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Inverse-Designed Narrowband THz Radiator for Ultrarelativistic Electrons
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  • Benedikt Hermann
    Benedikt Hermann
    Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland
    Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland
    Galatea Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), 2000 Neuchâtel, Switzerland
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    Orcidhttps://orcid.org/0000-0001-9766-3270
  • Urs Haeusler
    Urs Haeusler
    Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
    Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
    More by Urs Haeusler
    Orcidhttps://orcid.org/0000-0002-6818-0576
  • Gyanendra Yadav
    Gyanendra Yadav
    Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom
    Cockcroft Institute, Warrington, WA4 4AD, United Kingdom
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  • Adrian Kirchner
    Adrian Kirchner
    Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
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  • Thomas Feurer
    Thomas Feurer
    Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland
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  • Carsten Welsch
    Carsten Welsch
    Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom
    Cockcroft Institute, Warrington, WA4 4AD, United Kingdom
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  • Peter Hommelhoff
    Peter Hommelhoff
    Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
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  • Rasmus Ischebeck*
    Rasmus Ischebeck
    Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland
    *E-mail: [email protected]
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    Orcidhttps://orcid.org/0000-0002-5612-5828
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ACS Photonics

Cite this: ACS Photonics 2022, 9, 4, 1143–1149
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https://doi.org/10.1021/acsphotonics.1c01932
Published March 16, 2022

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Abstract

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THz radiation finds various applications in science and technology. Pump–probe experiments at free-electron lasers typically rely on THz radiation generated by optical rectification of ultrafast laser pulses in electro-optic crystals. A compact and cost-efficient alternative is offered by the Smith–Purcell effect: a charged particle beam passes a periodic structure and generates synchronous radiation. Here, we employ the technique of photonic inverse design to optimize a structure for Smith–Purcell radiation at a single wavelength from ultrarelativistic electrons. The resulting design is highly resonant and emits narrowbandly. Experiments with a 3D-printed model for a wavelength of 900 μm show coherent enhancement. The versatility of inverse design offers a simple adaption of the structure to other electron energies or radiation wavelengths. This approach could advance beam-based THz generation for a wide range of applications.

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Keywords

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Sources of THz radiation are of interest for numerous applications, including wireless communication, (1,2) electron acceleration, (3−5) and biomedical and material science. (6,7) Free-electron laser (FEL) facilities demand versatile THz sources for pump–probe experiments. (8) Intense, broadband THz pulses up to sub-mJ pulse energy have been demonstrated using optical rectification of high-power femtosecond lasers in lithium niobate crystals. (9,10) The Smith–Purcell effect (11) offers a compact and cost-efficient alternative for the generation of beam-synchronous THz radiation at electron accelerators. This effect describes the emission of electromagnetic waves from a periodic metallic or dielectric structure excited by electrons moving parallel to its surface. The wavelength of Smith–Purcell radiation at an angle θ with respect to the electron beam follows: (11)
(1)
where β is the normalized velocity of the electrons, a is the periodicity of the structure, and m is the mode order. Smith–Purcell emission from regular metallic grating surfaces has been observed in numerous experiments, first using 300 keV electrons (11) and later also using ultrarelativistic electrons. (12,13) If electron pulses shorter than the emitted wavelength are used, the fields from individual electrons add coherently, and the radiated energy scales quadratically with the bunch charge. (14) The typically used single-sided gratings emit a broadband spectrum, (15) which is dispersed by the Smith–Purcell relation (eq 1). To enhance emission at single frequencies, a concept called orotron uses a metallic mirror above the grating to form a resonator. (16,17) Dielectrics can sustain fields 1–2 orders of magnitude larger than metals (18) and are therefore an attractive material for strong Smith–Purcell interactions.
Inverse design is a computational technique that has been successfully employed to advance integrated photonics. (19) Algorithms to discover optical structures fulfilling desired functional characteristics are creating a plethora of novel subwavelength geometries: applications include wavelength-dependent beam splitters (19,20) and couplers, (21) as well as dielectric laser accelerators. (22)

Results

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The goal of our inverse design optimization was a narrowband dielectric Smith–Purcell radiator for ultrarelativistic electrons (E = 3.2 GeV, γ ≈ 6000). To simplify the collection of the THz radiation, a periodicity of a = λ was chosen, resulting in an emission perpendicular to the electron propagation direction, θ = 90°. The optimization was based on a 2D finite-difference frequency-domain (FDFD) simulation of a single unit cell of the grating (Figure 1a). Periodic boundaries in direction of the electron propagation ensure the desired periodicity, and perfectly matched layers in the transverse x-direction imitate free space. The design region extends 4.5 mm to each side of a 150 μm wide vacuum channel, large enough to facilitate the full transmission of the electron beam with a width of σx = 30 μm (RMS). The electric current spectral density J(x, y, ω) of a single electron bunch acts here as the source term of our simulation and is given by
with the electron wavevector ky = 2π/βλ and the line charge density q. The absolute value of q is irrelevant for the optimization, but rough agreement with 3D simulations is found by choosing q ∼ Q/d, where Q is the bunch charge and d the charge-structure distance. (23)

Figure 1

Figure 1. Inverse design and fabrication of THz radiator. (a) The design process is based on a 2D-FDFD simulation of a single unit cell of the grating (aspect ratio distorted). Applying periodic boundaries (green) in the longitudinal direction of the electron beam (blue) corresponds to the simulation of an infinitely long grating. In the transverse direction, we define perfectly matched layers (orange) to imitate free space. The design region (gray) extended 4.5 mm to each side of a 150 μm wide vacuum (white) channel for the electrons. The Poynting vector Sx was calculated outside the design region and served as the objective function of the optimization. (b) Optimized 2D design: structure material (black), vacuum (white), and associated electromagnetic field spectral density of the transverse-magnetic mode (red-blue). Three consecutive periods are shown. (c) 3D illustration of the extruded structure of (b) with 50 periods. The lower inset shows the electric field profile seen from the perspective of the electron obtained from a 3D-FDFD simulation. (d) Photograph of the inverse-designed structure fabricated by additive manufacturing. The dimensions of the entire structure are 6.5 × 6 × 45 mm (width × height × depth).

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The optimization problem was to find a design (parametrized by the variable ϕ) that maximizes the radiation to both sides of the grating. Exploiting the full symmetry of the double-sided, perpendicular emission process, we enforced mirror and point symmetry with respect to the center of a unit cell of the grating. The design is defined by its relative permittivity ε(x, y, ϕ) and can only take the two values of vacuum, ε = 1, or the structure material, ε = 2.79. For simplicity, we neglected the small imaginary part ε″ = 0.08 of the material. (24)
The objective function G, quantifying the performance of a design ϕ, is given by the line integral of the Poynting vector in the x-direction along the length of one period, evaluated at a point xS outside the design region:
The optimization problem can then be stated as
The design obtained from the gradient-based technique of adaptive moment estimation (Adam) (25) is depicted in Figure 1b. The structure features two rows of pillars, shifted by half a period with respect to each other. The rows of pillars are followed by three slabs on each side, which can be easily identified as distributed Bragg reflectors forming a microresonator around the electron channel. The channel width is 272 μm, even larger than the initially defined clearance of 150 μm. These slabs exhibit grooves, which perhaps act as a grating as well as a reflector. We note that these features are good examples of the superiority of inverse design over intuition-based designs.
To fabricate the geometry obtained with inverse design, we used an additive manufacturing process for poly(methyl methacrylate) (PMMA). A stereolithography device, featuring a resolution of 140 μm, is capable of reproducing the structure with subwavelength accuracy. The so-obtained structure is 6 mm high and 45 mm long (Figure 1d). The holder of the structure was manufactured together with the structure, and filaments connect the pillars and slabs on top of the structure for increased mechanical stability. We selected the Formlabs High Temperature Resin as a material for this study due to its excellent vacuum compatibility after curing in a heated vacuum chamber. (24) Afterward, the fabricated Smith–Purcell radiator was inserted into the ACHIP experimental chamber (26) at SwissFEL (27) (Figure 2a). The photoemitted electron bunch is accelerated to an energy of 3.2 GeV with the normal-conducting radio frequency accelerator at SwissFEL. A two-stage compression scheme using magnetic chicanes is employed to achieve an electron bunch length of approximately 30 fs at the interaction point. At this location, the transverse beam size was measured to be around 30 μm in the horizontal and 40 μm in the vertical direction.

Figure 2

Figure 2. Experimental setup. (a) Schematic of SwissFEL. The THz generation experiments were conducted at the ACHIP interaction chamber (26) located in the switch-yard to the Athos beamline. (b) Sketch of the Smith–Purcell THz generation and Michelson interferometer (MI) setup. The inset shows a typical autocorrelation measurement.

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An in-vacuum PMMA lens with a diameter of 25 mm collimated parts of the emitted radiation. A Michelson interferometer was used to measure the first-order autocorrelation of the electromagnetic pulse and to obtain its power spectrum via Fourier transform (Figure 2b and Methods). The measured spectrum is centered around 881 μm (0.34 THz) and has a full width at half-maximum of ∼9% (Figure 3).

Figure 3

Figure 3. Emission spectra. The Fourier transform of an autocorrelation measurement with a Michelson interferometer (black) is compared to 3D time-domain (green) and frequency-domain (orange) simulations. The gray area indicates the acceptance window of the spectrometer, defined by the angular acceptance of the Michelson interferometer. The narrowness of emission originates from the high mode density inside the microresonator formed by the two distributed Bragg reflectors on each side of the electron channel.

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Discussion

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The observed spectrum agrees well with a 3D finite-differences time-domain (FDTD) simulation of the experiment (Figure 3). In contrast, a finite-differences frequency-domain (FDFD) simulation reveals that the design can in principal emit even more narrowbandly, originating from the high mode density inside the Fabry–Perot cavity formed by the two distributed Bragg reflectors on both sides of the electron channel. The difference between the two simulations can be explained by their distinct grid resolutions. The FDFD simulation considers only a single period of the structure with periodic boundaries, corresponding to an infinitely long structure. Hence, the cell size is small, allowing to use a high grid resolution. The time-domain simulation, on the other hand, calculates the electromagnetic field of the entire 50-period-long structure for each time step. This high memory requirement comes at the cost of a lower spatial resolution. Since the experiment was similarly limited by the fabrication resolution of 140 μm, the FDTD simulation reproduced the measured spectrum much better. We also note that potential absorption losses in the structure can reduce its quality factor and broaden the radiation spectrum. Due to the small contribution from ε″ = 0.08, (24) absorption effects were not considered here but would dominate at higher quality factors.
We drove the structure with electron bunches with a duration of approximately 30 fs (RMS), which is much shorter than the resonant wavelength corresponding to a period of 3 ps. Hence, we expect to see the coherent addition of radiated fields. To experimentally verify this, we varied the bunch charge. Figure 4 shows the detected pulse energy for six bunch charge settings ranging from 0 pC to 11.8 pC. The scaling is well approximated by a quadratic fit, which confirms the expected coherent enhancement of the THz pulse energy. (14) We observe a slight deviation for the highest charge measurement from the quadratic fit, which might be a result of detector saturation (see Methods). We note that the quadratic scaling would enable THz pulse energies orders of magnitude larger by driving the structure at higher bunch charges.

Figure 4

Figure 4. Coherent scaling. The detected pulse energy is shown as a function of the bunch charge. In contrast to the linear fit (dashed red), the quadratic fit (solid blue) approximates the measurements within the uncertainties, which confirms the expected coherent enhancement. Vertical and horizontal error bars represent the RMS detector noise obtained from a background measurement and the uncertainty in the charge measurement, respectively.

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The THz pulse emitted perpendicular to the Smith-Purcell radiator possesses a pulse-front tilt of close to 45◦ since it is driven by ultrarelativistic electrons. Depending on the length of the radiator and the application, the tilt can be compensated for with a diffraction grating.
During and after our experiments, the structure did not show any signs of performance degradation or visible damage. It was used continuously for eight hours with a bunch charge of approximately 10 pC at a pulse repetition rate of 1 Hz.

Conclusion

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The here-presented beam-synchronous radiation source can be added to the beamline of an FEL to enrich capabilities for pump–probe experiments. For ultrarelativistic electrons, a second beamline may be used to compensate for the longer path length of the THz radiation and achieve simultaneous arrival with the X-ray radiation created in the undulator of the FEL (Figure 5a). Smith–Purcell radiation represents a cost-efficient alternative to the broadband generation of THz by optical rectification, which requires an external laser system and precise synchronization to the accelerator. Our inverse design approach to Smith–Purcell emitters can produce beam-synchronous narrowband THz radiation, which could propel pump–probe studies with THz excitations in solids, for instance, resonant control of strongly correlated electron systems, high-temperature superconductors, or vibrational modes of crystal lattices (phonons). (28,29)

Figure 5

Figure 5. Possible applications of the beam-driven THz source in pump–probe experiments. (a) For ultrarelativistic electrons, a second electron bunch may be used to compensate for the longer path length of the THz pulse. X-rays are generated in the undulators of an FEL. (b) For subrelativistic electrons, the generated THz pulse is delayed to achieve simultaneous arrival of electron and THz radiation. (c) The structure becomes a tunable light source if the periodicity changes along the invariant direction; exemplified with a rectangular grating.

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Further improvement of our THz structure can be achieved by higher fabrication accuracy and the use of a fully 3D-optimized geometry with a higher quality factor, resulting in more narrowband emission and higher pulse energy. Moreover, the inverse design suite could be extended to composite structures of more than one material, which could provide extra stability for complicated 3D designs. In the case of highly resonant structures, materials with low absorption, for example, polytetrafluoroethylene (PTFE), (24) are a necessity. The measured THz pulse energy can be increased by a factor of almost 300 by raising the driving bunch charge from the used 11.8 pC up to the 200 pC available at SwissFEL. Whether the currently used material can withstand such high fields and radiation remains to be investigated. Combining 3D optimization, longer structures, larger collection optics, and higher bunch charges will result in a THz pulse energy multiple orders of magnitude larger than observed in the presented experiment (0.6 pJ).
Our work naturally extends to the field of subrelativistic electrons. Here, simultaneous arrival of THz radiation and electron bunches is readily achieved by compensating for the higher velocity of the radiation with a longer path length (Figure 5b). Besides its application for pump–probe experiments, our structure can be more generally applied as a radiation source at wavelengths that are otherwise difficult to generate. An advantage lies in the tunability that arises from changing the periodicity, either by replacing the entire structure or using a design with variable periodicity (Figure 5c), or from tuning the electron velocity. For the visible to UV regime, the idea of a compact device with the electron source integrated on a nanofabricated chip has recently sparked interest. (30,31)

Methods

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Structure Parametrization

Our inverse design process was carried out with an open-source Python package (32) suitable for 2D-FDFD gradient-based optimizations (25) of the chosen objective function G(ϕ) with respect to the design parameter ϕ. A key step lies in the parametrization of the structure ε(ϕ) through the variable ϕ in a way that ensures robust convergence of the algorithm and fabricability of the final design. In the most rudimentary case, ε(x, y) = ϕ(x, y) is a two-dimensional array with entries ∈ [1, 2.79] for each pixel of the design area. Instead of setting bounds on the values of ϕ, we leave ϕ unbounded and apply a sigmoid function of the shape
where large values of α yield a close-to-binary design with few values between εmin = 1 and εmax = 2.79. To avoid small or sharp features in the final design, we convolved ϕ(x, y) with a uniform 2D circular kernel with radius 60 μm before projection onto the sigmoid function tanh(αϕ̃) with the convolved design parameter ϕ̃. By increasing α from 20 to 1000 as the optimization progresses, we found improved convergence. We further accelerated convergence by applying mirror and point symmetry with respect to the center of a unit cell of the grating, which reduces the parameter space by a factor of 4. An exemplary design evolution is shown in Figure 6.

Figure 6

Figure 6. Exemplary design evolution. Left to right: The first 100 steps of an exemplary inverse design optimization are shown above their respective objective value in relative units. Starting from a random design, the design evolves under stochastic gradient-based optimization. At multiple steps throughout the optimization, the design solution is disturbed by the addition of random noise and blurring of features, which tests the stability of the design and helps in exploring a larger design space. Such a procedure was repeated ∼50×, each time yielding a different design depending on the initial randomized design (similar to particle swarm optimization). We then selected those design groups that gave best performance, stability, and fabricability (similar to supervised learning). Continuing the optimization from there and repetitively disturbing the solution, a final design will have gone through more than 1000 steps of optimization before fabrication. The displayed structure evolution used slightly different optimization conditions than the design presented in this work.

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Ultrarelativistic Optimization

The simulation of ultrarelativistic electrons poses challenges that have so far prevented inverse design in this regime. (33) Here, we report on two main challenges. First, the electron velocity is close to the speed of light (β = 0.999999985 for E = 3.2 GeV), which requires a high mesh resolution. If the numerical error is too large due to a low mesh resolution, the simulation may not be able to distinguish between β < 1 and β > 1. In that case, the simulation could show Cherenkov radiation in vacuum instead of Smith–Purcell radiation.
Not only does a higher mesh resolution require more computational memory and time, but it may also hamper the inverse design optimization if the number of design parameters becomes too large. Hence, we parametrized our structures at a low resolution (mesh spacing λ/30), which is still above the fabrication accuracy of λ/5, and computed the fields at a high resolution (mesh spacing λ/150).
The second difficulty arises from the long-range evanescent waves of ultrarelativistic electrons. The spectral density of the electric field of a line charge decays with exp(−κ|x|), where κ = 2π/βγλ, with β ≈ 1 and γ ≈ 6000 for E = 3.2 GeV. (34) This means the evanescent waves will reach the boundaries of our simulation cell in the x-direction. Generalized perfectly matched layers (PMLs) (35) are chosen, such that they can absorb both propagating and evanescent waves.
A detailed look at Figure 1b reveals that our implementation of generalized PMLs is not fully capable of absorbing evanescent waves. Hence, we make use of symmetry to further reduce the effect of evanescent waves at the boundaries of the simulation cell. Note that the evanescent electric field for β ≈ 1 is almost entirely polarized along the transverse direction x. This means if the simulation cell is mirror symmetric with respect to the electron channel, antiperiodic boundaries can be applied after the PMLs to cancel out the effect of evanescent waves at the boundaries. This turned out to work well for us, although the structure is not mirror symmetric with respect to the electron axis.

Simulations

The 3D frequency-domain simulation was performed in COMSOL, based on the finite element method. The simulation cell, as shown in the lower right inset of Figure 1c, consists of a single unit cell of the grating, with a height of 4 mm and periodic boundaries along the electron propagation direction. An optional phase shift at the boundaries in longitudinal direction enables simulations for nonperpendicular Smith-Purcell emission, λ ≠ a. Perfectly matched layers are applied in all remaining, transverse directions. The electron beam (E = 3.2 GeV, Q = e) had a Gaussian shape of width σx = σz = 50 μm in the transverse direction.
The 3D time-domain simulation of the full structure, as shown in Figure 1c with the connecting filaments at the top and bottom, was performed in CST Studio Suite 2021. A single electron bunch (E = 3 GeV) with Gaussian charge distribution was assumed. Its width in the transverse direction was σx = σz = 0.1 mm and in the longitudinal direction σy = 0.2 mm with cutoff length 0.4 mm. The simulation was performed for a longer bunch length than the experimental bunch length due to computational resource limitations for smaller mesh cell resolutions. Nevertheless, we expect this approximation to yield a realistic emission spectrum, since the simulated bunch length is still substantially shorter than the central wavelength. A convergence test showed that a hexahedral mesh with a minimum cell size of 15 μm was sufficient. To imitate free space, perfectly matched layers and open-space boundary conditions were applied, where a λ/2 thick layer of vacuum was added after the dielectric structure. The radiation spectrum was then obtained via far-field approximations at multiple frequencies.

Accelerator Setup

The experiments used 10 pC electron bunches from the 3.2 GeV Athos beamline of SwissFEL (27) operated at a pulse repetition rate of 1 Hz to keep particle losses during alignment at a tolerable level. The standard bunch charge at SwissFEL is 200 pC at a repetition rate of 100 Hz. For the low charge working point, the aperture and intensity of the cathode laser are reduced. The normalized emittance of the electron beam with a charge of 9.5 pC was 110 nm rad in both planes and was measured with a quadrupole scan in the injector at a beam energy of 150 MeV. (36)
For the experiment, we scanned the charge from 0 to 11.8 pC by adjusting the intensity of the cathode laser, which results in a slight emittance degradation and mismatch of the transverse beam parameters. This is due to charge density changes in the space charge dominated gun region. Nevertheless, the beam size remained small enough for full transmission through the THz Smith–Purcell structure.
A bunch length of 30 fs (RMS) was measured for similar machine settings in a separate shift with a transverse deflecting cavity (TDC) in the Aramis beamline of the accelerator. Therefore, we expect the longitudinal dimension of the electron beam at the ACHIP chamber to be on the order of 10 μm, almost 2 orders of magnitude shorter than the period of the structure and radiated wavelength.
The transverse beam size at the interaction point was 30 μm in the horizontal and 40 μm in the vertical direction (for a charge of 9.5 pC), as measured with a scintillating YAG screen imaged with an out-of-vacuum microscope onto a CCD camera. After position and angular alignment of the structure using an in-vacuum hexapod, the beam could be transmitted without substantial losses through the 272 μm wide channel of the THz generating structure.

Structure Fabrication

The structure was fabricated with a commercial PMMA stereolithography device Formlabs Form 2. The resolution of the device is 140 μm, which provides subwavelength feature sizes for the geometry with a periodicity of 900 μm. The height of the structure (6 mm) was limited by the stability of the structure rods during the fabrication process. The high temperature resin used for this study can be heated to 235 °C. A sufficiently low outgassing rate for the installation at SwissFEL was achieved after baking the device for 5 h under vacuum conditions at 175 °C. (24) Thanks to the rapid improvements in SLA technology and other free-form manufacturing techniques, the geometry could certainly be fabricated also at shorter wavelengths and higher resolution for future experiments. An increased manufacturing quality is required to achieve an even narrower emission bandwidth.

Michelson Interferometer and THz Detector

For the spectrum measurements, we installed a Michelson interferometer outside the vacuum chamber. The THz pulse was first sent through an in-vacuum lens made of PMMA with a diameter of 25 mm and a focal length of 100 mm. The lens collimates radiation in the vertical plane, but it does not map the entire radiation of the 45 mm long structure onto the detector. The angular acceptance in the horizontal plane is calculated via ray tracing (see Figure 3). A fused silica vacuum window with about 50% transmission for the design wavelength of the structure (900 μm) is used as extraction port.
The beam splitter is made of 3.5 mm-thick plano–plano high-resistivity float-zone silicon (HRFZ-Si) manufactured by TYDEX. It provides a splitting ratio of 54/46 for wavelengths ranging from 0.1 to 1 mm. Translating one of the mirrors of the interferometer allowed us to measure the first-order autocorrelation, from which the power spectrum is obtained via Fourier transform.
The geometric acceptance angle of the Michelson interferometer Δθ in the plane of the electron beam and the THz radiation defines the accepted bandwidth of the setup. According to the Smith–Purcell relation (eq 1), it is given by
Around the orthogonal direction (θ = 90°), the accepted bandwidth covers the measured spectrum (Figure 3). We calculated the acceptance with ray tracing including the size of the emitting structure and the apertures of the collimating lens (25 mm) and the detector (12 mm).
A Schottky diode (ACST, Type 3DL 12C LS2500 A2) was used as THz detector, sensitive from 300 to 4000 μm. The manufacturer indicates a responsivity of 120 V/W at 900 μm, which we used to estimate the energy deposited on the detector. The signal from the detector is transmitted via a 20 m long coaxial cable to an oscilloscope outside of the accelerator bunker. For absolute pulse energy measurements, the detector setup including absorption in cables and the vacuum window should be characterized with a calibrated THz source. We calculated the pulse energy for different charges (Figure 4) by averaging over all shots during the oscillating autocorrelation measurement.
A typical autocorrelation measurement for a charge of 9.4 pC is depicted in Figure 2b. The shape of the autocorrelation is not perfectly symmetric in amplitude and stage position. The amplitude asymmetry could be a result of a nonlinear detector response (onset of saturation). This is in agreement with the slight deviation of the pulse energy from the quadratic fit (Figure 4). Since the length of only one arm is changed and the radiation might not be perfectly collimated, the position scan of the mirror is not creating a perfectly symmetric autocorrelation signal.

Author Information

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  • Corresponding Author
  • Authors
    • Benedikt Hermann - Paul Scherrer Institut, 5232 Villigen, PSI, Switzerland;  Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland;  Galatea Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), 2000 Neuchâtel, Switzerland;  Orcidhttps://orcid.org/0000-0001-9766-3270
    • Urs Haeusler - Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany;  Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom;  Orcidhttps://orcid.org/0000-0002-6818-0576
    • Gyanendra Yadav - Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom;  Cockcroft Institute, Warrington, WA4 4AD, United Kingdom
    • Adrian Kirchner - Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
    • Thomas Feurer - Institute of Applied Physics, University of Bern, 3012 Bern, Switzerland
    • Carsten Welsch - Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom;  Cockcroft Institute, Warrington, WA4 4AD, United Kingdom
    • Peter Hommelhoff - Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany
  • Author Contributions

    These authors contributed equally to this work. B.H., U.H., P.H., and R.I. conceived the project. U.H. optimized the design. B.H. fabricated the structure and performed the experiments with support from R.I. and A.K. Simulations in CST were performed by G.Y. All authors discussed the results and contributed to the manuscript.

  • Funding

    Gordon and Betty Moore Foundation (4744, “ACHIP”) and ERC Advanced Grant (884217, “AccelOnChip”).

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We thank the SwissFEL operations crew, the expert groups at PSI, and the entire ACHIP collaboration for their support. We thank Thomas Schietinger for careful proofreading. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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    In this paper, we will review both past and recent progresses in the generation, detection and application of intense terahertz (THz) radiation. We will restrict the review to laser based intense few-cycle THz sources, and thus will not include sources such as synchrotron-based or narrowband sources. We will first review the various methods used for generating intense THz radiation, including photoconductive antennas (PCAs), optical rectification sources (esp. the tilted-pulse-front lithium niobate source and the DAST source, but also those using other crystals), air plasma THz sources and relativistic laser-plasma sources. Next, we will give a brief introduction on the common methods for coherent THz detection techniques (namely the PCA technique and the electro-optic sampling), and point out the limitations of these techniques for measuring intense THz radiation. We will then review three techniques that are highly suited for detecting intense THz radiation, namely the air breakdown coherent detection technique, various single-shot THz detection techniques, and the spectral-domain interferometry technique. Finally, we will give an overview of the various applications that have been made possible with such intense THz sources, including nonlinear THz spectroscopy of condensed matter (optical-pump/THz-probe, THz-pump/THz-probe, THz-pump/optical-probe), nonlinear THz optics, resonant and non-resonant control of material (such as switching of supercond., magnetic and polarization switching) and controlling the nonlinear response of metamaterials. We will also provide a short perspective on the future of intense THz sources and their applications.
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    Nanni, E. A.; Huang, W. R.; Hong, K.-H.; Ravi, K.; Fallahi, A.; Moriena, G.; Dwayne Miller, R. J.; Kartner, F. X. Terahertz-driven linear electron acceleration. Nat. Commun. 2015, 6, 1– 8,  DOI: 10.1038/ncomms9486
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    Hibberd, M. T. Acceleration of relativistic beams using laser-generated terahertz pulses. Nat. Photonics 2020, 14, 755– 759,  DOI: 10.1038/s41566-020-0674-1
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    Acceleration of relativistic beams using laser-generated terahertz pulses
    Hibberd, Morgan T.; Healy, Alisa L.; Lake, Daniel S.; Georgiadis, Vasileios; Smith, Elliott J. H.; Finlay, Oliver J.; Pacey, Thomas H.; Jones, James K.; Saveliev, Yuri; Walsh, David A.; Snedden, Edward W.; Appleby, Robert B.; Burt, Graeme; Graham, Darren M.; Jamison, Steven P.
    Nature Photonics (2020), 14 (12), 755-759CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
    Abstr.: Particle accelerators driven by laser-generated terahertz (THz) pulses promise unprecedented control over the energy-time phase space of particle bunches compared with conventional radiofrequency technol. Here we demonstrate acceleration of a relativistic electron beam in a THz-driven linear accelerator. Narrowband THz pulses were tuned to the phase-velocity-matched operating frequency of a rectangular dielec.-lined waveguide for extended collinear interaction with 35 MeV, 60 pC electron bunches, imparting multicycle energy modulation to chirped (6 ps) bunches and injection phase-dependent energy gain (up to 10 keV) to subcycle (2 ps) bunches. These proof-of-principle results establish a route to whole-bunch linear acceleration of subpicosecond particle beams, directly applicable to scaled-up and multistaged concepts capable of preserving beam quality, thus marking a key milestone for future THz-driven acceleration of relativistic beams.
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    Xu, H. Cascaded high-gradient terahertz-driven acceleration of relativistic electron beams. Nat. Photonics 2021, 15, 426– 430,  DOI: 10.1038/s41566-021-00779-x
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    Cascaded high-gradient terahertz-driven acceleration of relativistic electron beams
    Xu, Hanxun; Yan, Lixin; Du, Yingchao; Huang, Wenhui; Tian, Qili; Li, Renkai; Liang, Yifan; Gu, Shaohong; Shi, Jiaru; Tang, Chuanxiang
    Nature Photonics (2021), 15 (6), 426-430CODEN: NPAHBY; ISSN:1749-4885. (Nature Portfolio)
    Abstr.: Terahertz-driven acceleration has recently emerged as a route for delivering ultrashort bright electron beams efficiently, reliably and in a compact set-up. Many working schemes and key technologies related to terahertz-driven acceleration have been successfully demonstrated and are being developeds1-10. However, the achieved acceleration gradient and energy gain remain low, and the potential physics and tech. challenges in the high-energy regime are still underexplored. Here we report whole-bunch acceleration of relativistic beams with an effective acceleration gradient of up to 85 MV m-1 in a single-stage configuration and demonstrate a cascaded terahertz-driven acceleration scheme of relativistic beams with an energy gain of 204 keV. These proof-of-principle results represent a crit. advance towards high-energy terahertz-driven acceleration of relativistic beams, are scalable and have great potential to provide high-quality beams, with implications for future terahertz-driven electron sources and related scientific discoveries.
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    Tanaka, K.; Hirori, H.; Nagai, M. THz nonlinear spectroscopy of solids. IEEE Trans. Terahertz Sci. Technol. 2011, 1, 301– 312,  DOI: 10.1109/TTHZ.2011.2159535
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    THz nonlinear spectroscopy of solids
    Tanaka, Koichiro; Hirori, Hideki; Nagai, Masaya
    IEEE Transactions on Terahertz Science and Technology (2011), 1 (1), 301-312CODEN: ITTSBX; ISSN:2156-342X. (Institute of Electrical and Electronics Engineers)
    We present a review of the recent progress in the generation methods of intense terahertz (THz) single-cycle pulses and their application to THz nonlinear spectroscopy in condensed matters. Special attentions are paid to various aspects of nonlinearity in semiconductors including dynamical Franz-Keldysh effect, ballistic acceleration of free carriers, and coherent control of the exciton system.
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    Son, J.-H. Terahertz Biomedical Science and Technology; CRC Press, 2014.
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    Schneidmiller, E. A.; Yurkov, M. V.; Krasilnikov, M.; Stephan, F. In Tunable IR/THz Source for Pump Probe Experiments at the European XFEL; Tschentscher, T., Tiedtke, K., Eds.; Advances in X-ray Free-Electron Lasers II: Instrumentation, International Society for Optics and Photonics, SPIE, 2013; Vol. 8778, pp 151– 156.
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    Zhang, X.; Jin, Y.; Ma, X. F. Coherent measurement of THz optical rectification from electro-optic crystals. Appl. Phys. Lett. 1992, 61, 2764– 2766,  DOI: 10.1063/1.108083
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    Coherent measurement of THz optical rectification from electro-optic crystals
    Zhang, X. C.; Jin, Y.; Ma, X. F.
    Applied Physics Letters (1992), 61 (23), 2764-6CODEN: APPLAB; ISSN:0003-6951.
    Results are reported of coherent measurement (phase and amplitude) of optical rectification from a variety of electrooptic crystals. A comparison is presented of the exptl. data with a theor. calcn.
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    Fülöp, J. A. Generation of sub-mj terahertz pulses by optical rectification. Opt. Lett. 2012, 37, 557– 559,  DOI: 10.1364/OL.37.000557
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    Smith, S. J.; Purcell, E. M. Visible light from localized surface charges moving across a grating. Phys. Rev. 1953, 92, 1069– 1069,  DOI: 10.1103/PhysRev.92.1069
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    Doucas, G.; Mulvey, J. H.; Omori, M.; Walsh, J.; Kimmitt, M. F. First observation of Smith-Purcell radiation from relativistic electrons. Phys. Rev. Lett. 1992, 69, 1761– 1764,  DOI: 10.1103/PhysRevLett.69.1761
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    First observation of Smith-Purcell radiation from relativistic electrons
    Doucas, G.; Mulvey, J. H.; Omori, M.; Walsh, J.; Kimmitt, M. R.
    Physical Review Letters (1992), 69 (12), 1761-4CODEN: PRLTAO; ISSN:0031-9007.
    A beam of 3.6-MeV electrons was used to study the generation of radiation in the far IR (FIR) by the Smith-Purcell mechanism. The dependence of wavelength on angle of emission, over angles from 56° to 150° and wavelengths from 350 to 1860 μm, is in excellent agreement with the Smith-Purcell dispersion relation. Comparison of the yield with that from a 5000-K source suggests that the spontaneous Smith-Purcell effect offers an easily tunable alternative to the synchrotron as a coherent FIR source, and that it could also form the basis of an inexpensive, compact free-electron laser.
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    Kube, G. Observation of optical Smith-Purcell radiation at an electron beam energy of 855 MeV. Phys. Rev. E 2002, 65, 056501,  DOI: 10.1103/PhysRevE.65.056501
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    Observation of optical Smith-Purcell radiation at an electron beam energy of 855 MeV
    Kube, G.; Backe, H.; Euteneuer, H.; Grendel, A.; Hagenbuck, F.; Hartmann, H.; Kaiser, K. H.; Lauth, W.; Schope, H.; Wagner, G.; Walcher, Th.; Kretzschmar, M.
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2002), 65 (5-2), 056501/1-056501/15CODEN: PRESCM ISSN:. (American Physical Society)
    Smith-Purcell radiation, generated when a beam of charged particles passes close to the surface of a diffraction grating, was studied in the visible spectral range at λ = 360 and 546 nm with the low emittance 855 MeV electron beam of the Mainz Microtron MAMI. The beam focused to a spot size of 4 μm (full width at half max.) passed over optical diffraction gratings of echelle profiles with blaze angles of 0.8°, 17.27°, and 41.12° and grating periods of 0.833 and 9.09 μm. Taking advantage of the specific emission characteristics of Smith-Purcell radiation a clear sepn. from background components, such as diffracted synchrotron radiation from upstream beam optical elements and transition radiation, was possible. The intensity scales with a modified Bessel function of the 1st kind as a function of the distance between electron beam and grating surface. Exptl. radiation factors were detd. and compared with calcns. from P.M. Van den Berg's (1973) theory. Fair agreement was found for gratings with large blaze angles while the measurement with the shallow grating (blaze angle 0.8°) is at variance with this theory. The optimal operational parameters of a Smith-Purcell radiation source in view of already existing powerful undulator sources are discussed.
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    Ishi, K. Observation of coherent smith-purcell radiation from short-bunched electrons. Phys. Rev. E 1995, 51, R5212– R5215,  DOI: 10.1103/PhysRevE.51.R5212
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    Observation of coherent Smith-Purcell radiation from short-bunched electrons
    Ishi, K.; Shibata, Y.; Takahashi, T.; Hasebe, S.; Ikezawa, M.
    Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics (1995), 51 (6-A), R5212-R5215CODEN: PLEEE8; ISSN:1063-651X. (American Physical Society)
    Coherent Smith-Purcell radiation, generated by the passage of short-bunched electrons of relativistic energy of 42 MeV above the surface of a metallic grating, has been obsd. in the wavelength region from 0.5 to 4.0 mm. The intensity of the radiation is proportional to the square of the beam current. The intensity at λ = 2.5 mm is enhanced by several orders of magnitude compared with the incoherent radiation. It is found that the intensity decreases proportionally to the square of the modified Bessel function [K0(2πh/λβγ)]2, as the beam height h from the surface of the grating increases.
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    Brownell, J. H. The angular distribution of the power produced by Smith-Purcell radiation. J. Phys. D: Appl. Phys. 1997, 30, 2478– 2481,  DOI: 10.1088/0022-3727/30/17/014
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    The angular distribution of the power produced by smith-purcell radiation
    Brownell, J. H.; Doucas, G.; Kimmitt, M. F.; Mulvey, J. H.; Omori, M.; Walsh, J. E.
    Journal of Physics D: Applied Physics (1997), 30 (17), 2478-2481CODEN: JPAPBE; ISSN:0022-3727. (Institute of Physics Publishing)
    The radiation produced by the interaction of an electron beam with a metallic grating (the Smith-Purcell radiation) can be described in terms of a theory based on the acceleration of the surface charges induced on the grating surface by the passing electrons. The calcd. spectral distribution of the emitted power is compared with recent exptl. results; the agreement between the two is found to be satisfactory.
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    Rusin, F.; Bogomolov, G. Orotron─an electronic oscillator with an open resonator and reflecting grating. Proc. IEEE 1969, 57, 720– 722,  DOI: 10.1109/PROC.1969.7049
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    Zhang, P.; Ang, L. K.; Gover, A. Enhancement of coherent smith-purcell radiation at terahertz frequency by optimized grating, prebunched beams, and open cavity. Phys. Rev. ST Accel. Beams 2015, 18, 020702,  DOI: 10.1103/PhysRevSTAB.18.020702
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    England, R. J. Dielectric laser accelerators. Rev. Mod. Phys. 2014, 86, 1337,  DOI: 10.1103/RevModPhys.86.1337
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    Dielectric laser accelerators
    England, R. Joel; Noble, Robert J.; Bane, Karl; Dowell, David H.; Ng, Cho-Kuen; Spencer, James E.; Tantawi, Sami; Wu, Ziran; Byer, Robert L.; Peralta, Edgar; Soong, Ken; Chang, Chia-Ming; Montazeri, Behnam; Wolf, Stephen J.; Cowan, Benjamin; Dawson, Jay; Gai, Wei; Hommelhoff, Peter; Huang, Yen-Chieh; Jing, Chunguang; McGuinness, Christopher; Palmer, Robert B.; Naranjo, Brian; Rosenzweig, James; Travish, Gil; Mizrahi, Amit; Schachter, Levi; Sears, Christopher; Werner, Gregory R.; Yoder, Rodney B.
    Reviews of Modern Physics (2014), 86 (4), 1337-1389CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
    The use of IR lasers to power optical-scale lithog. fabricated particle accelerators is a developing area of research that has garnered increasing interest in recent years. The physics and technol. of this approach is reviewed, which is referred to as dielec. laser acceleration (DLA). In the DLA scheme operating at typical laser pulse lengths of 0.1 to 1 ps, the laser damage fluences for robust dielec. materials correspond to peak surface elec. fields in the GV/m regime. The corresponding accelerating field enhancement represents a potential redn. in active length of the accelerator between 1 and 2 orders of magnitude. Power sources for DLA-based accelerators (lasers) are less costly than microwave sources (klystrons) for equiv. av. power levels due to wider availability and private sector investment. Because of the high laser-to-particle coupling efficiency, required pulse energies are consistent with tabletop microJoule class lasers. Combined with the very high (MHz) repetition rates these lasers can provide, the DLA approach appears promising for a variety of applications, including future high-energy physics colliders, compact light sources, and portable medical scanners and radiative therapy machines.
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    Molesky, S. Inverse design in nanophotonics. Nat. Photonics 2018, 12, 659– 670,  DOI: 10.1038/s41566-018-0246-9
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    Inverse design in nanophotonics
    Molesky, Sean; Lin, Zin; Piggott, Alexander Y.; Jin, Weiliang; Vuckovic, Jelena; Rodriguez, Alejandro W.
    Nature Photonics (2018), 12 (11), 659-670CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)
    Recent advancements in computational inverse-design approaches - algorithmic techniques for discovering optical structures based on desired functional characteristics - have begun to reshape the landscape of structures available to nanophotonics. Here, we outline a cross-section of key developments in this emerging field of photonic optimization: moving from a recap of foundational results to motivation of applications in nonlinear, topol., near-field and on-chip optics.
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    Su, L.; Piggott, A. Y.; Sapra, N. V.; Petykiewicz, J.; Vučković, J. Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer. ACS Photonics 2018, 5, 301– 305,  DOI: 10.1021/acsphotonics.7b00987
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    Inverse Design and Demonstration of a Compact on-Chip Narrowband Three-Channel Wavelength Demultiplexer
    Su, Logan; Piggott, Alexander Y.; Sapra, Neil V.; Petykiewicz, Jan; Vuckovic, Jelena
    ACS Photonics (2018), 5 (2), 301-305CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    In wavelength division multiplexing schemes, splitters must be used to combine and sep. different wavelengths. Conventional splitters are fairly large with footprints in hundreds to thousands of square microns, and exptl. demonstrated multimode-interference-based and inverse-designed ultracompact splitters operate with only 2 channels and large channel spacing (>100 nm). A 3-channel wavelength demultiplexer with 40 nm spacing (1500, 1540, and 1580 nm) with a footprint of 24.75 μm2 was inverse designed and exptl. demonstrated. The splitter has a simulated peak insertion loss of -1.55 dB with under -15 dB crosstalk and a measured peak insertion loss of -2.29 dB with under -10.7 dB crosstalk.
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    Su, L. Fully-automated optimization of grating couplers. Opt. Express 2018, 26, 4023– 4034,  DOI: 10.1364/OE.26.004023
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    Fully-automated optimization of grating couplers
    Su, Logan; Trivedi, Rahul; Sapra, Neil V.; Piggott, Alexander Y.; Vercruysse, Dries; Vuckovic, Jelena
    Optics Express (2018), 26 (4), 4023-4034CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
    We present a gradient-based algorithm to design general 1D grating couplers without any human input from start to finish, including a choice of initial condition. We show that we can reliably design efficient couplers to have multiple functionalities in different geometries, including conventional couplers for single-polarization and single-wavelength operation, polarization-insensitive couplers, and wavelength-demultiplexing couplers. In particular, we design a fiber-to-chip blazed grating with under 0.2 dB insertion loss that requires a single etch to fabricate and no back-reflector.
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    Sapra, N. V. On-chip integrated laser-driven particle accelerator. Science 2020, 367, 79– 83,  DOI: 10.1126/science.aay5734
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    On-chip integrated laser-driven particle accelerator
    Sapra, Neil V.; Yang, Ki Youl; Vercruysse, Dries; Leedle, Kenneth J.; Black, Dylan S.; England, R. Joel; Su, Logan; Trivedi, Rahul; Miao, Yu; Solgaard, Olav; Byer, Robert L.; Vuckovic, Jelena
    Science (Washington, DC, United States) (2020), 367 (6473), 79-83CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
    Particle accelerators represent an indispensable tool in science and industry. However, the size and cost of conventional radio-frequency accelerators limit the utility and reach of this technol. Dielec. laser accelerators (DLAs) provide a compact and cost-effective soln. to this problem by driving accelerator nanostructures with visible or near-IR pulsed lasers, resulting in a 104 redn. of scale. Current implementations of DLAs rely on free-space lasers directly incident on the accelerating structures, limiting the scalability and integrability of this technol. We present an exptl. demonstration of a waveguide-integrated DLA that was designed using a photonic inverse-design approach. By comparing the measured electron energy spectra with particle-tracking simulations, we infer a max. energy gain of 0.915 kilo-eV over 30μm, corresponding to an acceleration gradient of 30.5 mega-eV per m. On-chip acceleration provides the possibility for a completely integrated mega-eV-scale DLA.
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    Szczepkowicz, A.; Schächter, L.; England, R. J. Frequency-domain calculation of smith–purcell radiation for metallic and dielectric gratings. Appl. Opt. 2020, 59, 11146– 11155,  DOI: 10.1364/AO.409585
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    Frequency-domain calculation of Smith-Purcell radiation for metallic and dielectric gratings
    Szczepkowicz, Andrzej; Schaechter, Levi; England, R. Joel
    Applied Optics (2020), 59 (35), 11146-11155CODEN: APOPAI; ISSN:2155-3165. (Optical Society of America)
    The intensity of Smith-Purcell radiation from metallic and dielec. gratings (silicon, silica) is compared in a frequency-domain simulation. The numerical model is discussed and verified with the Frank-Tamm formula for Cherenkov radiation. For 30 keV electrons, rectangular dielec. gratings are less efficient than their metallic counterpar ts, by an order of magnitude for silicon, and two orders of magnitude for silica. For all gratings studied, radiation intensity oscillates with grating tooth height due to electromagnetic resonances in the grating. 3D and 2D numerical models are compared.
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    Kellermeier, M. Towards additive manufacturing of dielectric accelerating structures. J. Phys.: Conf. Ser. 2020, 1596, 012020,  DOI: 10.1088/1742-6596/1596/1/012020
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    Kingma, D. P.; Ba, J. Adam: A method for stochastic optimization. 3rd International Conference on Learning Representations; ICLR, 2015; Vols. 1–15.
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    Ferrari, E. The ACHIP experimental chambers at the Paul Scherrer Institut. Nucl. Instrum. Methods Phys. Res., Sect. A 2018, 907, 244– 247,  DOI: 10.1016/j.nima.2018.02.112
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    The ACHIP experimental chambers at the Paul Scherrer Institut
    Ferrari, Eugenio; Ischebeck, Rasmus; Bednarzik, Martin; Bettoni, Simona; Borrelli, Simona; Braun, Hans-Heinrich; Calvi, Marco; David, Christian; Dehler, Micha; Frei, Franziska; Garvey, Terence; Guzenko, Vitaliy A.; Hiller, Nicole; Hommelhoff, Peter; McNeur, Joshua; Orlandi, Gian Luca; Ozkan-Loch, Cigdem; Prat, Eduard; Reiche, Sven; Romann, Albert; Sarafinov, Blagoj; Rivkin, Leonid
    Nuclear Instruments & Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment (2018), 907 (), 244-247CODEN: NIMAER; ISSN:0168-9002. (Elsevier B.V.)
    The Accelerator on a Chip International Program (ACHIP) is an international collaboration, funded by the Gordon and Betty Moore Foundation, with the goal of demonstrating that laser-driven accelerator can be integrated on a chip to fully build an accelerator based on dielec. structures. PSI will provide access to the high brightness electron beam of SwissFEL to test structures, approaches and methods towards achieving the final goal of the project. In this contribution, we will describe the two interaction chambers installed on SwissFEL to perform the proof-of-principle expts. In particular, we will present the positioning system for the samples, the magnets needed to focus the beam to sub-micrometer dimensions and the diagnostics to measure beam properties at the interaction point.
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    Milne, C. J. SwissFEL: The Swiss X-ray free electron laser. Appl. Sci. 2017, 7, 720,  DOI: 10.3390/app7070720
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    Kampfrath, T.; Tanaka, K.; Nelson, K. A. Resonant and nonresonant control over matter and light by intense terahertz transients. Nat. Photonics 2013, 7, 680– 690,  DOI: 10.1038/nphoton.2013.184
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    Resonant and nonresonant control over matter and light by intense terahertz transients
    Kampfrath, Tobias; Tanaka, Koichiro; Nelson, Keith A.
    Nature Photonics (2013), 7 (9), 680-690CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
    A review. Electromagnetic radiation in the terahertz (THz) frequency range is a fascinating spectroscopic tool that provides resonant access to fundamental modes, including the motions of free electrons, the rotations of mols., the vibrations of crystal lattices and the precessions of spins. Consequently, THz waves have been extensively used to probe such responses with high sensitivity. However, owing to recent developments in high-power sources, scientists have started to abandon the role of pure observers and are now exploiting intense THz radiation to engineer transient states of matter. This Review provides an overview and illustrative examples of how the elec. and magnetic fields of intense THz transients can be used to control matter and light resonantly and nonresonantly.
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    Nicoletti, D.; Cavalleri, A. Nonlinear light–matter interaction at terahertz frequencies. Adv. Opt. Photonics 2016, 8, 401– 464,  DOI: 10.1364/AOP.8.000401
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    Roques-Carmes, C.; Kooi, S. E.; Yang, Y.; Massuda, A.; Keathley, P. D.; Zaidi, A.; Yang, Y.; Joannopoulos, J. D.; Berggren, K. K.; Kaminer, I.; Soljacic, M. Towards integrated tunable all-silicon free-electron light sources. Nat. Commun. 2019, 10, 1– 8,  DOI: 10.1038/s41467-019-11070-7
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    Towards integrated tunable all-silicon free-electron light sources
    Roques-Carmes, Charles; Kooi, Steven E.; Yang, Yi; Massuda, Aviram; Keathley, Phillip D.; Zaidi, Aun; Yang, Yujia; Joannopoulos, John D.; Berggren, Karl K.; Kaminer, Ido; Soljacic, Marin
    Nature Communications (2019), 10 (1), 1-8CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    Extg. light from silicon is a longstanding challenge in modern engineering and physics. While silicon has underpinned the past 70 years of electronics advancement, a facile tunable and efficient silicon-based light source remains elusive. Here, we exptl. demonstrate the generation of tunable radiation from a one-dimensional, all-silicon nanograting. Light is generated by the spontaneous emission from the interaction of these nanogratings with low-energy free electrons (2-20 keV) and is recorded in the wavelength range of 800-1600 nm, which includes the silicon transparency window. Tunable free-electron-based light generation from nanoscale silicon gratings with efficiencies approaching those from metallic gratings is demonstrated. We theor. investigate the feasibility of a scalable, compact, all-silicon tunable light source comprised of a silicon Field Emitter Array integrated with a silicon nanograting that emits at telecommunication wavelengths. Our results reveal the prospects of a CMOS-compatible elec.-pumped silicon light source for possible applications in the mid-IR and telecommunication wavelengths.
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    Ye, Y. Deep-ultraviolet smith–purcell radiation. Optica 2019, 6, 592– 597,  DOI: 10.1364/OPTICA.6.000592
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    Deep-ultraviolet Smith-Purcell radiation
    Ye, Yu; Liu, Fang; Wang, Mengxuan; Tai, Lixuan; Cui, Kaiyu; Feng, Xue; Zhang, Wei; Huang, Yidong
    Optica (2019), 6 (5), 592-597CODEN: OPTIC8; ISSN:2334-2536. (Optical Society of America)
    Smith-Purcell radiation (SPR) is electromagnetic radiation generated by free electrons passing over a periodic grating. Here, having the electron beam pass through 30 nm wide slots in an Al grating greatly shortens the SPR wavelength, and a directional, ultra-broadband, tunable light source spanning λ0 ≈ 230-1100 nm is demonstrated. By adjusting the electron energy, backward SPR can be tuned over λ0 = 251-340 nm. This work greatly extends the wavelength of SPR from the previously reported 320 nm to 230 nm, and provides a means of realizing an integrated free-electron broadband light source covering the deep UV.
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    Hughes, T. W.; Williamson, I. A.; Minkov, M.; Fan, S. Forward-mode differentiation of Maxwell’s Equations. ACS Photonics 2019, 6, 3010– 3016,  DOI: 10.1021/acsphotonics.9b01238
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    Forward-mode differentiation of Maxwell's equations
    Hughes, Tyler W.; Williamson, Ian A. D.; Minkov, Momchil; Fan, Shanhui
    ACS Photonics (2019), 6 (11), 3010-3016CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    The authors discuss the application of the forward-mode differentiation method to Maxwell's equations, which is useful for the sensitivity anal. of photonic devices. This approach yields exact gradients and is similar to the popular adjoint variable method but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as the authors analyze it in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical deriv. methods, based on finite-difference approxns. To demonstrate the usefulness of the method, they perform sensitivity anal. of two problems. First, they compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielec. const. Then, they compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor.
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    Hughes, T.; Veronis, G.; Wootton, K. P.; England, R. J.; Fan, S. Method for computationally efficient design of dielectric laser accelerator structures. Opt. Express 2017, 25, 15414– 15427,  DOI: 10.1364/OE.25.015414
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    Symmetric single-quadrupole-magnet scan method to measure the 2D transverse beam parameters
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  1. Hyoung-Taek Lee, Jeonghoon Kim, Joon Sue Lee, Mina Yoon, Hyeong-Ryeol Park. More Than 30 000-fold Field Enhancement of Terahertz Nanoresonators Enabled by Rapid Inverse Design. Nano Letters 2023, 23 (24) , 11685-11692. https://doi.org/10.1021/acs.nanolett.3c03572
  2. Tinglian Zhang, Rasmus Ischebeck, Uwe Niedermayer, Thomas Schietinger, Pavle Juranić. Boosting the efficiency of narrowband THz radiators via three-dimensional emission collection. Physical Review Accelerators and Beams 2025, 28 (5) https://doi.org/10.1103/PhysRevAccelBeams.28.054501
  3. Hossein Shirvani, Chih-Ying Lien, Yen-Chieh Huang. Periodically corrugated waveguides for slow-wave THz free-electron laser. Physical Review Accelerators and Beams 2025, 28 (4) https://doi.org/10.1103/PhysRevAccelBeams.28.040701
  4. Ke Chen, Dandan Li, Ziyang Liu, Chenyi Yang, Bingheng Lu, Yadong Yang, Qianqian Wang, , , . Design and verification of a dielectric laser accelerator test system for sub-relativistic electrons. 2024, 28. https://doi.org/10.1117/12.3035533
  5. Tomáš Chlouba, Roy Shiloh, Stefanie Kraus, Leon Brückner, Julian Litzel, Peter Hommelhoff. Coherent nanophotonic electron accelerator. Nature 2023, 622 (7983) , 476-480. https://doi.org/10.1038/s41586-023-06602-7
  6. Niclas Westerberg, Robert Bennett. Perturbative light–matter interactions; from first principles to inverse design. Physics Reports 2023, 1026 , 1-63. https://doi.org/10.1016/j.physrep.2023.07.005
  7. Zhaofu Chen, Leilei Mao, Renjun Yang, Mengmeng Jin, Ningfeng Bai, Xiaohan Sun. Effect of absorption loss on resonance-enhanced Smith–Purcell radiation from metal-plate arrays. Journal of the Optical Society of America B 2023, 40 (1) , 115. https://doi.org/10.1364/JOSAB.476006
  8. Sergey Belomestnykh, Xueying Lu. Summary of Working Group 3: Laser and High-Gradient Structure-Based Acceleration. 2022, 1-5. https://doi.org/10.1109/AAC55212.2022.10822893
  9. S. Ya. Tochitsky, N. Lemos, R. A. Simpson, E.S. Grace, A. Pak, T. Ma, J. Chou, F. Fiuza, D. J. Haberbergr, A. Haid, C. Joshi. Exploring Potential of 3D Printed Structures in PW Laser-Driven Ion Acceleration Experiments. 2022, 1-5. https://doi.org/10.1109/AAC55212.2022.10822937
  10. Zhaofu Chen, Mengmeng Jin, Leilei Mao, Xin Shi, Ningfeng Bai, Xiaohan Sun. Enhancement of Smith–Purcell radiation from cylindrical gratings by quasi-bound states in the continuum. Optics Letters 2022, 47 (11) , 2911. https://doi.org/10.1364/OL.455763
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  • Abstract

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    Figure 1

    Figure 1. Inverse design and fabrication of THz radiator. (a) The design process is based on a 2D-FDFD simulation of a single unit cell of the grating (aspect ratio distorted). Applying periodic boundaries (green) in the longitudinal direction of the electron beam (blue) corresponds to the simulation of an infinitely long grating. In the transverse direction, we define perfectly matched layers (orange) to imitate free space. The design region (gray) extended 4.5 mm to each side of a 150 μm wide vacuum (white) channel for the electrons. The Poynting vector Sx was calculated outside the design region and served as the objective function of the optimization. (b) Optimized 2D design: structure material (black), vacuum (white), and associated electromagnetic field spectral density of the transverse-magnetic mode (red-blue). Three consecutive periods are shown. (c) 3D illustration of the extruded structure of (b) with 50 periods. The lower inset shows the electric field profile seen from the perspective of the electron obtained from a 3D-FDFD simulation. (d) Photograph of the inverse-designed structure fabricated by additive manufacturing. The dimensions of the entire structure are 6.5 × 6 × 45 mm (width × height × depth).

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    Figure 2

    Figure 2. Experimental setup. (a) Schematic of SwissFEL. The THz generation experiments were conducted at the ACHIP interaction chamber (26) located in the switch-yard to the Athos beamline. (b) Sketch of the Smith–Purcell THz generation and Michelson interferometer (MI) setup. The inset shows a typical autocorrelation measurement.

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    Figure 3

    Figure 3. Emission spectra. The Fourier transform of an autocorrelation measurement with a Michelson interferometer (black) is compared to 3D time-domain (green) and frequency-domain (orange) simulations. The gray area indicates the acceptance window of the spectrometer, defined by the angular acceptance of the Michelson interferometer. The narrowness of emission originates from the high mode density inside the microresonator formed by the two distributed Bragg reflectors on each side of the electron channel.

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    Figure 4

    Figure 4. Coherent scaling. The detected pulse energy is shown as a function of the bunch charge. In contrast to the linear fit (dashed red), the quadratic fit (solid blue) approximates the measurements within the uncertainties, which confirms the expected coherent enhancement. Vertical and horizontal error bars represent the RMS detector noise obtained from a background measurement and the uncertainty in the charge measurement, respectively.

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    Figure 5

    Figure 5. Possible applications of the beam-driven THz source in pump–probe experiments. (a) For ultrarelativistic electrons, a second electron bunch may be used to compensate for the longer path length of the THz pulse. X-rays are generated in the undulators of an FEL. (b) For subrelativistic electrons, the generated THz pulse is delayed to achieve simultaneous arrival of electron and THz radiation. (c) The structure becomes a tunable light source if the periodicity changes along the invariant direction; exemplified with a rectangular grating.

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    Figure 6

    Figure 6. Exemplary design evolution. Left to right: The first 100 steps of an exemplary inverse design optimization are shown above their respective objective value in relative units. Starting from a random design, the design evolves under stochastic gradient-based optimization. At multiple steps throughout the optimization, the design solution is disturbed by the addition of random noise and blurring of features, which tests the stability of the design and helps in exploring a larger design space. Such a procedure was repeated ∼50×, each time yielding a different design depending on the initial randomized design (similar to particle swarm optimization). We then selected those design groups that gave best performance, stability, and fabricability (similar to supervised learning). Continuing the optimization from there and repetitively disturbing the solution, a final design will have gone through more than 1000 steps of optimization before fabrication. The displayed structure evolution used slightly different optimization conditions than the design presented in this work.

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      Recent advancements in computational inverse-design approaches - algorithmic techniques for discovering optical structures based on desired functional characteristics - have begun to reshape the landscape of structures available to nanophotonics. Here, we outline a cross-section of key developments in this emerging field of photonic optimization: moving from a recap of foundational results to motivation of applications in nonlinear, topol., near-field and on-chip optics.
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      Fully-automated optimization of grating couplers
      Su, Logan; Trivedi, Rahul; Sapra, Neil V.; Piggott, Alexander Y.; Vercruysse, Dries; Vuckovic, Jelena
      Optics Express (2018), 26 (4), 4023-4034CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
      We present a gradient-based algorithm to design general 1D grating couplers without any human input from start to finish, including a choice of initial condition. We show that we can reliably design efficient couplers to have multiple functionalities in different geometries, including conventional couplers for single-polarization and single-wavelength operation, polarization-insensitive couplers, and wavelength-demultiplexing couplers. In particular, we design a fiber-to-chip blazed grating with under 0.2 dB insertion loss that requires a single etch to fabricate and no back-reflector.
    22. 22
      Sapra, N. V. On-chip integrated laser-driven particle accelerator. Science 2020, 367, 79– 83,  DOI: 10.1126/science.aay5734
      22
      On-chip integrated laser-driven particle accelerator
      Sapra, Neil V.; Yang, Ki Youl; Vercruysse, Dries; Leedle, Kenneth J.; Black, Dylan S.; England, R. Joel; Su, Logan; Trivedi, Rahul; Miao, Yu; Solgaard, Olav; Byer, Robert L.; Vuckovic, Jelena
      Science (Washington, DC, United States) (2020), 367 (6473), 79-83CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
      Particle accelerators represent an indispensable tool in science and industry. However, the size and cost of conventional radio-frequency accelerators limit the utility and reach of this technol. Dielec. laser accelerators (DLAs) provide a compact and cost-effective soln. to this problem by driving accelerator nanostructures with visible or near-IR pulsed lasers, resulting in a 104 redn. of scale. Current implementations of DLAs rely on free-space lasers directly incident on the accelerating structures, limiting the scalability and integrability of this technol. We present an exptl. demonstration of a waveguide-integrated DLA that was designed using a photonic inverse-design approach. By comparing the measured electron energy spectra with particle-tracking simulations, we infer a max. energy gain of 0.915 kilo-eV over 30μm, corresponding to an acceleration gradient of 30.5 mega-eV per m. On-chip acceleration provides the possibility for a completely integrated mega-eV-scale DLA.
    23. 23
      Szczepkowicz, A.; Schächter, L.; England, R. J. Frequency-domain calculation of smith–purcell radiation for metallic and dielectric gratings. Appl. Opt. 2020, 59, 11146– 11155,  DOI: 10.1364/AO.409585
      23
      Frequency-domain calculation of Smith-Purcell radiation for metallic and dielectric gratings
      Szczepkowicz, Andrzej; Schaechter, Levi; England, R. Joel
      Applied Optics (2020), 59 (35), 11146-11155CODEN: APOPAI; ISSN:2155-3165. (Optical Society of America)
      The intensity of Smith-Purcell radiation from metallic and dielec. gratings (silicon, silica) is compared in a frequency-domain simulation. The numerical model is discussed and verified with the Frank-Tamm formula for Cherenkov radiation. For 30 keV electrons, rectangular dielec. gratings are less efficient than their metallic counterpar ts, by an order of magnitude for silicon, and two orders of magnitude for silica. For all gratings studied, radiation intensity oscillates with grating tooth height due to electromagnetic resonances in the grating. 3D and 2D numerical models are compared.
    24. 24
      Kellermeier, M. Towards additive manufacturing of dielectric accelerating structures. J. Phys.: Conf. Ser. 2020, 1596, 012020,  DOI: 10.1088/1742-6596/1596/1/012020
      There is no corresponding record for this reference.
    25. 25
      Kingma, D. P.; Ba, J. Adam: A method for stochastic optimization. 3rd International Conference on Learning Representations; ICLR, 2015; Vols. 1–15.
      There is no corresponding record for this reference.
    26. 26
      Ferrari, E. The ACHIP experimental chambers at the Paul Scherrer Institut. Nucl. Instrum. Methods Phys. Res., Sect. A 2018, 907, 244– 247,  DOI: 10.1016/j.nima.2018.02.112
      26
      The ACHIP experimental chambers at the Paul Scherrer Institut
      Ferrari, Eugenio; Ischebeck, Rasmus; Bednarzik, Martin; Bettoni, Simona; Borrelli, Simona; Braun, Hans-Heinrich; Calvi, Marco; David, Christian; Dehler, Micha; Frei, Franziska; Garvey, Terence; Guzenko, Vitaliy A.; Hiller, Nicole; Hommelhoff, Peter; McNeur, Joshua; Orlandi, Gian Luca; Ozkan-Loch, Cigdem; Prat, Eduard; Reiche, Sven; Romann, Albert; Sarafinov, Blagoj; Rivkin, Leonid
      Nuclear Instruments & Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment (2018), 907 (), 244-247CODEN: NIMAER; ISSN:0168-9002. (Elsevier B.V.)
      The Accelerator on a Chip International Program (ACHIP) is an international collaboration, funded by the Gordon and Betty Moore Foundation, with the goal of demonstrating that laser-driven accelerator can be integrated on a chip to fully build an accelerator based on dielec. structures. PSI will provide access to the high brightness electron beam of SwissFEL to test structures, approaches and methods towards achieving the final goal of the project. In this contribution, we will describe the two interaction chambers installed on SwissFEL to perform the proof-of-principle expts. In particular, we will present the positioning system for the samples, the magnets needed to focus the beam to sub-micrometer dimensions and the diagnostics to measure beam properties at the interaction point.
    27. 27
      Milne, C. J. SwissFEL: The Swiss X-ray free electron laser. Appl. Sci. 2017, 7, 720,  DOI: 10.3390/app7070720
      There is no corresponding record for this reference.
    28. 28
      Kampfrath, T.; Tanaka, K.; Nelson, K. A. Resonant and nonresonant control over matter and light by intense terahertz transients. Nat. Photonics 2013, 7, 680– 690,  DOI: 10.1038/nphoton.2013.184
      28
      Resonant and nonresonant control over matter and light by intense terahertz transients
      Kampfrath, Tobias; Tanaka, Koichiro; Nelson, Keith A.
      Nature Photonics (2013), 7 (9), 680-690CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
      A review. Electromagnetic radiation in the terahertz (THz) frequency range is a fascinating spectroscopic tool that provides resonant access to fundamental modes, including the motions of free electrons, the rotations of mols., the vibrations of crystal lattices and the precessions of spins. Consequently, THz waves have been extensively used to probe such responses with high sensitivity. However, owing to recent developments in high-power sources, scientists have started to abandon the role of pure observers and are now exploiting intense THz radiation to engineer transient states of matter. This Review provides an overview and illustrative examples of how the elec. and magnetic fields of intense THz transients can be used to control matter and light resonantly and nonresonantly.
    29. 29
      Nicoletti, D.; Cavalleri, A. Nonlinear light–matter interaction at terahertz frequencies. Adv. Opt. Photonics 2016, 8, 401– 464,  DOI: 10.1364/AOP.8.000401
      There is no corresponding record for this reference.
    30. 30
      Roques-Carmes, C.; Kooi, S. E.; Yang, Y.; Massuda, A.; Keathley, P. D.; Zaidi, A.; Yang, Y.; Joannopoulos, J. D.; Berggren, K. K.; Kaminer, I.; Soljacic, M. Towards integrated tunable all-silicon free-electron light sources. Nat. Commun. 2019, 10, 1– 8,  DOI: 10.1038/s41467-019-11070-7
      30
      Towards integrated tunable all-silicon free-electron light sources
      Roques-Carmes, Charles; Kooi, Steven E.; Yang, Yi; Massuda, Aviram; Keathley, Phillip D.; Zaidi, Aun; Yang, Yujia; Joannopoulos, John D.; Berggren, Karl K.; Kaminer, Ido; Soljacic, Marin
      Nature Communications (2019), 10 (1), 1-8CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      Extg. light from silicon is a longstanding challenge in modern engineering and physics. While silicon has underpinned the past 70 years of electronics advancement, a facile tunable and efficient silicon-based light source remains elusive. Here, we exptl. demonstrate the generation of tunable radiation from a one-dimensional, all-silicon nanograting. Light is generated by the spontaneous emission from the interaction of these nanogratings with low-energy free electrons (2-20 keV) and is recorded in the wavelength range of 800-1600 nm, which includes the silicon transparency window. Tunable free-electron-based light generation from nanoscale silicon gratings with efficiencies approaching those from metallic gratings is demonstrated. We theor. investigate the feasibility of a scalable, compact, all-silicon tunable light source comprised of a silicon Field Emitter Array integrated with a silicon nanograting that emits at telecommunication wavelengths. Our results reveal the prospects of a CMOS-compatible elec.-pumped silicon light source for possible applications in the mid-IR and telecommunication wavelengths.
    31. 31
      Ye, Y. Deep-ultraviolet smith–purcell radiation. Optica 2019, 6, 592– 597,  DOI: 10.1364/OPTICA.6.000592
      31
      Deep-ultraviolet Smith-Purcell radiation
      Ye, Yu; Liu, Fang; Wang, Mengxuan; Tai, Lixuan; Cui, Kaiyu; Feng, Xue; Zhang, Wei; Huang, Yidong
      Optica (2019), 6 (5), 592-597CODEN: OPTIC8; ISSN:2334-2536. (Optical Society of America)
      Smith-Purcell radiation (SPR) is electromagnetic radiation generated by free electrons passing over a periodic grating. Here, having the electron beam pass through 30 nm wide slots in an Al grating greatly shortens the SPR wavelength, and a directional, ultra-broadband, tunable light source spanning λ0 ≈ 230-1100 nm is demonstrated. By adjusting the electron energy, backward SPR can be tuned over λ0 = 251-340 nm. This work greatly extends the wavelength of SPR from the previously reported 320 nm to 230 nm, and provides a means of realizing an integrated free-electron broadband light source covering the deep UV.
    32. 32
      Hughes, T. W.; Williamson, I. A.; Minkov, M.; Fan, S. Forward-mode differentiation of Maxwell’s Equations. ACS Photonics 2019, 6, 3010– 3016,  DOI: 10.1021/acsphotonics.9b01238
      32
      Forward-mode differentiation of Maxwell's equations
      Hughes, Tyler W.; Williamson, Ian A. D.; Minkov, Momchil; Fan, Shanhui
      ACS Photonics (2019), 6 (11), 3010-3016CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      The authors discuss the application of the forward-mode differentiation method to Maxwell's equations, which is useful for the sensitivity anal. of photonic devices. This approach yields exact gradients and is similar to the popular adjoint variable method but provides a significant improvement in both memory and speed scaling for problems involving several output parameters, as the authors analyze it in the context of finite-difference time-domain (FDTD) simulations. Furthermore, it provides an exact alternative to numerical deriv. methods, based on finite-difference approxns. To demonstrate the usefulness of the method, they perform sensitivity anal. of two problems. First, they compute how the spatial near-field intensity distribution of a scatterer changes with respect to its dielec. const. Then, they compute how the spectral power and coupling efficiency of a surface grating coupler changes with respect to its fill factor.
    33. 33
      Hughes, T.; Veronis, G.; Wootton, K. P.; England, R. J.; Fan, S. Method for computationally efficient design of dielectric laser accelerator structures. Opt. Express 2017, 25, 15414– 15427,  DOI: 10.1364/OE.25.015414
      33
      Method for computationally efficient design of dielectric laser accelerator structures
      Hughes, Tyler; Veronis, Georgios; Wootton, Kent P.; England, Joel R.; Fan, Shanhui
      Optics Express (2017), 25 (13), 15414-15427CODEN: OPEXFF; ISSN:1094-4087. (Optical Society of America)
      Dielec. microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important figure of merit. To design structures with high acceleration gradients, we explore the adjoint variable method, a highly efficient technique used to compute the sensitivity of an objective with respect to a large no. of parameters. With this formalism, the sensitivity of the acceleration gradient of a dielec. structure with respect to its entire spatial permittivity distribution is calcd. by the use of only two full-field electromagnetic simulations, the original and 'adjoint'. The adjoint simulation corresponds phys. to the reciprocal situation of a point charge moving through the accelerator gap and radiating. Using this formalism, we perform numerical optimizations aimed at maximizing acceleration gradients, which generate fabricable structures of greatly improved performance in comparison to previously examd. geometries.
    34. 34
      Van den Berg, P. Smith–purcell radiation from a line charge moving parallel to a reflection grating. J. Opt. Soc. Am. 1973, 63, 689– 698,  DOI: 10.1364/JOSA.63.000689
      There is no corresponding record for this reference.
    35. 35
      Fang, J.; Wu, Z. Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media. IEEE Trans. Microwave Theory Technol. 1996, 44, 2216– 2222,  DOI: 10.1109/22.556449
      There is no corresponding record for this reference.
    36. 36
      Prat, E. Symmetric single-quadrupole-magnet scan method to measure the 2d transverse beam parameters. Nucl. Instrum. Methods Phys. Res., Sect. A 2014, 743, 103– 108,  DOI: 10.1016/j.nima.2014.01.021
      36
      Symmetric single-quadrupole-magnet scan method to measure the 2D transverse beam parameters
      Prat, Eduard
      Nuclear Instruments & Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment (2014), 743 (), 103-108CODEN: NIMAER; ISSN:0168-9002. (Elsevier B.V.)
      Precise measurements of the transverse beam parameters are essential to control and optimize all types of charged particle beams. In this paper we present a novel method that uses one quadrupole magnet and one profile monitor to measure the transverse beam emittance and optics. In comparison to a conventional single-quadrupole scan measurement, this new technique measures the two transverse planes simultaneously. This novel procedure is faster, more intuitive and allows keeping under control the required quadrupole gradient and the beam sizes at the profile monitor. The application of the method is illustrated with the SwissFEL Injector Test Facility.