We propose an analytical approach to characterize undulator radiation near resonance, when the presence of the vacuum-pipe considerably affects radiation properties. This is the case of the far-infrared undulator beamline at the Free-electron LASer (FEL) in Hamburg (FLASH), that will be capable of delivering pulses in the TeraHertz (THz) range. This undulator will allow pump-probe experiments where THz pulses are naturally synchronized to the VUV pulse from the FEL, as well as the development of novel electron-beam diagnostics techniques. Since the THz radiation diffraction-size exceeds the vacuum-chamber dimensions, characterization of infrared radiation must be performed accounting for the presence of a waveguide. We developed a theory of undulator radiation in a waveguide based on paraxial and resonance approximation. We solved the field equation with a tensor Green's function technique, and extracted figure of merits describing in a simple way the influence of the vacuum-pipe on the radiation pulse as a function of the problem parameters. Our theory, that makes consistent use of dimensionless analysis, allows treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability.
The law of photon radiation from electron beams passing through a photonic crystal in the presence of an undulator is considered. The spectral-angular distribution and the time evolution of radiation is found. It is shown that the characteristics of the radiation intensity in time demonstrate oscillations due to the interference between undulator and parametric (quasi-Cherenkov) radiations.
The radiation of twisted photons by undulators filled with a homogeneous dielectric dispersive medium is considered. The general formulas for the average number of radiated twisted photons are obtained. The radiation of undulators in the dipole regime and the radiation of the helical and planar wigglers are studied in detail. It is shown that the selection rules for radiation of twisted photons established for undulators in a vacuum also holds for undulators filled with a dielectric medium. In the case of a medium with plasma permittivity the lower undulator harmonics do not form. This fact ca…
The explicit expressions for the average number of twisted photons radiated by a charged particle in an elliptical undulator in the classical approximation as well as in the approach accounting for the quantum recoil are obtained. It is shown that radiation emitted by a particle moving along an elliptical helix which evolves around the axis specifying the angular momentum of twisted photons obeys the selection rule: $m+n$ is an even number, where $m$ is a projection of the total angular momentum of a twisted photon and $n$ is the harmonic number of the undulator radiation. This selection rule …
Recent theoretical and experimental studies have shown that Self-Amplified Spontaneous Emission Free Electron Laser (SASE FEL) with a planar undulator holds a potential for generation of relatively strong coherent radiation at the third harmonic of the fundamental frequency. Here we present detailed study of the nonlinear harmonic generation in the SASE FEL obtained with time-dependent FEL simulation code. Using similarity techniques we present universal dependencies for temporal, spectral, and statistical properties of the odd harmonics of the radiation from SASE FEL. In particular, we derive…
The crystalline undulator is a single crystal with periodically bent crystallographic planes. If ultrarelativistic charged particles channel through such a crystal, they emit hard radiation of undulator type. A crystalline undulator with a bending amplitude smaller than the distance between the bent planes and a bending period shorter than the period of channeling oscillations is proposed. Heretofore, it was believed that such a range of bending parameters was unsuitable for a crystalline undulator. This point of view is refuted. In fact, the undulator with a small amplitude and a short period…
A dielectric laser accelerator, operating at optical frequencies and GHz pulse rate, is expected to produce attosec electron bunches with a moderate beam current at high energy. For relativistic electrons, the attosec bunch has a spatial length of a few nanometers, which is well suited for generating high-brightness superradiance in the VUV, EUV, and x-ray spectra. Our study shows that the brilliance of coherent undulator radiation driven by a short-bunch beam with 1~10 fC bunch charge from a dielectric laser accelerator is comparable to or higher than that of a synchrotron in the 0.1 ~ 3 keV …
On-chip high energy photon radiation source based on microwave-dielectric undulator
Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academy of Sciences (CAS)（中国科学院上海光学精密机械研究所）；University of Chinese Academy of Sciences（中国科学院大学）
The general formula for the probability of radiation of a twisted photon by a classical current is derived. The general theory of generation of twisted photons by undulators is developed. It is proved that the probability to record a twisted photon produced by a classical current is equal to the average number of twisted photons in a given state. The general formula for the projection of the total angular momentum of twisted photons with given the energy, the longitudinal projection of momentum, and the helicity is obtained. The symmetry property of the average number of twisted photons produc…
This paper describes a theory of transverse coherence properties of Undulator Radiation. Our study is of very practical relevance, because it yields specific predictions of Undulator Radiation cross-spectral density in various parts of the beamline. On the contrary, usual estimations of coherence properties assume that the undulator source is quasi-homogeneous, like thermal sources, and rely on the application of van Cittert-Zernike (VCZ) theorem, in its original or generalized form, for calculating transverse coherence length in the far-field approximation. The VCZ theorem is derived in the f…
VFEL lasing in system with dynamical undulator is described. In this system radiation of long wavelength creates the undulator for lasing on shorter wavelength. Two diffraction gratings with different spatial periods form VFEL resonator. The grating with longer period pumps the resonator with long wavelength radiation to provide necessary amplitude of undulator field. The grating with shorter period makes mode selection for short wavelength radiation. Lasing of such a system in terahertz frequency range is discussed.
The laser-plasma accelerator has attracted great interest for constituting an alternative in the production of the relativistic electron beams of high peak current. But the generated electron beam has poor monochrome and emittance, which make it difficult to produce high brightness radiation. Here we propose a compact flexible laser undulator based on ponderomotive force to constitute a millimeter-sized synchrotron radiation source of X-ray. We demonstrate that it can produce bright radiation with tens of keV energies. This opens a new path to compact synchrotron source with high power laser.
If an ultrarelativistic charged particle channels inside a single crystal with periodically bent crystallographic planes, it emits hard electromagnetic radiation of the undulator type. Due to similarity of its physical principles to the ordinary (magnetic) undulator, such a device is termed as the crystalline undulator. Recent development of a new Monte Carlo code ChaS made possible a detailed simulation of particle channeling and radiation emission in periodically bent crystals. According to recent findings, energy of the electron beam below 1 GeV is sufficient to observe the undulator effect…
This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four ord…
We propose a scheme for generation of single 100 GW 300-as pulse in the X-ray free electron laser with the use of a few cycles optical pulse from Ti:sapphire laser system. Femtosecond optical pulse interacts with the electron beam in the two-period undulator resonant to 800 nm wavelength and produces energy modulation within a slice of the electron bunch. Following the energy modulator the electron beam enters the first part of the baseline gap-adjustable X-ray undulator and produces SASE radiation with 100 MW-level power. Due to energy modulation the frequency is correlated to the longitudina…
One goal of XFEL facilities is the production of narrow bandwidth X-ray radiation. The self-seeding scheme was proposed to obtain a bandwidth narrower than that achievable with conventional X-ray SASE FELs. A self-seeded FEL is composed of two undulators separated by a monochromator and an electron beam bypass that must compensate for the path delay of X-rays in the monochromator. This leads to a long bypass, with a length in the order of 40-60 m, which requires modifications of the baseline undulator configuration. As an attempt to get around this obstacle, together with a study of the self-s…
In this paper we analyze the image formation problem for undulator radiation through an optical system, accounting for the influence of the electron beam emittance. On the one hand, image formation with Synchrotron Radiation is governed by the laws of Statistical Optics. On the other hand, the widely used Gaussian-Shell model cannot be applied to describe the coherence properties of X-ray beams from third generation Synchrotron Radiation sources. As a result, a more rigorous analysis of coherence properties is required. We propose a technique to explicitly calculate the cross-spectral density …
The most promising way to increase the output power of an X-ray FEL (XFEL) is by tapering the magnetic field of the undulator. Also, significant increase in power is achievable by starting the FEL process from a monochromatic seed rather than from noise. This report proposes to make use of a cascade self-seeding scheme with wake monochromators in a tunable-gap baseline undulator at the European XFEL to create a source capable of delivering coherent radiation of unprecedented characteristics at hard X-ray wavelengths. Compared with SASE X-ray FEL parameters, the radiation from the new source ha…
A new algorithm to perform coherent mode decomposition of the undulator radiation is proposed. It is based in separating the horizontal and vertical directions, reducing the problem by working with one-dimension wavefronts. The validity conditions of this approximation are discussed. Simulations require low computer resources, and run interactively in a laptop. We study the focusing with lenses of the radiation emitted by an undulator in a fourth-generation storage ring (EBS-ESRF). Results are compared against multiple optics packages implementing a variety of methods for dealing with partial …
Ultraviolet and extreme ultraviolet electric-fields produced by relativistic electrons in an undulator of a synchrotron light source are characterized by using spectral phase interferometry for direct electric-field reconstruction (SPIDER). A tandem undulator with a phase shifter produces a pair of wavelength shifted wave packets with some delay. The interferogram between the pair of the wave packets is analyzed with a SPIDER algorithm, which is widely used for ultrashort pulse characterization. As a result, a 10-cycle square shaped electric-field is reconstructed. The waveform corresponds to …
Within the framework of a Hilbert space theory, we develop a maximum-``power'' variational principle (MPVP) applicable to classical spontaneous electromagnetic radiation from relativistic electron beams or other prescribed classical current sources. A simple proof is summarized for the case of three-dimensional fields propagating in vacuum, and specialization to the important case of paraxial optics is also discussed. The techniques have been developed to model undulator radiation from relativistic electron beams, but are more broadly applicable to synchrotron or other radiation problems, and …
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical situati…
The dynamical response of a relativistic bunch of electrons injected in a planar magnetic undulator and interacting with a counterpropagating electromagnetic wave is studied. We demonstrate a resonance condition for which the free electron laser (FEL) dynamics is strongly influenced by the presence of the external field. It opens up the possibility of control of short wavelength FEL emission characteristics by changing the parameters of the microwave field without requiring change in the undulator's geometry or configuration. Numerical examples, assuming realistic parameter values analogous to…
A robust method for producing half-cycle - few-cycle pulses in mid-infrared to extreme ultraviolet spectral ranges is proposed. It is based on coherent undulator radiation of relativistic ultrathin electron layers, which are produced by microbunching of ultrashort electron bunches by a TW power laser in a modulator undulator. According to our numerical calculations it is possible to generate as short as 10 nm long electron layers in a single-period modulator undulator having an undulator parameter of only K=0.25 and which is significantly shorter than the resonant period length. By using these…
Radiative emission from a semi-infinite unflanged circular cylindrical dielectric waveguide or optical fiber is studied for the case of axisymmetric modes of TM polarization on the basis of an iterative scheme. The first step of the scheme leads to approximate values for the reflection coefficients and the electromagnetic fields inside and outside the waveguide. In a numerical example the reflection back into the waveguide is appreciable. Correspondingly the radiation pattern of the outgoing radiation differs appreciably from the lowest order approximation in which reflection is neglected.
In this letter, the leakage radiation microscopy (LRM) is extended into characterization of planar waveguide modes (WMs) rather than surface plasmon polaritons (SPPs) taking advantages of the coupling between WMs and fluorescence emission. Propagation constants of different WMs allowed in the same planar waveguide can be simultaneously and rapidly derived from the Fourier plane image of fluorescence based LRM. Numerical simulations are also carried out to calculate propagation constants of these modes, which are consistent with experimental results. Our experiments provide a simple but high ef…
Recently it was suggested that Hawking radiation may be observed in a nonlinear electromagnetic waveguide upon propagation of an optical pulse. We show that the spectral characteristics of the Hawking effect in such a waveguide are indistinguishable from the well-known effect of frequency broadening of an optical pulse due to self-phase modulation. Furthermore, we derive an estimate on the critical optical power at which Hawking effect is dominated by the self-phase modulation. It appears that optical experiments reported so far are clearly dominated by self-phase modulation.
A numerical study of the radiation in coupled bent waveguides is presented. Such arrangements of curved waveguides in reduced radiation-loss configurations can be used to enhance the quality factor of integrated micro-resonators. 3D full vector computations of the complex modal fields (and propagation constants) and the transient propagation effects have been performed. The results obtained agree qualitatively with former 2D FDTD analyses. At the same time, the calculations presented meet the accuracy requirements for the design of practical implementations that are unattainable with 2D approa…
