Showing papers on "High harmonic generation published in 1992"
TL;DR: It is found that ions can produce harmonics comparable in strength to those obtained from neutrals, and that the emission extends to much higher order.
Abstract: We present calculated optical harmonic spectra for atoms and ions in the high intensity regime to current short-pulse experiments. We find that ions can produce harmonics comparable in strength to those obtained from neutrals, and that the emission extends to much higher order. Simple scaling laws for the strength of the harmonic emission and the maximum observable harmonic are suggested. These results imply that the photoemission observed in recent experiments in helium and neon contains contributions from ions as well as neutrals.
1,155 citations
TL;DR: A two-dimensional, axisymmetric, relativistic fluid model describing the propagation of intense laser pulses in plasmas is formulated and numerically evaluated.
Abstract: A two-dimensional, axisymmetric, relativistic fluid model describing the propagation of intense laser pulses in plasmas is formulated and numerically evaluated. Relativistic guiding is ineffective in preventing the diffractive spreading of short laser pulses and long pulses become modulated due to relativistic and wake-field effects. Laser pulses can be propagated over many Rayleigh lengths by use of a performed plasma density channel or by tailoring the pulse profile. Ultrahigh axial electric fields can be generated behind the laser pulse.
359 citations
TL;DR: This method is based on the direct use of the acceleration of the atomic electron rather than the dipole moment of the atom, which produces a more exact numerical evaluation of the spectrum.
Abstract: We present a method for calculating the spectrum emitted by an atom in an intense laser field. This method is based on the direct use of the acceleration of the atomic electron rather than the dipole moment of the atom. We show, using a numerical calculation in one dimension, that this method produces a more exact numerical evaluation of the spectrum. This technique is particularly important in determining the background to the high harmonics emitted by the atom.
330 citations
TL;DR: It allows us to understand why efficient phase matching can be achieved in a strong-field regime for the laser-atom interaction, and how the harmonic fields build up in the nonlinear medium through a series of interferences.
Abstract: We perform detailed calculations of harmonic conversion in a 15-Torr jet of xenon into which a 1064-nm-wavelength 36-ps-pulse-width laser has been tightly focused, so that the peak intensity ranges from 5\ifmmode\times\else\texttimes\fi{}${10}^{12}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{13}$ W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. The single-atom emission rates are obtained by integrating the time-dependent Schr\"odinger equation. We employ an improved atomic model which includes excitation and ionization through states with both low-lying ionic cores. The propagation equations are solved using a general and efficient finite-difference technique. Excellent agreement with experimental data is obtained. We consider the effect of the defocusing of the pump beam by the free electrons in the saturation regime, and find it to be small for the conditions studied here. The spatial, temporal, and spectral profiles of the harmonic emission are presented. Significant blueshifts of the harmonics' spectral line shapes are observed in the saturation regime. Finally, using model polarizations, we discuss how the harmonic fields build up in the nonlinear medium, through a series of interferences. It allows us to understand why efficient phase matching can be achieved in a strong-field regime for the laser-atom interaction.
179 citations
TL;DR: In this paper, the development of compact high-intensity laser, made possible by the technique of chirped pulse amplification, is reviewed, including the complexities of high-power laser implementation, such as the generation of short pulses, pulse cleaning, widebandwidth amplification, temporal stretching and compression, and the requirements for high average powers.
Abstract: The development of compact high‐intensity lasers, made possible by the technique of chirped pulse amplification, is reviewed. This includes the complexities of high‐power laser implementation, such as the generation of short pulses, pulse cleaning, wide‐bandwidth amplification, temporal stretching and compression, and the requirements for high‐average powers. Details of specific solid‐state laser systems are given. Some applications of these lasers to short‐pulse coherent short‐wavelength [x‐ray ultraviolet (XUV)] sources are also reviewed. This includes several nonlinear effects observed by focusing a subpicosecond laser into a gas; namely, an anomalous scaling of harmonic generation in atomic media, an upper limit on the conversion efficiency of relativistic harmonics in a plasma, and the observation of short‐pulse self‐focusing and multifoci formation. Finally, the effects of large ponderomotive pressures (100 Mbars) in short‐pulse high‐intensity laser–plasma interactions are discussed, with relevance both to recombination x‐ray lasers and a novel method of igniting thermonuclear fusion.
153 citations
TL;DR: The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas is rich in a wide variety of new phenomena as discussed by the authors, including laser excitation of large-amplitude plasma waves (wake fields), relativistic optical guiding of laser pulses in preformed plasma channels, laser frequency amplification by ionization fronts and plasma waves, and stimulated backscattering from plasma and electron beams, and cooling of electron beams by intense lasers.
Abstract: The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas is rich in a wide variety of new phenomena. Advances in laser science have made possible compact terawatt lasers capable of generating subpicosecond pulses at ultrahigh powers (≥1 TW) and intensities (≥1018 W/cm2). These ultrahigh intensities result in highly relativistic nonlinear electron dynamics. This paper briefly addresses a number of phenomena including (i) laser excitation of large‐amplitude plasma waves (wake fields), (ii) relativistic optical guiding of laser pulses in plasmas, (iii) optical guiding by preformed plasma channels, (iv) laser frequency amplification by ionization fronts and plasma waves, (v) relativistic harmonic generation, (vi) stimulated backscattering from plasmas and electron beams, (vii) nonlinear Thomson scattering from plasmas and electron beams, and (viii) cooling of electron beams by intense lasers. Potential applications of these effects are also discussed.
128 citations
TL;DR: In this article, a linear theory using Laplace transforms for gyrotron traveling wave amplifiers (TWTs) and gyro-backward-wave oscillators (gyro-BWOs) is presented.
Abstract: A linear theory using Laplace transforms which is applicable to both gyrotron traveling wave amplifiers (gyro-TWTs) and gyrotron backward-wave oscillators (gyro-BWOs) is presented. The validity of the linear theory is verified by comparing it with an existing nonlinear self-consistent theory based on a different approach. In conjunction with a time-dependent multimode particle simulation code, the linear theory is applied to study the stability of harmonic gyro-TWTs. It is shown that a harmonic gyro-TWT can be made stable to all forms of spontaneous oscillations by employing a multistage interaction structure and that it can generate power levels far in excess of those possible for a fundamental gyro-TWT. The linear bandwidth of a second-harmonic gyro-TWT amplifier is also calculated. >
93 citations
TL;DR: In this paper, the focusing of an intense 1053-nm, 1-ps laser pulse in an argon gas vapor has been studied and it is shown that defocusing can occur and that it is sensitive both to the incident laser power and to the argon pressure in the experimental chamber.
Abstract: The focusing of an intense 1053-nm, 1-ps laser pulse in an argon gas vapor has been studied. Experimental results are reported for different gas pressures and incident laser powers. In this paper we show that defocusing can occur and that it is sensitive both to the incident laser power and to the argon gas pressure in the experimental chamber. It is suggested that such a phenomenon is due to the refractive index of the plasma created by optical-field-induced ionization of the gas in the leading edge of the laser pulse. We show that it is not possible to obtain simultaneously a high focused intensity (>1017 W/cm2) and a high electron density (>1019 cm−3).
81 citations
TL;DR: In this paper, high-order harmonic generation results obtained with different laser systems, a 1 ps 1053 nm Ndglass laser, a 2 ps 616 nm synchronously pumped dye laser, and a 36 ps 1064 nm mode-locked Nd-YAG laser and the second harmonics (308 nm and 532 nm) were investigated.
Abstract: The authors present high-order harmonic generation results obtained with different laser systems, a 1 ps 1053 nm Nd-glass laser, a 2 ps 616 nm synchronously pumped dye laser, a 36 ps 1064 nm mode-locked Nd-YAG laser and the second harmonics (308 nm and 532 nm) of the latter two systems. They investigate the influence of the laser pulse width, the excitation wavelength (from the near infrared to the ultraviolet) and the atomic medium on the number of photons produced and on the maximum energy attained. Harmonic generation also depends strongly on the focusing conditions. By using simple arguments and results of numerical calculations in xenon, they show that the conversion efficiency in general follows a simple b3 power law, b denoting the laser confocal parameter, up to a transition regime where the coherence length of the process becomes equal to the medium length. By applying the b3 scaling as a normalization factor, they can then compare experimental results obtained in different focusing geometries. Their experimental data show that the optimization of the photon energy produced is favoured by using long incident wavelengths and light atomic systems with a high ionization energy.
75 citations
TL;DR: In this article, an extremely high power second-harmonic gyro-TWT has been designed, evaluated and optimized with a self-consistent nonlinear numerical simulation code, which is based on the magnetron-injection-gun (MIG)-type beam.
Abstract: For pt.I, see ibid., vol.20, no.3, p.155-162 (1992). Based on an analytical study of the stability problems of gyrotron traveling wave amplifiers (gyro-TWTs), an extremely high power second-harmonic gyro-TWT has been designed, evaluated and optimized with a self-consistent nonlinear numerical simulation code. The design, which is based on the magnetron-injection-gun (MIG)-type beam, is presented. Using a 100 kV, 25 A MIG beam with alpha =1 and an axial velocity spread of 5%, nonlinear self-consistent analysis of a three-stage second-harmonic gyro-TWT amplifier predicts a peak output power of 533 kW, peak efficiency of 21.3% and a 7.4% saturated bandwidth, which verifies the theoretical predictions that a stable harmonic gyro-TWT can generate power levels an order of magnitude higher than those possible from a fundamental gyro-TWT. It is shown that the positioning of the electron beam is very important. A multistage structure is used to recover the loss in gain resulting from shortening the interaction sections to ensure stability. >
64 citations
01 Jan 1992
TL;DR: A simple phase-matching scheme, based on a resonant density modulation, is proposed and analyzed, and the nonlinear phase velocity and the renormalized electron mass due to plasmon screening are calculated.
Abstract: When an intense, plane-polarized, laser pulse interacts with a plasma, the relativistic nonlinearities induce a third-harmonic polarization. A phase-locked growth of a third-harmonic wave can take place, but the difference between the nonlinear dispersion of the pump and driven waves leads to a rapid unlocking, resulting in a saturation. What become third-harmonic amplitude oscillations are identified here, and the nonlinear phase velocity and the renormalized electron mass due to plasmon screening are calculated. A simple phase-matching scheme, based on a resonant density modulation, is then proposed and analyzed.
TL;DR: The observed decrease of the harmonic efficiencies with increasing harmonic order is much weaker than predicted by perturbative theories.
Abstract: Illuminating a gold surface by strong (5 GW/${\mathrm{cm}}^{2}$) picosecond neodymium-doped yttrium aluminum garnet laser pulses at grazing incidence, we observed a generation of coherent beams of both even and odd harmonics up to fifth order in the reflected direction with efficiencies ${10}^{\mathrm{\ensuremath{-}}10--}$${10}^{\mathrm{\ensuremath{-}}13}$. The observed decrease of the harmonic efficiencies with increasing harmonic order is much weaker than predicted by perturbative theories.
TL;DR: In this article, a scanning probe microscope was integrated into a microwave resonator tunable from 2.2 to 3.4 GHz with a quality factor Q larger than 1000, which caused generation of higher harmonics when rf fields in the range of 109 V/m were applied between tip and sample.
Abstract: A scanning probe microscope has been integrated into a microwave resonator tunable from 2.2 to 3.4 GHz with a quality factor Q larger than 1000. Nonlinear phenomena caused generation of higher harmonics when rf fields in the range of 109 V/m were applied between tip and sample. Higher harmonic signals were detected at a bandwidth of 10 kHz on conductor surfaces as well as on thin insulating films and were used as feedback to the control loop for imaging graphite surface features and oxidized silicon surfaces with subnanometer resolution.
TL;DR: In this paper, the authors analyzed the dynamics of the laser-electron interaction using a fully nonlinear, relativistic, cold fluid model valid to all orders in the amplitude of the pump laser.
Abstract: A comprehensive analysis is presented that describes the generation of harmonic radiation by the stimulated backscattering of intense laser fields from electron beams and from plasmas. The dynamics of the intense laser-electron interaction are analyzed using a fully nonlinear, relativistic, cold fluid model valid to all orders in the amplitude of the pump laser. In general, the backscattered radiation, from an electron beam or stationary plasma, occurs at odd harmonics of the Doppler-shifted incident laser frequency. The strength of the harmonics is strongly dependent on the incident laser intensity. The growth rate and saturation level of the backscattered harmonics are calculated, and the limitations due to thermal, space-charge, and collisional effects are discussed. Significant radiation generation at high harmonics requires sufficiently intense pump laser fields and sufficiently cold axial electron distributions. This mechanism may provide a practical method for producing coherent radiation in the xuv regime.
TL;DR: In this article, a systematic study of high-order harmonic generation in rare gases has been made for the first time with intense (2*1014 W cm-2, 616 nm) dye laser pulses, where the harmonic radiation up to the 41st order in He, the 37th in Ne, the 19th in Ar, the 17th in Kr and the 13th in Xe is observed.
Abstract: A systematic study of high-order harmonic generation in rare gases has been made for the first time with intense (2*1014 W cm-2, 616 nm) dye laser pulses, where the harmonic radiation up to the 41st order in He, the 37th in Ne, the 19th in Ar, the 17th in Kr and the 13th in Xe is observed. The individual harmonic distributions represent a plateau that is preceded by an intensity minimum and formed from an energy region near the ionization limit. The importance of dynamic resonances and shifting ionization limit is discussed to illustrate the plateau formation process observed.
06 Apr 1992
TL;DR: A comprehensive analysis is presented which describes the generation of harmonic radiation by the stimulated backscattering of intense laser fields from electron beams and from plasmas, and may provide a practical method for producing coherent radiation in the XUV regime.
Abstract: A comprehensive analysis is presented which describes the generation of harmonic radiation by the stimulated backscattering of intense laser fields from electron beams and from plasmas. The dynamics of the intense laser-electron interaction are analyzed using a fully nonlinear, relativistic cold fluid model valid to all orders in the amplitude of the pump laser. In general. the back-scattered radiation, from an electron beam or stationary plasma, occurs at odd harmonics of the doppler shifted incident laser frequency. The strength of the harmonics is strongly dependent on the incident laser intensity. The growth rate and saturation level of the backscattered harmonics are calculated and limitations due to thermal, space charge and collisional effects are discussed. Significant radiation generation at high harmonics requires sufficiently intense pump laser fields and sufficiently cold axial electron distributions. This mechanism may provide a practical method for producing coherent radiation in the XUV regime.
TL;DR: In this paper, a frequency- or phase-modulated optical signal becomes intensity modulated through dispersion in single-mode optical fibres, and this effect is supported by observation of 12% intensity modulation at the 60 GHz harmonic of a 4 GHz signal applied to a three-contact DFB laser.
Abstract: A frequency- or phase-modulated optical signal becomes intensity-modulated through dispersion in single-mode optical fibres. New theoretical results describing this effect are presented, and supported by observation of 12% intensity modulation at the 60 GHz harmonic of a 4 GHz signal applied to a three-contact DFB laser.
TL;DR: The data suggest that the highest harmonic order produced depends on the highest intensity seen by the atom before photoionization, and the extension of the harmonic plateau with increasing laser intensity.
Abstract: We observe harmonics of 526-nm laser light up to the 45th order, 11.7 nm, in helium. We discuss the extension of the harmonic plateau with increasing laser intensity. The data suggest that the highest harmonic order produced depends on the highest intensity seen by the atom before photoionization. Harmonics are generated predominantly from neutrals. Harmonic generation from ions is weak owing to poor phase matching between the fundamental and harmonic fields at high electron densities.
TL;DR: In this paper, femtosecond laser pulses were focused onto the surface of metal films and glass targets, and a relatively intense, well-collimated second harmonic was observed in the specular direction.
Abstract: Plasmas were produced by tightly focusing femtosecond laser pulses onto the surface of metal films and glass targets A relatively intense, well-collimated second harmonic could be observed in the specular direction The conversion efficiency reached 10/sup -4/ for focused intensities around 10/sup 16/ W/cm/sup 2/ Detailed measurements of the angular dependence, the polarization properties, and the second-harmonic frequency spectra were performed Time-resolved pump-probe experiments revealed interesting information about the dynamics of the plasmas It is suggested that resonant absorption plays an important role in second-harmonic generation >
TL;DR: The design and performance of the 3 x 3 arrays of potassium dihydrogen phosphate crystal plates used for phase-matched harmonic conversion of the Nova 0.74-m diameter beams are described and an alternate type-I-type-II phasematching configuration is described that improves third-harmonic conversion efficiency.
Abstract: To provide high-energy, high-power beams at short wavelengths for inertial-confinement fusion experiments, we routinely convert the 1.05-microm output of the Nova, Nd:phosphate-glass, laser system to its second- or third-harmonic wavelength. We describe the design and performance of the 3 x 3 arrays of potassium dihydrogen phosphate crystal plates used for type-II-type-II phase-matched harmonic conversion of the Nova 0.74-m diameter beams. We also describe an alternate type-I-type-II phasematching configuration that improves third-harmonic conversion efficiency. These arrays provide conversion of a Nova beam of up to 75% to the second harmonic and of up to 70% to the third harmonic.
TL;DR: Theoretical analysis and some experiments are performed on nonlinearly generated harmonic components in bounded sound beams emitted from a rectangular aperture source as mentioned in this paper, which takes account of nonlinearity, dissipation, and diffraction effects in the beams, numerically solved by means of the alternating direction implicit difference method.
Abstract: Theoretical analysis and some experiments are performed on nonlinearly generated harmonic components in bounded sound beams emitted from a rectangular aperture source The Khokhlov–Zabolotskaya–Kuznetsov equation, which takes account of nonlinearity, dissipation, and diffraction effects in the beams, is numerically solved by means of the alternating direction implicit difference method Using a planar source of size 24×44 cm, axial sound pressures and beam patterns of the first three harmonics are measured in air for initially sinusoidal ultrasounds of 25‐ and 30‐kHz frequency, and are compared with the theory They are in relatively good agreement Deformation of the source face from circular to rectangular shape results in the unclear appearance of pressure peaks and dips with propagation Within the framework of these studies, the harmonic pressure levels in the far field are almost the same as from a circular aperture source with equal face area and equal initial pressure, independent of the source le
TL;DR: The spectra obtained from ensemble-averaged atomic dipoles qualitatively reproduce the main features of those recently observed in experiments and allow, in particular, discussion of the occurrence of a plateau in the distribution of harmonic intensities as a function of their order.
Abstract: We present the results of our investigations of the dynamics of a classical hydrogen atom submitted to an intense classical radiation field with a relatively low frequency as compared to the characteristic Kepler frequency of the atomic system. We discuss here the harmonic spectra which can be deduced from a Fourier analysis of the time evolution of the strongly driven atomic dipole, associated either with a single trajectory or with ensembles of trajectories evolving from an initial microcanonical distribution. The spectra obtained from ensemble-averaged atomic dipoles qualitatively reproduce the main features of those recently observed in experiments and allow, in particular, discussion of the occurrence of a plateau in the distribution of harmonic intensities as a function of their order. The possible competition between harmonic generation and multiphoton ionization, which both take place in the same laser-intensity range, is also discussed.
TL;DR: Experimental measurements of harmonic generation in xenon using a 1064-nm 40-psec Nd-doped yttrium aluminum garnet laser shows regular oscillations whose period decreases with increasing harmonic order and which can be interpreted as phase-matching effects due to the tight focusing geometry.
Abstract: We present experimental measurements of harmonic generation in xenon using a 1064-nm 40-psec Nd-doped yttrium aluminum garnet laser. The harmonic yield is studied as a function of the position of the laser focus in the atomic beam. It shows regular oscillations whose period decreases with increasing harmonic order and which can be interpreted as phase-matching effects due to the tight focusing geometry. Moreover, the amplitudes of the oscillations vary rapidly with the laser intensity, a signature of resonance effects in the harmonic generation process.
TL;DR: In this article, a nonlinear self-consistent simulation code is employed to investigate the behavior of the slotted gyrotron traveling-wave amplifier (gyro-TWT), in which an axis-encircling electron beam synchronously interacts with a high-order azimuthal mode in a magnetron-type waveguide.
Abstract: A nonlinear self-consistent simulation code is employed to investigate the behavior of the slotted gyrotron traveling-wave amplifier (gyro-TWT), in which an axis-encircling electron beam synchronously interacts with a high-order azimuthal mode in a magnetron-type waveguide. The efficiency of a fourth-harmonic device with an ideal 60 kV, 5 A beam is shown to reach 30% for alpha identical to nu /sub perpendicular to // nu /sub z/=2. The growth rate for the pi mode is roughly 25% larger than for the 2 pi mode. The efficiency increases for lower voltage and the device is found to be moderately sensitive to the radial spread of the beam's guiding center position and extremely sensitive to the axial velocity spread. For an ideal 60 kV, 5 A beam with alpha =1.5, the efficiency of a second-harmonic gyro-TWT is 42% and falls to 10% for an eighth-harmonic device. The design of a 35 GHz, 60 kV, 5A, alpha =1.5, eight-vane, fourth-harmonic gyro-TWT with 7% axial velocity spread is presented. It is predicted that this design will yield a peak output power of 90 kW, a peak efficiency of 30%, and 6.3% saturated bandwidth. >
TL;DR: A nonperturbative method based on the numerical computation of solutions of the Schr\"odinger equation, to obtain the generation of harmonics of the incident laser.
Abstract: The interaction between a laser field and a crystalline solid is considered. The electron wave function in the crystal is obtained from an appropriately chosen pseudopotential. The dipole approximation is introduced, and only vertical transitions are taken into account. We present a nonperturbative method based on the numerical computation of solutions of the Schr\"odinger equation, to obtain the generation of harmonics of the incident laser. Particular numerical results are presented for the case of pure silicon. The mechanisms to enhance harmonic generation without excessive excitation of electrons to the conduction band are analyzed.
TL;DR: In this paper, the fourth and fifth harmonic of a Nd:YLF laser-regenerative amplifier system for the purpose of generating short (<70 ps), intense electron pulses was studied.
Abstract: Linear photoemission from pure metal surfaces has been studied using the fourth (263 nm) and fifth (211 nm) harmonic of a Nd:YLF laser‐regenerative amplifier system for the purpose of generating short (<70 ps), intense electron pulses. Capacitive charge limitations for the pulsed mode of operation of a laser‐driven photodiode are used to explain the observed current‐voltage characteristics. Quantum efficiencies at the two different wavelengths for eleven photocathode materials are presented.
TL;DR: The time-dependent Schroedinger equation for the helium atom with a model potential is solved on a numerical grid and it is found that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV.
Abstract: The time-dependent Schroedinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.
TL;DR: It is seen that the acceleration form provides a more satisfactory and accurate framework for the study of the photoemission HG spectrum at very intense fields, particularly when ionization becomes appreciable.
Abstract: We present a study of the high-order harmonic-generation (HG) spectra of atomic hydrogen at 248 nm based on the Fourier transform of the expectation values of the induced dipole moment and acceleration. The calculations were performed by extending a fast-Fourier-transformation split-operator technique (in spherical coordinates) to the solution of the time-dependent wave functions in intense laser fields. It is seen that the acceleration form provides a more satisfactory and accurate framework for the study of the photoemission HG spectrum at very intense fields, particularly when ionization becomes appreciable.
01 Jul 1992-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, the design parameters of a harmonic generation FEL experiment at the accelerator test facility (ATF) at BNL were presented as a proof-of-principle for the proposed UV-FEL user's facility.
Abstract: We present the design parameters of a harmonic generation FEL experiment to be carried out at the accelerator test facility (ATF) at BNL. This experiment will be carried out as a proof-of-principle for the proposed UV-FEL user's facility at BNL. In the experiment we plan to triple the frequency of a CO2 seed laser by utilizing two superconducting wigglers and a dispersive section. The first wiggler will be used in conjunction with the CO2 seed laser to generate a ponderomotive force that will bunch the electron beam. The bunching will then be enhanced by the dispersion section. The second wiggler, tuned to the third harmonic of the seed laser will follow. In the beginning of the second wiggler the bunched beam will produce superradiant emission (characterized by a quadratic growth of the radiated power), then the radiation will be amplified exponentially. The last part of the wiggler will be tapered. We plan to study the evolution of the various radiation growth mechanisms as well as the coherence of the tripled and exponentially amplified radiation.