Abstract
PHYSICAL REVIEW A VOLUME 35, NUMBER 8 APRIL 15, 1987 Theory of short-wavelength lasing from channeled projectiles: Nondegenerate dipole transitions G. Kurizki Chemical Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel M. Strauss and J. Oreg The Negev Nuclear Research Center, Beer Sheva 84190, Israel N. Rostoker Physics Department, of California, Irvine, California 9271 7 (Received 28 August 1986) University A theory is developed for lasing action from ensembles of relativistically or subrelativistically propagating emitters whose motion is bound in the direction(s) transverse to the direction of propa- gation. These include relativistic electrons and positrons channeled in crystals or other hollow- channel structures, as well as fast ions wherein a bound electron is perturbed by the crystal potential or laser light. Apart from planar-channeled positrons in crystals, the confining potentials for all other emitters in this category are strongly anharmonic. Therefore, their spectral dipolar transitions are nondegenerate, each involving a different pair of nearly discrete levels of the confining potential. This implies that stimulated emission from such systems can exhibit coherence in the Glauber sense. The theoretical framework presented here consists of Heisenberg equations which have the Maxwell-Bloch form with modifications resulting from the high velocity of the emitters. Steady- state semiclassical solutions of these equations are obtained. It is shown that previous approaches, based on the assumption that the cross section for stimulated emission is uniform throughout the system, do not account for the spatial variation of the polarization at high velocities. As a result, these approaches do not yield the correct gain coefficient whenever the characteristic lengths for the dephasing of the dipole oscillation and for emission amplification are comparable. The latter condi- tions are realizable in structures composed of channels much wider than in crystals. Lasing schemes are investigated and the prospects for achieving gain in these schemes at wavelengths below 100 A are discussed. I. INTRODUCTION (vacuum uv Many types of stimulated short-wavelength and x-ray) radiation sources that have been suggested over the years employ beams of high-velocity (relativistic or subrelativistic) emitters. The appeal of such sources lies in the fact that the emission is continuously Doppler shifted towards shorter wavelengths and becomes progres- sively more collimated about the beam direction as the beam velocity is increased. Such sources may be grouped into two categories. (a) Free electron lasers (FE-L's), encompassing structures wherein a spatially periodic perturbation acts either on the electron beam (as in magnetic undulators, ' light and crystals serving as coherent bremsstrah- wigglers, or on the emitted radiation (due to lung amplifiers) periodic changes in the refraction index, e.g. , in superlat- devices tices acting as transition-radiation ). The emis- sion features in FEL's are determined by transfer of discrete momentum (wiggler quanta or reciprocal lattice vectors) to the structure from the emitter or the field. Generally, many quantum states of the emitting electron are involved in the dynamics, which is governed by equa- As a re- tions of the Raman-Nath or Mathieu type. ' FEL radiation is, in principle, not sult, short-wavelength non- coherent (in the Glauber sense), ' exhibiting Poissonian photon statistics. In the quantum regime of operation, quantum recoil (which is responsible for gain) hampers coherence and, during the start-up stage, many- particle effects lead to thermal statistics. ' In the classical steady-state regime, too, small deviations from coherence are predicted. ' (TCE's), i. e. , emitters confinement (b) Transverse emitters whose motion is bound in the direction(s) trans- verse to the direction of propagation. These include rela- tivistic electrons and positrons channeled in crystals' or other hollow structures, ' as well as fast ions wherein a bound electron is perturbed by the crystal potential' or laser light. The emission wavelengths are determined by the nearly discrete spectrum of their transverse-energy states and by the Doppler shift due to their longitudinal motion. Planar channeled positrons in crystals are the only TOE's whose nearly harmonic transverse confining potential requires the inclusion of many states in the dynamical description. All other emitters in this category are confined by strongly anharmonic potentials and there- fore their dynamics involves directly only the upper and lower nearly discrete states of a particular spectral (nonde- generate) transition. Hence, these systems can, in princi- ple, exhibit true lasing (coherent stimulated emission). The American Physical Society
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.