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Physical review. B, Condensed matter

Interaction of a tunable probe beam with a high-intensity pulsed C O2 -laser beam in p -type germanium

R. B. James, Darryl Lyle Smith

Published Feb 15, 1984• 2 citations
Publisher

Abstract

A theoretical study is presented of the interaction between a high-intensity pump beam with a wavelength of 10.6 \ensuremath{\mu}m and a low-intensity probe beam which is tunable in the (9-11)-\ensuremath{\mu}m region. The dominant absorption mechanism of the optical beams in $p$-type Ge is direct intervalence-band transitions between states in the heavy- and light-hole bands. The hole states in resonance with the pump tend to saturate at sufficiently high intensities due to changes in the occupation probabilities of the initial and final states. When the material is simultaneously irradiated by the pump and probe beams, there is a nonlinear response which produces a component in the hole population difference between the heavy- and light-hole bands which oscillates at the beat frequency. This oscillating component in the population difference acts as a spatial and temporal grating which mixes the two beams. The absorption of the probe beam is modified by the presence of the pump beam by both the saturation of the intervalence-band transitions and by the oscillating population difference, which can scatter pump photons into the direction of the probe beam with the frequency shifted to that of the probe. Calculations of the probe absorption as a function of the frequency difference between the probe and pump beams are presented. These calculations of the absorption spectrum are compared with experimental results and good agreement is found. In addition to modifying the probe absorption spectrum, the oscillating population difference leads to a current-density component which oscillates at the pump frequency plus the beat frequency. If the pump and probe beams are nearly phase matched, this current-density component can generate a new optical beam that oscillates at the pump frequency plus the beat frequency. The intensity of this generated wave is estimated as a function of the beat frequency and the pump and probe intensities.

DOI
10.1103/physrevb.29.2036

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 3, 1994•0 citations
A theoretical study is presented of the interaction between a high-intensity pump beam with a wavelength of 10.6 \ensuremath{\mu}m and a low-intensity probe beam which is tunable in the (9-11)-\ensuremath{\mu}m region. The dominant absorption mechanism of the optical beams in ppp-type Ge is direct intervalence-band transitions between states in the heavy- and light-hole bands. The hole states in resonance with the pump tend to saturate at sufficiently high intensities due to changes in the occupation probabilities of the initial and final states. When the material is simultaneously irradiated by the pump and probe beams, there is a nonlinear response which produces a component in the hole population difference between the heavy- and light-hole bands which oscillates at the beat frequency. This oscillating component in the population difference acts as a spatial and temporal grating which mixes the two beams. The absorption of the probe beam is modified by the presence of the pump beam by both the saturation of the intervalence-band transitions and by the oscillating population difference, which can scatter pump photons into the direction of the probe beam with the frequency shifted to that of the probe. Calculations of the probe absorption as a function of the frequency difference between the probe and pump beams are presented. These calculations of the absorption spectrum are compared with experimental results and good agreement is found. In addition to modifying the probe absorption spectrum, the oscillating population difference leads to a current-density component which oscillates at the pump frequency plus the beat frequency. If the pump and probe beams are nearly phase matched, this current-density component can generate a new optical beam that oscillates at the pump frequency plus the beat frequency. The intensity of this generated wave is estimated as a function of the beat frequency and the pump and probe intensities.
We investigate spectral changes induced by high-power CO2laser radiation in the direct intervalence band absorption of p-type germanium. Using a model of inhomogeneously broadened two-level systems, we deduce a room-temperature saturation intensity of 4 MW/ cm2from published observations of saturation of this absorption. The applicability of the two-level model to transitions between two electronic bands is discussed. We relate the linear absorption coefficient to the saturation intensity and the effective population difference, where the latter is obtained in a spherical band approximation. The result yields a value of 0.55 ps for the geometric mean of the phase and energy relaxation times. The meaning of these times is explained for our system, and quantitative agreement is found with published data on optical and acoustical lattice scattering probabilities. Specifically, we find a very short phase relaxation time of 0.09 ps. This allows the prediction of a burnt-hole spectral width of 57 cm-1(HWHM) at small saturation. In a preliminary experiment, we have observed the modulation of a CW CO2laser beam by intense nanosecond pulses of a second CO2laser offset in frequency by up to 140 cm-1.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
Through the use of modulation spectroscopy we have measured the absorption spectrum experienced by a weak probe beam in the presence of a saturating pump beam at two different wavelengths within the broad homogeneous absorption band of alexandrite. At 584 nm the absorption saturates at high pump intensities, and a hole (of width 612 Hz) appears at frequencies near that of the pump laser. However, at 457 nm the absorption demonstrates the inverse of normal saturation because of strong excited-state absorption, and an antihole appears at the pump frequency. These results are in good quantitative agreement with the predictions of a model that ascribes the origin of these spectral features to the temporal modulation of the ground-state population at the beat frequency between the pump and the probe beams. These population oscillations are treated properly within a rate-equation approximation in which the amplitude modulation of the total optical intensity caused by the beating of the pump and the probe beams is taken into account.
We employ the Dynamical Projective Operatorial Approach (DPOA) to investigate the ultrafast optical excitations of germanium under intense, ultrashort pump pulses. The method has very low resource demand relative to many other available approaches and enables detailed calculation of the residual electron and hole populations induced by the pump pulse. It provides direct access to the energy distribution of excited carriers and to the total energy transferred to the system. By decomposing the response into contributions from different multi-photon resonant processes, we systematically study the dependence of excited-carrier density and absorbed energy on key pump-pulse parameters: duration, amplitude, and photon energy. Our results reveal a complex interplay between these parameters, governed by resonant Rabi-like dynamics and competition between different multi-photon absorption channels. For the studied germanium setup, we find that two-photon processes are generally dominant, while one- and three-photon channels become significant under specific conditions of pump-pulse frequency, duration, and intensity. This comprehensive analysis offers practical insights for optimizing ultrafast optical control in semiconductors by targeting specific multi-photon pathways.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
The numerical simulations of two coaxial laser beams, pump and probe, propagating in a three-level absorber are presented. The fixed-pump beam frequency and the variable-probe beam frequency are near-resonant to the adjacent transitions. Depending on the ratio of the population relaxation rates, either absorption or amplification of the probe field may occur, both demonstrating symmetric Rabi-splitted spectra of the absorption coefficient if the on-resonance pump intensity is high enough. In contrary to this, the spectra of the probe beam transmitted intensity are shown to be asymmetric due to the frequency-sensitive saturated refraction induced by the pump beam. The competition of level population changes and Rabi splitting is shown to cause the nontrivial induced lenses responsible for the complicated dependence of spectral asymmetry upon the pump intensity.