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IEEE Journal of Quantum Electronics

Infrared saturation spectroscopy in p-type germanium

F. Keilmann

Published Oct 1, 1976• 79 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1976.1069045

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

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We study sub-Doppler saturation resonances at cesium molecular transitions in the absorption band B1Πu ← X1∑g+ near 780 nm by using a commercial diode laser. The saturation power is measured as low as 5.7 mW with the laser beam diameter of 0.1 cm. Optical saturation is associated with the optical pumping of molecular ground-state levels. The long relaxation time of ground-state levels could attract interest to electromagnetically induced transparency and quantum state memory in the molecular gas. We propose to use the molecular transitions as references for doubled-frequency sources in the communication band around 1550 nm.

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Radiationless relaxation and optical dephasing of molecules excited by wide- and narrow-band lasers. II. Pentacene in low-temperature mixed crystals

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One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g→1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and μ=0.7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h//μ⋅ε) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h//μ⋅ε) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ε. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ’’complete’’ level structure of pentacene (ground‖0〉, singlet ‖p〉, and triplet {‖l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 μsec, the time constants by which pentacene spontaneously decays to ‖0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and μ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ’’accepting’’ phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ’’conventional’’ dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {‖l〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (∼15 μsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.

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Journal of the Optical Society of America•May 1, 1983•5 citations
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.
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 study sub-Doppler saturation resonances at cesium molecular transitions in the absorption band B1Πu ← X1∑g+ near 780 nm by using a commercial diode laser. The saturation power is measured as low as 5.7 mW with the laser beam diameter of 0.1 cm. Optical saturation is associated with the optical pumping of molecular ground-state levels. The long relaxation time of ground-state levels could attract interest to electromagnetically induced transparency and quantum state memory in the molecular gas. We propose to use the molecular transitions as references for doubled-frequency sources in the communication band around 1550 nm.
One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g→1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and μ=0.7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h//μ⋅ε) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h//μ⋅ε) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ε. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ’’complete’’ level structure of pentacene (ground‖0〉, singlet ‖p〉, and triplet {‖l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 μsec, the time constants by which pentacene spontaneously decays to ‖0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and μ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ’’accepting’’ phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ’’conventional’’ dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {‖l〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (∼15 μsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.
The behaviour of an optically thick column of barium vapour resonantly 10 -2 illuminated at 553.5m by a 50 ns, 10 Wm pulse from a flashlamp pumped dye 19 21 -3 laser system was investigated for barium number densities in the range 10 -10 m in the presence of He buffer gas at 100 Torr.A variety of optical saturation effects associated with the principal resonance transition were studied.In marked contrast to earlier work, saturation of the intensity of the scattered light near 553.5 nm with increasing laser power was found for a suitable geometry of the collection optics but at a laser intensity typically two orders of magnitude higher than that predicted by simple theory, despite the fact that this theory was found to describe correctly transmission measurements along the length of the vapour column.The apparent contradiction between the fluorescence and transmission results, which indicated that the scattered radiation intensity continued to rise with incident laser power, despite the population of the upper resonance level having reached a limiting saturation value, could be understood in terms of a simple model which took into consideration the spectral distribution of the scattered light and its transfer through the unexcited vapour.However, in common with other similar experiments, saturation of the scattered radiation intensity with laser power could not be totally achieved when a more usual collection optics geometry was employed.This was interpreted as a consequence of laser intensity variation across the face of the laser beam.A number of subsidiary experiments were performed.These included spatially resolved intensity measurements of the scattered radiation and time resolved metastable level population measurements.In addition, evidence for laser induced ionization was sought using two different methods and this enabled an upper limit of 10% ionization to be placed on the experiments in the present work.
A nonperturbative analysis (in one of the fields) of the Rayleigh-type optical-mixing signal in an absorbing medium shows that it is more sensible to saturation than the effect that could be expected from ``absorption saturation arguments.'' We also report the observation of such high-order effects in the organic dye malachite green. We have found that an effective two-level system model with a longitudinal relaxation time of 1.1\ifmmode\pm\else\textpm\fi{}0.2 ps, a transverse relaxation time of 0.13\ifmmode\pm\else\textpm\fi{}0.05 ps, and a transition moment of 1.2 D account for the deviation from the third-order regime. However, the frequency region of the data that follows the predicted spectral deformation is power dependent and it shrinks as power increases.
We present the results of degenerate four-wave mixing (DFWM) studies in three samples of p-type Ge with a wide range of absorptive properties. Three mechanisms for DFWM are observed in this material. A model, which includes the mechanisms of the inhomogeneously broadened saturable absorption of p-type Ge and the optical Kerr effect that is due to bound electrons in Ge but not the mechanism of bulk plasma formation that occurs only at extremely high pump intensities, is developed and compared with the experimental results. Pump-beam attenuation by the medium is shown to be an important effect in modeling DFWM. The model, which has no free parameters, fits the experimental data well for samples with small-signal transmission of greater than 20%.