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Physical Review A

Modeling a semiconductor laser with an intracavity atomic absorber

Cristina Masoller, Marcos Oriá, Ramon A. Vilaseca

Published Jul 28, 2009• 2 citations
Publisher

Abstract

The dynamics of a semiconductor laser with an intracavity atomic absorber is studied numerically. The study is motivated by the experiments of Barbosa et al. [Opt. Lett. 32, 1869 (2007)], using a semiconductor junction as an active medium, with its output face being antireflection coated, and a cell containing cesium vapor placed in a cavity that was closed by a diffraction grating (DG). The DG allowed scanning the lasing frequency across the ${D}_{2}$ line in the Cs spectrum, and different regimes such as frequency bistability or dynamic instability were observed depending on the operating conditions. Here we propose a rate-equation model that takes into account the dispersive losses and the dispersive refractive index change in the laser cavity caused by the presence of the Cs vapor cell. These effects are described through a modification of the complex susceptibility. The numerical results are found to be in qualitative good agreement with some of the observations; however, some discrepancies are also noticed, which can be attributed to multi-longitudinal-mode emission in the experiments. The simulations clearly show the relevant role of the Lamb dips and crossover resonances, which arise on top of the Doppler-broadened ${D}_{2}$ line in the Cs spectrum, and are due to the forward and backward intracavity fields interacting resonantly with the Cs atoms. When the laser frequency is locked in a dip, a reduction in the frequency noise and of the intensity noise is demonstrated.

DOI
10.1103/physreva.80.013830

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Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
The dynamics of a semiconductor laser with an intracavity atomic absorber is studied numerically. The study is motivated by the experiments of Barbosa et al. [Opt. Lett. 32, 1869 (2007)], using a semiconductor junction as an active medium, with its output face being antireflection coated, and a cell containing cesium vapor placed in a cavity that was closed by a diffraction grating (DG). The DG allowed scanning the lasing frequency across the D2{D}_{2}D2​ line in the Cs spectrum, and different regimes such as frequency bistability or dynamic instability were observed depending on the operating conditions. Here we propose a rate-equation model that takes into account the dispersive losses and the dispersive refractive index change in the laser cavity caused by the presence of the Cs vapor cell. These effects are described through a modification of the complex susceptibility. The numerical results are found to be in qualitative good agreement with some of the observations; however, some discrepancies are also noticed, which can be attributed to multi-longitudinal-mode emission in the experiments. The simulations clearly show the relevant role of the Lamb dips and crossover resonances, which arise on top of the Doppler-broadened D2{D}_{2}D2​ line in the Cs spectrum, and are due to the forward and backward intracavity fields interacting resonantly with the Cs atoms. When the laser frequency is locked in a dip, a reduction in the frequency noise and of the intensity noise is demonstrated.
In this work we investigate the transmission in an optical cell containing an atomic vapor, when a laser is tuned to the wings of the Doppler line, presenting inhomogeneous broadening. The experiment is designed to detect the transmission of a laser beam through a an atomic cesium vapor within a quartz cell. Due to the high atomic density in the 1 mm cell, the laser beam is totally absorbed at resonance. On the other hand, when the detuning by few GHz from the center of the line an oscillatory signal is observed as a function of the laser frequency. The amplitude of the transmission signal varies linearly with the laser intensity. These oscillations exhibit diferent behavior as we change some parameters of the system, and the rate of the oscillations vary with laser detuning and on the atomic density. The phase of the transmited field is also sensitive to the angle of incidence of the laser beam in the cell, which allows to vary the lineshape of the signal without changing the parameters of the laser (intensity, frequency, ...) or atomic vapor. Out of resonance with the atomic vapor, the parallel windows of commercial optical cell cavity works as a low finesse Fabry-Pérot with a free spectral range of 150 GHz. However, in resonance, the optical path of the cavity changes varies with frequency due to the dispersive response of the atomic vapor. This study experimentally characterized the transmission signal through a cavity containing resonant vapor as a function of intensity and frequency of the laser, as well as its dependence on the angle of incidence of the beam. A numerical model that allows to determine the collisional broadening of the atomic vapor adjusting the spectral curves of the transmission signal was developed. As an application, exploring the oscillations in the wings of the resonance, we can lock the laser frequency at a few GHz off the center of the atomic resonance. The lock was performed in the frequency range between 0,8 GHz and 2,4 GHz from the center of the D2 line of cesium. To characterize the locking stability we measure the optical beat signal between two similar experiments, using the same locking technique.
This paper discusses the case of a Doppler-broadened gas laser with a saturable intracavity absorber gas. The semiclassical equations governing the field intensities and the atomic density-matrix elements are set up. The latter are written as Fourier series, the components of which are shown to obey coupled difference equations. In this paper the exact steady-state solution in single-mode operation is obtained. The lowest approximation (rate-equation approximation) is used to compute detailed characteristics of the system. In particular, the influence of the pumping rates in the two cells are investigated and displayed in the figures. The regions of bistable operation are determined and conditions for the occurrence of an inverted Lamb dip are given. The effect of a slow modulation of the pumping rates is discussed. The range of validity of the lowest approximation is investigated both analytically and numerically. Finally, there is a brief discussion of the influence of pressure on the parameters of the theory.
Coherent population oscillations (CPO), an ubiquitous mechanism inducing slow and fast light (SFL), is present in any active medium provided that a strong optical beam saturates this medium. Thus, CPO must be present in any single frequency laser since the oscillating beam acts as a strong pump which saturates the active medium. This effect could be observed using an external probe whose angular frequency is detuned with respect to the oscillating mode, by less than the inverse of the population inversion lifetime. This effect should be visible in the laser excess noise, using the spontaneous emission present in the non-lasing side longitudinal modes of a single-frequency laser as probe of the CPO effect. Class-A vertical external cavity surface emitting semiconductor lasers (VECSELs) [1] recently developed for their low noise characteristics make them perfectly suited for the observation of CPO induced SFL in their noise spectrum. The single-frequency laser used in our experiment is a VECSEL which operates at ∼ 1 µm. We focus on the excess noise due to the beat notes between the laser line and the spontaneous emission noise at neighboring longitudinal mode frequencies [2,3]. At the pthFSR frequency pΔ, the noise spectrum is thus the sum of two Lorentzian peaks due to the beat notes of the lasing mode with the corresponding sidebands (pthand −pthmodes). When the pumping rate is increased, we found experimentally that the excess noise consists of two peaks separated by δf = fp− f−p∼ 100 kHz (inset of Fig.1(a)). This frequency shift is given by: δf ≈ ν0Lmover L+n0Lm(δnp+δn−p), where n0 is the bulk refractive index of the semiconductor structure, L and Lmare the length of the cavity and the gain medium respectively. δn±pare the modifications of the refractive index of the structure experienced by the ±p side modes and induced by the dispersion associated with the CPO effect. In a semiconductor active medium, thanks to the Bogatov effect [4], the dispersion is not an odd function of the frequency detuning with respect to ½0. Thus, δnp≠ −δn−pand the two beat note frequencies fpand f−pcorresponding to the p and −p modes occur at slightly different frequencies, as evidenced by the double peak of Fig.1(a). This CPO induced index modification can be derived from the gain medium rate equation including the phase-intensity coupling coefficient α (Henry's factor) that is responsible for the Bogatov effect. This CPO effect is also responsible for the modification of the refractive index seen by the side modes which modifies the round-trip phase accumulated by each side mode Fig.1(b). Notice also that since the cavity FSR Δ is sufficiently large that we are probe the wings of the dispersion profile of Fig.1(b), i. e., in the slow light regime. In conclusion, we experimentally evidenced the existence of intracavity slow light effects in a laser induced by the CPO mechanism. These effects are probed by the laser spontaneous emission noise present in the non lasing modes.
This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.
Atomic clocks are a vital technology in the day to day operation of modern society. While passive Rb and Cs microwave atomic clocks find widespread practical applications today, active atomic clocks have the potential to surpass them in frequency stability, compactness, and simplicity. This dissertation is a comprehensive study of the physics of an active atomic clock based on modelocked external cavity semiconductor laser with 85Rb vapor cell saturable absorber. As the starting point for establishing our concept, this study encompasses optical interrogation in the traditional D1 (5S1/2-5P1/2, 795 nm wavelength) line in 85Rb atoms, as well as in the less used and less studied 5S1/2-6P3/2 (420 nm) line, which has very different absorption characteristics. The theoretical and experimental work in this dissertation establish a foundational background for the active atomic clock laser, yielding novel results in the field of semiconductor lasers and atomic physics.
The equation of motion for the slowly varying field amplitude of the laser containing an intracavity saturable absorber (LSA) is where a is the net gain (pump parameter) and b is a saturation parameter of the laser. In our experiment the absorber saturates faster than the amplifier and the parameter b is positive. q(t) is a complex Gaussian white noise random process representing spontaneous emission noise. From Eq. (1) we obtain for the steady-state probability density of light intensity I = | E |2. From this equation various moments of light intensity can be calculated and compared with experimentally measured quantities. For b > 0 the LSA exhibits bistability and a first order phase transition occurs at a = -3b2/16. For negative values of b there is a continuous transition at a = 0. Experiments were carried out on a He—Ne laser with an intracavity Ne absorber cell. The laser was operated close to the center of the absorption line. Slow drifts of light intensity were controlled by an electronic feedback loop. The parameter b was varied by changing the current in the absorber tube. Pump parameter a was then varied by changing passive losses in the cavity by means of an adjustable knife edge. The main beam from the LSA was allowed to fall on a detector/am- plifier combination. The voltage output from the detector was digitized by a multichannel analyzer and a histogram of voltage amplitudes was built up. Since the voltage output from the detector is directly proportional to the light intensity incident on the detector, voltage histogram is a direct representative of the intensity probability distribution. From the measured histogram moments of light intensity were calculated. These results are compared with the theoretical predictions.