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Quantum Electronics and Laser Science Conference

Anomalous spectral response and propagationl instability for pump-probe propagation in a two-level medium

Michael E. Crenshaw, C. M. Bowden

Published May 12, 1991• 0 citations
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Abstract

We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.

Related papers

Spectral response and propagational instability for pump-probe propagation in a two-level medium

Michael E. Crenshaw, C. M. Bowden

The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.

Physical Review Letters•Sep 2, 1991•4 citations

Effect of propagation on pulsed four-wave mixing

P. Weisman, A. D. Wilson‐Gordon, Harry Friedmann

We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.

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Noise in dead zones

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We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system in the Doppler-broadening limit in which the so-called ``dead zone'' of the absorption spectrum is formed. We find that the plot of the noise as a function of the pump-probe detuning (which we shall refer to as the ``noise spectrum'') is hardly affected by the Doppler broadening for the case of a resonant pump. It consists of a large central peak flanked by two smaller peaks at the edges of the dead zone, which are at the Rabi sideband frequencies. Thus the dead zone, which is produced when absorption and gain regions of the absorption spectrum are averaged by Doppler broadening, is a rather noisy region, indicating the occurrence of many competing absorption and emission processes. The probe noise spectrum for a detuned pump is quite different in the presence and absence of Doppler broadening as is the absorption spectrum. On Doppler broadening the absorption spectrum consists of a dead zone centered at the Rayleigh resonance frequency with asymmetric absorption peaks on either side. The noise spectrum has a peak at the center with two sidebands at the edges of the dead zone. The sidebands are of almost the same intensity for short path lengths, but the peak on the side of the three-photon scattering becomes larger than the other peak as the path length increases.

Physical Review A•Dec 1, 1995•6 citations

Instabilities of counterpropagating waves in a two-level medium

Israel Bar-Joseph, Yaron R. Silberberg

We have previously shown that counterpropagating waves in a Kerrlike medium exhibit spontaneous oscillations above a certain threshold intensity. The period of these oscillations was related to the medium length and to its response time. These oscillations were explained as results of parametric gain and feedback supplied by the grating formed through the nonlinear interaction. In this paper we extend the theory to a two-level medium. The complexity of the parametric interaction in this medium provides a reach spectrum of behaviors. The power exchange due to this interaction, between waves of different frequencies, is usually maximized when the frequency difference is the Rabi frequency. However, another maximum, which is smaller in magnitude, occurs in certain limits when the frequency difference is T1. Our derivation is based on performing a linear stability analysis to the steady-state solutions of the Maxwell-Bloch equations. We assumed a small signal absorption and large detuning from resonance. The solutions were studied in the limit of pure radiative broadening (T2 = T1) and rapid collisional dephasing (T2 ≪ T1). It is found that for most cases Rabi frequency self-oscillations are dominant. However, for T2 ≪ T1 and for large interaction length, we found slower oscillations, with a period of T1. We show that the results can be understood by the gain feedback model. We also discuss the effect of inhomogeneous broadening and present experimental parameters required for observation of T1 oscillations.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Rabi-side bands generation in optically thick medium

F. P. Mattar, P. R. Berman

By adopting phase‐integral methods we compute how an off‐resonant probe coherently extracts more energy from an on‐resonance pump in an optically thick three‐level atom than a resonant probe from a larger pump. In both situations the time‐integrated area of the pump must exceed 5π. The population accumulated in the intermediate level exhibits a peak at a detuning equal to the pump Rabi frequency. This is a generalization of the Rabi side bands since propagation effects are accounted for. The pulse shape or pulse length affects the interaction.

AIP conference proceedings•Jan 1, 1988•0 citations

Spatial solitary like weak probe wave in the three-level Λ-type atoms

Ljiljana Stevanović, Aleksandra Maluckov, Nikola Filipović +1 more

We study the interaction of the medium composed of three-level atoms in A configuration interacting with two laser fields: weak probe field and strong control field. The probe field enters the medium under a certain angle, and it is initially in the form of the spatial soliton, while the control field is periodically modulated. The system of optical Bloch equations is analytically solved in the stationary regime by the perturbation method in order to obtain linear and third-order nonlinear susceptibility of the medium with respect to the probe field. After a straightforward algebraic procedure, using the approximation of the slow-varying field envelope, the nonlinear Schrödinger equation for the probe field is obtained. It is numerically solved by applying the spectral Fourier split-step method. It is found that, for properly chosen values of the probe and control field detunings and control Rabi frequency, the probe field behaves as a solitary wave whose direction does not depend on the incident angle. Moreover, the regime consisting of Bloch-like oscillations can be identified. The simulation is performed by choosing the corresponding levels of Mg atoms.

AIP conference proceedings•Jan 1, 2019•0 citations
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.
The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.
We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.
We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system in the Doppler-broadening limit in which the so-called ``dead zone'' of the absorption spectrum is formed. We find that the plot of the noise as a function of the pump-probe detuning (which we shall refer to as the ``noise spectrum'') is hardly affected by the Doppler broadening for the case of a resonant pump. It consists of a large central peak flanked by two smaller peaks at the edges of the dead zone, which are at the Rabi sideband frequencies. Thus the dead zone, which is produced when absorption and gain regions of the absorption spectrum are averaged by Doppler broadening, is a rather noisy region, indicating the occurrence of many competing absorption and emission processes. The probe noise spectrum for a detuned pump is quite different in the presence and absence of Doppler broadening as is the absorption spectrum. On Doppler broadening the absorption spectrum consists of a dead zone centered at the Rayleigh resonance frequency with asymmetric absorption peaks on either side. The noise spectrum has a peak at the center with two sidebands at the edges of the dead zone. The sidebands are of almost the same intensity for short path lengths, but the peak on the side of the three-photon scattering becomes larger than the other peak as the path length increases.
We have previously shown that counterpropagating waves in a Kerrlike medium exhibit spontaneous oscillations above a certain threshold intensity. The period of these oscillations was related to the medium length and to its response time. These oscillations were explained as results of parametric gain and feedback supplied by the grating formed through the nonlinear interaction. In this paper we extend the theory to a two-level medium. The complexity of the parametric interaction in this medium provides a reach spectrum of behaviors. The power exchange due to this interaction, between waves of different frequencies, is usually maximized when the frequency difference is the Rabi frequency. However, another maximum, which is smaller in magnitude, occurs in certain limits when the frequency difference is T1. Our derivation is based on performing a linear stability analysis to the steady-state solutions of the Maxwell-Bloch equations. We assumed a small signal absorption and large detuning from resonance. The solutions were studied in the limit of pure radiative broadening (T2 = T1) and rapid collisional dephasing (T2 ≪ T1). It is found that for most cases Rabi frequency self-oscillations are dominant. However, for T2 ≪ T1 and for large interaction length, we found slower oscillations, with a period of T1. We show that the results can be understood by the gain feedback model. We also discuss the effect of inhomogeneous broadening and present experimental parameters required for observation of T1 oscillations.
By adopting phase‐integral methods we compute how an off‐resonant probe coherently extracts more energy from an on‐resonance pump in an optically thick three‐level atom than a resonant probe from a larger pump. In both situations the time‐integrated area of the pump must exceed 5π. The population accumulated in the intermediate level exhibits a peak at a detuning equal to the pump Rabi frequency. This is a generalization of the Rabi side bands since propagation effects are accounted for. The pulse shape or pulse length affects the interaction.
We study the interaction of the medium composed of three-level atoms in A configuration interacting with two laser fields: weak probe field and strong control field. The probe field enters the medium under a certain angle, and it is initially in the form of the spatial soliton, while the control field is periodically modulated. The system of optical Bloch equations is analytically solved in the stationary regime by the perturbation method in order to obtain linear and third-order nonlinear susceptibility of the medium with respect to the probe field. After a straightforward algebraic procedure, using the approximation of the slow-varying field envelope, the nonlinear Schrödinger equation for the probe field is obtained. It is numerically solved by applying the spectral Fourier split-step method. It is found that, for properly chosen values of the probe and control field detunings and control Rabi frequency, the probe field behaves as a solitary wave whose direction does not depend on the incident angle. Moreover, the regime consisting of Bloch-like oscillations can be identified. The simulation is performed by choosing the corresponding levels of Mg atoms.