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Optica Acta International Journal of Optics

Chirped Steady π-pulses of Light of an Arbitrary Duration in a Lossy, Exactly Resonant Inverted Medium

Hari Prakash, G. S. Bhatnagar

Published Apr 1, 1979• 0 citations
Publisher

Abstract

It is shown that the steady π -pulses of light in a lossy, resonant inverted medium can have an arbitrary duration greater than a critical value and are in general chirped. The non-chirped π -pulses of fixed duration (for a given population inversion) obtained by Arecchi and Bonifacio and by Lamb is a special case of our results when the pulse duration is set equal to the critical value. We find expressions for the pulse profile, propagation number, envelope velocity and atomic variables, and show that the expression for the area of the pulse in this case is different from that used commonly, and that the product of the envelope and mean phase velocities is equal to the square of the velocity of non-resonant light.

DOI
10.1080/713820021

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It is shown that the steady π -pulses of light in a lossy, resonant inverted medium can have an arbitrary duration greater than a critical value and are in general chirped. The non-chirped π -pulses of fixed duration (for a given population inversion) obtained by Arecchi and Bonifacio and by Lamb is a special case of our results when the pulse duration is set equal to the critical value. We find expressions for the pulse profile, propagation number, envelope velocity and atomic variables, and show that the expression for the area of the pulse in this case is different from that used commonly, and that the product of the envelope and mean phase velocities is equal to the square of the velocity of non-resonant light.
We analyze the phase modulation, or chirping, of coherent lossless light pulses propagating without distortion through resonant absorbers. In order to do this, we generalize the pioneering work of McCall and Hahn in two different directions. In the first place, of course, we abandon their assumption that the phase of the pulses has no temporal dependence. We prove that for slowly varying single pulses, chirping is not possible. However, we describe many multiple-pulse trains which are necessarily chirped, even under the slowly varying envelope restriction, and also describe the envelope modulations which produce large chirps. We show that certain zero-$\ensuremath{\pi}$ chirped pulse trains are contained as special cases of our general results. Our second generalization of the McCall-Hahn work concerns the background material in which the two-level resonant atoms are suspended. We allow the host medium to possess significant nonresonant nonlinearities. We find that undistorted lossless single pulses are possible in such a medium and that they are necessarily chirped.
The exact solution describing steady-state resonant pulse propagation in a two-level inverted medium is given. This steady-state pulse is often referred to as a 180° or π-pulse. No approximation of a slowly varying envelope is made, and hence the solution satisfies the second-order wave equation as well as the equations of motion of the density matrix of the system. As a result the theory is able to describe very short pulses, whose width can be of the order of the period of the optical carrier. The model for the system includes a nonresonant loss and a finite value of the transverse relaxation time T2, but neglects dispersion in the host medium. The steady-state pulse is found to be frequency modulated and asymmetric in shape.
We consider the propagation of a light pulse in a medium with a single resonance. If the frequency of the pulse is tuned far from resonance and the pulse duration is much shorter than the lifetime of the excited state of the resonant particles in the medium (atoms in a gas, impurity ions in a solid, etc.), the group velocity of the pulse is appreciably reduced. It is shown that the slowing down of the group velocity of the pulse is accompanied with a pulse chirp, which produces a pulse broadening in time. It is proposed to use two samples in sequence with opposite chirps (up chirp and down chirp or vice versa) compensating the pulse broadening. Then the pulse can be delayed with almost no losses, distortion, and broadening. However, there is a maximum distance, beyond which the pulse experiences corruption. Pumping with an auxiliary laser beam can control the delay time of the light pulse in the medium. Conditions to eliminate the contribution of the dephasing processes in the pulse propagation are considered.
A theoretical analysis of the propagation of near resonant and linearly chirped light pulses through a resonant medium is presented under the restriction that the pulses are far enough off resonance or weak enough so that they do not significantly alter the atomic populations. If the pulses are of duration comparable to or less than the phase memory time T(2) of the atoms, it is found that the transient response of the medium gives rise to amplitude-and phase-modulating effects. Analytic solutions are presented to describe the propagation of an off-resonant pulse which is very short compared with T(2) and an off-resonant rectangular pulse. The evolution of a Gaussian pulse having a positive linear chirp is studied numerically.
A steady-state solution describing\Pi-pulse propagation in a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. For a given model of dispersion, the solution satisfies exactly the second-order wave equation together with the equations of motion for the density matrix of the two-level resonant system. The salient feature of the solution is that a small amount of dispersion in the host group velocity causes a large monotonic frequency sweep during the pulse. The effects of this chirp on the pulse properties are described in detail, and the relation of the theory to experiments is discussed.