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IEEE Journal of Quantum Electronics

Pulse propagation in the amplifier of a high-power iodine laser

H. Saito, Taro Uchiyama, Tomoo Fujioka

Published Apr 1, 1978• 13 citations
Publisher

Abstract

Pulse propagations in an amplifier in the case of the photodissociation iodine laser are investigated with the use of semiclassical treatments, especially when the input pulse fed into the amplifier has a width comparable to or shorter than the transverse relaxation time of the amplifier medium. In our semiclassical equations for pulse propagation in an iodine amplifier, the populations of all hyperfine levels [2P1/2(F= 3, 2),2P3/2(F = 4, 3, 2, 1)], the polarizations of optically allowed transitions (\DeltaF = 0, \pm 1), and the Doppler detuning effects were taken into consideration. Based on the numerical integrations of the semiclassical equations, the propagated pulse shape and the population distributions of the hyperfine levels are discussed. From our calculations, it has been made clear that bandwidth limitations of pulses in the range of pulsewidths of 0.1 ns and below can be avoided by making use of the nonlinear amplification that results from the coherent interaction between the propagated pulse field and the amplifier medium.

DOI
10.1109/jqe.1978.1069781

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•Jan 1, 1965•5 citations
Pulse propagations in an amplifier in the case of the photodissociation iodine laser are investigated with the use of semiclassical treatments, especially when the input pulse fed into the amplifier has a width comparable to or shorter than the transverse relaxation time of the amplifier medium. In our semiclassical equations for pulse propagation in an iodine amplifier, the populations of all hyperfine levels [2P1/2(F= 3, 2),2P3/2(F = 4, 3, 2, 1)], the polarizations of optically allowed transitions (\DeltaF = 0, \pm 1), and the Doppler detuning effects were taken into consideration. Based on the numerical integrations of the semiclassical equations, the propagated pulse shape and the population distributions of the hyperfine levels are discussed. From our calculations, it has been made clear that bandwidth limitations of pulses in the range of pulsewidths of 0.1 ns and below can be avoided by making use of the nonlinear amplification that results from the coherent interaction between the propagated pulse field and the amplifier medium.
Equations appropriate for amplification of short pulses in the multilevel atomic iodine amplifier are developed from the Maxwell-Bloch equations with homogeneous line broadening. The equations are implemented in the form of a two-dimensional time-dependent finite-difference computer code with six population densities, six medium polarization densities, and adaptive propagation capabilities. The Sandia atomic iodine laser was used to examine the adequacy of the theoretical description for amplification conditions covering the full range of gain saturation. Whole-beam self-focusing is observed with a strongly saturating small-waist beam in agreement with predictions. Calculations predict that this self-focusing instability may be controlled by tuning the multiline amplifier bandwidth.
A superradiant and amplified spontaneous transition pulse is obtained from an iodine photodissociation laser amplifier which uses i-C3F7I as an active molecule and is pumped with a flashlamp (full width at half maximum=3 μs). We have observed a sharp leading pulse of superradiance whose rise time is less than 50 ns, and the amplified spontaneous emission follows the superradiance during the pumping flash. By measuring the population inversion density in the active medium of the amplifier, we have obtained the threshold condition for the superradiance to take place. Also, the buildup time and peak intensity of the pulse are measured as a function of the flashlamp input energy. By placing a reflecting mirror at a varying distance (from 173 to 673 cm) behind the amplifier, we have found a periodic intensity fluctuation in the superradiance; the period (Δt) depends linearly on the distance (d), i.e., Δt=2d/c, where c is the light velocity.
A review of basic analytical results on coherent propagation of optical pulses through nondegenerate amplifying media is presented. Original numerical results concerning pulse coherent amplification by degenerate media and, in particular, by the amplifying medium of an iodine laser are described also. Furthermore, some analytical results on coherent effects in the pulsed mode of laser generation are given. We have pointed out that the stochastic mode of laser radiation is related also to the coherency of interaction of a laser field with matter.
The problem of a light pulse propagating in a nonlinear laser medium is investigated. The electromagnetic field is treated classically and the active medium consists of thermally moving atoms which have two electronic states with independent decay constants ${\ensuremath{\gamma}}_{a}$ and ${\ensuremath{\gamma}}_{b}$ in addition to the decay constant ${\ensuremath{\gamma}}_{\mathrm{ab}}$ describing the phase memory. The self-consistency requirement that the field sustained by the polarized medium be equal to the field inducing the polarization leads to coupled equations of motion for the density matrix, and equations of propagation for the electromagnetic field. Although the theory is developed for a Doppler-broadened gaseous medium, it may also be applied to a solid medium with inhomogeneous broadening. A unified treatment is given encompassing a wide range of pulse durations from cw signals to psec pulses. Continuous pumping is allowed, as well as any amount of detuning of the carrier frequency of the pulse from the atomic resonance frequency. The three independent decay constants ${\ensuremath{\gamma}}_{a}$, ${\ensuremath{\gamma}}_{b}$, and ${\ensuremath{\gamma}}_{\mathrm{ab}}$ provide greater flexibility than that obtained by using 1T1\frac{1}{{T}_{1}}T1​1​ and 1T2\frac{1}{{T}_{2}}T2​1​. The equations are solved analytically in a few specialized cases and numerically in the general case. Flow charts for accomplishing the numerical integration are given. Among the special problems considered is the apparent paradox of pulses propagating faster than the velocity of light under circumstances described by Basov et al. It is shown that this contradiction with relativity arises from the use of an unphysical initial condition.
An analysis is made of the interaction of radiation with a two-level medium at a high particle density. An explicit allowance is made in the interaction Hamiltonian for the interaction between dipoles induced by a resonance field. A semiclassical description is used to obtain a system of equations describing the propagation of a pulse in the active medium. The equations contain nonlinear terms allowing for the interaction in question. An approximate solution of the equations is obtained for the case of amplification of a weak noncoherent pulse describing pulse compression in the amplifying medium. The theory is compared with experimental results.
Using semiclassical radiation theory, a formalism similar to that used by Lamb in his Theory of an Optical Maser is developed for studying the amplification of vector traveling waves in a laser-type medium. The effect of the medium on the waves is given in terms of space (or time) dependent field amplitudes and phases and a nonlinear index of refraction. With particular emphasis on typical gaseous media, the effects of Doppler broadening are treated in detail for arbitrary ratios of natural to Doppler linewidths. Polarization and propagation vectors in various directions are considered, and the nonlinear effects are found to make an isotropic medium effectively anisotropic. Lowest order nonlinear effects (due to a polarization cubic in the field amplitudes) are studied extensively, and the frequency dependence of several of these processes is presented in graphical form. In particular, the introduction of fields at new frequencies and polarization effects are considered. The characteristics of these nonlinear processes peculiar to Doppler broadened lines are discussed, and the processes are interpreted in terms of saturation and coherent modulation of the population inversion density. Strong nonlinear effects are considered in a more approximate way and are found to consist of saturation of the various linear and nonlinear processes previously considered. These strong nonlinear effects should occur at low enough intensities to be easily observed in practice on a CW basis. With the present formalism, the analytical results of Gordon, White and Rigden regarding gain saturation in laser amplifiers are obtained, and the extension is made to include frequencies away from line center and the effects of multiple spectral components. Again, the introduction of fields at new frequencies is considered in detail. These results are also discussed in terms of saturation and coherent modulation of the populations and hole burning.