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Theoretical and Experimental Investigations of Saturation Effects in a Gas Laser

Maeda, Hisatoshi

Published Feb 12, 2018• 0 citations
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Abstract

Theoretical studies of standing and traveling wave lasers are presented. The spectral behavior of the amplified spontaneous emission (superradiance) in a pencil-shaped column is investigated theoretically and experimentally. Spectral narrowing followed by rebroadening has been observed as predicted by the theory. A geometrical representation of an interacting two-level atomic system has been developed and applied to an optical laser. A semi-classical model for a standing wave laser has been examined using the rotating wave approximation, and compared to the exact solution. Depth and width of the Lamb dip are determined theoretically and experimentally. The effect of radial profile of the laser field has been studied using the self-consistent-field approach, and the radius of the beam was measured at various positions from the window.

DOI
10.7907/k70k-gs53

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Theoretical studies of standing and traveling wave lasers are presented. The spectral behavior of the amplified spontaneous emission (superradiance) in a pencil-shaped column is investigated theoretically and experimentally. Spectral narrowing followed by rebroadening has been observed as predicted by the theory. A geometrical representation of an interacting two-level atomic system has been developed and applied to an optical laser. A semi-classical model for a standing wave laser has been examined using the rotating wave approximation, and compared to the exact solution. Depth and width of the Lamb dip are determined theoretically and experimentally. The effect of radial profile of the laser field has been studied using the self-consistent-field approach, and the radius of the beam was measured at various positions from the window.
The resonance condition is used to describe theoretically the three main kinds of standing waves with E\ensuremath{\perp}B (linear) and E?B (helicoidal and circular polarizations) that can be produced by the same laser and their nonlinear interaction with an atomic medium. It is shown that the saturation behavior of a single-mode gas laser is drastically modified by the nature of the operating standing wave. The predictions are checked experimentally with a laser from which each kind of standing wave can be generated with the same losses. The anisotropic structure of the saturation and in particular of the Lamb dip is isolated in each case. Very good agreement is observed between experiments and theory.
Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters. Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory. The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s2 → 3p4) transition and a J = 1 to J = 1 (3s2 → 3p2) transition. The input signals were tuned to the centers of their respective resonant gain lines. The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s2) level quadrupole moment decay rate, the dipole moment decay rates for the 3s2 → 3p4 and 3s2 → 3p2 transitions, and the effects of various types of collision processes on these decay rates.
Previous theoretical results on the influence of a laser on the line shape of a coupled transition-laser-induced line narrowing-have been restricted to the case where the laser is detuned from the center of its atomic gain profile or is in the form of a traveling wave. This paper extends those results to include the case where the laser is an intense standing-wave field tunable to the center of its atomic gain profile (conditions for Lamb dip). The effect may be observed either in transmission, by probing the coupled transition with a weak traveling-wave field coaxial with the laser field, or else in spontaneous emission from the coupled transition viewed along the axis of the laser field. It is now well known that for a laser detuned from the center of its atomic gain profile, two narrow Lorentzian resonances of different widths appear superimposed upon the broad background signal at frequencies symmetrically located about the corresponding line center. When the laser is tuned to the center of its gain profile, however, additional fine structure develops. This structure, which is particularly significant when the laser field is intense, may have important applications in highresolution spectroscopy and laser-frequency stabilization. In this paper the laser frequency may be smaller or larger than the frequency of the coupled transition. In the latter case an intense laser introduces additional splitting effects, even when the laser is detuned. Splitting effects due to weakly saturating laser fields are also discussed. The problem is formulated by expanding elements of the ensemble-averaged density matrix in an infinite series of spatial Fourier components. A perturbation technique is employed, valid for a weak probe field and a standing-wave field of arbitrary intensity. One obtains an expression for emission induced by the probe field due to atoms moving with one velocity, written in terms of continued fractions in the general case and with Bessel functions in an important special case. This expression is integrated over the atomic velocity distribution by means of a computer to obtain the total emission due to atoms moving with all velocities. In some cases the integrated expressions may be written in closed algebraic form. A detailed discussions of line shapes and of the physical processes involved is included.
The optical spectra corresponding to complex intensity pulsation patterns near line-center tuning of single-mode, standing-wave gas lasers contain some simple indicators of the origins of their complexity. Heterodyne measurements show that on detuning of the laser the power density in each component of the optical spectrum undergoes a Lamb-dip-like reduction as it passes through resonance with the zero-velocity atoms. These observations help to explain the sensitive dependence of the dynamics of standing-wave gas lasers on detuning within the Lamp dip and distortions of the Lamb-dip shapes when the lasers are unstable.
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.