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Applied Physics Letters

Experimental observation of transverse effects in microchip solid-state lasers

Stefano Longhi, Giulio Cerullo, Stefano Taccheo, Vittorio C. Magni, P. Laporta

Published Dec 12, 1994• 13 citations
Publisher

Abstract

We report on the observation of transverse effects in a microchip solid-state laser due to gain-guiding, demonstrating that the transverse modulation of the gain profile and detuning play a fundamental role in the control of the longitudinal lasing mode. The observed behavior is interpreted in the framework of the Maxwell–Bloch equations as a symmetry breaking between the two sides of the atomic resonance.

DOI
10.1063/1.112498

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Physical Review A•Mar 1, 1998•1 citation
We report on the observation of transverse effects in a microchip solid-state laser due to gain-guiding, demonstrating that the transverse modulation of the gain profile and detuning play a fundamental role in the control of the longitudinal lasing mode. The observed behavior is interpreted in the framework of the Maxwell–Bloch equations as a symmetry breaking between the two sides of the atomic resonance.
Field confinement in a microchip laser with transversely varying gain and plane–plane cavity mirrors is theoretically discussed with a semiclassical treatment. We show that the common notion of a transverse cavity mode becomes closely linked to that of a longitudinal cavity mode owing to the key role that detuning of the longitudinal cavity frequency from the atomic resonance plays in the formation of the transverse field profile. In particular, we show that as the pump size decreases the laser emission is pulled toward the atomic resonance frequency on the negative detuning side. Strong mode pulling is interpreted as being due to the index-antiguiding effect induced by the pump and manifests itself as a ring pattern in the far-field spatial intensity.
We consider the dynamics of an inhomogeneously broadened unidirectional ring laser formulated in the traditional Maxwell-Bloch configuration of a two-level atom with transverse modes. We numerically analyze the model for a single-longitudinal mode in the paraxial approximation, using the uniform field limit with cylindrical symmetry and a Gaussian profile for inhomogeneous broadening. Several domains of solutions are found for the resonant case in the good cavity limit. The laser threshold is found to be dependent on the mode spacing as well as on the gain and scaled Doppler broadening. Hysteresis between stable and unstable solutions is obtained in realistic operating conditions for both increasing (decreasing) gain and increasing (decreasing) mode spacing (i.e., for changes in the initial conditions).
The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.
We consider an inhomogeneously broadened, unidirectional ring laser formulated in the traditional Maxwell–Bloch configuration of a two-level atom with transverse modes. We numerically analyze the steady state for a single longitudinal mode in the paraxial approximation, using the uniform-field limit with cylindrical symmetry and Gaussian profile for inhomogeneous broadening. Several domains of steady-state solutions are found for the resonant case in the good-cavity limit. Both single- and multiple-transverse mode solutions are observed; the expected TEM00 mode is seen in the limit of single-mode operation. The laser threshold is found to depend on the mode spacing (A1) as well as on the gain (2C) and the scaled Doppler broadening (σD). This means that as A1 is increased, the laser requires a larger gain to operate, up to a critical gain; beyond this critical gain, the laser threshold is independent of A1. Hysteresis between zero- and nonzero-intensity solutions at the laser threshold is obtained under realistic operating conditions for both increasing and decreasing 2C and A1 (i.e., for changes in the initial conditions). These distinct, but overlapping, domains of parameter space where both single- and multiple-mode steady states exist are qualitatively the same for increasing values of σD ≥ 1 and may indicate the presence of competing attractors.
Of the Lorenz-type instabilities expected in optical systems, the single-mode instability in optical bistability has been the subject of detailed theoretical and experimental work by our groups. A treatment employing the plane-wave and mean-field limits of the Maxwell-Bloch equations predicts a rich variety of higher-order bifurcations including period doublings and intermittency.1 An extension of this work to include the transverse dependence of the intracavity field reveals no significant qualitative differences between the plane-wave theory and the Gaussian beam theory as regards the stability boundaries obtained from a linearized analysis.2 The instability persists in the presence of a Gaussian transverse profile and the boundaries are not radically modified compared with those obtained from the plane-wave theory. However, numerical integration of the Maxwell-Bloch equations in the single transverse mode approximation does not show the wealth of higher-order dynamic states present in the plane-wave case. An experimental investigation of optical bistability for two-level atoms in a single transverse, single longitudinal mode cavity exhibits limit cycle oscillation with stability boundaries that agree well with the boundaries obtained from the work in Ref. 2. However, for the range of values C < 300, |Δ| < 5, |θ| < 50, X ~ 102, the experimental results do not show the diversity of higher dynamic states expected from the plane-wave theory, in agreement with our numerical results. In addition the measurements support the existence of a single transverse mode oscillation. The sum of our theoretical and experimental work provides a quantitative statement for the role of the transverse effects in optical instabilities.
Transverse effects in the laser threshold, originated by electronic-vibrational coupling in the active centers, are analyzed theoretically by means of the semiclassical two-level Maxwell-Bloch equations. A single longitudinal mode is considered. It is found that the first laser threshold suffers modifications depending on the electronic-vibrational coupling strength. This coupling imposes certain conditions for the selection of a particular transverse spatial state and provides the minimum wavelength that can appear in the transverse pattern. The nature of the bifurcation and the stability of the homogeneous and critical traveling waves are analyzed.