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Journal of Physics D Applied Physics

Transient behaviour analysis of injection-locked lasers

Alireza Bahrampour, Mohammad Hossein Zandi

Published Jan 7, 2005• 1 citation
Publisher

Abstract

In this paper, we present a theory for analysing the transient behaviour of injection-locked lasers with monochromatic injection, wherein homogeneously broadened wide-band lasers with injection are analysed. In addition to boundary conditions, the initial distribution of the laser and the monochromatic injection signal fields are necessary for solving the governing equations. The Maxwell–Bloch equations are reduced to a system of ordinary differential equations with the initial conditions. In this paper, two approximation methods are introduced. These approximations are named the De-satellite signal approximation and the finite number satellite signal approximation, respectively. The finite number satellite signal approximation is used to study the transient behaviour of the satellite signal around the laser frequency in injection-locked lasers. The results are in good agreement with the data published by the previous studies on this topic.

DOI
10.1088/0022-3727/38/2/008

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In this paper, we present a theory for analysing the transient behaviour of injection-locked lasers with monochromatic injection, wherein homogeneously broadened wide-band lasers with injection are analysed. In addition to boundary conditions, the initial distribution of the laser and the monochromatic injection signal fields are necessary for solving the governing equations. The Maxwell–Bloch equations are reduced to a system of ordinary differential equations with the initial conditions. In this paper, two approximation methods are introduced. These approximations are named the De-satellite signal approximation and the finite number satellite signal approximation, respectively. The finite number satellite signal approximation is used to study the transient behaviour of the satellite signal around the laser frequency in injection-locked lasers. The results are in good agreement with the data published by the previous studies on this topic.
The theory of the laser amplifier is developed for conditions in which the strength of the input signal is increased from small values, where the amplification is linear, to larger values, where the amplification becomes nonlinear. The below-threshold laser amplifier oscillates at a single frequency equal to that of the input signal, and its properties are found by solution of the nonlinear equation of motion for the single excitation amplitude. For the above-threshold laser amplifier, the effects of the nonlinear behavior are to shift the laser frequency from its free-running value and to transfer intensity from the laser line to the signal frequency and to a range of satellite lines, whose frequency detunings are integer multiples of the signal detuning. The intensities of the various emission lines of the laser are calculated by power-series expansions of the field amplitudes up to terms of fourth order in the input signal strength. The onset of injection locking is determined by the conditions for which the intensity at the shifted free-running laser frequency falls to zero. The injection-locked state is characterized by a single excitation frequency equal to that of the input signal, and its properties are found by solution of the same nonlinear equation of motion as for the below-threshold amplifier. The ranges of input signal strength and detuning are determined for which the injection-locked state is stable. The energy conservation properties of the laser amplifier are considered for each of its operating states. \textcopyright{} 1996 The American Physical Society.
Abstract : A semiclassical analysis of injected lasers with stable and unstable resonators and arbitrary outcoupling fractions was performed. Homogeneously broadened lasers with Fabry-Perot and with positive branch, confocal unstable resonators were modeled. Both time-dependent and steady-state analyses of free-running and injected lasers were performed. Because of deficiencies in the standing wave semiclassical and the simple saturable gain models, a new semiclassical theory of homogeneously broadened lasers were developed. The theory is predicted upon the following assumptions: the atoms are two-level, a single longitudinal mode exists in the cavity, the transverse mode structure can be adequately modeled by the geometric optics mode, and the laser electric fields can be described by a pair of counterpropagating planar, cylindrical, or spherical traveling waves with different amplitudes. A general semiclassical theory was first developed, and then specialized to the Fabry-Perot and positive branch, confocal unstable resonator cases. Both the Maxwell-Bloch and rate equation approximation forms of the theory were derived. The general theory is sufficiently broad to allow the modeling of the geometric optics mode of any standing wave resonator configuration. The theory was shown to reduce to the simple saturable gain and standing wave semiclassical models in the appropriate limits. The analysis of the injected lasers were performed with the new semiclassical theory. Both time-dependent and steady-state analyses were performed.
We present an ab initio treatment of the steady-state of lasers with injected signals that describes a regime, valid for microlasers, in which the locking transition is dominated by cross saturation and spatial hole burning. The theory goes beyond standard approaches and treats multimode lasing with injected signals and finds the possibility of partially locked states and as well as repulsion of the free-running frequencies from the injected signal. The theory agrees well with exact integration of the full wave and matter equations for the system. It can also describe accurately complex modern lasers structures and is applied to the example of deformed disk lasers. We show that in the case of a one-dimensional cavity in the locked or regenerative amplifier regime the theory reduces to an improved version of the Adler equations in the appropriate limit.
The behavior of a single-mode class-C laser in the presence of an injected signal is investigated theoretically in detail. We have determined the ranges of input signal strength and the frequency detuning for which the oscillations of the cavity electric field and the atomic induced dipole moment are simultaneously stable and have only one oscillation component with the frequency equal to that of the input signal (injection-locked state). One can reproduce all the previous results corresponding to class-A and class-B lasers from our results by using their relevant conditions. Finally, the energy conservation law is demonstrated for both the below-threshold and the injection-locked states of class-C laser amplifiers.
A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.