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Europhysics Letters (EPL)

Amplification process in a laser injected by a narrow band weak signal

S. Blin, Guy Michel Stéphan, R. Gabet, Pascal Besnard, Daniel C. Kilper

Published Oct 1, 2000• 6 citations
Publisher

Abstract

The process of amplification of light by a laser set above its oscillation threshold is studied. This laser has a wide bandwidth (typically 100 MHz) and is injected by a signal whose bandwidth is much narrower, which allows to separate the amplified signal from the ordinary laser spectral density. Theoretical calculations are based on simple semiclassical formulas and agree with the experimental results which are performed at 1.55 μm using single-mode semiconductor lasers. The amplification arises from a progressive channeling of energy from the wider laser line onto the narrow injected signal.

DOI
10.1209/epl/i2000-00404-8

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The process of amplification of light by a laser set above its oscillation threshold is studied. This laser has a wide bandwidth (typically 100 MHz) and is injected by a signal whose bandwidth is much narrower, which allows to separate the amplified signal from the ordinary laser spectral density. Theoretical calculations are based on simple semiclassical formulas and agree with the experimental results which are performed at 1.55 μm using single-mode semiconductor lasers. The amplification arises from a progressive channeling of energy from the wider laser line onto the narrow injected signal.
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.
We calculate the passage-time statistics of a gain-switched single-mode semiconductor laser with a weak, detuned injected signal. Results are given in terms of a relevant scaling parameter. We find that a weak injected signal can be detected by measurements of the mean passage time or its variance whenever its frequency is close to the one of the semiconductor lasers in the on state. In this case, the external signal is resonant with the laser field at the time when amplification becomes possible, and hence it triggers the switch-on more efficiently. The detection bandwidth is of the order of 50 GHz for the case considered.
The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The fundamental concern of this investigation is the spectral behavior of the radiation in the nonlinear regime; hence, the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. These expressions should be easily susceptible to detailed experimental observations. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed with some detail. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is extensively explored in several numerical examples. The connections of this study with the time-domain work of Risken and Nummedal, on self-pulsing in a ring-laser configuration, are clearly established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ("Raman-type terms"), and saturation phenomena. The predicted narrowing-rebroadening rate is compared with expressions found in previous literature.
The amplification before detection of the carrier of a modulated optical signal by a narrow-band quantum amplifier enhances the signal-to-noise ratio, particularly when the signal wave-front is distorted. A further improvement is obtained by using a combination of wide-band and narrow-band quantum amplifiers. The practical application of these schemes requires a degenerate regenerative ring-type amplifier capable of amplifying arbitrary transverse field configurations. Experiments show that such an amplifier with a gain of 24 dB and a bandwidth of 1 MHz is feasible. The incident beam axis can be displaced by as much as ten times the beam-waist radius without losing more than 4 dB in gain. Frequency modulation may be converted into amplitude modulation by the phase shift introduced in the carrier.