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Amplitude noise of injection locked lasers: Quantum theory using a linearised input/output method

Timothy C. Ralph, C. C. Harb, Hans‐A. Bachor

Published Jul 14, 1996• 0 citations
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Abstract

The search for ever quieter light sources has fueled experimental interest in the noise properties of injection locked lasers [ 1,2,3], Ref. 1 showed that the injection of a small signal into a pump noise suppressed semi-conductor laser could suppress small longitudinal side modes whilst leaving the non-classical noise characteristics of the free running laser unaffected. In contrast [2] and [3] found that in Nd:YAG lasers the free running noise characteristics were suppressed and the output noise was an amplified version of the injected signal.

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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.

Physical Review A•Dec 1, 1996•18 citations
The search for ever quieter light sources has fueled experimental interest in the noise properties of injection locked lasers [ 1,2,3], Ref. 1 showed that the injection of a small signal into a pump noise suppressed semi-conductor laser could suppress small longitudinal side modes whilst leaving the non-classical noise characteristics of the free running laser unaffected. In contrast [2] and [3] found that in Nd:YAG lasers the free running noise characteristics were suppressed and the output noise was an amplified version of the injected signal.
The quantum noise properties of injection-locked semiconductor laser oscillators are investigated. Included in the analysis are pump-noise suppression and squeezing of the injection signal. It is shown that the main effect of injection locking is the reduction of the phase noise of the outgoing laser light field. The influence that squeezing of the injection signal state has on the output state is shown to be strongly dependent on the value of the linewidth enhancement factor. In general, little or no noise reduction stands to be gained by squeezing the injection signal. It is also shown that under idealized conditions, the spectral uncertainty product of the outgoing field will approach, but never go below, the minimum uncertainty value given by the Heisenberg uncertainty relation.
Experimental investigations illustrating the intensity noise properties of injection-locked solid-state lasers were performed. The measured results are predicted by a quantum mechanical model. The theory describes the intensity noise transfer to the slave laser’s output for large modulation signals as well as for signals at the quantum noise level. Different frequency regions in the intensity noise spectrum are identified and it is shown that there exist different minimum noise levels in these regions. Under appropriate conditions, injection-locked lasers can generate non-classical light.
We derive analytical expressions for the quantum-noise spectra of an atomic laser using a linearized input-output method. We generalize the method to the problem of injection-locked lasers. We identify three distinct spectral noise regimes in the solution, unifying previous results. The approach offers insights into the physical processes and is especially suited for comparison with experiment. The quantum spectral noise properties of the pump laser and the injected laser appear explicitly in the solution. \textcopyright{} 1996 The American Physical Society.
We have investigated the intensity and phase noise of single-mode laser diodes, either free-running or using different types of line narrowing techniques at room temperature, namely feedback from an external grating and injection locking. We have measured an intensity squeezing of 1.2 dB in the first case, and 1.4 dB in the second case (respectively, 1.6 dB and 2.3 dB inferred at the laser output). We have observed that the intensity noise of a free-running 'single-mode' laser diode actually results from a cancellation effect between large anticorrelated fluctuations of the main mode and of weak longitudinal side modes. It is also shown that free-running diodes exhibit very large excess phase noise. Typically more than 80 dB above shot noise at 10 MHz, which can be significantly reduced by the above-mentioned techniques.
Amplitude-squeezed light has been generated by semiconductor quantum well lasers in numerous optical configurations, at both room and cryogenic temperatures. Various intensity noise sources associated with nonideal laser operation, in particular mode partition and polarization-dependent noise, can introduce intensity fluctuations that limit or remove amplitude squeezing. We discuss amplitude noise reduction in low-temperature free-running and injection-locking laser configurations and room-temperature injection locking and external-cavity laser configurations. Drive-current modulation with a nonclassical SNR improvement is achieved with an injection-locked laser.
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.