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Physical Review A

Intensity noise of injection-locked lasers: Quantum theory using a linearized input-output method

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

Published Nov 1, 1996• 62 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.4359

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Theory of laser-amplifier injection locking

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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
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 present experimental results that illustrate how laser intensity noise near the quantum-noise limit is transferred in an injection-locked cw Nd:(yttrium aluminum garnet) nonplanar ring-oscillator laser. We show that these results are in extremely good agreement with our quantum-mechanical model describing the injection locking process [T. C. Ralph, C. C. Harb, and H.-A. Bachor, Phys. Rev. A]. Three regions in the intensity-noise spectrum are identified and we show that different minimum noise levels exist in these regions. Finally, we show that the injection-locked laser can generate and preserve nonclassical states. \textcopyright{} 1996 The American Physical Society.
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.
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.
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.
The quantum noise of an injection-locked laser oscillator is analyzed by the operator Langevin equation. The problem is also treated by the Fokker-Planck equation and the same results are obtained in the same regimes of applicability. The steady-state solution of the Fokker-Planck equation gives the probability distribution of amplitude and phase, the Langevin equation arrives more directly at the spectrum of amplitude and phase. The phase of the injection-locked oscillator is related to the phase of the injection signal and thus constitutes a measurement of phase. In the limit of complete inversion and zero internal loss of the laser resonator, the associated uncertainty is twice that dictated by the uncertainty principle. This result is interpreted by comparing it with the uncertainty introduced by a linear amplifier which can perform a simultaneous measurement of amplitude and phase.
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.