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Physical Review A

Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers

Alberto Bramati, Jean‐Pierre Hermier, V. Jost, E. Giacobino

Published Sep 13, 2000• 5 citations
Publisher

Abstract

A fully quantum model is used to derive both the intensity noise of a laser operating with an electronic feedback loop and the nonlinear corrections to the noise of the free-running laser. The implementation of a nonstandard feedback loop on a ${\mathrm{N}\mathrm{d}:\mathrm{Y}\mathrm{V}\mathrm{O}}_{4}$ microchip laser pumped with an amplitude squeezed diode laser permits us to decrease the intensity of the relaxation oscillation noise peak while leaving the low-frequency part of the spectrum unaffected. This procedure also results in a decrease of the noise in the low-frequency region, showing evidence for nonlinear effects in the noise spectrum. The latter are found to be in good agreement with the theoretical predictions. Good agreement between the experimental results and theoretical predictions is also found over the complete frequency range.

DOI
10.1103/physreva.62.043806

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Optics Letters•Sep 1, 1994•30 citations
A fully quantum model is used to derive both the intensity noise of a laser operating with an electronic feedback loop and the nonlinear corrections to the noise of the free-running laser. The implementation of a nonstandard feedback loop on a Nd:YVO4{\mathrm{N}\mathrm{d}:\mathrm{Y}\mathrm{V}\mathrm{O}}_{4}Nd:YVO4​ microchip laser pumped with an amplitude squeezed diode laser permits us to decrease the intensity of the relaxation oscillation noise peak while leaving the low-frequency part of the spectrum unaffected. This procedure also results in a decrease of the noise in the low-frequency region, showing evidence for nonlinear effects in the noise spectrum. The latter are found to be in good agreement with the theoretical predictions. Good agreement between the experimental results and theoretical predictions is also found over the complete frequency range.
A fully quantum-mechanical model of feedback to the pump source of a four-level laser is developed with a view to predicting the achievable intensity noise reduction. For solid-state lasers, the model shows that quantum noise sources due to laser dynamics have a significant impact on the optimization of the feedback loop. Experimental results obtained with a diode pumped neodymium:yttrium aluminum garnet (Nd:YAG) laser are found to be in good agreement with the theoretical model. The ultimate limit to the noise suppression comes from the quantum noise due to the measurement processes in the feedback loop. A scheme to overcome this limit using a squeezed vacuum is theoretically demonstrated to be a highly efficient method of generating bright intensity squeezed light, particularly in the kHz regime where bright squeezing is otherwise difficult to obtain.
We investigate theoretically the intensity and phase correlations in the quantum-noise-driven dynamics of two spatially coupled microchip lasers. These correlations induce noise reduction phenomena for which simple analytic expressions are derived. We predict a complete suppression of the dominant relaxation oscillation peaks in the intensity difference noise spectrum, as well as photon statistics approaching the standard quantum limit. The correlations and consequent noise reduction effects are robust against frequency detuning and persist for pump powers well above threshold.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.
We examine the quantum-limited behavior of an electro-optical intensity feedback loop and present a simple theory and experimental data showing excellent agreement. We show that, although the light incident upon the in-loop detector may be sub-Poissonian, this light has unique properties different from those of a freely propagating beam of intensity squeezed light. We support this by presenting the results of homodyne measurements of the phase noise of light extracted from the loop. The utility of the in-loop field is discussed, and it is shown that in all cases in which linear optical components are used, no advantage in signal-to-noise ratio is gained by taking measurements by using this light rather than a coherent source. We also discuss effects seen in the extracted or out-of-loop light. We demonstrate the existence of, and derive an expression for, an optimum gain for suppressing low-level classical noise. Conversely, in the high-gain limit, we demonstrate that the extra noise seen in the out-of-loop photocurrent that is due to the feedback process is expressible purely in terms of the mean photocurrents involved. Lastly, we introduce the novel concept of using an intensity feedback loop in conjunction with a squeezed source and show that the feedback loop has the capability of electronically transferring squeezing from one light beam to another.
We have produced amplitude-squeezed light whose noise is reduced by ~10 dB below the quantum noise limit in four different feedback systems. In our experimental method we have directly compared the noise power spectrum of the laser diode with the quantum noise limit in the low-frequency region, where the classical noise is stronger than the quantum noise. In addition to the well-known methods for extracting the out-loop beams from the feedback system by use of a 50:50 beam splitter, a polarizing beam splitter, or the leakage light from the rear side of a laser diode, we also have tried to use the spatial coherence of the laser light. We also have examined the vacuum fluctuations that prohibited the out-loop beam from being amplitude squeezed. In all these systems we have verified that the noise power spectrum for the in-loop beam is reduced below the quantum noise limit but not that for the out-loop beam; the difference arises mainly because vacuum fluctuations enter each system differently.
We present the theory and measurements of the amplitude noise spectrum from a semiconductor laser with weak optical feedback (P(fb)/P(out) approximately 10(-6)) from an external cavity containing an element of dispersive loss. The laser noise is found to be reduced over most of the low-frequency spectrum, although an increase in the noise is observed at frequencies corresponding to multiples of the external-cavity free spectral range. The low-frequency noise reduction closely follows theoretical predictions, and a reduction of as much as 7 dB is measured at an injection current of 1.5 times the threshold current. The potential of this method for contributing to the production of amplitude-squeezed light is discussed.