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IEEE Journal of Quantum Electronics

Heterodyne detection with an injection laser I. principle of operation and conversion efficiency

Dietrich Marcuse

Published Jan 1, 1990• 9 citations
Publisher

Abstract

If a light signal is passed into the resonant cavity of an actively oscillating injection laser, an electrical signal at the difference between the laser and light signal frequencies flows through the wire supplying the DC bias to the laser. A small-signal analysis of heterodyne detection with such a laser oscillator that is based solely on rate equations and introduces the externally applied signal as a source term into the photon rate equation is discussed. Since neither Maxwell's equations nor the wave equation are involved, this analysis is deemed simpler and more transparent than that reported earlier. Gain saturation of the active medium of the laser, which is responsible for broadening of the relaxation resonance, is taken into account.

DOI
10.1109/3.44920

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Superregenerative detection: experiment and theory

Ian C. M. Littler, Stefan Balle, Klaas Bergmann +2 more

The initiation time for the intensity of an injection seeded laser is measured as a function of the externally injected signal strength. The operation of a radiation detector based on the measurement of initiation times is demonstrated, with a dynamic range of 7 orders of magnitude, bandwidth resolution of 5 MHz, and tuning range limited by the active medium of the laser employed. Such a detector, based on the Q-switched operation of an oscillator, is known as a superregenerative receiver. We report experimental measurements of the characteristics of such a receiver and explain the behavior with reference to a simple stochastic model of a laser with an injected signal. The weakest signals that can be detected are shown to be comparable to the level of spontaneous emission into the cavity mode, which corresponds to an average photon number less than unity for our system.

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Population Inversion, Saturation, and Laser Systems

Surendra Singh

This chapter begins with a heuristic derivation of atomic population rate equations which include changes to level populations due to stimulated transitions as well as level relaxations and pump. These equations are used to study the saturation of population inversion with increasing light intensity and its dependence on the type of gain medium (three-level gain media vs. four-level gain media), lineshape and nature of line broadening (homogeneous vs inhomogeneous broadening). How saturation affects lineshape and thus gain and absorption giving rise to phenomena like power broadening and spectral hole burning is also discussed. The chapter summarizes the equations of motion for atomic polarization, inversion and the cavity field describing their nonlinear dynamical coupling. These equations, known as the Maxwell-Bloch equations, provide a complete description of atom-field interaction in a laser. Approximations of these equations, including the rate equation approximation, to deal with different laser classes are briefly described. These will be used in the next few chapters to explore and understand the rich and varied behavior of lasers. The chapter ends with a summary of select gain media for different types of commonly used lasers.

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Coherent laser detection by frequency-shifted optical feedback

Éric Lacot, R. Day, F. Stoeckel

The dynamical response of a laser to frequency-shifted optical feedback is investigated both theoretically and experimentally. The ultrahigh sensitivity of a class-B laser (i.e., a laser with a cavity damping rate ${\ensuremath{\gamma}}_{c}$ higher than the population damping rate ${\ensuremath{\gamma}}_{1})$ to external light injection is demonstrated by the optical detection of weak optical feedback. Compared to a conventional optical beating, the intensity modulation induced by the coherent interaction between the laser electric field and the frequency-shifted reinjected electric field can be several orders of magnitude higher. This method permits high sensitive interferometry and hence imaging. We call this laser detection technique laser optical feedback imaging (LOFI). When the optical frequency shift is resonant with the laser relaxation frequency, the intracavity amplification of the beating is maximum and the enhancement is given by the laser damping rate ratio ${\ensuremath{\gamma}}_{c}/{\ensuremath{\gamma}}_{1}.$ This amplification is of the order of ${10}^{6}$ for a microchip laser. We also show that without optical feedback the strong fluctuations of the laser output power are well described by the Langevin noise process. In a broad range around the laser relaxation frequency the laser quantum noise is also resonantly amplified and is then several orders of magnitude higher than the detector noise. In these conditions, the LOFI is a shot noise limited detection technique. Reflectivity as low as ${10}^{\ensuremath{-}13}$ is then easily detectable with a laser output power of a few milliwatts with a detection bandwidth of 1 kHz. Experimentally, for weak optical feedback the laser fluctuations are principally composed of the LOFI modulation signal at the shifted frequency and of the laser quantum noise amplified at the relaxation frequency. For strong optical feedback, nonlinear effects appear in the laser dynamics. In these conditions, harmonics and parametrics peaks appear in the power spectrum. The LOFI detection system is then saturated.

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Self-pulsing in other optical systems

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This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.

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In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.

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Gain, dispersion, and emission characteristics of three-level molecular laser amplifier and oscillator systems

J. S. Uppal, Robert G. Harrison, Jerome V. Moloney

Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.

Physical Review A•Nov 1, 1987•31 citations
If a light signal is passed into the resonant cavity of an actively oscillating injection laser, an electrical signal at the difference between the laser and light signal frequencies flows through the wire supplying the DC bias to the laser. A small-signal analysis of heterodyne detection with such a laser oscillator that is based solely on rate equations and introduces the externally applied signal as a source term into the photon rate equation is discussed. Since neither Maxwell's equations nor the wave equation are involved, this analysis is deemed simpler and more transparent than that reported earlier. Gain saturation of the active medium of the laser, which is responsible for broadening of the relaxation resonance, is taken into account.
The initiation time for the intensity of an injection seeded laser is measured as a function of the externally injected signal strength. The operation of a radiation detector based on the measurement of initiation times is demonstrated, with a dynamic range of 7 orders of magnitude, bandwidth resolution of 5 MHz, and tuning range limited by the active medium of the laser employed. Such a detector, based on the Q-switched operation of an oscillator, is known as a superregenerative receiver. We report experimental measurements of the characteristics of such a receiver and explain the behavior with reference to a simple stochastic model of a laser with an injected signal. The weakest signals that can be detected are shown to be comparable to the level of spontaneous emission into the cavity mode, which corresponds to an average photon number less than unity for our system.
This chapter begins with a heuristic derivation of atomic population rate equations which include changes to level populations due to stimulated transitions as well as level relaxations and pump. These equations are used to study the saturation of population inversion with increasing light intensity and its dependence on the type of gain medium (three-level gain media vs. four-level gain media), lineshape and nature of line broadening (homogeneous vs inhomogeneous broadening). How saturation affects lineshape and thus gain and absorption giving rise to phenomena like power broadening and spectral hole burning is also discussed. The chapter summarizes the equations of motion for atomic polarization, inversion and the cavity field describing their nonlinear dynamical coupling. These equations, known as the Maxwell-Bloch equations, provide a complete description of atom-field interaction in a laser. Approximations of these equations, including the rate equation approximation, to deal with different laser classes are briefly described. These will be used in the next few chapters to explore and understand the rich and varied behavior of lasers. The chapter ends with a summary of select gain media for different types of commonly used lasers.
The dynamical response of a laser to frequency-shifted optical feedback is investigated both theoretically and experimentally. The ultrahigh sensitivity of a class-B laser (i.e., a laser with a cavity damping rate ${\ensuremath{\gamma}}_{c}$ higher than the population damping rate ${\ensuremath{\gamma}}_{1})$ to external light injection is demonstrated by the optical detection of weak optical feedback. Compared to a conventional optical beating, the intensity modulation induced by the coherent interaction between the laser electric field and the frequency-shifted reinjected electric field can be several orders of magnitude higher. This method permits high sensitive interferometry and hence imaging. We call this laser detection technique laser optical feedback imaging (LOFI). When the optical frequency shift is resonant with the laser relaxation frequency, the intracavity amplification of the beating is maximum and the enhancement is given by the laser damping rate ratio ${\ensuremath{\gamma}}_{c}/{\ensuremath{\gamma}}_{1}.$ This amplification is of the order of 106{10}^{6}106 for a microchip laser. We also show that without optical feedback the strong fluctuations of the laser output power are well described by the Langevin noise process. In a broad range around the laser relaxation frequency the laser quantum noise is also resonantly amplified and is then several orders of magnitude higher than the detector noise. In these conditions, the LOFI is a shot noise limited detection technique. Reflectivity as low as ${10}^{\ensuremath{-}13}$ is then easily detectable with a laser output power of a few milliwatts with a detection bandwidth of 1 kHz. Experimentally, for weak optical feedback the laser fluctuations are principally composed of the LOFI modulation signal at the shifted frequency and of the laser quantum noise amplified at the relaxation frequency. For strong optical feedback, nonlinear effects appear in the laser dynamics. In these conditions, harmonics and parametrics peaks appear in the power spectrum. The LOFI detection system is then saturated.
This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.
In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.
Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.