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Physical Review A

Low-frequency dynamics of a Nd-doped glass laser

Björn Peters, Jörg Hünkemeier, Valery M. Baev, Yakov I. Khanin

Published Jul 18, 2001• 13 citations
Publisher

Abstract

We study a Nd-doped microchip glass laser that emits in two polarizations and in many longitudinal modes. Saturation of the inversion by standing waves causes spatial inhomogeneity of both the longitudinal and azimuthal distributions of the laser gain. These nonlinear inhomogeneities couple the modes and result in low-frequency oscillations (10--500 kHz) of the light flux in the individual laser modes. These oscillations are steadily driven by quantum noise and appear as 15% fluctuations of the power in each mode. In-phase fluctuations in the laser modes appear at the frequency of the main relaxation oscillation of the total laser power. Antiphase fluctuations appear at other frequencies in individual longitudinal and polarization laser modes only. The dominant frequency of these fluctuations is determined by the light power in the mode. Numerical simulations of rate equations, including Langevin forces, satisfactorily reproduce the experimental results. These phenomena must be taken into account when lasers are applied as stable coherent optical light sources, and also with sensitive absorption measurements in the laser cavity.

DOI
10.1103/physreva.64.023816

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We study the dynamics of a laser oscillating on L optical transitions connecting a common upper level and L lower sublevels. Each transition is single mode. The minimal generalization of the rate equations to explain the experimental observations includes the low-frequency coherence dynamics [Europhys. Lett. 45, 307 (1999)]. These equations are studied analytically. We prove that such a laser has a low intensity self-pulsing threshold corresponding to the destabilization of the lowest of the relaxation oscillation frequencies. It also displays antiphased dynamics in the time-periodic regime, resulting in a vanishingly small oscillation amplitude of the total intensity while modal intensities have finite amplitude oscillations. The physical origin of this behavior is found to be the enhancement of stimulated absorption by quantum interference.
Fluctuations in the amplitude, frequency, and polarization of the light emitted by semiconductor laser diodes limit the performance and reliability of many optical systems, such as communication links, optical radar, and optical disk read/write memories. Although it seems logical to explain this noise as random or stochastic, such erratic behavior can arise from completely deterministic models of lasers that retain the dynamics of the coherently induced polarization. This has been shown to be true for the simple model of a laser based on a two-level resonance, which results in the coupled Maxwell-Bloch equations. These equations are termed coherent because the Bloch equations describe, not only the inversion, but also the induced polarization of the gain media. The Maxwell-Bloch equations predict an array of instabilities and novel operation conditions for a laser: the output light may oscillate regularly or pulsate chaotically. Such behavior is not found in the incoherent population rate equation that adiabatically eliminated the dynamics of the polarization. However, the Maxwell-Bloch equations apply only to dilute materials in which the total gain is described by an ensemble average over many noninteracting molecules, such as gas lasers.
In a LiNdP 4 O 12 microchip laser pumped by a diode laser, atomic interference arise due to the simultaneous oscillation on two transitions forming a Λ configuration. For a microchip laser, the low-frequency coherence is an important dynamical variable. It is coupled to the low spatial frequency of the population inversion grating. This results in modal intensities which are self-pulsing while the total intensity remains nearly constant. In addition, the modal power spectra display combinations of the relaxation oscillation frequencies which are absent in the power spectrum of the total output power.
Quantum fluctuations in the radiation of multitransverse-mode laser are investigated theoretically and numerically, based on quantum c-number Langevin stochastic equations for the complex amplitudes of transverse modes. It is shown that strong antiphase quantum fluctuations of transverse-mode amplitudes occur, which corresponds to spatial fluctuations of the laser field. Fluctuation spectra are calculated, showing that antiphase fluctuations dominate at low frequencies (smaller than relaxation oscillation frequency), and in-phase oscillations prevail at high frequencies.
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.
We study the field correlation functions and the natural laser spectrum for a slow-inversion laser with the thresholdless intensity fluctuations. In such a laser, the spontaneous-emission-driven relaxation oscillations are responsible for some unique features: The field correlation function oscillates with the frequency of relaxation oscillations ${\ensuremath{\omega}}_{r}$ and the laser line changes its profile. We show that appreciably above threshold the laser spectrum consists of three lines. In addition to the main line at the frequency of the lasing mode ${\ensuremath{\omega}}_{c}$ appear two lines at frequencies ${\ensuremath{\omega}}_{c}+{\ensuremath{\omega}}_{r}$ and ${\ensuremath{\omega}}_{c}\ensuremath{-}{\ensuremath{\omega}}_{r}$. The spontaneous emission noise in such lasers gives rise to nonlinear stochastic effects: Quantum noise affects the oscillation frequency ${\ensuremath{\omega}}_{r}$ and the decay rates of the field correlation function.