IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 8, AUGUST 1998 1469 Multilongitudinal-Mode Dynamics in a Semiconductor Laser Subject to Optical Injection John K. White, J. V. Moloney, A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus Abstract—Multilongitudinal-mode dynamics in a semiconduc- tor laser subject to optical injection are investigated both exper- imentally and numerically. We found that there are parameter regimes for which the slave laser hops into an adjacent longitu- dinal mode as we vary the detuning of the optical frequencies between the master and slave laser. A traveling wave model is used to numerically investigate the mode hopping. Good qualita- tive agreement is found between the numerical computations and the experimental observations. Index Terms—Laser modes, laser stability, modeling, nonlinear differential equations, nonlinear optics, optical communications, optoelectronic devices, semiconductor lasers. I. INTRODUCTION S EMICONDUCTOR lasers are widely used as coherent light sources in technological applications such as optical communications. For high-speed and reliable transmission of data, it is essential that the semiconductor laser exhibits stable single-mode operation with a narrow linewidth and may be modulated at high frequencies with little chirping. It was found that injection locking of a slave laser to a master laser may enhance the spectral stability of a laser significantly. The injection-locked slave laser exhibits stable single-mode operation for a specific locking band region [1], its linewidth may be reduced significantly [2], the chirping is minimized in modulated semiconductor lasers [3], and also squeezing can be realized [4]. To employ this locking technique successfully it is essen- tial to know the stability boundaries for a laser subject to optical injection and to understand the underlying dynamical properties beyond these boundaries. The injection-lock band was investigated by many authors experimentally, numerically, and analytically [1], [5]–[11] and was found to be asymmetric due to the coupling of the phase and amplitude as expressed by the linewidth enhancement factor . Unstable behavior is especially found for positive detunings, meaning the master laser is detuned to the shorter wavelength with respect to the slave laser. In this regime, multimode operation and leakage of energy into sidemodes has been observed in [8] and [12]. Manuscript received December 22, 1997. This work was supported by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under Grant AFOSR-94-1-0144 DEF and Grant AFOSR-04-1-0463. The work of A. Hohl was supported by the National Research Council. J. K. White and J. V. Moloney are with the Arizona Center for Mathematical Sciences, University of Arizona, Tucson, AZ 85721 USA. A. Gavrielides, V. Kovanis, A. Hohl, and R. Kalmus are with the Nonlinear Optics Group, Phillips Laboratory PL/LIDD, Kirtland AFB, NM 87117-5776 USA. Publisher Item Identifier S 0018-9197(98)05407-4. Mode hopping has been observed in solitary semiconductor lasers as the pump current or the temperature of the laser are varied [13]–[19] or due to external feedback from a reflector [20]. The physical cause of mode hopping has been widely attributed to nonlinear gain and it has been shown that including the nonlinear gain into numerical computations is sufficient to induce mode hopping, yet the origin of the nonlinearity is not entirely understood. Some authors attribute the nonlinearity in the gain to spectral hole burning and longitudinal mode beating that modulate the refractive index [13], [14], [16]–[18], while others attribute the nonlinear gain to dynamic carrier heating effects [21]. A natural way to account for multimode behavior is to include the longitudinal dependence into the semiconductor laser rate equations. Models that reduce the laser equations to a system of coupled ordinary differential equations (ODE’s) [22] are limited to studying the energy in a single mode, usually the lasing mode. Even multimode decompositions [23] where modes are represented by coupled ODE’s fail to capture the gain dispersion accurately. Furthermore, all ODE models assume a uniform carrier density. For lasers where one end is antireflection (AR) coated there arise strong longitudinal dependencies in the carriers. Our model addresses all of these issues in a simple self-consistent manor by resolving the longitudinal structure of the forward field, backward field, and carrier density. The paper is organized as follows. We first report on the experimental arrangement and observations on mode hopping due to external optical injection. The description of the model follows and the numerically computed optical spectra are discussed. We conclude with a summarizing section. II. EXPERIMENTAL APPARATUS AND OBSERVATIONS In the experiment two commercially available GaAlAs Fabry–Perot lasers (Sharp LT015, double heterojunction diodes in a V-channeled substrate inner stripe (VSIS) structure) were used in a master–slave configuration. Both lasers were lasing at 835 nm and during the experiment, both were operated from a low-noise current supply (ILX Lightwave LDC-3722), and the temperature was stabilized to better than 0.01 K. The optical spectrum was monitored with a scanning Fabry–Perot interferometer (Newport SR-240C) which had a free spectral range of 2 THz. Isolators of 50-dB attenuation were used to insure that no light was injected into the master laser and no back reflections from the Fabry–Perot were injected into either laser. The slave laser was pumped at above threshold, where and and 0018–9197/98$10.00  1998 IEEE