Kenju Otsuka

Transient and modulation dynamics of a multimode Fabry-Pérot laser

Abstract The two-mode rate equations for a laser in a Fabry-Perot cavity are studied, taking into account the dynamics of spatial holeburning. We prove analytically that each mode intensity has a transient behavior characterized by two damped oscillation frequencies, while the total intensity displays a domain where only the largest oscillation frequency remains; this domain appears to display antiphase dynamics. These results are generalized to N lasing modes. We then analyze the response of the two-mode laser to a periodic pump modulation. For small modulation depth, the two oscillation frequencies are clearly displayed as resonances on the response curve. For deeper modulation depth, the beating of the modulation frequency and the largest internal oscillation frequency produces a subharmonic sequence to chaos. This chaotic domain disappears in a crisis when it collides with the branch of stable periodic oscillations associated with the smaller oscillation frequency which coexists with the subharmonic cascade.

Intensity Fluctuations in Multimode Lasers with Spatial Hole Burning

The intensity fluctuations in multimode lasers with spatial hole burning are investigated. We give experimental evidence for a self-organized collective behavior resulting from the cross saturation dynamics of spatially hole-burned lasers, in which each mode is characterized by N relaxation oscillation frequencies ωl (l=1, 2, 3,, N; N: number of oscillating modes), while the total output exhibits a unique relaxation oscillation at the highest frequency in ωl which coincides with that in a single mode laser.

EXPERIMENTAL SUPPRESSION OF CHAOS IN A MODULATED MULTIMODE LASER

Suppressing chaotic behavior by addition of a weak second periodic perturbation signal, which is nearly resonant to a subharmonic of the fundamental system frequency, is observed in a modulated microchip LiNdP(4)O(12) multimode laser by a highly sensitive self-mixing modulation technique. The stabilization of the unstable period-2 orbit embedded in a chaotic attractor is demonstrated in a wide parameter region. The chaos-suppressing experiments are well reproduced by simulations of globally coupled modulated Tang-Statz-deMars [J. Appl. Phys. 34 8289 (1963)] multimode laser equations, including a spatial hole-burning effect.

Laser rate equations with phase sensitive interactions

A set of multimode rate equations which couple the complex fields to the mean number of amplifiers is derived. It is shown that in the case of semiconductor lasers, phase-sensitive interactions must be retained. The resulting equations are studied and bifurcation diagrams are presented that display the steady, periodic, and quasiperiodic solutions. >

Modulation dynamics and spatiotemporal pattern generation in a microchip multimode laser

N- 1 different periodic oscillations are obtained experimentally in a microchip N-mode laser by different combinations of modulations at multiple relaxntion oscillation frequencies that appear on the basis of antiphase dynamics among lasing modes. Application of mode-dependent periodic oscillations to generation of dynamic spatial patterns is demonstrated using a shear plate interferometer. Complex multi-longitudinal-mode laser dynamics has recently been attracting an increasing interest as an intriguing subject for the study of nonlinear dy- namics in optical systems. Indeed, self-organization and antiphase dynamics among oscillating modes re- sulting from the cross-saturation of population inver- sion in the longitudinal direction have been demon- strated for class-B lasers in which polarization dynamics can be adiabatically eliminated ( l-61. In particular, we found a generic feature of such N-mode class-B multi-mode lasers: an individual mode shows antiphase motion featuring N relaxation oscillation frequencies f, >f2 > . . . > fN, while the total intensity exhibits a unique single relaxation oscillation at fi, just like a single mode laser ( l-3 1. In this paper, we investigate the response of a mi- crochip multimode laser to modulation at different combinations of relaxation oscillation frequencies v,, fi, . . . . fN), paying special attention to mode-depen- dent temporal evolutions. We report that 2N- 1 dif- ferent periodic oscillations are excited by a weak loss modulation based on the simple technique of highly- sensitive self-mixing laser-Doppler velocimetry ( 7 1. Application of mode-dependent periodic oscillation to spatiotemporal pattern generation with a shear- plate interferometry is demonstrated. The experiments used a LiNdP4012 (LNP) micro- chip solid-state laser. The LNP crystal was L = 1 mm thick and both ends of the crystal were directly coated with dielectric mirrors (transmission of 0.1 and 1 percent at 1.32 pm). An argon laser (L=514.5 nm) served as a pump. The 1.32 pm LNP laser radiation was linearly polarized along the pseudoorthorhom- bit c-axis. The oscillation threshold was Pti = 185 mW and the slope efficiency was 15 percent. Two-longi- tudinal-mode oscillation was obtained above w= PIP th = 1.2; three-longitudinal-mode oscillation was observed above w= 1.8. The light beam of the TEMoo mode LNP laser was split into two beams by a beam splitter. One beam was passed through a spectrome-

Antiphase Dynamics in a Modulated Multimode Laser

Antiphase periodic oscillations and clustering in a modulated microchip multimode solid-state laser have been demonstrated experimentally. Chaotic relaxation oscillations featuring intermode statistical non-independence that result from cross-saturation dynamics among oscillating modes have been observed.

Modulation dynamics in a multimode laser with feedback

Abstract The response of an N -mode solid-state laser when the output field is reinjected in the cavity after N frequency shifts is analyzed. The results obtained with up to four modes are described and it is tried to infer general rules. The emphasis is on comparing the dynamics of the partial and the total mode intensities.

Modulation of a two-mode laser

We analyze a two-mode laser, described by rate equations, whose gain is periodically modulated. The nature of the response varies significantly with the modulation amplitude. We study both the small modulation in which the pump parameter remains always above the lasing threshold for the second mode, and the deep modulation in which the pump parameter is located during part of the cycle between the single-mode and the two-mode thresholds. Apart from the strong McCumber nonlinear resonance at the relaxation oscillation frequency, we describe a rich variety of nonlinear properties such as multistability among periodic and quasi-periodic solutions, and small resonances in the vicinity of the second (and lower) internal frequency. We also identify domains that suggest the occurrence of the traditional routes to chaos. >

Universal dynamical properties of three-mode Fabry-Perot lasers

We present an asymptotic study of a three-mode Fabry - Perot laser with arbitrary relative modal gains in the rate equation limit. Dynamical modes are defined as the eigenvectors of the stability or Jacobian matrix. The associated eigenvalues are the decay rates and the relaxation oscillation frequencies. We show that if the modal gains are not equal, the ratio of the relaxation oscillation frequencies may display rational ratios which will lead to resonances. We classify the various states of the modal field intensities as in-phase, partial and perfect antiphase and find universal relations between the peak heights in the power spectra of the total and of the modal intensities at each of the relaxation oscillation frequencies. Our theoretical results are confirmed by numerical computation using the full rate equations. Experimental results obtained for the noise spectrum of an LNP microchip laser fully support our theoretical results. We also conjecture some properties of lasers operating in an arbitrary N-mode regime.

Parametric resonance in a modulated microchip multimode laser

A nonlinear response of a laser-diode-pumped microchip LiNdP(4)O(12) (LNP) multimode laser that is subjected to multiple-frequency modulations is investigated. Clustering and breathing motions featuring intermode parametric resonances are demonstrated when the LNP laser was modulated by rational frequencies chosen to be nearly resonant to multiple relaxation-oscillation frequencies inherent in multimode lasers. A simple correspondence between the modulation signal patterns and the total-output power-spectrum patterns is demonstrated.