The effect of optical injection was studied by observation of the dependence of the .... Owing to the coupled. ELECTRONICS LETTERS 21st January 1993 Vol.
THE SEMICONDUCTOR LASER BEYOND THE LOCKING RANGE OF OPTICAL INJ ECTlON
almost copied the spectrum of the injected light. At larger detuning, i.e. beyond the locking range, the spectrum was composed as follows. First, we observed a strong but slightly 20
G. H. M. van Tartwijk, G. Muijres, D. Lenstra, M. P. van Exter a n d J. P. W o e r d m a n
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Indexinq terms ' Semiconductor lasers, Laser.?
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The voltage of a current-driven optically injected semiconductor laser has been measured. The experiments not only show the well known phenomenon of injection locking but also reveal unprecedented dispersive-like structures around the relaxation oscillation frequencies. Based on the singlemode rate equations a theoretical explanation of both phenomena is given. The dispersive-like structures are shown to be caused by four wave mixing.
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Introduction: In recent years, injection locking of a semiconductor laser with light from an external source has proven to he a powerful tool for obtaining detailed information about the dynamical properties of a semiconductor laser [l, 21. The injected power induces a change in the population inversion which results in a change in voltage A V over the injected laser [3]. This generated AV depends on the detuning between the frequency of the injected light and the unperturbed laser eigenfrequency. Hui et al. [2] were the first to measure A V on optical injection as a function of the detuning. They showed that the linewidth-enhancement factor a of a DFB laser can be determined from the voltage-detuning characteristics. This technique was then shown by Van Exter and Woerdman [4] to be quite similarly applicable to a Fabry-Perot-type (FP) laser. We report the voltage measurements of an FP-type laser for detunings extending beyond the locking range. We found dispersive structures around the relaxation oscillation frequencies, which to our knowledge have not been dealt with before. Based on the singlemode rate-equation model, we give a theoretical explanation of these structures as well as analytical expressions describing both the locking and nonlocking behaviour. The explanation for the novel structures is based on the mixing of two dominant solitary laser waves at frequency w, and the injected wave at frequency w,, producing a fourth wave at frequency Zw, -U,. As the charge-carrier relaxation dynamics is that of a damped harmonic oscillator, the above FWM process is indeed resonantly enhanced when the detuning w , - w, equals the relaxation oscillation frequencies fw,, as observed in the experiment.
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Fig. 1 Change in ooltage against frequency detuning ~
0 measured data points theoretical results for both locking and nonlocking case
- - - - transition between the two cases
shifted dominant central line with accompanying weak sidebands. Secondly, two weak additional peaks were observed, one of which was located at the injection frequency, and the other was found at a new frequency symmetrically disposed on the opposite side of the central dominant peak. A more complete description of these experiments is given elsewhere.* Theory: We start with the well known rate equations for a singlemode diode laser that describe the temporal behaviour of the complex slowly varying envelope E(t) of the optical field E(t) exp (iw, t ) and the number of carriers (electron-hole pairs) N ( t ) . Injection of an external optical field E , exp (iw,t) results in an additional term in the rate equation for E(t). After linearisation around the solitary laser (i.e. without injection) operation point, the rate equations are
d -E(/) dt
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* > A S EXTER, M. P., BiEVER, r., and WOERDMAN, J P.: 'Effect Of optical injection on bias voltage and spectrum of a semiconductor laser', submitted 10 IEEE J. Quantum Electron., ELECTRONICS LETTERS 21st January 1993
Vol. 29
No. 2
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