A theoretical analysis for gigabit/second pulse code modulation of semiconductor lasers

Abstract

Document VersionPublisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Danielsen, M. (1976). A theoretical analysis for gigabit/second pulse code modulation of semiconductor lasers. I E E E Journal of Quantum Electronics, 12(11), 657-660.IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-12, NO. 11,NOVEMBER 1976 657 A Theoretical Analysis for GigabitAecond Pulse Code Modulation of Semiconductor LasersAbstract-Investigation of the rate equations of a semiconductor laser suggests that bit rates of 3-4 Gbit/s can be achieved. Delay, ringing hansients, and charge-storage effects can be removed by adjusting the dc-bias current and the peak and width of the current pulse to values prescribed by simple analytical expressions. Also, simple approximate formulas for the light pulse maximum, width, delay, and integrated values are given. INTRODUCTIONP ULSE modulation of a semiconductor laser presents three problems [1]-[SI, when high bit rates are required: a time delay between the applied current pulse and the light pulse, ringing transients, and the charge-storage effect of preceding pulses on the light pulse form and magnitude.This work presents a pulse modulation model which avoids these disadvantages. A dc-bias current near threshold reduces the delay. The first spike of the ringings is suggested to be exploited as a light pulse. This is done by switching off the current pulse immediately after the light pulse appeared. The influence of the charge storage, making the height of the photon pulses dependent on preceding pulses, is overcome by giving the height and duration of the applied current pulses such values that the electron and photon densities return to the start values at the end of the pulse. This makes the start condition identical for each pulse.Numerical solutions show that the detailed current pulse form is not significant. Only the charge delivered by the current has to fulfill some requirements. Analytical formulas, derived for square current pulses, are therefore at least qualitatively applicable for a wide range of pulse forms.The following analysis is based on the rate equations including spontaneous emission as reported in [ 51 ,where n, J , S electron, current, and photon densities, respectively; d active layer thickness; e electronic charge;T~, rp electron and photon lifetimes. The gain of the laser is g = a(n -No) [SI ,[6] , where No and cx are constants. The factor 0 is the fraction of spontaneous light that goes into the the lasing modes. In [7] it has been shown that the spectrum of a narrow pulse is determined by the dc bias, and is almost independent of the current pulse height.Therefore fi is taken to depend on the prebias current only and to be constant during a pulse. The value of 0 is estimated to be of the order of when one mode is active, and is taken to be proportional to the number of active modes [8].For simplicity, effects like mode locking, mode coupling, Qswitching, electron diffusion, and circuit parasitics have been disregarded in this analysis. T...

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“…To calculate the phase </>(ω), we use the Hilbert transform theory according to which the phase can be calculated from the magnitude as [20] 7Γ Jo " 2 -'^2 ω Α ■ dr\ (8) resulting in <7(/'ω) = \G(joe)\eJ*^ (9) provided that the transfer function is minimum phase, i.e., has no poles or zeros in the right half plane. Minimum phase be havior is expected since the gain factor, the delay factor, and the transfer function of the equivalent circuit all show mini mum phase behavior [16], [17], [19].…”