Modelling of chirping laser diodes for microwave generation and transmission over dispersive fibres

Abstract

For a sinusoidal modulation of the injection current we present optical and photocurrent spectra computed by a numerical large signal LD model, and compare the outcome to previous analytical and experimental results [2]. We also treat successfully some cases of overmodulation, where temporarily the current falls below threshold. For lower modulation frequencies and below-threshold currents the optical power becomes significantly determined by spontaneous emission; in these cases our present deterministic model fails. I IntroductionThe commercial impact of extended subscriber services with higher transmission capacity seems to be tremendous, if cost-effective means of connecting to subscribers can be employed. A very promising way is to upgrade existing copper or optical fibre cables by hybrid fibre radio networks, where wireless transmission channels employing the microwave and mm-wave frequency range 20. . .70 GHz bridge inexpensively the 'last mile' to a subscriber. The direct modulation of a laser diode (LD) has the potential to be very cost-effective, especially if harmonic upconversion by transmission over a fibre or any other suitable dispersive element is exploited 11) 12). For an optimization of this technique a model of a chirping LD is needed, which we discuss in the following. I1 Laser diode spectrumThe optical output field of a LD is represented by an analytic signal a(t) with complex amplitude A(t), phase cp(t), and total output power P,(t) leaving the resonator (time t, angular optical frequency wg = 27rf0, vacuum speed of light c , vacuum wavelength XO, frequency fo = ./A,, elementary charge e, Planck's constant h, time constant T R from finite resonator mirror reflectivities, photon lifetime r p = 3 ps, effective carrier lifetime 7 ,~ = 3ns, differential quantum efficiency vd = T~/ T R = 0.28, field confinement factor r = 0.2). Further, the normalized quantities Z(t) for the photon number N p ( t ) , Y ( t ) for the carrier number N~c ( t )inside the active volume VI< sz 0.16 x 3 x 420pm3, and n(t) for the injection current I ( t ) (threshold values indexed by S, threshold current 1s = 41 mA, bias pumprate 170 = 3 with corresponding approximate DC values y0 = 1, 2 0 = 2, 20 N Pao = 18mW) are introduced, Further parameters are the normalized gain GN with the normalized transparency carrier number & = 0.82, the normalized differential gain d G~/ t l Y = G N~ M 1 / ( 1 -yt) = 5.56, the threshold gain rGs x l / r p , the gain saturation parameter EG = 10 x 10-17cm3, its normalized version EG = 0.075, the adiabatic angular frequency shift w, = 27r x 8.0GHzI the Henry factor of amplitude-phase coupling Q = 3.5, and the factor of spontaneous emission Q = We adopt the notation X ( t ) = Xo + X l ( t ) for any quantity X ( t ) dependent on time t around a constant operating point Xo; this formulation does not necessarily imply a small signal approximation for X,(t).The quasi-stationary resonance frequency w(t) = WO + w l ( t ) of ,a single-mode field in a laser resonator with length L, effective modal r...

A new electro-optical phase shifter for optically generated microwave signals

“…However, external modulators as well as laser diodes suitable for modulation frequencies above 2 GHz are expensive. On the other hand, it is well known that the direct intensity modulation (IM) of a semiconductor laser has side effects as frequency modulation (chirp) due to the dependence of the refractive index on the carrier density, which gives rise to higher harmonics of the modulation signal in the demodulated optical signal [5] [6] [7]. Higher harmonics can be also produced by operating an inexpensive laser in the nonlinear regime near the threshold current.…”