Microwave Generation And Transmission With Chirping Laser Diodes And Dispersive Fibres

Abstract

Microwave generation and transmission is possible using directly modulated laser diodes (LD) and optical fibres. The chirp of the LD together with the fibre dispersion influences the microwave spectrum significantly. We calculate the optical spectrum of the LD and the photocurrent spectrum before and after fibre transmission analytically, and compare them with experimental results. We also report on bit error rate measurements for various operating conditions and show that FM-AM conversion in the fibre counterbalances the attenuation when increasing the transmission length. Introduction Hybrid fibre rad0 (HFR) networks upgrade existing copper or optical fibre cables by wireless transmission channels, employing the microwave and mm-wave frequency range 20. . .70 GHz. HFR may be used for future micro and pico-cell broadband mobile communication systems, for wireless in-house connections, or for bridging inexpensively the 'last mile' to a subscriber having no access to a fibre or coax system. Three main technologies exist for transmitting and generating microwave signals by optical means, namely direct intensity modulation (IM) of a laser diode (LD), suppressed carrier modulation with an external Mach-Zehnder modulator , and heterodyne techniques in which optical waves of different frequencies are coherently mixed. We discuss the direct IM of a chirping LD with a sinusoidal subcarrier at fm = 1.95; 2.52; 3.52 and 3.716 GHz for producing at a remote location the lcth harmonic ( I C = 9; 7; 5 and 5) microwave signal at lcfm = 17.6 and 18.58 GHz. We calculate the optical and the photocurrent spectra for an m o d u l a t e d subcarrier at various LD modulation current amplitudes without and with transmission over a dispersive fibre, and compare these spectra to measurements. Decreased bit error rate (BER) power penalties for zncreaszng transmission lengths are explained by these results. I1 Rate equation approach The rate equations for the phase p of the power amplitude a of the electric field, for the photon number Np N la12, and for the carrier concentration n~ [l, Eq. (2.77, 74, 78)] [a, Eq. (3.89)] as a function of the injection current represent a highly nonlinear system of dfferential equations, from which the (optical) Fourier spectrum ii of the power amplitude a may be calculated only numerically. To gain more physical insight, we simplify the problem as follows. Simplified approach The optical output field of a LD is represented by an analytic signal a with amplitude A and total output power Pa leaving the resonator (time t , angular frequency wo = 2 ~ f 0 , vacuum speed of light c, vacuum wavelength XO, frequency fo = c/Xo, Planck's constant h, time constant T R from h t e resonator mirror reflectivities), Spectrum of chirping laser diode a ( t ) = Ao(t) eJwut , Ao(t) = /Ao(t)/eJ'PO(t), P,(t) = $ la(t)I2 = N p ( t ) h f o / ~ ~ . (1) Following the analysis of [3] (also cited in [I, Eq. (5.2)-(5.4)] [2, Eq. (3.222, 3.146)]), the instantaneous frequency deviation (frequency chirp) Afo(t) from the mean frequency fo may be calculated. With the Henry factor of amplitude-phase coupling a 2 0 in the definition [2, Eq. (3.106)], the adiabatic angular frequency shift w s 2.fs for aPa(t) = 2Pa(0), and its constituents gain saturation parameter EG, field confinement factor r, photon lifetime 'rp, differential quantum efficiency v d = T P / T R and resonator volume VK, we write (neglecting spontaneous emission and any spatial inhomogeneity of n ~ ) 3-4