Theoretical Study On The Vertical-Cavity Semiconductor Optical Amplifiers

As a new type of optical amplifiers, vertical cavity semiconductor optical amplifiers(VCSOAs) have many intrinsic advantages over the tranditional edge emitting semiconductor optical amplifiers(SOAs) and erbium-doped fiber amplifiers(EDFAs), which lead to their potential applications in many fields of optical fiber communications. Up to now, plenty of research works, both theoretically and experimentally, have been done on VCSOAs and many great results have been obtained. Based on those research findings, this work concentrated on many properties of VCSOAs such as the stationary state gain, optical gain bandwidth, modulation bandwidth, short optical pulse amplification and the small signal frequency response.On the basis of the theory of multilayer dielectric films, a transfer matrix model of VCSOAs is established by treating one VCSOA as a whole, which differs from the commonly used effective cavity model in many theoretical studies. The transfer matrix model includes the dicontinuities of the refractive indice of the media in the resonant cavity and the logitudinal distributions of the carriers and optical intensity within the active region. By using such model, the reflectivities of the ditributed Bragg reflector (DBR), the effective cavity length, the gain enhancement factor as well as the coupling efficiency of the input signal into the cavity are no longer necessary to be calculated seperately, which brings more convenience to the theoretical study.In the steady state region, this transfer matrix model has been ultilized to study the influence of the input optical power on the distribution of the carrier concentration, the optical bandwidth, and the gain saturation characteristics of VCSOA under continous wave operation in reflection mode. The results show that the power of input signal give a strong impact on the spatial distribution of the carriers and only in the small signal regime the assumption of uniform distribution of the carriers can be used; the periods of DBR influnces the optical bandwidth and the input saturation power greatly, and the reduction in the period would result in the broadening of optical bandwidth and the improvement of the gain saturation characteristics; within certain range the input power affect the optical bandwidth to some extent; and the standing wave effect can not be decribed in a correct way by the transfer matrix model unless the reflection and refraction occuring at the interfaces between different medium in the cavity are taken into account.Such transfer matrix model has then been extended to the dynamic region to be suitable for the pulse amplification operation. Based upon the dynamic model the operation properties of VCSOA during short pulse amplification in reflection mode were studied numerically, such as the distortion of the amplified optical pulse, the evolution process of the carrier density and the temporal gain, and the energy gain characteristics. The simulations results indicate that the distortion of the output pulse can be attributed to the gain saturation induce by the enhancement of stimulated emission within the active region during the input pulse injection; the energy gain during pulse amplification is affected by the pump optical power, the DBR periods as well as the input pulse energy; under a fixed pump level the reduction in DBR periods can improve the energy gain saturation characteristics. Additionly, it is also shown that the input pulse width takes little effect on the energy gain saturation property provided that the input pulse has a width much shorter than the carrier lifetime, while with certain DBR period the increment in the pump power would diminish the saturation input pulse energy.Finally, from the start of rate equations of VCSOA, with the aid of small signal analysis and the consideration of the logarithmic relation between the gain coefficient and carrier concentration in the quantum well medium, the modulation and the small signal frequency response properties were both investigated. The analytical expressions of modulation bandwidth, the peak response frequency and the 3dB frequency response bandwidth in the small signal regime of VCSOA were obtained. The results show that the strengthment of the pump power or the input optical power would increase the modulation bandwidth; in the unsaturation region the modulation bandwidth would be broadened with the enhancement of the spontaneous emission; when operated in the saturated region the modulation bandwidth of VCSOA can reach 1.8GHz, which agree well with the reported experimental data; the peak response frequency can be increased with the increment of the pump power or the decrement of the input optical power, while the dynamic frequency response range dwindles simultaneously; the enhancement of the spontaneous emission can also broaden the 3dB frequency response bandwidth.The theory models and the corresponding results in this paper are helpful for analyzing the performance, optimizing the design sheme of VCSOA.