垂直腔半导体光放大器理论研究
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摘要
垂直腔半导体光放大器(VCSOA)作为一种新型的光放大器有着许多传统边发式半导体光放大器(SOA)以及掺铒光纤放大器(EDFA)都无法比拟的优点，在众多光纤通信领域都有着潜在的应用前景。到目前为止关于VCSOA的理论和实验方面的研究已经取得了一系列成果，本文的工作是建立在已有的研究成果基础上，围绕着VCSOA的稳态增益、光学带宽、调制响应、光脉冲放大以及小信号频率响应等工作特性而展开，具体内容包括：
针对现有VCSOA的理论研究模型多采用等效腔的现状，基于VCSOA由多层介质交替生长的结构特点，将其视为一个整体，构建其传输矩阵模型。该模型考虑了谐振腔内介质折射率的不连续性和有源区内载流子浓度和光强的纵向分布。使用该模型不再需要对分布布拉格反射镜(DBR)的反射率、有效腔长度、增益增强因子以及输入信号注入耦合效率等参数分别计算，方便了理论上的讨论。
在稳态工作条件下，利用这个传输矩阵模型研究了VCSOA在反射模式的输入光功率对腔内载流子浓度分布的影响、光学带宽、以及增益饱和等特性。结果表明，输入光功率的大小直接影响腔内载流子密度纵向空间分布的均匀性，在小信号光情况下可以使用载流子分布均匀的假设，而当输入光功率接近饱和区时载流子的空间分布很不均匀；顶部DBR的周期数对VCSOA的光学带宽和输入饱和功率有很大影响，适当减少其周期可以拓宽VCSOA的工作带宽，改善VCSOA的增益饱和特性；一定范围内输入光功率对VCSOA的带宽特性也有比较大的影响；在传输矩阵模型中必须考虑腔内不同介质间界面上的光反射和折射对模型才能够真实反映周期增益结构中的驻波效应。
将传输矩阵模型扩展到动态工作范围，数值模拟了反射工作模式下，VCSOA在短脉冲通过后发生的时域波形畸变、有源区内载流子密度和增益在脉冲放大过程中的变化以及脉冲放大的能量增益等VCSOA的脉冲工作特性。结果表明：随着脉冲的注入，因受激辐射增强而引起的增益饱和效应使得输出光脉冲的时域波形发生畸变；抽运光功率、DBR周期数以及输入脉冲能量都对脉冲放大的能量增益有一定影响；在同样偏置条件下减小DBR周期数可以改善脉冲放大中的能量增益饱和特性。另外，在输入脉冲宽度远小于载流子寿命时脉宽对VCSOA的能量增益饱和特性几乎没有影响，而在DBR周期一定时抽运光功率的增大会导致能量增益饱和特性的劣化。
从VCSOA的速率方程组出发，考虑了量子阱材料中的增益和载流子浓度之间的对数关系后，借助小信号分析法，对VCSOA的调制特性和小信号频率响应特性进行了研究，得到了VCSOA的调制带宽、小信号峰值响应频率和3dB小信号频率响应带宽的解析表达式。结果表明，提高输入信号功率或抽运光强度可以增大VCSOAs的调制带宽；在VCSOAs的未饱和区时调制带宽随自发辐射的增强而有所增大：当输入光功率增大到饱和区时，VCSOAs的调制带宽可以达到1.8GHz，这与文献报导的实验数据符合较好；提高抽运光功率或减小输入光功率能提高VCSOA的峰值响应频率，但同时缩小其动态响应频率范围；自发辐射的增强也会扩展其3dB频率响应带宽。
本文的理论模型和相关结论对于分析VCSOA的性能、优化其设计方案具有一定的参考作用。
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.
针对现有VCSOA的理论研究模型多采用等效腔的现状，基于VCSOA由多层介质交替生长的结构特点，将其视为一个整体，构建其传输矩阵模型。该模型考虑了谐振腔内介质折射率的不连续性和有源区内载流子浓度和光强的纵向分布。使用该模型不再需要对分布布拉格反射镜(DBR)的反射率、有效腔长度、增益增强因子以及输入信号注入耦合效率等参数分别计算，方便了理论上的讨论。
在稳态工作条件下，利用这个传输矩阵模型研究了VCSOA在反射模式的输入光功率对腔内载流子浓度分布的影响、光学带宽、以及增益饱和等特性。结果表明，输入光功率的大小直接影响腔内载流子密度纵向空间分布的均匀性，在小信号光情况下可以使用载流子分布均匀的假设，而当输入光功率接近饱和区时载流子的空间分布很不均匀；顶部DBR的周期数对VCSOA的光学带宽和输入饱和功率有很大影响，适当减少其周期可以拓宽VCSOA的工作带宽，改善VCSOA的增益饱和特性；一定范围内输入光功率对VCSOA的带宽特性也有比较大的影响；在传输矩阵模型中必须考虑腔内不同介质间界面上的光反射和折射对模型才能够真实反映周期增益结构中的驻波效应。
将传输矩阵模型扩展到动态工作范围，数值模拟了反射工作模式下，VCSOA在短脉冲通过后发生的时域波形畸变、有源区内载流子密度和增益在脉冲放大过程中的变化以及脉冲放大的能量增益等VCSOA的脉冲工作特性。结果表明：随着脉冲的注入，因受激辐射增强而引起的增益饱和效应使得输出光脉冲的时域波形发生畸变；抽运光功率、DBR周期数以及输入脉冲能量都对脉冲放大的能量增益有一定影响；在同样偏置条件下减小DBR周期数可以改善脉冲放大中的能量增益饱和特性。另外，在输入脉冲宽度远小于载流子寿命时脉宽对VCSOA的能量增益饱和特性几乎没有影响，而在DBR周期一定时抽运光功率的增大会导致能量增益饱和特性的劣化。
从VCSOA的速率方程组出发，考虑了量子阱材料中的增益和载流子浓度之间的对数关系后，借助小信号分析法，对VCSOA的调制特性和小信号频率响应特性进行了研究，得到了VCSOA的调制带宽、小信号峰值响应频率和3dB小信号频率响应带宽的解析表达式。结果表明，提高输入信号功率或抽运光强度可以增大VCSOAs的调制带宽；在VCSOAs的未饱和区时调制带宽随自发辐射的增强而有所增大：当输入光功率增大到饱和区时，VCSOAs的调制带宽可以达到1.8GHz，这与文献报导的实验数据符合较好；提高抽运光功率或减小输入光功率能提高VCSOA的峰值响应频率，但同时缩小其动态响应频率范围；自发辐射的增强也会扩展其3dB频率响应带宽。
本文的理论模型和相关结论对于分析VCSOA的性能、优化其设计方案具有一定的参考作用。
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.
引文
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