摘要
作为密集波分复用技术的关键器件，阵列波导光栅波分复用与解复用器有着分辨率高、集成度高、通道数大等优点，成为光通信领域的研究热点。
由瑞利—索末菲标量衍射积分公式出发，推导出平面波导基模衍射远场分布表达式和中央亮条纹强度半最大值处的空间频率所满足的方程。分析了中央亮条纹的全宽度和半最大值全宽度随波导参数和传输距离的关系。这为波导参数的测量提供理论基础，也为分析阵列波导光栅的焦场理论及其特性参数提供准备。
在现有的文献中，大多仅对复合光波从中心波导输入时的阵列波导光栅焦场性质进行分析，而且计算都很复杂。本文在平面波导场横向分布用高斯近似条件下，利用求两次傅立叶变换的方法推导出计算中心波长的光波从任一波导输入的阵列波导光栅的焦场和插入损耗的简单表达式，这为阵列波导光栅的设计提供简便的设计依据。
提出用脉冲响应函数法来对焦场进行分析，这种方法简单，物理意义鲜明。指出了AWG系统不是线性空间不变系统，中心波长光波从不同波导输入，输出特性不同，文中做了详尽的比较。最后，我们还利用已求的脉冲响应函数对串扰特性、损耗特性和相位误差对传输特性的影响进行了分析。
Arrayed waveguide grating, the key component of dense wavelength division multiplexing, has the advantage of high resolution, high integration and more channels, etc. It has become the research hotspot in the optical communication field.
Based on Rayleigh-Sommerfeld diffraction scalar integral formula, the distributing formula of far diffraction field of planar waveguide and the equation of spatial frequency at half maximum intensity of central bright fringe of far diffraction field of planar waveguide in TEo mode are educed. The relation between the width of central bright fringe together with full width at half maximum of central bright fringe and every waveguide parameter is analyzed. The conclusions are useful to measure parameter of planar waveguide and to analyse focal field distribution of arrayed waveguide grating.
In most existing literature, the focal field property of arrayed waveguide grating is analyzed only when complex lightwave input from central waveguide, and its method is complicated. In this paper, on the condition that the transverse field of planar waveguide is expressed in gauss function, the simple expression of the focal field distribution and insert loss of arrayed waveguide grating is derived by computing two Fourier transform, which affords handy theoretical basis for designing arrayed waveguide grating.
One new method to analyse focal field of arrayed waveguide grating is brought forward, which is named the impulse response function method. The method is simple and feasible. The system of AWG is not linear shift-invariant system, so the output characteristic of the central wavelength inputting from different waveguide is different. Their different characteristic is compared. Lastly, crosstalk characteristic, loss
characteristic and phase error of AWG are analyzed.
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