Gratings In Optical Waveguides And Lasers

Gratings play a crucial role in Distributed Bragg reflector (DBR) lasers, influencing their performance and characteristics. The focus of this work is aimed at the design of DBR lasers that significantly impact the laser's spectral and temporal behavior, making it a key component in optimizing DBR laser functionality. The SMU developed grating software, compared with commercially available photonics software, has improved accuracy and much smaller computation times. The improved accuracy and reduced computation times compared with commercial photonics software occur because commercial software is typically based on numerical methods such as finite-difference time-domain (FDTD), eigenmode expansion and beam propagation methods that require specifying grids and setting finite boundary conditions. The SMU software is based on Floquet-Bloch theory that avoids such constraints. Enhanced Coupling Strength grating designs developed here, yield small grating lengths for required feedback in first-order and outcoupling in second-order gratings, features that are required in silicon photonics and photonic integrated circuits. Analytic expressions of a planar current source to replicate the effects of a periodic layer for both TE and TM mode coupling coefficients are derived. The resulting expressions match numerical results for structures with shallow gratings and small index differences between different layers forming the laser structure. While several published analytic expressions for TM modes yield significantly different results, two of the previously published expressions are in close agreement with our exact, correct Floquet-Bloch analysis. The correct TM coupling coefficients as a function of 2πd/λ, under certain conditions, exhibit a unique and unexpected behavior: the coupling coefficient initially increases, reaches a maximum, decreases to zero, then increases again to a second maximum before decreasing as a function of 2πd/λ. Analytic expressions for TE and TM gain are derived. For identical waveguide material gain, and wavelength, the TE modal gain due to gain in the middle layer may be larger or smaller than the TM modal gain. In the case of gain in one or both outer layers, the TM mode, unexpectedly, is found in some cases to have an effective gain coefficient greater than 1, which cannot occur in TE modes. Notably, the sum of the TM modal gain confinement factors for all layers can exceed unity. The resulting analytic equations provide accurate results that are indistinguishable to three or more decimal points from the exact numerical results, even for large values of power gain or loss (~10,000/cm).