A simple mathematical formulation is proposed for tailoring the transmission characteristics of a one-dimensional (1D) finite optical grating for its applications in the pass band and stop band regions without using anti reflection coating (ARC). In this formulation, a frequency dependent continuity function derived from effective boundary condition is shown to determine the envelope function of the transmittance curve. Using this envelope function along with the dispersion relation, the optimization of the grating parameters can be performed to achieve the desired transmittance profile over the predetermined pass band. Meanwhile, using the appropriate part of the transmittance function, the result of optimization for the stop band was also demonstrated for a specific system.
- Bloch–Floquet theorem
- effective medium
- One dimensional optical grating
- photonic band structure