Photonic band gap structure simulator

A system for designing a photonic bandgap structure, comprising:

• means for representing components of a photonic bandgap structure as a linear equation corresponding to a unit cell, said linear equation represents a Helmholtz equation that models the properties exhibited by said components of said photonic bandgap structure;
• means for representing a boundary condition for the unit cell, the boundary condition to be applied to a solution of said Helmholtz equation defined for the unit cell;
• means for approximating the linear equation using a Hermitian matrix;
• and
• means for calculating an eigenvalue of the Helmholtz equation in a Hermitian matrix form for the unit cell.

A method of designing a photonic bandgap structure, comprising the steps of:

• representing components of a photonic bandgap structure as a linear equation corresponding to a unit cell, said linear equation represents a Helmholtz equation that models the properties exhibited by said components of said photonic bandgap structure;
• representing a boundary condition for the unit cell, the boundary condition to be applied to a solution of said Helmholtz equation defined for the unit cell;
• approximating the linear equation using a Hermitian matrix corresponding to the unit cell;
• and
• calculating an eigenvalue of the Helmholtz equation by solving the Hermitian matrix equation.