
Y. Jiao,
S. H. Fan, and D. A. B. Miller, "Designing for beam propagation in
periodic and nonperiodic photonic nanostructures: Extended Hamiltonian
method," Phys. Rev E70, No. 3, Pt. 2, 0. 036612 (Sept. 2004)
We use Hamiltonian optics to
design and analyze beam propagation in twodimensional (2D) periodic
structures with slowly varying nonuniformities. We extend a conventional
Hamiltonian method, adding equations for calculating the width of a beam
propagating in such structures, and quantify the range of validity of
the extended Hamiltonian equations. For calculating the beam width, the
equations are more than 10(3) times faster than finite difference time
domain (FDTD) simulations. We perform FDTD simulations of beam
propagation in large 2D periodic structures with slowly varying
nonuniformities to validate our method. Beam path and beam width
calculated using the extended Hamiltonian method show good agreement
with FDTD simulations. By contrasting the method with ray tracing of the
bundle of rays, we highlight and explain the limitations of the extended
Hamiltonian method. Finally, we use a frequency demultiplexing device
optimization example to demonstrate the potential applications of the
method.
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