Chip-scale WDM devices using photonic crystals

Issued as final reportAir Force Office of Scientific Researc

Analytical solution of linear ordinary differential equations by differential transfer matrix method

We report a new analytical method for exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the $n$th-order differential equation to a system of $n$ linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method. We show that the Abel-Liouville-Ostogradski theorem can be easily recovered through this approach

Two-center holographic recording

We describe a two-center holographic recording method for the storage of persistent holograms in doubly doped lithium niobate crystals. We use a two-center model, and we show that our experimental observations can be explained by the model. We describe experimental methods for finding the unknown material parameters of LiNbO3:Fe:Mn crystals for the two-center model, and we discuss the optimization of two-center recording

Theoretical analysis of two-step holographic recording with high-intensity pulses

We develop a full numerical as well as an approximate analytic solution for two-step holographic recording with high intensity pulses in LiNbO3:Fe crystals. We find the unknown material parameters by fitting the numerical solution to the experimental results. The two important parameters that were unknown so far and found in this work are the bulk photovoltaic coefficient and absorption cross section for the excitation of the electrons from small polarons in LiNbO3 with infrared light. We show that the approximate analytic solution agrees very well with the numerical solution (as well as the experimental results) for most practical applications. We use the analytic solution to explain the experimental observations that were not understood before

Multiplexing holograms in LiNbO3FeMn crystals

Persistent holograms are recorded with red light in lithium niobate crystals doped with manganese and iron. Different erasure mechanisms are investigated, and a recording schedule for multiplexing holograms with equal diffraction efficiencies is proposed. To test the recording schedule experimentally, we multiplex 50 plane-wave holograms with the proposed recording schedule

System Measure for Persistence in Holographic Recording and Application to Singly-Doped and Doubly-Doped Lithium Niobate

We define a measure for persistence in holographic recording. Using this measure and the known measures for dynamic range and sensitivity, we compare the performance of singly-doped and doubly-doped LiNbO3 crystals. We show that the range of performance that can be obtained using doubly-doped crystals is much larger than that obtained using singly-doped ones

Secondary Grating Formation by Readout at Bragg-null Incidence

We show that when a dynamic hologram is read out by illumination at the Bragg nulls of a previously recorded grating the diffracted beam inside the medium can result in the recording of two secondary gratings that alter the final selectivity curve. This is confirmed experimentally. This effect can cause cross talk in hologram multiplexing that is stronger than interpage cross talk when a small number of holograms with high diffraction efficiencies are multiplexed