We recently demonstrated a phase compensated metalens that cannot only achieve super-resolution, but also possesses the Fourier transform capability. The metalens consists of a metamaterial slab and a plasmonic waveguide coupler (PWC). We have now ascertained the requirements for the metamaterial and the detailed design principles for the PWCs. Simulations of metalenses with a new type of PWC geometry have confirmed that the new metalenses also possess super-resolution and the Fourier transform function. The hyperbolic metalens shows an anomalous focus shifting behavior, which may be used to design exotic optical systems with new functionalities.
Thermooptic switches are viable options for rapidly and reliably switching and routing optical signals in planar
lightwave circuits. We present modeling and fabrication of a thermooptic switch made of the polymer SU-8, an epoxy
resin commonly used as a MEMS structural material. SU-8 is a good candidate material for use in planar waveguides
due to its high refractive index, good transmission properties in the visible and infrared, and excellent thermal and
mechanical stability. Furthermore, it has great advantages in fabrication since it is used as a negative photoresist, and
so can be patterned directly using photolithography. Light is guided by a refractive index gradient generated by
embedded MEMS microheaters, which activate the thermal nonlinearity of the polymer. The thermooptic change in
refractive index imparts an inhomogeneous phase shift to the beam in the waveguide, which guides the input into one of
two or more outputs. The switch design and operation parameters have been optimized using simulations of the
thermal profile using finite element modeling and of the optical propagation using the beam propagation method.
The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.
The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. We present results of simulations combining this method with finite element modeling of thermal effects using Comsol FEMLAB software. These simulations were developed and are used to examine propagation of optical signals in polymer waveguides in which inhomogeneous temperature profiles are induced using MEMS microheaters, for example, for use in switching applications. Thermal modeling combined with values of the thermo-optic nonlinearity yields three-dimensional refractive index profiles in the active regions of a variety of waveguide structures. The change in the refractive index profile of cladding induces mode deformations and transmission losses due to leakage at the core/cladding interface, in addition to phase shifts in the propagating beams. These effects are used to design thermo-optic switches in both multimode and single mode waveguides, and study the direct effect on propagation due to changes in the applied heater power. In addition, we demonstrate the utility of applying the method to assessing losses due to thermally induced inhomogeneities in planar lightwave circuits such as optical interconnects.