Where | Me) 1S ad propagalllg Moge WIW) WaVeVeclor K alld ITEQUuellCy @; I Waveguide Mm, 1 ne Mode | Me) 1s
a localized mode of the resonator pair next of waveguide mode m, c=e, o for the even and odd modes,
respectively; @, is its frequency. The coefficients Vineme ANd Vinemk represent the coupling between the
corresponding modes. We have neglected the coupling between the propagating modes of different
waveguides as discussed by Xu et. al.
If we follow the standard group theoretical approach and choose a basis function according irreducible
representations, the problem becomes extremely difficult to analyze. The hardest part lies in constructing <
mode that has zero backscattering amplitude, which is required for an ideal OADM. Our experiences witl
a number of basis functions have shown that the following choice offers the most convenience in the study
Finite Difference Time Domain (FDTD) simulations are generally performed to study the non-parallel
surface cases quantitatively. But such simulations are time consuming, and may become prohibitive for the
cases of high wavelength and angular sensitivities. High wavelength sensitivity demands fine grids; high
angular sensitivity requires a very wide incident beam so that the angular spread of the incident beam is
small, and the wide beam leads to a large simulation region.
Fig. 3 (a) Beams inside photonic crystal (and exiting beams) overlap significantly in space after a round-trip internal
reflection inside a photonic crystal slab. A negative refraction case is presented, although the beam overlap/separation
appears regardless of negative refraction. For simplicity, only one round-trip internal reflection is drawn. (b) Beams
separate after one-round trip reflection. The single-interface refraction problem must be solved to obtain the intensity each
of exiting beam. (c) Multiple internal reflections for non-parallel surfaces. Our theory can address all three cases.
Conventional theory can only address case (a).
Fig. 4 (a) Electron beam nanolithography facility at (a) Center for Nano- and Molecular Science Technology.
(b) Microelectronics Research Center, both part of the University of Texas at Austin.
SEL EE ONIN ISR ENA AMET, ASL ie Rp eNS NNT I
Photonic crystals are periodic ‘structures with feature sizes comparable to the wavelength of light. Fo
communication wavelengths around 1.55 um, the feature sizes lie in the submicron range, which presents <
challenge to the conventional photolithography techniques. Electron beam lithography is usually employed
to pattern photonic crystals for visible and infrared wavelengths. We have used electron beam lithography
to pattern structures on polymer films to fabricate two-dimensional(2D) photonic crystals. Several suits of
electron beam lithography tools are available at the University of Texas at Austin. Some nano-lithography
facilities at the University of Texas at Austin are shown in Fig. 4.
Fig. 5 A segment of photonic crystal fabricated on a multi-layer polymer film.
We have integrated photonic crystals and conventional channel waveguides on a multi-layer polymer film.
First, the bottom cladding layer and core layer of the waveguides are spin-coated on a silicon wafer.
Conventional photolithography is employed to pattern the waveguide core layer, followed by reactive ion
etching(RIE). Subsequently, the top cladding layer is applied. By careful design and fabrication, the top
surface of the polymer film stack can usually be planarized easily despite the undulating core layer
underneath. The planarization of the top surface is important for the successful patterning by electron beam
lithography that follows because the depth of focus of the electron beam is usually fairly small. A segment
of photonic crystal fabricated on a polymer multi-layer film is shown in Fig. 5. We are able to achieve
holes of very high aspect ratios around 7:1 with hole radii in the submicron range. Optical tests show that
the out-of-plane radiation loss“*° for the short segment of holes shown in Fig. 5 is low. We compare a
straight waveguide and a waveguide with this short segment of photonic crystal inserted in the middle of its
length, the difference in insertion loss is on average below 1dB, with a variation from 0 to 3 dB. The loss
and loss variation are attributed to a number of factors, including the roughness of holes’ walls, hole size
uniformity, out-of-plane loss, and polymer curing conditions. Further improvement is underway. Detailed
analysis of the origin of the loss will be presented elsewhere.
