Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session S43: Photonic Crystals |
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Sponsoring Units: DCMP Chair: Mark Sherwin, University of California, Santa Barbara Room: Colorado Convention Center 506 |
Wednesday, March 7, 2007 2:30PM - 2:42PM |
S43.00001: Theory of Band Structure of Thin Photonic Crystals Jeffrey Sokoloff There exist several highly successful methods for calculating the band structure of thick photonic crystals (PC's), constructed from parallel dielectric rods, which are long compared to their diameters and spacings. None of these methods, however, can accurately calculate the band structure of the technologically important case of thin PC's (i.e., PC's consisting of a periodic array of dielectric rods or holes in a dielectric material of length comparable to or smaller than the hole or rod diameter and spacing). Methods analogous to approximate methods traditionally used to calculate the band structure of crystalline solids, such as the tight binding method (where the rods or holes which are resonant cavities play the role of atoms) or the augmented plane wave method will be applied to this problem. The resulting band structure for thin PC's is much different from that of thick PC's. For example, there exist lower/higher frequency flat bands, resulting from the tight binding functions constructed from linear combinations of the resonant modes of the rods/holes. [Preview Abstract] |
Wednesday, March 7, 2007 2:42PM - 2:54PM |
S43.00002: Quasi-phase-matched Cerenkov radiation generation in a two-dimensional nonlinear photonic crystal waveguide S.N. Zhu, Y. Zhang, Z. Qi, G. Zhao , W. Wang In this report, we present a new type of quasi-phase-matched Cerenkov radiation generation from a two-dimensional nonlinear photonic crystal waveguide: a hexagonally poled LiTaO$_{3}$ waveguide. The waveguide was fabricated by field poling followed by proton exchange technique. The fundamental source was a LD-pumped, 90-ns pulsed Q-switch double wavelength Nd:YAG laser at 1064-$\mu $m and 1319-$\mu $m. The pulse repetition rates was 8-kHz. When the fundamental beams at 1064-$\mu $m and 1319-$\mu $m were collinearly focused into the waveguide and propagated along its x-axis, three sets of hexagonal patterns, with red, yellow and green colors, were respectively exhibited on the projection screen behind the waveguide at the same time. They were confirmed to be the second-harmonic generation (red and green patterns) and sum-frequency generation (yellow pattern) for these two fundamental waves, respectively. These frequency conversion processes were realized by guided-to-radiated mode interaction. Phase-matching for these processes in the waveguide was automatically achieved by a quasi-phase-matched Cerenkov configuration. [Preview Abstract] |
Wednesday, March 7, 2007 2:54PM - 3:06PM |
S43.00003: ABSTRACT WITHDRAWN |
Wednesday, March 7, 2007 3:06PM - 3:18PM |
S43.00004: Thermal emission from two-dimensional metallo-dielectric photonic crystals Mohit Diwekar, Z.V. Vardeny We studied thermal light emission from a sub-wavelength hole arrays with square lattice of 4 $\mu $m periodicity fabricated in aluminum (Al) and silver (Ag) films on silicon (Si) substrates by conventional photolithography. The emission spectra were obtained using a FTIR setup with a port for an external cryostat configured for thermal emission measurements. These patterned films show extraordinary transmission bands in the mid-IR spectral range, which can be well explained as due to light coupling to surface plasmons on the two film interfaces. The thermal emission spectrum from these photonic crystals followed the transmission spectrum characteristics; however it differs significantly from the obtained absorption spectrum, in contrast to the Kirchhoff's law of radiation. We conclude that the fabricated photonic structures behave as radiation filters where the emission radiation is suppressed in the frequency range outside the transmission bands in the spectrum. [Preview Abstract] |
Wednesday, March 7, 2007 3:18PM - 3:30PM |
S43.00005: Berry phase for optical wavepacket propagation in deformed photonic crystals Kei Sawada, Shuichi Murakami, Naoto Nagaosa We develop a theory for a trajectory of an optical wavepacket propagating through a photonic crystal with a deformation $[1]$. Naively one might expect that the trajectory of an optical beam is always perpendicular to the wave front, which is expected in a conventional geometrical optics derived from Fermat's principle. We reveal an anomalous behavior of such electromagnetic beams beyond this naive expectation. We derive a set of equations motion which includes multiple scatterings and a geometrical phase called Berry phase associated with the wave dynamics. We find that such a Berry phase correction to geometrical optics gives rise to a shift of the center position of an wavepacket. Remarkably, at the edge of a photonic band gap, such a coordinate shift is enhanced by a factor $\omega / \Delta \omega$, where $\omega$ is a frequency of light and $\Delta \omega$ is a size of a photonic band gap. An amount of the enhancement factor is $\omega / \Delta \omega \sim 10$ or $\sim 10^2$ for photonic crystals. Especially, in the case of an x-ray dynamical diffraction, the factor can be $\omega / \Delta \omega \sim 10^6$, which implies that an atomic crystal deformation gives a macroscopic shift of a wavepacket.\\ $[1]$ K. Sawada, S. Murakami and N. Nagaosa, Phys. Rev. Lett. \textbf{96}, 154802 (2006). [Preview Abstract] |
Wednesday, March 7, 2007 3:30PM - 3:42PM |
S43.00006: Terahertz transmittance of single-mode photonic crystal slabs Cristo Yee, Nathan Jukam, Mark Sherwin Terahertz (THz) radiation lies in the gap between optical and electronic frequencies. Its importance has grown during the past few years due to applications ranging from security to biomedicine to quantum information processing. These applications often require manipulating electromagnetic radiation on-chip, and THz Photonic Crystals (PC) are a natural solution. Terahertz PCs have two advantage: Silicon has a negligible absorption and the large PC dimensions makes fabrication defects negligible. In this work we report the first measurement of a transmission through a single mode THz PC Slab . The PC slab consist on an triangular array of holes with lattice constant a=64 $\mu $m, radius r=0.3a and thickness d=0.74a. The PC slab was fabricated with Reactive Ion Etching on a high-resistivity Si wafer. FTIR transmission spectrum along the J orientation shows an optical bangap from 1.2 to 1.6 THz for the TE mode, in good agreement with our FDTD calculations. The PC slab is the starting point for testing devices like waveguides and cavities. [Preview Abstract] |
Wednesday, March 7, 2007 3:42PM - 3:54PM |
S43.00007: Multi-layered photonic crystals \textit{de novo}: new formalism, results, insights, and analytic possibilities Frank Szmulowicz A new formalism for calculating the photonic band structure of multi-layer photonic gap (PBG) materials is derived. The formalism expresses all boundary conditions in terms of tangents rather than exponential functions. The formalism is compact, algorithmically simple, and physically appealing, and provides a new conceptual framework for describing the photonic band structure of layered materials. Its simplicity makes it possible to represent eigenfrequency conditions using geometric constructs, find a factored form of the secular equation, and derive analytic eigenfrequency conditions and analytic wave functions for multi-layer structures. Computationally, the new formalism makes it possible to find \underline {explicitly} the complete band structure of multi-layer PBG materials with integer ratios of optical path lengths (e.g., any combination of quarter-wave, half-wave, etc., stacks) through a \underline {single} diagonalization of a low order secular equation, the alternative being an \underline {implicit} root search via the transfer matrix formalism. The formalism is demonstrated on multi-layered structures arranged in the Fibonacci sequence and half-wave-quarter-wave-eighth-wave PBG. [Preview Abstract] |
Wednesday, March 7, 2007 3:54PM - 4:06PM |
S43.00008: The Rayleigh Hypothesis and Scattering at Photonic Crystal Surfaces Prabasaj Paul, Kyaw Nyein, Robert Choudury We examine the Rayleigh hypothesis in the context of scattering of light off photonic crystal interfaces. First, the hypothesis -- which was initially suggested for scattering of waves off rough surfaces between homogeneous media -- is rephrased to apply to photonic crystal interfaces. Next, some exact and explicit functional forms are presented that map plane photonic crystal surfaces to periodic rough surfaces in free space, so that known criteria for the validity of the Rayleigh hypothesis for scattering at rough surfaces can be applied directly to scattering at the photonic crystal surfaces. The same maps also allow the scattering problem to be solved exactly. We present numerical results for scattering amplitudes at a photonic crystal surface using both the exact method (based on a surface integral formulation) and an approximate method (based on the Rayleigh hypothesis). The results are found to be consistent with the analytical criteria for the range of validity of the approximate method. [Preview Abstract] |
Wednesday, March 7, 2007 4:06PM - 4:18PM |
S43.00009: Optical Characterization of 3D Photonic Crystals Fabricated by Holographic Lithography Ying-Chieh Chen, Joseph B. Geddes III, Paul V. Braun, Pierre Wiltzius Holographic lithography is a promising technique for fabricating photonic crystals. Due to the large area, defect-free nature of the crystals created, they are expected to be good model systems for the study of their optical properties. However, the crystals created experimentally do not always meet theoretical expectations. We will present our current understanding of the optical response by comparing the experimental and simulated optical spectra. These spectra were taken from holographically fabricated crystals having FCC geometry. Optical spectra were simulated using a frequency domain algorithm for both the ideal photonic crystal and cross-sectional SEM images from the fabricated crystals as inputs to the simulation. Experimental issues associated with inconsistencies between measured and predicted results of the optical response will be discussed. [Preview Abstract] |
Wednesday, March 7, 2007 4:18PM - 4:30PM |
S43.00010: Tunable Mesoporous Defects in Photonic Crystals F.C. Peiris, J.R. Rodriguez, V. Kitaev , G.A. Ozin Similar to doping in semiconductors, the incorporation of defects into photonic crystals introduces defect-based states in the photonic bad gap, resulting in an increase in its functionality. In this work, we have introduced a planar-defect into a colloidal photonic crystal, and have investigated the evolution of its optical properties with respect to the infiltration of various foreign constituents. A periodic mesoporous silica film (i.e., the defect) was deposited on a silica-based colloidal photonic crystal, and a second photonic crystal was deposited subsequently to encompass the defect-layer. UV-VIS spectroscopy, scanning electron microscopy and X-ray diffraction experiments confirm the existence of the meso-layer. Subsequently, water vapor and tetramethyl orthosilicate (TMOS) were infiltrated into the structure and the defect-based signature corresponding to the optical spectra was monitored. In both cases, a noticeable shift in wavelength was observed, providing evidence that the structure performs as a chemical sensor. [Preview Abstract] |
Wednesday, March 7, 2007 4:30PM - 4:42PM |
S43.00011: Robust Optimization of Aperiodic Photonic Structures Omid Nohadani, Kwong Meng Teo, Dimitris Bertsimas In engineering design, the physical properties of a system can often only be described by numerical simulation. Optimization of such systems is usually accomplished heuristically without taking into account that there are implementation errors that lead to very suboptimal, and often, infeasible solutions. We present a novel robust optimization method for electromagnetic scattering problems with large degrees of freedom, and report on results when this technique is applied to optimization of aperiodic dielectric structures. The spatial configuration of 50 dielectric scattering cylinders is optimized to match a desired target function such that the optimal arrangement is robust against placement and prototype errors. Our optimization method inherently improves the robustness of the optimized solution with respect to relevant errors and is suitable for real-world design of materials with novel electromagnetic functionalities. [Preview Abstract] |
Wednesday, March 7, 2007 4:42PM - 4:54PM |
S43.00012: Enhanced and Tailored Emission from Luminescent Three-Dimensional Ru(bpy)$_{3}$(PF$_{6})_{2}$ Inverse-Opal Photonic Crystals Andrew Brzezinski, Jyh-Tsung Lee, Jason Slinker, Pierre Wiltzius, George Malliaras, Paul Braun Three-dimensional inverse opal structures, with various lattice constants are made by infilling polystyrene colloid templates with luminescent Ru(bpy)$_{3}$(PF$_{6})_{2}$. The passive photoluminescent structures and active electroluminescent organic light-emitting-diode structures were characterized via electron microscopy and solid-angle-resolved spectroscopy. A model is presented, explaining light propagation within and emission from the crystal. Results show angular emission profiles are tailored by choice of lattice constant, which determines directions inside the crystal for which propagation of frequencies emitted from Ru(bpy)$_{3}$(PF$_{6})_{2}$ are either enhanced or suppressed. Enhanced emissive flux is achieved by suppressing propagation in near parallel directions relative to the air interface. [Preview Abstract] |
Wednesday, March 7, 2007 4:54PM - 5:06PM |
S43.00013: ABSTRACT WITHDRAWN |
Wednesday, March 7, 2007 5:06PM - 5:18PM |
S43.00014: A direct time integration of Maxwell equations in dielectric and magnetic dispersive materials for FDTD modelling of metamaterials Jesus Manzanares-Martinez, Jorge Gaspar-Armenta A new procedure of integration for the Maxwell equations is present to study dielectric and magnetic dispersive materials using the Finite Difference Time Domain Method. Our method is based on a direct application of the Fourier Transform for the temporal and frequency integrations of the constitutive relations. We study Drude and Lorentz dispersive media. We present different results for the light reflection of a pulse impinging dispersive dielectric, dispersive magnetic, or both dispersive media. [Preview Abstract] |
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