Sharp Resonance Features Research Articles

Integrated Optics Utilizing GaN-Based Layers on Silicon Substrates

ABSTRACTIt is now apparent that future generations of fast electronics and compact sensors may need to rely increasingly on integrated optical components. But integration of electronics and photonics in today's IC's is challenging. Silicon, the ubiquitous electronic material, is neither ideally suited for most photonic functions nor readily integrated with most of the common photonic materials, such as GaAs. The approach we describe here relies on GaN-based films, which can be grown directly on silicon substrates and hence can be potentially integrated with state-of-the-art Si-based electronics. We have demonstrated the fabrication of GaN structures on silicon wafers ranging in overall size from sub-micron to several millimeters, all containing highly accurate individual features on the nm scale. As proof of concept, we have fabricated GaN optical waveguides and photonic crystals containing optical cavities by patterning GaN membranes grown directly on Si wafers. Our optical cavities were designed to have resonant modes within the spectral region of the broad defect-induced luminescence of GaN. We have measured sharp resonant features associated with these cavities by optically pumping above the GaN band edge, and have compared the data to numerical simulations of the spectra. Our results to date demonstrate the feasibility of fabricating high-quality GaN photonic structures directly on Si wafers, thereby providing a possible path to achieving true integration of electronics and photonics in future generations of IC's.

Single Quantum Dot Spontaneous Emission in a Finite-Size Photonic Crystal Waveguide: Proposal for an Efficient “On Chip” Single Photon Gun

Spontaneous emission rate enhancements from a single quantum dot embedded in a finite-size, planar photonic-crystal waveguide are investigated. Short waveguide lengths of only 10 to 20 unit cells are found to produce very large Purcell factors associated with a waveguidelike sharp resonance feature in the local density of photon states. Aided by theoretical insight and rigorous computational calculations, we explain the physics behind these remarkable emission enhancements and subsequently propose a "single-photon gun" with on-chip unidirectional collection efficiencies greater than 60% into an output wire waveguide. The advantages over recent proposals for infinitely long photonic-crystal waveguides are highlighted.

The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy

We measure the normal-incidence transmission coefficient of photonic crystal slabs with hexagonal arrays of air holes in silicon. The transmission spectra exhibit sharp resonant features with Fano line shapes. They are produced due to the coupling of the leaky photonic crystal modes, called guided resonances, to the continuum of free-space modes. We investigate the effects of several types of structural disorder on the spectra of these resonances. Our results indicate that guided resonances are very tolerant to disorder in the hole diameter and to interface roughness, but very sensitive to disorder in the lattice periodicity.

Scattering T-matrix theory in wave-vector space for surface-enhanced Raman scattering in clusters of nanoscale spherical metal particles

Very large enhancements up to 14 orders of magnitude in the Raman cross section from a molecule adsorbed on a single cluster of a few nanoscale metal particles has been reported recently. The enhancement is believed mainly due to the enhanced electric field because of the excitation of the localized surface plasmon modes. We have developed a Green's function theory using scattering matrix approach in the wave-vector space to solve the Maxwell equations for the enhanced field near a spherical metal particle cluster. The advantage of working in the wave-vector space is that one does not need to use complicated translational addition theorem required in the real space as used in earlier calculations. Therefore our theory can be easily extended to any shape or size of the cluster. We consider clusters of two, three, and four spherical particles forming a linear chain, triangle, and square and calculate their localized surface modes. These modes have much more localized field near the cluster compared to those of single metal sphere and are redshifted. We find the enhancement in the Raman cross section can reach up to 10 orders of magnitude due to the resonant excitation of these modes for silver particle clusters and is in a broad frequency range. We also find new results that chainlike clusters of three or more particles have very sharp resonant features that give a dramatic increase in the enhancement near the resonance. The results for gold particle clusters are also presented.

Multimode electron transport through quantum waveguides with spin-orbit interaction modulation: Applications of the scattering matrix formalism

We present a formulation of the scattering matrix method for spin-dependent electron transport in a quantum waveguide with spin-orbit interaction (SOI). All the required Hamiltonian matrices needed in the implementation of the formulation are represented in a basis of the transverse spatial eigenstates and the spin eigenstates of the leads. Thus the method has great flexibility and can be easily applied to systems with complex geometrical structure, potential distribution, and SOI strength profile. Also, the method is numerically stable and can be used to treat spin-dependent multisubband scattering processes accurately. We have applied the method to the spin-dependent electron transport in quasi-one-dimensional (Q1D) conductors, with a region of the Rashba SOI of uniform strength and with a region containing a Rashba SOI superlattice, made from a semiconductor heterostructure. The total conductance, spin-dependent conductances, and spin polarization of the system are calculated for a fully spin-polarized electron beam injected from a lead into the SOI region. For the Q1D conductor with a single region of the Rashba SOI, it is found that when the Fermi energy is set at a value, for which the total conductance is at a plateau, the spin-dependent conductances show regular oscillations with increasing SOI strength. This is approximately true even when the total conductance is at a high plateau and thus multiple subbands in the waveguide are open for conduction. However, when the Fermi energy is set at a value close to the onset of a subband (with the subband index $n\ensuremath{\geqslant}2$), the spin-polarized conductances plotted against the SOI strength and the SOI region length show sharp resonance features or complex fluctuations. These irregular conductance characteristics arise from SOI-induced strong coupling between subbands. For the Q1D conductor modulated by an array of strong Rashba SOI stripes, the total conductance shows regular superlattice behavior, while the spin-dependent conductances show complex behavior with regions of slow oscillations and regions of rapid oscillations. As in the Q1D conductor with a single SOI region, the slow oscillations are found in the energy regions where the total conductance is at plateaus. However, the rapid oscillations appear at energies close to the onsets of subbands with the subband index $n\ensuremath{\geqslant}2$. These oscillations originate from strong spin scattering by localized states formed in the SOI-modulated superlattice region.

Quantum wave packet study of [formula omitted] inelastic scattering

Time dependent quantum wave packet calculations have been carried for the astrophysically important Li + H 2 + collision process. The state-to-state and state-to-all inelastic probabilities for the entitled collision have been calculated. Sharp resonance features are observed in all transition probabilities at low collision energies. J-shifting approximation has been employed to estimate the inelastic integral cross-sections.

Quantum wave-packet dynamics of H+HLi scattering: reaction cross section and thermal rate constant.

The channel specific and initial state-selected reaction cross section and temperature-dependent rate constant for the title system is calculated with the aid of a time-dependent wave-packet approach and using the ab initio potential energy surface of Dunne et al. [Chem. Phys. Lett. 336, 1 (2001)]. All partial-wave contributions up to the total angular momentum J=74 are explicitly calculated within the coupled states (CS) approximation. Companion calculations are also carried out employing the standard as well as the uniform J-shifting (JS) approximation. The overall variation of reaction cross sections corresponds well to the behavior of a barrierless reaction. The hydrogen exchange channel yielding HLi+H products is seen to be more favored over the HLi depletion channel yielding Li+H(2) products at low and moderate collision energies. Sharp resonance features are observed in the cross-section results for the HLi depletion channel at low energies. Resonance features in the reaction cross sections average out with various partial-wave contributions, when compared to the same observed in the individual reaction probability curve. Except near the onset of the reaction, the vibrational and rotational excitation of the reagent HLi, in general, does not dramatically influence the reactivity of either channel. The thermal rate constants calculated up to 4000 K show nearly Arrhenius type behavior. The rate constant decreases with vibrational excitation of the reagent HLi, indicating that the cold HLi molecules are efficiently depleted in the reactive encounter with H at relatively low temperatures. The results obtained from the JS approximation are found to agree well qualitatively with the CS results.

Vacuum Rabi splitting for multilevel electromagnetically induced transparency system

We discuss the vacuum Rabi splitting (VRS) from multilevel atoms under electromagnetically induced transparency condition within the framework of linear absorption-dispersion theory. Sharp resonance features superimposed on usually occurring VRS doublet to three-peaked structure spectra are obtained here which can be engineered to have absorptive, dispersive, or dip like profiles according to the choice of system parameters such as radiative damping constants, atomic detunings and driving field strengths etc.

Photonic band-structure effects in the reflectivity of periodically patterned waveguides

We report sharp resonant features in the reflectivity spectra of semiconductor waveguides patterned with periodic lattices of deep holes. The resonances arise from coupling of incident light to the photonic bands of the lattice. By varying the reflection geometry, large parts of the photonic band structure are determined. A scattering matrix treatment is used to obtain theoretical spectra which agree well with experiment. The waveguide is shown to have an important influence on the band structure, including marked polarization mixing and significant energy up-shifts.

Resonant coupling of near-infrared radiation to photonic band structure waveguides

Sharp resonance features are observed in the polarized reflectivity spectra of semiconductor photonic crystals fabricated by deep periodic patterning of AlGaAs surface waveguides. Both one- (1-D) and two-dimensional (2-D) lattices are studied by angular dependent reflectivity. By comparison with theory we show that the sharp features in reflectivity arise from resonant coupling of the external radiation to the folded band structure of the photonic crystal waveguides. Wavevector selective coupling to heavy photon states at the edge of the photonic Brillouin zone is demonstrated for the 1-D lattices. In the case of the 2-D lattices we observe polarization mixing of the photonic hands. Theoretical reflectivity spectra were obtained from a numerical solution of Maxwells equations for the patterned waveguide and were found to be in very good agreement with experiment.

Guided mode resonance filters using polymer films

Guided-mode resonance optical filters are made from thin-film structures which consist of azopolymer films deposited on top of slab waveguides. Surface relief gratings can be optically induced on the azopolymer films. The transmission and reflection spectra as a function of the angle of incidence of the probe beam exhibit very sharp resonance features which correspond to coupling into the waveguide modes. Coupling into the overlying azopolymer film is also observed.

Quantum mechanical three-dimensional wavepacket study of the Li+HF→LiF+H reaction

A three-dimensional time-dependent quantum mechanical wavepacket method is used to calculate the state-to-state reaction probabilities at zero total angular momentum for the Li + HF → LiF +H reaction. Reaction probabilities starting from several different initial HF vibrational–rotational states (v=0,j=0,1,2) and going to all possible open channels are computed over a wide range of energies. A single computation of the wavepacket dynamics yields reaction probabilities from a specific initial quantum state of the reactants to all possible final states over a wide range of energies. The energy dependence of the reaction probabilities shows a broad background structure on which resonances of varying widths are superimposed. Sharp resonance features seem to dominate particularly at low product translational energies. There are marked changes in the energy dependence of the reaction probabilities for different initial or final diatom rotational quantum numbers, but it is noticeable that, for both reactants and products, odd and even rotational quantum numbers give rise to similar features. Our results clearly identify some resonance features which are present in the reaction probability plots for all product and initial states, though they appear in the form of sharp peaks in some plots and sharp dips in others. We speculate that these features arise from reactive scattering resonances which serve to redistribute the flux preferentially to particular product quantum states. The present calculations extend to higher energies than previously published time-independent reactive scattering calculations for this system.

Resonant states of helium atoms scattered from the Pt(110)-(1×2) surface

The specular intensity of helium atoms scattered from the missing-row reconstructed clean Pt(110)-(1×2) surface is measured as a function of the helium beam energy. Sharp resonance features were observed from which four eigenvalues of the He–Pt interaction potential could be determined; ε 0=−6.05±0.05 meV, ε1=−2.93±0.05 meV, ε2=−1.05±0.05 meV, and ε3=−0.32±0.05 meV. Several model potentials were examined and the potential parameters were fitted to these bound states. Excellent agreement with the experimental results is obtained with the shifted-Morse-hybrid (SMH)-potential with a well depth D=−8.17 meV. The shape of the so determined potential is discussed and compared to results from previous studies of the same system.

Resonance properties of dielectric waveguide gratings: theory and experiments at 4-18 GHz

The guided-mode resonance characteristics of dielectric waveguide gratings are presented. The sharp resonance features predicted theoretically are experimentally observed in the microwave region (4-18 GHz) and are shown to be in agreement with theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New features of the Mott-Hubbard insulator gap of parent HTS compounds found by resonance Raman scattering and UV-excited ordinary Raman scattering

Optical absorption at the insulating gap in the parent phase of cuprate superconductors shows a broad exciton-like peak near 1.7 eV, followed by a gradual decrease in absorption persisting 1 eV above the gap. By using ultraviolet laser lines to excite Raman spectra, we have found a Raman peak 0.2 eV below the first absorption peak in insulating cuprates. The Raman peak is much narrower than the absorption peak and hasA2g symmetry. We assign it to an exciton consisting of a hole transition from Cu\(d_{x^2 - y^2 } \) to a linear combination of Cudxy and nearest neighbor Opπ orbitals. We have also studied the resonance Raman profile for two-magnon Raman scattering in the same samples. We find a sharp resonance feature at about 2.7 eV, and little Raman intensity for photon energies at the 1.7 eV absorption peak. The state created at the peak must therefore be an inappropriate intermediate state for the double spin-flip Raman process.

The theoretical design and fabrication of a prism-coupled polarization conversion ferroelectric liquid crystal light modulator

It is possible to probe directly the optical dielectric tensor configuration within thin smectic layers (less than 6 μm thick) of ferroelectric liquid crystals (FLCs) by the propagation of optical prism-coupled leaky Fabry-Pérot modes. Incident polarized monochromatic light couples into the resonant modes of the system and may be coupled out of the cell in an orthogonal polarization. The observed reflectivity is a series of sharp peaks on a low background response at certain well-defined incident angles. These sharp resonant features make the prism-coupling technique a possible route for commercial fabrication of voltage-modulated devices. However, previous prism-coupled cells with sharp resonant guided mode features are not practical from a device point of view because they incorporate silver layers not used in conventional cell design. In this paper we demonstrate for the first time operating a leaky guided mode FLC cell with conventional surface layers, in a sp-mixed polarization mode of operation, allows sharp features to be observed which are modulated in intensity by an applied d.c. voltage. The prism-coupled cells used here are designed to be compatible with current FLC device technology.

Optical characterization of liquid crystals by means of half-leaky guided modes

Optical excitation of half-leaky guided modes has been used, for the first time to our knowledge, to characterize in detail the optical tensor profile in a liquid-crystal layer. The thin liquid-crystal layer is sandwiched between a high-index pyramid, with an index greater than the maximum index of the liquid crystal, and a glass substrate with an index lower than the minimum index of the liquid crystal. Analysis of this geometry shows that over a small angle range encompassed by a pseudocritical angle and a critical angle associated with the pyramid–liquid crystal and the pyramid–glass-substrate boundaries, respectively, there may exist sharp resonant features in the angle-dependent optical reflectivity. More particularly, if the director is tilted and twisted out of the plane of incidence there is strong TE-to-TM optical conversion over this small angular window, which is sensitive to details of the director profile. A 90° twisted, homogeneously aligned nematic liquid-crystal layer has been studied with this technique at two different wavelengths, 632.8 and 514.5 nm. Greater than 60% conversion from TM incident radiation to TE output has been recorded from sharp resonances in the half-leaky guided-wave angle window. If one fits these resonances with predictions from multilayer optics theory, one obtains extraordinary detail of the director profile in the cell. Since no metallic coatings are used, and all that is required are two glass plates of high and low index, respectively, the technique offers the potential of extremely useful applications in the examination of detailed director profiles in commercially fabricated cells.

Energy dependent photochemistry in the predissociation of V(OCO)+

Photofragmentation of the V(OCO)+ molecular ion in the visible shows sharp resonant absorption features and two distinct dissociation pathways: V+(OCO)+→V++CO2 and V(OCO)+→VO++CO. The photodissociation excitation spectrum reveals two low frequency vibrational modes in the upper state of this molecule at 105 and 196 cm−1. This spectrum indicates that the same photoexcited state in V(OCO)+ is the precursor to both V+ and VO+ products. The branching ratio for VO+/V+ production depends on the excitation energy and upper state vibrational mode. An estimate of the barrier to the production of VO+ of 13 000 cm−1 (37 kcal/mole) above the ground state of V(OCO)+ is made from this data.

SO(4) Symmetry of the Hubbard Model and its Experimental Consequences

The one band Hubbard model on a bi-partite lattice possess a global SO(4) symmetry group which is a direct product of the spin SU(2) and the pseudospin SU(2) symmetry group. Recently, the group theorectical consequence of this symmetry property has been investigated systematically. It is shown that this symmetry property can be used to reduce the complexity of diagonalizing the Hubbard Hamiltonian, and classify all the eigenstates according to the representation of the SO(4) group. It also leads to an exact one-to-one corespondence of the eigenstates at half-filling to that away from half-filling. Most importantly however, it is shown that this symmetry property leads to a direct experimental prediction for the high Tc superconductivity. If the high Tc superconductivity is correctly described by the Hubbard model, then the SO(4) symmetry dictates the existence of a collective mode that only appears below the superconducting transition temperature. Such a mode can be detected in an electron energy loss experiment as a sharp resonance feature. The location of the peak measure the parameters in the Hubbard model, the intensity is proportional to the superconducting order parameter and the width measures the departure of the Hubbard model from reality.

Direct determination of scattering time delays using the R-matrix propagation method

A direct method for determining time delays for scattering processes is developed using the R-matrix propagation method. The procedure involves the simultaneous generation of the global R matrix and its energy derivative. The necessary expressions to obtain the energy derivative of the S matrix are relatively simple and involve many of the same matrix elements required for the R-matrix propagation method. This method is applied to a simple model for a chemical reaction that displays sharp resonance features. The test results of the direct method are shown to be in excellent agreement with the traditional numerical differentiation method for scattering energies near the resonance energy. However, for sharp resonances the numerical differentiation method requires calculation of the S-matrix elements at many closely spaced energies. Since the direct method presented here involves calculations at only a single energy, one is able to generate accurate energy derivatives and time delays much more efficiently and reliably.