Showing papers on "Photonic crystal published in 2002"
TL;DR: In this article, the authors present a three-dimensional analysis of guided resonances in photonic crystal slab structures that leads to a new understanding of the complex spectral properties of such systems.
Abstract: We present a three-dimensional analysis of guided resonances in photonic crystal slab structures that leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and reflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes and the strength of the index modulation.
1,273 citations
TL;DR: In this paper, the authors reported on stimulated Raman scattering in an approximately 1-meter-long hollow-core photonic crystal fiber filled with hydrogen gas under pressure, which was guided and confined in the 15-micrometer-diameter hollow core by a two-dimensional photonic bandgap.
Abstract: We report on stimulated Raman scattering in an approximately 1-meter-long hollow-core photonic crystal fiber filled with hydrogen gas under pressure. Light was guided and confined in the 15-micrometer-diameter hollow core by a two-dimensional photonic bandgap. Using a pulsed laser source (pulse duration, 6 nanoseconds; wavelength, 532 nanometers), the threshold for Stokes (longer wavelength) generation was observed at pulse energies as low as 800 ± 200 nanojoules, followed by a coherent anti-Stokes (shorter wavelength) generation threshold at 3.4 ± 0.7 microjoules. The pump-to-Stokes conversion efficiency was 30 ± 3% at a pulse energy of only 4.5 microjoules. These energies are almost two orders of magnitude lower than any other reported energy, moving gas-based nonlinear optics to previously inaccessible parameter regimes of high intensity and long interaction length.
961 citations
TL;DR: In this article, the authors describe an all-angle negative refraction effect that does not employ a negative effective index of refraction and involves photonic crystals, and demonstrate this phenomenon using a microsuperlens.
Abstract: We describe an all-angle negative refraction effect that does not employ a negative effective index of refraction and involves photonic crystals. A few simple criteria sufficient to achieve this behavior are presented. To illustrate this phenomenon, a microsuperlens is designed and numerically demonstrated.
914 citations
TL;DR: In this paper, an out-of-plane coupler for butt-coupling from fiber to compact planar waveguides is proposed based on a short second-order grating or photonic crystal, etched in a waveguide with a low-index oxide cladding.
Abstract: We have designed and fabricated an out-of-plane coupler for butt-coupling from fiber to compact planar waveguides. The coupler is based on a short second-order grating or photonic crystal, etched in a waveguide with a low-index oxide cladding. The coupler is optimized using mode expansion-based simulations. Simulations using a 2-D model show that up to 74% coupling efficiency between single-mode fiber and a 240-nm-thick GaAs-AlO/sub x/ waveguide is possible. We have measured 19% coupling efficiency on test structures.
687 citations
TL;DR: In this article, slow group velocities of light, which are readily achievable in photonic-crystal systems, can dramatically increase the induced phase shifts caused by small changes in the index of refraction.
Abstract: We demonstrate how slow group velocities of light, which are readily achievable in photonic-crystal systems, can dramatically increase the induced phase shifts caused by small changes in the index of refraction. Such increased phase sensitivity may be used to decrease the sizes of many devices, including switches, routers, all-optical logical gates, wavelength converters, and others. At the same time a low group velocity greatly decreases the power requirements needed to operate these devices. We show how these advantages can be used to design switches smaller than 20 µm×200 µm in size by using readily available materials and at modest levels of power. With this approach, one could have ∼105 such devices on a surface that is 2 cm×2 cm, making it an important step towards large-scale all-optical integration.
645 citations
TL;DR: The design and drawing of a hollow optical fibre lined with an interior omnidirectional dielectric mirror is reported, demonstrating that low attenuation can be achieved through structural design rather than high-transparency material selection.
Abstract: Conventional solid-core optical fibres require highly transparent materials. Such materials have been difficult to identify owing to the fundamental limitations associated with the propagation of light through solids, such as absorption, scattering and nonlinear effects. Hollow optical fibres offer the potential to minimize the dependence of light transmission on fibre material transparency. Here we report on the design and drawing of a hollow optical fibre lined with an interior omnidirectional dielectric mirror. Confinement of light in the hollow core is provided by the large photonic bandgaps established by the multiple alternating submicrometre-thick layers of a high-refractive-index glass and a low-refractive-index polymer. The fundamental and high-order transmission windows are determined by the layer dimensions and can be scaled from 0.75 to 10.6 micro m in wavelength. Tens of metres of hollow photonic bandgap fibres for transmission of carbon dioxide laser light at 10.6 micro m wavelength were drawn. The transmission losses are found to be less than 1.0 dB m(-1), orders of magnitude lower than those of the intrinsic fibre material, thus demonstrating that low attenuation can be achieved through structural design rather than high-transparency material selection.
640 citations
TL;DR: It is proposed that these 3D metallic photonic crystals can be used to integrate various photonic transport phenomena, allowing applications in thermophotovoltaics and blackbody emission.
Abstract: Three-dimensional (3D) metallic crystals are promising photonic bandgap structures: they can possess a large bandgap, new electromagnetic phenomena can be explored, and high-temperature (above 1,000 degrees C) applications may be possible. However, investigation of their photonic bandgap properties is challenging, especially in the infrared and visible spectrum, as metals are dispersive and absorbing in these regions. Studies of metallic photonic crystals have therefore mainly concentrated on microwave and millimetre wavelengths. Difficulties in fabricating 3D metallic crystals present another challenge, although emerging techniques such as self-assembly may help to resolve these problems. Here we report measurements and simulations of a 3D tungsten crystal that has a large photonic bandgap at infrared wavelengths (from about 8 to 20 microm). A very strong attenuation exists in the bandgap, approximately 30 dB per unit cell at 12 microm. These structures also possess other interesting optical properties; a sharp absorption peak is present at the photonic band edge, and a surprisingly large transmission is observed in the allowed band, below 6 microm. We propose that these 3D metallic photonic crystals can be used to integrate various photonic transport phenomena, allowing applications in thermophotovoltaics and blackbody emission.
608 citations
TL;DR: A new regime of guidance is identified in which the spectral properties of these structures are largely determined by the thickness of the high-index layers and the refractive-index contrast and are not particularly sensitive to the period of the cladding layers.
Abstract: We propose a simple analytical theory for low-index core photonic bandgap optical waveguides based on an antiresonant reflecting guidance mechanism. We identify a new regime of guidance in which the spectral properties of these structures are largely determined by the thickness of the high-index layers and the refractive-index contrast and are not particularly sensitive to the period of the cladding layers. The attenuation properties are controlled by the number of high/low-index cladding layers. Numerical simulations with the beam propagation method confirm the predictions of the analytical model. We discuss the implications of the results for photonic bandgap fibers.
576 citations
TL;DR: In this article, the authors showed that these core−shell particles could be assembled into long-range ordered lattices (or photonic crystals) over large areas that exhibited optical properties different from those crystallized from silica colloids.
Abstract: Gold nanoparticles have been coated with amorphous silica to form spherical colloids with a core−shell structure The thickness of silica shells could be conveniently controlled in the range of tens to several hundred nanometers by changing the concentration of the sol−gel precursor or the coating time These core−shell colloids could serve as the building blocks to fabricate photonic devices In one demonstration, we showed that these core−shell particles could be assembled into long-range ordered lattices (or photonic crystals) over large areas that exhibited optical properties different from those crystallized from silica colloids Transmission spectra of these crystals displayed both features that correspond to the Bragg diffraction of a periodic lattice and the plasmon resonance absorption of gold nanoparticles Reflectance spectra taken from these crystals only showed peaks caused by Bragg diffraction In another demonstration, these core−shell colloids were assembled into chains of different config
537 citations
TL;DR: In this paper, a scattering-matrix-based numerical method was proposed to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensional, periodic photonic crystal slab of finite thickness.
Abstract: We formulate a scattering-matrix-based numerical method to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensionally periodic photonic crystal slab (PCS) of finite thickness. The square symmetry (point group C4v) is taken for the illustration of the method, but it is quite general and works for any point group symmetry for one-dimensional (1D) and 2D PCS’s. We show that the appearance of well-pronounced dips in the transmission spectra of a PCS is due to the interaction with resonant waveguide eigenmodes in the slab. The energy position and width of the dips in transmission provide information on the frequency and inverse radiative lifetime of the quasiguided eigenmodes. We calculate the energies, linewidths, and electromagnetic fields of such quasiguided eigenmodes, and analyze their symmetry and optical activity. The electromagnetic field in such modes is resonantly enhanced, which opens possibilities for use in creating resonant enhancement of different nonlinear effects.
527 citations
TL;DR: This work demonstrates photonic crystal fibers with ultra-flattened, near zero dispersion with micro-structured fibers showing dispersion of 0 +/- 0.6 ps/nm from 1.24 microm-1.6 microm wavelength.
Abstract: We demonstrate photonic crystal fibers with ultra-flattened, near zero dispersion. Two micro-structured fibers showing dispersion of 0 ± 0.6 ps/nm.km from 1.24 μm-1.44 μm wavelength and 0 ± 1.2 ps/nm.km over 1 μm-1.6 μm wavelength have been measured.
TL;DR: The first observations of lasing in three-dimensional photonic crystals, in the cholesteric blue phase II are reported, showing that distributed feedback is realized in three dimensions, resulting in almost diffraction-limited lasing with significantly lower thresholds than in one dimension.
Abstract: Photonic-bandgap materials, with periodicity in one, two or three dimensions, offer control of spontaneous emission and photon localization. Low-threshold lasing has been demonstrated in two-dimensional photonic-bandgap materials, both with distributed feedback and defect modes. Liquid crystals with chiral constituents exhibit mesophases with modulated ground states. Helical cholesterics are one-dimensional, whereas blue phases are three-dimensional self-assembled photonic-bandgap structures. Although mirrorless lasing was predicted and observed in one-dimensional helical cholesteric materials and chiral ferroelectric smectic materials, it is of great interest to probe light confinement in three dimensions. Here, we report the first observations of lasing in three-dimensional photonic crystals, in the cholesteric blue phase II. Our results show that distributed feedback is realized in three dimensions, resulting in almost diffraction-limited lasing with significantly lower thresholds than in one dimension. In addition to mirrorless lasing, these self-assembled soft photonic-bandgap materials may also be useful for waveguiding, switching and sensing applications.
TL;DR: In this article, the optical properties of polycrystalline inverse opals were modified in predictable manners by numerous methods, including tailoring the pore size, filling the pores with fluids of various refractive indices, and changing the compositions of the solid material.
Abstract: Colloidal crystal-templating methods have been used to prepare inverse opal photonic crystals of silica, mercaptopropyl-functionalized silica, titania, and zirconia. Ordered arrays of uniformly sized polymer spheres were infiltrated with fluid precursors capable of condensation or crystallization. After solidification of the material in the void spaces between the spheres, the polymer templates were removed by calcination or solvent extraction, leaving inverse replicas of the template arrays. By carefully controlling the synthetic procedures, gram-scale quantities of powdered macroporous materials exhibiting photonic crystal properties were obtained. For materials with crystalline walls (titania and zirconia), this required minimization of the size of the nanocrystalline grains. Because the periodicity introduced into the wall structure by the colloidal crystal templates was on the order of optical wavelengths, Bragg diffractions from the planes produced photonic stop bands in the visible spectra of these materials. The stop bands were manifested as brightly colored reflections and an optical filtering behavior of the materials. A crystallographic indexing of the optical spectrum of a polycrystalline inverse opal confirmed the fcc ordering of the pores. The optical properties of these materials were modified in predictable manners by numerous methods, including tailoring the pore size, filling the pores with fluids of various refractive indices, and changing the compositions of the solid material. The wavelengths of the colorful reflections (stop bands) were found to be proportional to the pore size and to vary linearly with the refractive index of the fluid filling the pores. The physical and synthetic modifications reported here allowed for the preparation of powders with optical reflections and bright colors spanning the entire visible spectrum.
TL;DR: The coherence of the supercontinuum is shown to depend strongly on the input pulse's duration and wavelength, and optimal conditions for the generation of coherent supercontinua are discussed.
Abstract: Numerical simulations have been used in studies of the temporal and spectral features of supercontinuum generation in photonic crystal and tapered optical fibers. In particular, an ensemble average over multiple simulations performed with random quantum noise on the input pulse allows the coherence of the supercontinuum to be quantified in terms of the dependence of the degree of first-order coherence on the wavelength. The coherence is shown to depend strongly on the input pulse’s duration and wavelength, and optimal conditions for the generation of coherent supercontinua are discussed.
TL;DR: In this paper, the authors showed that sharp and asymmetric line shapes can be created in the response function by placing two partially reflecting elements into the waveguides, and numerically demonstrated this effect by simulating the propagation of electromagnetic waves in a photonic crystal.
Abstract: We show that, for an optical microcavity side coupled with a waveguide, sharp, and asymmetric line shapes can be created in the response function by placing two partially reflecting elements into the waveguides. In such a system, the transmission coefficient varies from 0% to 100% in a frequency range narrower than the full width of the resonance itself. We numerically demonstrate this effect by simulating the propagation of electromagnetic waves in a photonic crystal.
TL;DR: In this paper, an ultrabroadband octave-spanning white-light continuum is generated with 60-ps pump pulses of subkilowatt peak power, and the primary mechanism of spectral broadening is identified as the combined action of stimulated Raman scattering and parametric four-wave mixing.
Abstract: Supercontinuum generation is investigated experimentally and numerically in a highly nonlinear index-guiding photonic crystal optical fiber in a regime in which self-phase modulation of the pump wave makes a negligible contribution to spectral broadening. An ultrabroadband octave-spanning white-light continuum is generated with 60-ps pump pulses of subkilowatt peak power. The primary mechanism of spectral broadening is identified as the combined action of stimulated Raman scattering and parametric four-wave mixing. The observation of a strong anti-Stokes Raman component reveals the importance of the coupling between stimulated Raman scattering and parametric four-wave mixing in highly nonlinear photonic crystal fibers and also indicates that non-phase-matched processes contribute to the continuum. Additionally, the pump input polarization affects the generated continuum through the influence of polarization modulational instability. The experimental results are in good agreement with detailed numerical simulations. These findings demonstrate the importance of index-guiding photonic crystal fibers for the design of picosecond and nanosecond supercontinuum light sources.
TL;DR: A method for optically encoding micrometre-sized nanostructured particles of porous silicon using a periodic electrochemical etch and a simple antibody-based bioassay using fluorescently tagged proteins demonstrates the encoding strategy in biologically relevant media.
Abstract: Strategies to encode or label small particles or beads for use in high-throughput screening and bioassay applications focus on either spatially differentiated, on-chip arrays or random distributions of encoded beads. Attempts to encode large numbers of polymeric, metallic or glass beads in random arrays or in fluid suspension have used a variety of entities to provide coded elements (bits)--fluorescent molecules, molecules with specific vibrational signatures, quantum dots, or discrete metallic layers. Here we report a method for optically encoding micrometre-sized nanostructured particles of porous silicon. We generate multilayered porous films in crystalline silicon using a periodic electrochemical etch. This results in photonic crystals with well-resolved and narrow optical reflectivity features, whose wavelengths are determined by the etching parameters. Millions of possible codes can be prepared this way. Micrometre-sized particles are then produced by ultrasonic fracture, mechanical grinding or by lithographic means. A simple antibody-based bioassay using fluorescently tagged proteins demonstrates the encoding strategy in biologically relevant media.
TL;DR: In this paper, the femtosecond pulses from an unamplified Ti:sapphire laser with energies up to 4 nJ were used, and the resultant spectra from several photonic crystal fibers and taper structures were compared and analyzed.
Abstract: Broadband continua extending from 400 to 1600 nm are generated in photonic crystal fibers and in tapered conventional optical fibers. The continuum is generated in the fundamental fiber mode. Femtosecond pulses from an unamplified Ti:sapphire laser with energies up to 4 nJ are used, and the resultant spectra from several photonic crystal fibers and taper structures are compared and analyzed.
02 Jun 2002
TL;DR: Guided-wave singlemode propagation of sub-ps terahertz (THz) pulses in a plastic photonic crystal fiber has been experimentally demonstrated for the first time to the best of our knowledge as discussed by the authors.
Abstract: Guided-wave single-mode propagation of sub-ps terahertz (THz) pulses in a plastic photonic crystal fiber has been experimentally demonstrated for the first time to the best of our knowledge. The plastic photonic crystal fiber is fabricated from high density polyethylene tubes and filaments. The fabricated fiber exhibits low loss and relatively low dispersive propagation of THz pulses within the experimental bandwidth of 0.1 /spl sim/ 3 THz. The measured loss and group velocity dispersion are less than 0.5 cm/sup -1/ and -0.3 ps/THz/spl middot/cm above 0.6 THz, respectively.
TL;DR: In this paper, the authors combine quantum entanglement with nanostructured metal optics in the form of optically thick metal films perforated with a periodic array of subwavelength holes, which act as photonic crystals that may convert entangled photons into surface-plasmon waves.
Abstract: The state of a two-particle system is called entangled when its quantum mechanical wave function cannot be factorized in two single-particle wave functions Entanglement leads to the strongest counter-intuitive feature of quantum mechanics, namely nonlocality Experimental realization of quantum entanglement is relatively easy for the case of photons; a pump photon can spontaneously split into a pair of entangled photons inside a nonlinear crystal In this paper we combine quantum entanglement with nanostructured metal optics in the form of optically thick metal films perforated with a periodic array of subwavelength holes These arrays act as photonic crystals that may convert entangled photons into surface-plasmon waves, ie, compressive charge density waves We address the question whether the entanglement survives such a conversion We find that, in principle, optical excitation of the surface plasmon modes of a metal is a coherent process at the single-particle level However, the quality of the plasmon-assisted entanglement is limited by spatial dispersion of the hole arrays This spatial dispersion is due to the nonlocal dielectric response of a metal, which is particularly large in the plasmonic regime; it introduces "which way" labels, that may kill entanglement
TL;DR: Numerical investigations using the finite-difference time-domain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 10;5 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum.
Abstract: The design of high quality factor (Q) optical cavities in two dimensional photonic crystal (PC) slab waveguides based upon a momentum space picture is presented. The results of a symmetry analysis of defect modes in hexagonal and square host photonic lattices are used to determine cavity geometries that produce modes which by their very symmetry reduce the vertical radiation loss from the PC slab. Further improvements in the Q are achieved through tailoring of the defect geometry in Fourier space to limit coupling between the dominant momentum components of a given defect mode and those momentum components which are either not reflected by the PC mirror or which lie within the radiation cone of the cladding surrounding the PC slab. Numerical investigations using the finite-difference timedomain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 105 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum.
TL;DR: In this article, the authors developed an effective medium description of a two-dimensional photonic band-gap medium composed of dielectric cylinders of large Dielectric constant, and derived an effective permittivity and permeability for the composite.
Abstract: We develop an effective medium description of a two-dimensional photonic band-gap medium composed of dielectric cylinders of large dielectric constant. Using the transfer matrix method we have calculated reflection coefficients for a slab of the composite and plane-wave incidence, as well as the (complex) wavevector for the infinite system. From these quantities we derive an effective permittivity and permeability for the composite. In the case of p-polarized incidence the composite displays a negative magnetic permeability at microwave frequencies due to single-scatterer resonances in the medium.
TL;DR: The fabrication and properties of soft glass photonic crystal fibers for supercontinuum generation have zero or anomalous group velocity dispersion at wavelengths around 1550 nm, and approximately an order of magnitude higher nonlinearity than attainable in comparable silica fibers.
Abstract: We report the fabrication and properties of soft glass photonic crystal fibers (PCF's) for supercontinuum generation. The fibers have zero or anomalous group velocity dispersion at wavelengths around 1550 nm, and approximately an order of magnitude higher nonlinearity than attainable in comparable silica fibers. We demonstrate the generation of an ultrabroad supercontinuum spanning at least 350 nm to 2200 nm using a 1550 nm ultrafast pump source.
TL;DR: In this article, a photonic crystal nanocavity laser was fabricated based on a high-quality factor design that incorporates fractional edge dislocations, and the laser was optically pumped with 10 ns pulses, and lased at threshold pumping powers below 220 μW.
Abstract: We have fabricated photonic crystal nanocavity lasers, based on a high-quality factor design that incorporates fractional edge dislocations. Lasers with InGaAsP quantum well active material emitting at 1550 nm were optically pumped with 10 ns pulses, and lased at threshold pumping powers below 220 μW, the lowest reported for quantum-well based photonic crystal lasers, to our knowledge. Polarization characteristics and lithographic tuning properties were found to be in excellent agreement with theoretical predictions.
TL;DR: In this article, the validity of the effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals is tested against the full-vectorial three-dimensional finite-difference time-domain calculations.
Abstract: The validity of the two-dimensional approximation by the effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals is tested against the full-vectorial three-dimensional finite-difference time-domain calculations. A good agreement over a wide frequency range is obtained for the band structures of two-dimensional photonic crystals in a low-index-contrast heterostructure. For high-index-contrast heterostructures, the effective index method is still valid, but only for much narrower frequency range.
TL;DR: The design and fabrication of a multilayered macroscopic fiber preform and the subsequent drawing and optical characterization of extended lengths of omnidirectional dielectric mirror fibers with submicrometer layer thickness are reported.
Abstract: We report the design and fabrication of a multilayered macroscopic fiber preform and the subsequent drawing and optical characterization of extended lengths of omnidirectional dielectric mirror fibers with submicrometer layer thickness. A pair of glassy materials with substantially different indices of refraction, but with similar thermomechanical properties, was used to construct 21 layers of alternating refractive index surrounding a tough polymer core. Large directional photonic band gaps and high reflection efficiencies comparable to those of the best metallic reflectors were obtained. Potential applications of these fibers include woven fabrics for radiation barriers, spectral authentication of cloth, and filters for telecommunications.
TL;DR: In this article, the dispersion properties of dielectric slabs perforated with two-dimensional photonic crystals (PCs) of square symmetry were analyzed, in three dimensions, for all k-vectors in the first Brillouin zone, and not only along the characteristic high symmetry directions.
Abstract: We analyze, in three dimensions, the dispersion properties of dielectric slabs perforated with two-dimensional photonic crystals (PCs) of square symmetry. The band diagrams are calculated for all k-vectors in the first Brillouin zone, and not only along the characteristic high-symmetry directions. We have analyzed the equal-frequency contours of the first two bands, and we found that the square lattice planar photonic crystal is a good candidate for the self-collimation of light beams. We map out the group velocities for the second band of a square lattice planar PC and show that the group velocity is the highest in the region of maximum self-collimation. Such a self-collimated beam is predicted to show beating patterns due to the specific shape of the equal-frequency contours. A geometrical transformation maps the region of the first and second photonic bands where self-collimation takes place one onto the other and gives additional insights on the structural similarities of self-collimation in those two bands.
TL;DR: It is shown how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings, which becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory.
Abstract: We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.
TL;DR: In this paper, the quality factor of a dipole defect mode in free-standing membranes is expressed in terms of the Fourier transforms of its field components and the reduction in radiation loss can be achieved by suppressing the mode's wavevector components within the light cone.
Abstract: We express the quality factor of a mode in terms of the Fourier transforms of its field components and prove that the reduction in radiation loss can be achieved by suppressing the mode's wavevector components within the light cone. Although this is intuitively clear, our analytical proof gives us insight into how to achieve the Q factor optimization, without the mode delocalization. We focus on the dipole defect mode in free-standing membranes and achieve Q > 10/sup 4/, while preserving the mode volume of the order of one half of the cubic wavelength of light in the material. The derived expressions and conclusions can be used in the optimization of the Q factor for any type of defect in planar photonic crystals.