Biomedical subjects

Sajeev John

Publications and source records attributed to Sajeev John.

13 recordsLinked to original sources

PubMed2006

Nonlinear Bloch waves in resonantly doped photonic crystals.

We demonstrate the existence of self-consistent Bloch modes in resonant nonlinear photonic crystals with a complex, intensity-dependent, and frequency-dependent dielectric function. Such a dielectric response may arise by "doping" the photonic crystal with resonant quantum dots, atomic impurities, or other two-level light emitters. These exact solutions of the nonlinear electromagnetic wave equation exhibit Bloch periodicity and describe fundamental eigenmodes of an active photonic crystal under incoherent pumping. In a simple model two-dimensional photonic crystal, doped with active two-level atoms, the optical field intensity of these waves shows a laserlike threshold behavior with pumping. This appears to be a universal property of active, nonlinear photonic crystals and photonic band gap materials, arising from multidirectional distributed feedback. We describe an iterative technique for computing the detailed properties of these exact, self-consistent nonlinear waves in strongly scattering photonic crystal architectures with regions of gain and loss.

Journal Article↗

PubMed2006

Photonic band-gap formation by optical-phase-mask lithography.

We demonstrate an approach for fabricating photonic crystals with large three-dimensional photonic band gaps (PBG's) using single-exposure, single-beam, optical interference lithography based on diffraction of light through an optical phase mask. The optical phase mask (OPM) consists of two orthogonally oriented binary gratings joined by a thin, solid layer of homogeneous material. Illuminating the phase mask with a normally incident beam produces a five-beam diffraction pattern which can be used to expose a suitable photoresist and produce a photonic crystal template. Optical-phase-mask Lithography (OPML) is a major simplification from the previously considered multibeam holographic lithography of photonic crystals. The diffracted five-beam intensity pattern exhibits isointensity surfaces corresponding to a diamondlike (face-centered-cubic) structure, with high intensity contrast. When the isointensity surfaces in the interference patterns define a silicon-air boundary in the resulting photonic crystal, with dielectric contrast 11.9 to 1, the optimized PBG is approximately 24% of the gap center frequency. The ideal index contrast for the OPM is in the range of 1.7-2.3. Below this range, the intensity contrast of the diffraction pattern becomes too weak. Above this range, the diffraction pattern may become too sensitive to structural imperfections of the OPM. When combined with recently demonstrated polymer-to-silicon replication methods, OPML provides a highly efficient approach, of unprecedented simplicity, for the mass production of large-scale three-dimensional photonic band-gap materials.

Journal Article↗

PubMed2005

Photonic band gap templating using optical interference lithography.

We describe the properties of three families of inversion-symmetric, large photonic band-gap (PBG) template architectures defined by iso-intensity surfaces in four beam laser interference patterns. These templates can be fabricated by optical interference (holographic) lithography in a suitable polymer photo-resist. PBG materials can be synthesized from these templates using two stages of infiltration and inversion, first with silica and second with silicon. By considering point and space group symmetries to produce laser interference patterns with the smallest possible irreducible Brillouin zones, we obtain laser beam intensities, directions, and polarizations which generate a diamond-like (fcc) crystal, a novel body-centered cubic (bcc) architecture, and a simple-cubic (sc) structure. We obtain laser beam parameters that maximize the intensity contrasts of the interference patterns. This optimizes the robustness of the holographic lithography to inhomogeneity in the polymer photo-resist. When the optimized iso-intensity surface defines a silicon to air boundary (dielectric contrast of 11.9 to 1), the fcc, bcc, and sc crystals have PBG to center frequency ratios of 25%, 21%, and 11%, respectively. A full PBG forms for the diamond-like crystal when the refractive index contrast exceeds 1.97 to 1. We illustrate a non-inversion symmetric PBG architecture that interpolates between a simple fcc structure and a diamond network structure. This crystal exhibits two distinct and complete photonic band gaps. We also describe a generalized class of tetragonal photonic crystals that interpolate between and extrapolate beyond the diamond-like crystal and the optimized bcc crystal. We demonstrate the extent to which the resulting PBG materials are robust against perturbations to the laser beam amplitudes and polarizations, and template inhomogeneity. The body centered cubic structure exhibits the maximum robustness overall.

Journal Article↗

PubMed2005

Slanted-pore photonic band-gap materials.

We present a detailed analysis of three-dimensional photonic band-gap materials consisting of lattices of slanted pores with n = 2 , 3, and 4 pores per unit cell. These slanted pores emanate from one or two masks consisting of a two-dimensional square or triangular lattice of holes placed on the top surface of the crystal. We also consider the case in which the top surface is "polished" at an angle after the first set of slanted pores is generated from the first mask. A second set of slanted pores is then generated from a second mask placed on the new angled surface. Using these architectures, we demonstrate photonic band gaps of up to 25% of the gap center frequency when the crystal is made from materials with a dielectric constant ratio of 11.9:1 (silicon with air pores). The proposed structures are amenable to microfabrication using established techniques such as x-ray lithography or two-photon direct writing in a polymer template, followed by inversion and replication of the template with polycrystalline silicon. They can also be microfabricated by direct plasma etching in single crystal semiconductors. An alternative fabrication protocol consists of photoelectrochemical etching of deep pores in a single crystal semiconductor followed by focused ion beam or reactive ion etching of the second lattice of directed pores.

Journal Article↗

PubMed2005

Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules, and simulations.

We demonstrate on-chip, single-mode, waveguiding of light in air for a variety of 2D-3D photonic band gap (PBG) heterostructures. These include square spiral, woodpile, slanted pore, and inverse opal three-dimensional (3D) photonic crystals intercalated with a 2D (planar) photonic crystal microchip. Design rules are established to yield maximal single-mode waveguiding bandwidths of up to roughly 180 nanometers centered at a wavelength of 1.5 microns . This can be achieved with 3D PBG materials with gaps as small as 15% of the PBG center frequency. Finite-difference time-domain (FDTD) simulations of light flow in optical mirocircuits within such heterostructures reveal tolerance to layer misalignment and other fabrication-related structural disorder. We provide an interpretation of the universal mechanism for diffractionless light propagation in 2D-3D photonic crystal heterostructures. We demonstrate that planar, on-chip, optical microcircuitry similar to that of two-dimensional (2D) photonic crystals is almost universally achievable within the engineered electromagnetic vacuum of 3D PBG materials.

Journal Article↗

PubMed2004

Photonic band gap enhancement in frequency-dependent dielectrics.

We illustrate a general technique for evaluating photonic band structures in periodic d -dimensional microstructures in which the dielectric constant epsilon (omega) exhibits rapid variations with frequency omega . This technique involves the evaluation of generalized electromagnetic dispersion surfaces omega ( k--> ,epsilon) in a (d+1) -dimensional space consisting of the physical d -dimensional space of wave vectors k--> and an additional dimension defined by the continuous, independent, variable epsilon . The physical band structure for the photonic crystal is obtained by evaluating the intersection of the generalized dispersion surfaces with the "cutting surface" defined by the function epsilon (omega) . We apply this method to evaluate the band structure of both two- and three-dimensional (3D) periodic microstructures. We consider metallic photonic crystals with free carriers described by a simple Drude conductivity and verify the occurrence of electromagnetic pass bands below the plasma frequency of the bulk metal. We also evaluate the shift of the photonic band structure caused by free carrier injection into semiconductor-based photonic crystals. We apply our method to two models in which epsilon (omega) describes a resonant radiation-matter interaction. In the first model, we consider the addition of independent, resonant oscillators to a photonic crystal with an otherwise frequency-independent dielectric constant. We demonstrate that for an inhomogeneously broadened distribution of resonators impregnated within an inverse opal structure, the full 3D photonic band gap (PBG) can be considerably enhanced. In the second model, we consider a coupled resonant oscillator mode in a photonic crystal. When this mode is an optical phonon, there can be a synergetic interplay between the polaritonic resonance and the geometrical scattering resonances of the structured dielectric, leading to PBG enhancement. A similar effect may arise when resonant atoms that are coupled radiatively through resonance dipole-dipole interaction are placed in a photonic crystal.

Journal Article↗

PubMed2004

Lasing in a random amplifying medium: spatiotemporal characteristics and nonadiabatic atomic dynamics.

We study the dynamics of lasing from photonic paints excited by short, localized, optical pulses, using a time-dependent diffusion model for light propagating in the medium containing active atoms. The full time-dependent, nonadiabatic nonlinear response of the atomic system to the local optical field intensity is described using the Einstein rate equations for absorption and emission of light. Solving the time-dependent diffusion equation for the light intensity in the medium with nonlinear gain and loss, we derive detailed information on the spectral, spatial, and temporal properties of the emitted laser light. Our model recaptures the effects of scatterers to narrow the emission spectral linewidth and to narrow the emitted pulse duration, at a specific threshold pump intensity. Our model also describes how this threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results.

Journal Article↗

PubMed2004

Theory of photon statistics and optical coherence in a multiple-scattering random-laser medium.

We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.

Journal Article↗

PubMed2004

Photonic band gap architectures for holographic lithography.

Using symmetry considerations, we identify three families of large photonic band-gap (PBG) architectures defined by the isointensity surfaces of four beam laser interference. For particular choices of beam intensities, directions, and polarizations, we obtain a diamondlike crystal, a novel body-centered cubic architecture, and a simple cubic structure with PBG to center frequency ratios of 25%, 21%, and 11%, respectively, when the isointensity surface defines a silicon (dielectric constant of 11.9) to air boundary.

Journal Article↗

PubMed2003

Blueprint for wafer-scale three-dimensional photonic band-gap synthesis by photoelectrochemical etching.

We present an architecture for three-dimensional photonic band-gap (PBG) material synthesis by oblique angle photoelectrochemical pore etching. This technique provides high aspect ratio pores, in which the pore diameter can be modulated by changing light intensity during the etch process. The naturally occurring "Kielovite" structure is a stretched version of the face-centered-cubic lattice of crisscrossing pores and exhibits a PBG to center frequency ratio of 8% in a background dielectric constant of 11.9 (silicon). We demonstrate that by modulating the pore radius in between pore intersections, the PBG can be doubled in size to nearly 16%. The enlarged PBG is robust against a number of structural perturbations.

Journal Article↗

PubMed2003

Photonic band gaps based on tetragonal lattices of slanted pores.

We describe broad new classes of three-dimensional (3D) structures which, when made of silicon, exhibit robust 3D photonic band gaps of up to 25% of the gap center frequency. The proposed photonic crystals are readily amenable to very high precision microfabrication using established techniques such as x-ray lithography and template inversion. Each architecture consists of a set of oriented cylindrical pores emanating from a two-dimensional (2D) square lattice mask with a two-point basis. Large bandwidth, microcircuits for light may be incorporated within the resulting photonic band gaps using an intercalated 2D photonic crystal layer.

Journal Article↗

PubMed2003

Diffractionless flow of light in all-optical microchips.

We introduce the concept of a hybrid 2D-3D photonic band gap (PBG) heterostructure which enables both complete control of spontaneous emission of light from atoms and planar light-wave propagation in engineered wavelength-scale microcircuits. Using three-dimensional (3D) light localization, this heterostructure enables flow of light without diffraction through micron-scale air waveguide networks. Achieved by intercalating two-dimensional photonic crystal layers containing engineered defects into a 3D PBG material, this provides a general and versatile solution to the problem of "leaky modes" and diffractive losses in integrated optics.

Journal Article↗

PubMed2002

Square spiral photonic crystals: robust architecture for microfabrication of materials with large three-dimensional photonic band gaps.

We provide a blueprint for microfabricating photonic crystals with very large and robust three-dimensional photonic band gaps (PBG's). These crystals are based on interleaving polygonal spiral posts and can be efficiently manufactured on a large scale in a one-step process using the recently introduced technique of glancing angle deposition. We classify various families of spiral photonic crystals based on (i) the parent three-dimensional (3D) point lattice to which they are most closely related, (ii) the crystallographic axis of the parent lattice around which the spiral posts wind, and (iii) the set of points of the parent lattice which the spiral arms connect or nearly connect. We obtain optimal geometries for the spiral photonic crystals by detailed mapping of the size and location of the PBG within a multidimensional parameter space which characterizes the shape of each spiral post. For the optimum PBG, the spiral arms and elbows may deviate significantly from the points of the original point lattice. The largest 3D PBG's are obtained for square spiral posts that wind around the [001] axis of diamond (or face centered cubic) lattice and in which the spiral arm segments approximately connect either the fifth or first nearest-neighbor points of the parent lattice. In the case of silicon posts (with a dielectric constant of 11.9) in an air background, whose arm segments nearly connect fifth nearest-neighbor point of the diamond lattice, the full PBG can be as large as 16% of the gap center frequency. For the corresponding air posts in a silicon background, the maximum PBG is 24% of the gap center frequency. We compute both the total electromagnetic density of states and the electromagnetic field distributions near the PBG. It is suggested the PBG in an optimized structure is highly tolerant to various forms of disorder that may arise during the manufacturing process.

Journal Article↗