Unexpected and novel new physical phenomena result when light interacts with a shock wave or shock-like dielectric modulation propagating through a photonic crystal. These theoretically predicted new phenomena include the capture of light at the shock wave front and re-emission at a tunable pulse rate and carrier frequency across the photonic crystal bandgap, and bandwidth narrowing as opposed to the ubiquitous bandwidth broadening. To our knowledge, these effects do not occur in any other physical system. Reversed Doppler shifts are also predicted to be observable. The generality of these effects make them amenable to observation in a variety of time-dependent photonic crystal systems, which may have interesting technological implications.

We have investigated the miniaturization of photonic devices for ultimate photon localization, and have demonstrated two-dimensional photonic crystal nanolasers with two important quantum nanostructures-quantum wells (QWs) and quantum dots (QDs). Photonic crystal cavities with QW active material, are simple, but powerful nanolasers to produce intense laser output for signal processing. On the other hand, when located in a high-quality factor (Q) nanocavity, because QD(s) strongly couple with the intense optical field, QD photonic crystal cavities are expected to be good experimental setups to study cavity quantum electrodynamics, in addition to high speed and compact laser sources. Our photonic crystal nanolasers have shown as small thresholds as 0.12mW and 0.22mW for QD-photonic crystal lasers and QW-photonic crystal lasers, respectively, by proper cavity designs and nanofabrication. For QD-photonic crystal lasers, whispering gallery modes in square lattice were used together with coupled cavity designs and, for QW-photonic crystal lasers, quadrapole modes in triangular lattice with fractional edge dislocations were used to produce high-Q modes with small mode volume.

Two examples of integrating active and passive photonic crystal devices are discussed. A first example integrates two tunable laser diodes with a passive photonic crystal Y-coupler structure. The tunable laser diode is defined by two photonic crystal channel waveguides that are coupled longitudinally through photonic crystal coupling sections. The waveguides have slightly different lengths and hence exhibit slightly different longitudinal mode spacings. The front and rear reflectors are realized by photonic crystal mirrors with lattice dimensions chosen to achieve the desirable mirror reflectivities. Secondly, a passive superprism structure is discussed that can be integrated with an array of photo diodes to build highly integrated receivers for optical networks.

Infrared spectral transmission, reflection and thermal emission from diffraction gratings with differing periods, groove widths and groove depths were experimentally and theoretically studied. The structural dimensions are comparable to the measured spectral wavelengths in the range 2.5 to 25 microns. For calculating the optical properties (transmission and reflection spectra), we have used an in-house S-Matrix Propagation Algorithm (SMPA) technique which is unconditionally stable versus changes in structural dimensions, optical constants and truncation order. We have experimentally studied the planar angular transmission and reflection spectrum of Si and GaAs grating samples, using FTIR spectrometry over the spectral range from 2.5 μm to 25 μm. At λ < Λ, the transmitted intensity is quasi-periodic with respect to wave number. A similar property also appears in the reflection spectra. The theoretical results for spectral transmission are in good agreement with the experimental results for the wavelength range 2.5 to 25 μm.

In this paper we present a study of infrared spectral thermal emission from varius grating structures. The structures include various lamellar grating layers of metals, silicon or GaAs on the same semiconductor substrate. The gratings have different periods, groove widths and groove depths, with feature sizes comparable to the radiated measurement wavelengths (2.5 - 25 μm). The measurement temperatures for all samples were in the range 27 to 740°K. Lateral and vertical optical confinement in the grating layers can occur. In the semiconductor grating layer in the case where the material is partially transparent lateral optical coupling exist which affect the spectral emission. In addition vertical confinement of the electromagnetic field exists which corresponds to "organ-pipe" like modes. The vertical confinement is enhanced in the case where the grating scructure is coated with metal or degenerate semiconductor. These phenomena resulted in thermal emission spectral oscillation for the wavelength range larger than the grating period.

We consider Maxwell's equations in two-dimensional periodic dielectric media cast as an eigenvalue problem Multidomain spectral methods are applied in order to compute spectrally accurate eigenfrequencies, which provide the band structures of the photonic crystals. The domain is divided into subdomains whose interfaces include the edges of the different media so that the analytic solution of the eigenproblem is infinitely smooth in each subdomain. This promises that the multidomain spectral approximations perform the exponential rate of convergence to the analytic solution. The band structure calculations are carried out for simple domain structures, and their results are demonstrated.

An analytical approximate method is introduced for obtaining wave vector diagrams for planar 1-D photonic crystal. Based on the best separable wave solution, a variational formula provides the best estimate to the propagation constant. The wave vector diagram and the wave profile are obtained for a typical PCVD technology. Due to the iterative nature of the method, any wave amplitude nonlinearity can also be modeled easily.

In this paper, we presented a new algorithm for the band structure calculation of photonic crystal slabs (PCS) based on the plane wave expansion method (PWEM) with perfectly matched layers (PMLs). The introduction of PMLs is used to truncate the computational region in the vertical direction. In addition, the effective medium tensor is applied to improve the convergence. By using PWM, a general complex eigenvalue problem is then obtained. Two criterions are presented to distinguish the guided modes from the PML modes. The presented scheme can accurately determine the band structure both above and below the light cone. The results obtained using this algorithm have been compared with those by using Finite-difference Time-Domain (FDTD) method and found to agree very well.

In this paper, a procedure for optimizing two-dimensional (2D) photonic crystals (PhC) is presented. In this procedure, the unit cell of a PhC structure is discretized into small grids and converted into a binary sequence. A direct binary search (DBS) method is then used to search through a terrain of possible solutions in order to find a more optimal one. This process is designed for improving the absolute band gap, opening a new one, for a predefined PBG structure. By applying this procedure on a honeycomb array of dielectric rods in air background, the maximum absolute gap-to-midgap ratio (MAGTMR) is increased to more than twice that of the initial structure. To further prove the validity of this procedure, this procedure is also applied to two best-found hexagonal and square lattice structures. The band gap improvements in these two cases indicate that besides structure type, structure symmetry, fill factor, index contrast, and size, shape and orientation of the constituent objects, there are other unknown factors, which affect the absolute band gap of a photonic crystal as well. The convergence property of this procedure is also discussed in this paper. The idea of this procedure can be applied to find the global optimal solution by using a global optimization algorithm, such as simulated annealing (SA), genetic algorithm (GA).

Photonic crystals have seen major advances in the past few years in the optical range. The association of in-plane waveguiding and two-dimensional (2D) photonic crystals (PCs) in thin-slab or waveguide structures leads to good 3D confinement with easy fabrication. Such structures, much easier to fabricate than 3D PCs, open many exciting opportunities in optoelectronic devices and integrated optics. We review the basics of these structures, with emphasis on basic properties and loss performance, as well as modeling tools, which show that 2D PCs etched through waveguides supported by substrates are a viable route to high-performance PC-based photonic integrated circuits (PICs). A companion paper by Benisty et al. in these proceedings illustrates further high performance building blocks and integrated devices.

The existence of three-dimensional photonic bandgaps in square spiral thin films, made using the Glancing Angle Deposition (GLAD) method, was recently verified. We further demonstrate the flexibility of the GLAD process to fabricate silicon photonic bandgap crystals with customizable bandgap centre frequencies. GLAD combines physical vapor deposition at highly oblique flux incidence angles with dual axis substrate motion control, creating porous thin films with three-dimensional submicrometer topographies. This makes it a near-ideal approach for diamond lattice based photonic crystal fabrication, with manipulation of the photonic properties through the deposition parameters. We have produced a range of different square spiral thin films, and present characterization results indicating bandgaps at wavelengths close to 2 micrometers. Such low wavelength bandgaps have not previously been achieved for square spiral architectures. Ongoing work towards optimization of the process holds the promise of square spiral photonic crystals with even lower bandgap centre wavelengths, approaching the telecommunications windows. In addition to its flexibility and mass-production suitability, we present how GLAD can be used to engineer defects inside the photonic crystals during the one-step growth process. Such defects may potentially be employed as stand-alone waveguides, or as elements of more complex photonic device and circuitry designs involving subsequent micromachining of the GLAD thin films.

Since the launching of the photonic bandgap concept in 1987, the development of the corresponding structures has expanded very rapidly, in particular for two-dimensional semiconductor-based structures. In the case of sol-gel derived materials, the main emphasis has been on one-dimensional mutilayer stacks and, in particular, on three-dimensional structures of the opal and inverse opal type. In this work, one-dimensional multilayer stacks of periodically alternating low refractive index (SiO₂) and high index (TiO₂) materials have been deposited by spin-coating onto silica or single crystal Si substrates, in the form of dielectric mirrors (distributed Bragg reflectors) and Fabry-Perot microcavities, both single and coupled (double). Some of the microcavities were doped with rare-earth elements (Er and Yb). These structures have been characterized by X-ray diffraction, infrared spectroscopy and field emission-scanning electron microscopy; their optical properties have also been measured, namely the stop band of high reflectivity and, in the case of the microcavities, the cavity modes and the photoluminescence behavior of the rare-earth ions inserted in the cavity layers. The presence of Er in both cavity layers of coupled microcavities was found to lead to a substantial increase in photoluminescence signal intensity and width, compared to the cases where Er was present only in one of the cavities. The possibility of an antenna effect between Yb³⁺ and Er³⁺ ions is also examined.

Optical characteristics of a circular photonic crystal (CPC) in the frequency range of 0 to 20 GHz were investigated. The sample was made by alumina rods of 2 mm in radius and 300 mm in length. The alumina rods were arrayed in the form of concentric circles with 6-fold symmetry. The transmission spectra were calculated at various radical distances. When the radical distance was 8 mm, a photonicgap was obtained around 12 GHz. The experimental results were in good agreement with the calculations. Although the lattice positions were shifted from the ones of the CPC, the same transmission spectrum was obtained in the phase-shifted CPC. Phase-shift is a useful means for eliminating translational symmetries that would often appear in the exterior part of a CPC composed of numerous concentric circles. Isotropic photonicgaps were obtained for both a CPC and the phase-shifted CPC.

Practical realizations of 2D (planar) photonics crystal (PhC) are either on a membrane or etched through a conventional heterostructure. While fascinating objects can emerge from the first approach, only the latter approach lends itself to a progressive integration of more compact PhC's towards monolithic PICs based on InP. We describe in this talk the various aspects from technology to functions and devices, as emerged from the European collaboration "PCIC." The main technology tour de force is deep-etching with aspect ratio of about 10 and vertical sidewall, achieved by three techniques (CAIBE, ICP-RIE, ECR-RIE). The basic functions explored are bends, splitters/combiners, mirrors, tapers, and the devices are filters and lasers. At the end of the talk, I will emphasize some positive aspects of "broad" multimode PhC waveguides, in view of compact add-drop filtering action, notably.

We describe a photonic bandgap polarization selector based on a photonic crystal placed at junction of two 90° intersecting waveguides to form an ultra-compact device. The photonic crystal consists of 7 layers of a triangular lattice with a radius to pitch ratio (r/a) of 0.24 and a lattice constant of 0.386μm. The PBG is orientated so that the light is incident and collected at 45° to the Γ-K crystallographic direction. Modeling of the PBG shows that TM polarized light is strongly reflected while TE light passes largely into the crystal. Measurements of the fibre-to-fibre transmitted power of the device for each polarization show that the TM collected power is ~6dB higher than the TE light for equal input polarization powers. Further evidence of the strong reflection of TM light comes from an equivalent sample without a 2-D lattice at the waveguide junction. In these samples, no TM light is detected at the output. Furthermore, by taking into account the TE and TM gains within the active waveguides, the TM to TE polarization selection of the PBG is estimated to be up to 22dB.

We have fabricated high-quality planar photonic crystal defect waveguides in InP/InGaAsP material. Using Fourier analysis of the Fabry-Perot fringes obtained in transmission, we derive the propagation losses. Values as small as 1.8 dB/mm for waveguides consisting of 3 rows of missing holes ("W3") were measured. To the best of our knowledge, this is the smallest loss in III-V semiconductor photonic crystal waveguides reported to date. We believe that the reduction in losses is due to the high quality of etching carried out using a new regime of chemically assisted ion beam etching.

We investigate both experimentally and theoretically the waveguiding properties of the novel design of channel waveguides in silicon-on-insulator (SOI) photonic crystal slabs. It is known that the channel waveguides defined by a missing of one row of holes in a triangular-lattice photonic crystal are characterized by a very narrow transmission bandwidth limited by large group velocity dispersion. In order to increase the bandwidth we investigate an alternative design, where the conventional single-mode strip waveguide is embedded into a photonic crystal slab -- a so-called double-trench waveguide. Such a design is intended to combine the best features of photonic crystal slabs, such as suppression of radiation losses at bends and imperfections, with broad bandwidth and small group velocity dispersion. We report the successful demonstration of this broad-bandwidth photonic crystal waveguide with propagation losses as low as 35 dB/cm, which are among the lowest reported in the literature. Furthermore, we found that the modes of positive (quasi-TE) and negative (quasi-TM) parity significantly interact in our structures due to the absence of the oxide layer on top of the SOI slab and the resulting asymmetry. As a result of this interaction multiple mini-stopbands appear in the areas of anti-crossing of the positive and negative parity modes. The results are successfully modeled by the plane-wave calculations confirming the nature of the experimentally observed mini-stopbands. To the best of our knowledge this is the first demonstration of the effects of asymmetry on the transmission characteristics of the photonic crystal slabs.

We investigate theoretically and experimentally photonic crystal waveguides and bends realized in glass-like amorphous materials. Efficient photonic crystal waveguide bends with transmissions up to 75% per bend and low loss photonic crystal waveguides with propagation losses as low as 1.7 dB/mm were fabricated and characterized.

The tuning of the light propagation and localization properties in photonic crystal (PhC) slabs by using microactuators was demonstrated numerically and experimentally. A micromechanical actuator controls the position of the exterior structural element, which is located close to the PhC slab, and modulates the PhC properties through the change of the evanescent interaction of light confined in the PhC slab with the exterior element. When the exterior structural element approaches to a line-defect PhC waveguide, intensity and phase modulations occur. In the preliminary experiment using a line-defect PhC waveguide, we demonstrated the optical switching operation with an extinction ratio of ~10 dB at a wavelength of 1.55 μm. The localized state of light in a point-defect cavity can also be controlled. The tuning of the resonant wavelength over the spectral range of ~60nm at around the wavelength of 1.55 μm was numerically demonstrated by combining two PhC slabs. The approach discussed here can be widely employed for realizing functional and tunable PhC slab devices.

In this paper, we review the confinement mechanism of self-collimation in planar photonic crystals. In this mechanism, an approximately flat equi-frequency contour (EFC) below the light cone of the planar photonic crystal can be used to laterally confine the light and total internal reflection (TIR) provides vertical confinement. To this end, self-collimation in both low-index and high-index planar photonic crystals are investigated using the three-dimensional (3D) finite-difference time-domain (FDTD) method and the 3D iterative plane wave method (PWM). It is found that low-loss self-guiding is achievable in both the valence and conduction bands for high-index planar photonic crystals. However, for low-index planar photonic crystals, low-loss self-guiding can be only observed in the valence band. Experimental results show a propagation loss of as low as 1.1 dB/mm for the self-guiding in a high-index planar photonic crystals.

Photonic crystal based structures have been considered for optical communication applications. A class of novel symmetric structures consisting of cavities and waveguides have been proposed to serve as optical add-drop multiplexers. Light transfer processes in these structures are analyzed briefly. The problem of deviating from the perfect accidental degeneracy is addressed for practical designs, and the backscattering intensities are shown low for the slight deviations. Anomalous light refraction at a surface of a photonic crystal has also been studied. The limitations of prior theoretical methods for the transmission problem are discussed. An outline of a new analytic theory that overcomes these limitations is presented. Photonic crystals are fabricated on polymer multi-layer films and integrated with conventional channel waveguides.

We emphasize the importance of optical confinement in the vertical direction for a successful two-dimensional photonic crystal waveguide (2D-PCW) performance by presenting optical properties of a 2D-PCW that has a special feature to provide a strong vertical confinement. The 2D-PCW, which was designed to operate in microwave regime, was composed of two parts: an ordinary 2D-PCW composed of alumina rods in air for lateral optical confinement and a pair of aluminum metal plates forming a metal waveguide in the vertical direction. Cylindrical alumina rods, each being 2 mm in diameter, were arranged in a square-lattice with its spatial period of 9 mm, which according to a simple photonic band calculation produces a photonic bandgap in the frequency range of 14.7~16.5 GHz for TM-polarized light (E-field parallel to the rods). This 2D-PCW was then embedded between two aluminum metal plates. Light propagation loss for a straight waveguide, which was estimated from transmission measurement as a function of waveguide length, is as low as 0.05 dB/cm whereas most of transmission loss could be attributed to the input and output couplings due to mode mismatch. When multiple 90°-bends were incorporated, on the other hand, estimated bending loss was only 0.1 dB/bend, which indicates that high performance 2D-PCWs are indeed possible if an appropriate strong confinement in the vertical direction is provided. Fabry-Perot oscillations seen in transmission spectra, whose oscillation period was observed dictated only by total waveguide length regardless of the number of bends, are another strong evidence for the low propagation and bending losses of our waveguide structure.

Electromagnetic modes of photonic-crystal slabs can be excited by charged particles which remain outside the slab. The theory assumes a classical trajectory for the particle and computes the dielectric response of the slab photonic structure to the Coulomb fields emitted by the moving charge. The power applied by this response force on the charged particle describes the energy transfer between the charge and the electromagnetic modes of the slab. It is shown that the photonic crystal film responds according to an effective dielectric function which is easily calculated using a transfer matrix scheme.

Complex photonic bands and strong anisotropic dispersion characteristics of artificially engineered periodic dielectric structures have been widely investigated. In this paper we explore the self-guiding effect possessed by photonic crystals and the possible applications for integrated photonics. Since this approach does not require a full photonic bandgap, low refractive index materials (i.e. glass or organic polymers) are considered as an alternative with advantages over conventional semiconductor materials. Sensitivity analysis reveals how structural variations influence the performance of this type of photonic crystal based system.

In solid core Microstructured Optical Fibers (MOFs), guidance of light is due to a finite number of layers of holes surrounding a solid core. Because the potential barrier is finite, all modes are leaky, blurring the distinction between guided and non-guided modes. Through simulations using a multipole formulation, we clarify the definition of modal cutoff in MOFs. We establish that the fundamental mode of MOFs undergoes a transition between modal confinement and non-confinement similar to modal cutoff. An asymptotic analysis gives us a better understanding of mode properties on each side of the cutoff but also near cutoff and leads us to define a cutoff point and a cutoff region for the fundamental mode. Three operation regimes with very different mode properties can be distinguished. Only two of these are of practical interest, one with strong mode confinement and another with broader field distributions. The former is of interest for single-mode guidance with strong confinement, whereas the latter, the cutoff region, is where highly adjustable chromatic dispersion can be achieved. We provide a map of the parameter space (MOF "phase diagram") summarizing the operating regimes of MOFs, and show for a few examples how this map can be used for deterministic MOF design.

In this paper, an analysis of long period gratings in photonic nanostructured fibers and waveguides is presented. With the finite-difference time-domain (FDTD) method, a detailed quantitative study on the relationship between the spectral response shift of the gratings and the parameters of the photonic nanostructures is performed. It is found that the unique photonic nanostructures can substantially enhance the tuning capability of the spectral response of the gratings, which can lead to many practical applications in optical sensors and communications, such as optical sensors with ultra high sensitivity and wavelength filters with wide tuning range.

We investigate the potentials of using a far-field technique for tunable coupling to high-order guided modes of photonic crystal fibers. The field distribution matched for coupling to the fiber is generated by the optical Fourier transform of grating-based phase patterns dynamically encoded on a spatial light modulator. Tuning the parameters of phase-only binary diffractive patterns can modulate both amplitude and phase of the coupling field. Experiments demonstrate tunable and spatially controllable coupling to the second-order mode of a commercially available index-guided micro-structured fiber with a triangular lattice air-hole structure.

•A two-dimensional optically controlled phased array antenna (PAA) system is proposed. The system employs highly dispersive photonic crystal fibers (HDPCFs) to provide the true-time-delays (TTD). Independent azimuth and elevation control is obtained through a mid-stage optical wavelength conversion process. The dispersion of the fabricated is as high as -600 ps/nmkm around 1550 nm which is 33 times of conventional telecom SMF. By employing the PCFs to increase the dispersion, the TTD module size can be proportionally reduced. A 64-element (8x8) PCF-based PAA system is under construction. Simulation results operating at X-band are shown in this paper.

Microstructured Polymer Optical Fibers (MPOF) were first made in 2001, and subsequent development has aimed at exploiting the material and design opportunities they present. Most effort has been focused on developing approaches for high bandwidth MPOF, and investigating the properties of multimode microstructured fibers. We also consider new applications in endoscopy and photonic interconnects, as well as the use of organic dopants in MPOF.

Photonic crystal fibers (PCFs) are normally holey fibers, made of silica glass, which is opaque in the mid- and far-infrared spectral range 3-20 μm. We have fabricated novel PCFs by multiple extrusions of silver halide (AgCl_xBr_1-x) crystalline materials, which are highly transparent in this spectral range. These PCFs are composed of two solid materials: the core consists of pure AgBr (n=2.16), and the cladding includes small diameter fiberoptic elements, made of AgCl (n=1.98). These AgCl fiberoptic elements are arranged in two concentric hexagonal rings around the core. This structure gives rise to a cladding region of lower refractive index, thus ensuring total internal reflection. Flexible PCFs of outer diameter 1mm and length of about 1m were fabricated, and their optical properties were measured. Measurements of numerical aperture, laser power transmission and evanescent wave spectroscopy indicated that the PCFs behave like a core-clad structure. There was a good agreement between the results and those obtained by theoretical simulations. Silver halide PCFs would be extremely useful for IR laser power transmission, for IR radiometery and for IR spectroscopy.

The optical loss behavior of index guiding PC fibers made from high purity silica, was investigated with regard to the preform preparation steps and drawing procedure. Loss effects in the 1.4 µm region are caused mostly by incorporation of hydroxide groups during PC preform preparation. Typical sources are flame heat treatment procedures. However, hydroxide based absorption by water permeation into the holey structure was not observed, not even by storage in humid atmosphere over days. PCFs show additional NIR attenuation, possibly caused by drawing induced atomic defects in the pure silica material. By advanced PC preform preparation the minimum attentuation in the NIR range can be depressed down to 2.9 dB/km at 1.3 μm. PCFs have a reduced tensile strength in comparison with compact silica fibers. The mechanical stability increases with the cross section area of the solid outer cladding. This resembles the behavior of single capillary fibers without inner holey or cobweb structure. The tensile strength of PCFs decreases after a few days of hole contamination with condensed water.

Using both analytic theory, and first-principles finite-difference time-domain simulations, we introduce several novel mechanically tunable photonic crystal structures consisting of coupled photonic crystal slabs. These structures exploit guided resonance effects which give rise to strong variation of transmission for normally incident light. First, when the two slabs are separated apart by a few wavelengths, such a coupled slab structure behaves as a miniaturized Fabry-Perot cavity with two photonic crystal slabs acting as highly reflecting mirrors. Therefore, the transmission through the structure is highly sensitive to the spacing between the slabs. Second, when the two slabs are in proximity to each other, the evanescent tails of the resonance start to overlap. Exploiting the evanescent tunneling, we introduce a new type of optical all-pass filter. The filter exhibits near complete transmission for both on and off resonant frequencies, and yet generates large resonant group delay. Thus, we expect the coupled photonic crystal slab structures to play important roles in micro-mechanically tunable optical sensors and filters.

We investigate methods for actively tuning two-dimensional photonic crystal devices by modulating the index of refraction of the constituent materials. The index of refraction is modulated by infiltrating liquid crystals into a photonic crystal lattice of air cylinders in silicon. Moreover, the orientation of the liquid crystal molecules within the cylinders is actively modulated in order to induce a change in the dielectric tensor; thereby, tuning the optical properties of the photonic crystal. We validate and characterize the tunability of these devices both experimentally and with three-dimensional finite-difference time-domain method simulations. Furthermore, we integrate these tunable devices to demonstrate their enhancement of WDM photonic crystal applications.

Periodic inhomogeneities of linear dielectric materials are known to give rise to highly complex transmission spectra, widely adjustable by tuning geometric parameters. In this work, the theory of optical periodic structures is extended to materials exhibiting the nonlinear Kerr effect. A new computational scheme, based on the transfer-matrix method, is introduced in order to perform, in a selfconsistent way, the simultaneous adjustment of the refractive index and transisting electric field and compute the intensity-dependent transmittance of nonlinear films. For adequate geometries and with a suitably adjusted frequency, hysteresis loops can appear in the transmittance vs. intensity diagrams, signaling bistability. We observe that a bistable behavior can appear without the construction of a Fabry-Perot structure. For a nonlinear film structured by a periodic side variation of the refractive index, we provide evidence that bistability can also take place for frequencies corresponding to Fano resonances. Depending on the geometry of the film, we observe a wide variety of shapes for the transmittance hysteresis loops.

We show that inside a multi-layer dielectric stack, consideration of higher-order, fast-oscillating interference terms between counter-propagating waves can dramatically change the dynamics of second harmonic generation, and thus lead to an unusual result: field confinement and overlap can be far better optimized, and conversion efficiencies further enhanced, in the presence of a phase mismatch. One may therefore conclude that phase matching is not always a necessary condition to provide optimized nonlinear frequency conversion efficiency.

We experimentally demonstrate very efficient non-phase-matched second- and third-harmonic generation from a macroporous GaP. The generated second-harmonic signal is independent of crystallographic orientation, and its enhancement is believed to be due to the light localization for which conditions exist in the studied samples of porous GaP. The nonlinear optical results are correlated with linear optical scattering studies and atomic-force microscopic images of the studied surfaces.

An unconventional approach to passively expand the field-of-view of optical receivers for free-space laser communications is presented. Our device exploits the negative refractive behavior exhibited by photonic crystals. The particularity of this approach is seen by placing the device behind a lens, where the illumination area given by the ensemble of the focal spots of light received at different angle within a given angular range is reduced to a smaller area without any expansion in the propagation angle of the light for each individual spot. The fundamental idea of this approach is based on a combination of the crystal's negative refractive behavior and properly bended crystal boundaries interfacing with air. In a sample calculation, the reduction of the illumination area is estimated by the ray trace method and the preservation of propagation angles of the incoming beams is confirmed. Since the discrete structure of photonic crystals only approximates a bended boundary with an aribtrary inclination angle, a slight modification is introduced into the crystal's structure to allow a more flexible design. Although such a modification influences the negative refractive behavior, the function of field-of-view expansion is still verified and confirmed by means of electromagnetic computation.

We show that propagation of the envelope of the optical beams inside a periodic structure can be approximately modeled using a linear transformation solely based on its band structure. Using this model a simple description of the diffraction is obtained which relies on the shape of the equal-frequency contours of the photonic crystal band structure. This model provides intuitive insight on how to design these structures for diffraction-based applications. We consider various methods to modify the band structure, or to excite appropriate regions of the band structure to realize different functionalities inside the photonic crystal. Applications like diffraction-free propagation, frequency separation in space (superprism-based devices), and diffraction compensation are discussed in more detail.

Here we report a new type of dispersive structure for wavelength multiplexing/demultiplexing, based on a planar 1-D photonic crystal prism. We introduce a computationally efficient technique for simulating this structure. Simulations are carried out to determine the angular dispersion as a function of period, slant angle in the prism area and prism apex angle. The design has been optimized for good performance in a moderate refractive index contrast system (silica and silicon nitride) and promises reduced scattering losses when compared with existing 2-D superprism designs.

The superprism is known as a highly dispersive phenomenon in photonic crystals, which is expected to realize a narrow band filter, beam deflector, dispersion compensator, etc. Thus far, its large angular dispersion has been theoretically discussed worldwide through the dispersion surface analysis. In general, however, incidence of a finite width beam to a photonic crystal excites a wide angular spectrum of Bloch waves, which leads to a significant beam divergence. The dispersion surface analysis including such a property indicates that a large angular dispersion and a high quality beam propagation are achieved simultaneously under some limited conditions for incident angles, beam widths and wavelength range. A high resolution will be possible, but the length of the photonic crystal required is of cm to 10 cm order and beam width of 100 micron order. To solve these problems, we proposed a k-vector super-prism, which utilizes a large angular dispersion of k-vector and an angled output end of the photonic crystal. In this prism, the length of the PC is significantly shortened to 100 micron order with maintaining a high resolution. In addition, latitudes for the beam width and wavelength range are greatly expanded, so the butt-joint of a singlemode fiber and operation over C- to L bands will be possible. The FDTD simulation demonstrates the light propagation, which agrees with these expectations, but also showed some peculiar light diffraction, which should be cared in designing a high efficiency filter.

Effects of the enhancement of photoconductivity in 2D photonic macroporus silicon structures were investigated. Dependence of photoconductivity on the angle of incidence of the electromagnetic radiation is observed with maxima at normal incidence of electromagnetic radiation, in the region of the angle of full internal reflection respective to macropore walls and at a grazing angle of incidence respective to the surface of structure. The absolute maximum of photoconductivity is measured at distance between macropores, corresponding to two lengths of the electron free run, i.e. by the maximal transfer of the amplified electric components from a macropore surface in a silicon matrix. Angular dependences of photoconductivity, as well as enhancement of the photoconductivity in comparison with monocrystal silicon, primary absorption p-component of electromagnetic radiation testified to formation of surface electromagnetic waves in illuminated macroporous silicon structures. Its effects result in amplification of a local electric field on a surface of macroporous silicon structure and a macropore surface. The measured value of the built-in electric field on a macropore surface achieves 10⁶ V/cm, the signal photoconductivity amplifies 10² times, and Raman scattering -- up to one order of value.

In this paper, a novel effective index method for modeling high index contrast planar photonic crystals is introduced. In this effective index method, the frequency axis is divided into many regions, and the effective index for each region is obtained using the central frequency of this region. Dispersion relationship in a wide frequency region can then be calculated using the effective index for each region to obtain the states in this region with a 2-D simulation and integrating all states in all frequency regions. The validity of this effective index method in approximating an intense three-dimensional (3-D) simulation required by the finite thickness of planar photonic crystals with a less intense two-dimensional simulation is examined. As an example, this method is applied to calculate the band diagram of a planar photonic crystal waveguide. By comparing with the results obtained with the full 3D simulation, we find that this method is valid for all states below the light cone in many bands, and the wider the waveguide, the more the number of bands, which agree with the full 3D results.

We investigate the characteristics of resonant mode of a cavity with two-dimensional (2D) photonic crystal (PC) mirrors using the finite difference time domain simulation. The employed PC mirrors are composed of a square array of dielectric rods in air. As the dielectric constant of the rods increases, the frequency of resonant mode decreases whereas its Q factor increases. However, both the frequency and Q factor of a resonant mode increases as the number of dielectric rod increases. To clarify the mechanism that determines the frequency of resonant modes, we have studied the characteristics of resonant modes of one-dimensional PC cavities made of PCs. Our study of one-dimensional PC cavity demonstrates that both the phase change due to the reflection at the surface of PC mirror and the optical path length between PC mirrors play important roles in the determination of the position of resonant frequency. We also discuss the tunable PC filters implemented with the PC mirrors composed of some materials, such as liquid crystal, whose dielectric constant depends on an external field. In this case, the phase change due to the reflection can be controlled by changing the dielectric constant of liquid crystals in the PC mirrors.

We have designed channel-drop filters with two line defects and a resonance system based on the two-dimensional triangular-lattice-hole photonic-crystal structure by two-dimensional and three-dimensional finite-difference time-domain simulations. The quality factors have been calculated to be around 3,500 of a two-dimensional channel-drop filter and to be around 300 of a resonance system based on the triangular-lattice hole-based photonic-crystal slab structure.

We propose the diffractive optical element using the sub-wavelength scale pillar array structure. The equivalent microscopic refractive index can be controlled by changing pillar width and the pillar lattice constant. Advantages of using the sub-wavelength scale structure to manipulate the equivalent index in such a manner are that the optical functional elements can be fabricated by a single-etch-step process, and that the anisotropic optical characteristics can be realized using isotropic materials. In this paper, we have designed and fabricated the Fresnel lens with sub-wavelength structure on the Si substrate. The equivalent refractive index, n_eff, as a function of the pillar width and the lattice constant was calculated by the EMT (Effective Medium Theory). The width of pillar at the n-th lattice point, a_n, was determined by n_eff and required the local optical length of the target diffractive optical element. The design wavelength, λ, was set at 1.6 μm, the lattice constant, Λ, was 0.45 μm, the pillar height, h, was 1.21 μm, and the refractive index of Si, n_si, was 3.48, respectively. These parameter values satisfied the sub-wavelength condition of λ > n_si × Λ. The Fresnel lens with a focal length of 20 mm and the effective diameter of 1.8 mm was designed and fabricated.

A novel implementation of a variable beam splitter using a photonic crystal (PhC) is proposed. The beam splitter consists of two periodic structures: a non-channel dispersion guiding region and a band gap based splitting structure. The dispersion guiding PhC structure is used to route the optical wave by exploiting the dispersion properties of the lattice. Arbitrary power ratio between output beams can be achieved by varying the parameters of the splitting structure. Within the studied range of splitting structures, high output power was observed and verified experimentally.

We fabricate aniostropic porous silicon structures, which exhibit 1-D photonic crystal properties. Both second and third harmonics are generated from these structures. We observe a significant enhancement of nonlinear optical signals from nanoporous materials with respect to crystalline materials. These findings are attributed to the nanocrystalline structure of porous Si. The phase matching of nonlinear optical processes becomes possible in birefringent porous Si structures. The variation of symmetry of the nonlinear optical response from the surface of multilayered anisotropic structures is observed.

We propose to use onion-like resonators to approximate spherically symmetric Bragg resonators. Such Bragg onion resonators have been realized in silicon based material systems. We develop an analytical theory that calculates the resonant frequencies and the quality factors of the onion cavity modes. We demonstrate that it is possible to achieve Q factors exceeding 5 x 10⁶ in a cavity of a few microns in dimension. The onion resonators allow full control over the spontaneous emission process, which may lead to the thresholdless lasers. The onion resonators may also find many other applications in cavity quantum electrodynamics.

We show that light pulses can be stopped and stored all-optically, with a process that involves an adiabatic and reversible pulse bandwidth compression occurring entirely in the optical domain. Such a process overcomes the fundamental bandwidth-delay constraint in optics, and can generate arbitrarily small group velocities for any light pulse with a given bandwidth, without the use of any coherent or resonant light-matter interactions. We exhibit this process in optical resonator systems, where the pulse bandwidth compression is accomplished only by small refractive index modulations performed at moderate speeds. The optically achievable ultra low speeds can also generate extremely large non-linearities using non-resonant interactions, and thus enable decoherence-free single photon quantum gates.