Highly dispersive photonic band-gap prism

Compact high-resolution spectrometer based on super-prism and local-super-collimation effects of photonic crystal

We propose a design of the compact high-resolution photonic crystal (PhC) spectrometer with a wide working bandwidth based on both super-prism and local-super-collimation (LSC) effects. The optimizing methods, finding the ideal incident angle and oblique angle of PhC for a wider working bandwidth and ideal incident beam width and PhC size for a certain resolution requirement, are developed. Besides the theoretical work, for the first time, the experiment of such a PhC spectrometer is conducted in the microwave frequency range, and the beam-splitting effects for different frequencies in a wide working bandwidth agree very well with the theoretical predictions. According to the scalability, with the condition to control the deviations in the fabrication processes the design could be extended to optical frequency ranges, e.g., infrared, visible-light, and ultraviolet ranges. The spectrometer in optical frequencies can be implemented on silicon-on-insulator (SOI) chips as a thin-slab structure so that the operating bandwidth can be expanded further through the multi-layer design. Theoretically, the size of the ultra-high-resolution PhC spectrometer in optical frequency ranges based on our design could be two orders smaller than the traditional design.

Experimental realization of a Fresnel hologram as a super spectral resolution optical element

A highly dispersive, diffractive optical element is designed and realized for an extremely high spectral resolution spectroscopy for exoplanet telescope application. Our design uses an annular Fresnel hologram to transform incident starlight directly into a spectrogram. The recording of the hologram is accomplished using two spherical waves of different radius of curvature. The resultant hologram consists of an annular grating structure with a gradually shrinking period as a function of increasing radius. The variable period not only could bring the incoming star-light into focus, but also exhibits a large on-axis chromatic behavior. We demonstrate a dispersion of wavelength 430–700 nm over 190 mm on-axis distance, leading to a super fine spectral resolution 0.0266 nm at wavelength 515 nm for a detector size of 20 µm.

Angular dependent strong coupling between localized waveguide resonance and surface plasmon resonance in complementary metamaterials

We give direct evidence of both surface plasmon resonance (SPR) and localized waveguide resonance (LWR) contribution to the extraordinary optical transmission in complementary metamaterials. Strong coupling between SPR and LWR are also observed with clear evidence of Rabi splitting and anti-crossing phenomena. The splitting introduces sharp phase shift, which in turn enhances group velocity delay by the incident angle without geometric parameter change. The results not only clarify SPR and LWR effects in the extraordinary optical transmission, but also provide a novel route to control light-metamaterial interaction by angular modulation for on-chip slow light devices.

Design of flat-band superprism structures for on-chip spectroscopy

We present a systematic design procedure of photonic crystal (PhC) superprism structures for on-chip spectroscopic applications. In specific, we propose a new figure of merit, namely the angular-group-dispersion-bandwidth-product (AGDBP) to quantitatively describe the spectroscopic performance of PhC superprism structures, and an optimum PhC structure for spectroscopic applications should have large angular group dispersion over a large bandwidth, i.e., a flat-top dispersion profile. We demonstrate the advantage of such a new design consideration by optimizing the geometry of a two-dimensional parallelogram-lattice PhC superprism structure. The performance of such a superprism spectrometer is further analyzed numerically using finite-difference time-domain simulations, which out-performs current implementations in terms of the number of achievable output spectral channels.

Robust topology optimization of three-dimensional photonic-crystal band-gap structures

We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for robust topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.

Light trapping and near-unity solar absorption in a three-dimensional photonic-crystal

We report what is to our knowledge the first observation of the effect of parallel-to-interface-refraction (PIR) in a three-dimensional, simple-cubic photonic-crystal. PIR is an acutely negative refraction of light inside a photonic-crystal, leading to light-bending by nearly 90 deg over broad wavelengths (λ). The consequence is a longer path length of light in the medium and an improved light absorption beyond the Lambertian limit. As an illustration of the effect, we show near-unity total absorption (≥98%) in λ=520-620 nm and an average absorption of ~94% over λ=400-700 nm for our α-Si:H photonic-crystal sample of an equivalent bulk thickness of t˜=450 nm. Furthermore, we have achieved an ultra-wide angular acceptance of light over θ=0°-80°. This demonstration opens up a new door for light trapping and near-unity solar absorption over broad λs and wide angles.

First experimental demonstration of a photonic band gap channel-drop filter at 240 GHz

We have designed, fabricated, and tested a novel photonic band gap (PBG) channel-drop filter (CDF) operating at around 240 GHz. A PBG CDF is a device that allows the channeling of selected frequencies from continuous spectra into separate waveguides through select defects in a PBG structure. It is compact and configurable, and thus, it can be employed for millimeter-wave spectrometry with applications in communications, radio astronomy, and radar receivers for remote sensing and nonproliferation. In this paper we present the design, modeling, and fabrication methods used to produce a silicon-based PBG CDF, and demonstrate its ability to filter the frequency of 240 GHz with a linewidth of approximately 1 GHz and transmission of 25 dB above background.

Linearly damped modes at gap edges of photonic crystals

It is shown that for one-dimensional dielectric photonic crystals, the Bloch modes, a vital tool in the analysis of these structures, cannot provide a complete representation of the electromagnetic field at the edges of bandgaps. On these points, the couple of Bloch modes representing the propagation on both sides of the crystal reduces to a single one, with a stationary field, and a complete representation of the field inside the crystal illuminated by a plane wave must include a linearly damped mode (LDM), the amplitude of which behaves linearly in space. The theory of transfer matrices and the use of basic properties of the field allow a precise description of the LDM from a few parameters. An extension to two-dimensional photonic crystals is proposed.

Why a harmonic solution for lossless, perfectly homogeneous, left-handed material cannot exist

In a preceding paper [J. Opt. Soc. Am. A21, 122 (2004)], we proposed proof of the nonexistence of harmonic solutions for a perfectly homogeneous left-handed material with both relative permittivity and relative permeability equal to -1 using the theorem of analytic continuation of an analytic function. The use of this theorem of analyticity has been questioned in a recent paper [Phys. Rev. E73, 046608 (2006)], arguing the possible inadequacy of the conditions of application of the theorem. We avoid the use of the analyticity theorem and propose a direct and simple proof of the nonexistence of such solutions. Furthermore, this proof is extended to any left-handed material with negative permeability and permittivity.

Enhancement of the superprism effect based on the strong dispersion effect of ultrahigh-order modes

It is demonstrated that the superprism effect is greatly enhanced in the configuration of a symmetrical metal-cladding waveguide owing to the strong dispersion effect of ultrahigh-order modes. The experimental result shows that a notable spatial displacement of the reflected beam as large as 0.9 mm is achieved within a variation of 0.15 nm in wavelength.

Experimental demonstration of self-collimation inside a three-dimensional photonic crystal

We present our experimental demonstration of self-collimation inside a three-dimensional (3D) simple cubic photonic crystal at microwave frequencies. The photonic crystal was designed with unique dispersion property and fabricated by a high precision computer-controlled machine. The self-collimation modes were excited by a grounded waveguide feeding and detected by a scanning monopole. Self-collimation of electromagnetic waves in the 3D photonic crystal was demonstrated by measuring the 3D field distribution, which was shown as a narrow collimated beam inside the 3D photonic crystal but a diverged beam in the absence of the photonic crystal.

Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal

We study the radiation emitted by an oscillating dipole moving with a constant velocity in a photonic crystal, and analyze the effects that arise in the presence of a photonic band gap. It is demonstrated through numerical simulations that the radiation strength may be enhanced or inhibited according to the photonic band structure, and anomalous effects in the sign and magnitude of the Doppler shifts are possible, both outside and inside the gap. We suggest that this effect could be used to identify the physical origin of the backward waves in recent metamaterials.

Photonic bandgap properties of void-based body-centered-cubic photonic crystals in polymer

We report on the fabrication and characterization of void-based body-centered-cubic (bcc) photonic crystals in a solidified transparent polymer by the use of a femtosecond laser-driven microexplosion method. The change in the refractive index in the region surrounding the void dots that form the bcc structures is verified by presenting confocal microscope images, and the bandgap properties are characterized by using a Fourier transform infrared spectrometer. The effect of the angle of incidence on the photonic bandgaps is also studied. We observe multiple stop gaps with a suppression rate of the main gap of 47% for a bcc structure with a lattice constant of 2.77 microm, where the first and second stop gaps are located at 3.7 microm and 2.2 microm, respectively. We also present a theoretical approach to characterize the refractive index of the material for calculating the bandgap spectra, and confirm that the wavelengths of the observed bandgaps are in good correlation with the analytical predictions.

Anomalous reflections at photonic crystal surfaces

We explore the reflection phenomena when a light beam propagating in a photonic crystal is incident upon the interfaces between the crystal and a uniform dielectric. We prove that a generalized wave-vector conservation relation still applies even when the interface is not aligned with special crystal directions. Using this conservation relation, we show that neither the phase velocity nor the group velocity directions of the reflected beam satisfies Snell's law. Rather, the system exhibits remarkable and unusual reflection effects. In particular, total internal reflection is absent except at discrete angular values. The direction of the reflected beam can also be pinned along special crystal directions, independent of the orientation of the interface. And finally, at glancing incidences, strong backward reflections may occur. These effects may be important for creating integrated photonic circuits, and for on-chip image transfer.

Negative refraction at infrared wavelengths in a two-dimensional photonic crystal

We report on the first experimental evidence of negative refraction at telecommunication wavelengths by a two-dimensional photonic crystal field. Samples were fabricated by chemically assisted ion beam etching in the InP-based low-index constrast system. Experiments of beam imaging and light collection show light focusing by the photonic crystal field. Finite-difference time-domain simulations confirm that the observed focusing is due to negative refraction in the photonic crystal area.

Broadband blazing with artificial dielectrics

The efficiency of conventional diffractive optical elements with échelette-type profiles drops rapidly as the illumination wavelength departs from the blaze wavelength. We use high dispersion of artificial materials to synthesize diffractive optical elements that are blazed over a broad spectral range (approximately 1 octave) or for two different wavelengths.

Superprism effect based on phase velocities

The superprism effect has been studied in the past by use of the anomalous group velocities of optical waves in photonic crystals. We suggest the possibility of realizing agile beam steering based on purely phase-velocity effects. We present designs of photonic crystal prisms that might make experimental observation of this effect possible.

Mode matching interface for efficient coupling of light into planar photonic crystals

In order to integrate superdispersive elements based on photonic crystals, such as the superprism, with conventional integrated optics, insertion losses at the interface to the photonic crystal need to be reduced to an acceptable level. We describe a mode matching interface composed of cascaded diffraction gratings that generates the field profile of the photonic crystal Bloch mode from a slab mode. We calculate with three-dimensional finite-difference time-domain computation that by interposing such a multilayered grating between an unpatterned slab and a planar photonic crystal, the insertion efficiency is enhanced from 9% to 84%. Each diffraction grating consists of a row of holes and does not require any additional process steps from those used to fabricate the planar photonic crystal. In order to optimize the efficiency of the mode matching interface, constructive interference conditions are imposed between successive gratings and reflections from individual gratings are suppressed. We fabricate devices in silicon on insulator material and show experimental evidence of the Bloch mode structure and of the mode matching mechanism.

Perfect lenses made with left-handed materials: Alice's mirror?

In a recent paper, Pendry [Phys. Rev. Lett. 86, 3966 (2000)] mentioned the possibility of making perfect lenses by using a slab of left-handed material with relative permeability and permittivity equal to -1, a property first stated by Veselago [Sov. Phys. Usp. 10, 509 (1968)]. Pendry gave a demonstration of the vital effect of the evanescent waves in this process, arguing that these waves are amplified inside the slab. We present first a very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to -1 cannot exist, even for a unique frequency. This demonstration shows that the perfect lens proposed by Pendry can be interpreted as a means to move in real space the virtual perfect image of a point source given by a plane mirror. We show that, owing to evanescent waves, the concept of effective medium for heterogeneous materials is questionable, even when the wavelength of the incident light is much larger than the size of the heterogeneities. The effect of heterogeneities is compared with that of absorption. We conclude that a material able to focus the light more efficiently than the current devices (but not perfectly) could exist.

Optically tunable superprism effect in nonlinear photonic crystals

An analysis of the tunable superprism effect in a two-dimensional nonlinear photonic crystal is presented. We show that, by shifting the photonic bands of the crystal through the Kerr effect induced by a pump beam, one can tune the refraction angle of a transmitted signal beam over tens of degrees. We also demonstrate that the optical power required to tune the refracted angle is dramatically reduced if the frequency of the pump beam is close to a bandgap edge.

Multilayer thin-film structures with high spatial dispersion

We demonstrate how to design thin-film multilayer structures that separate multiple wavelength channels with a single stack by spatial dispersion, thus allowing compact manufacturable wavelength multiplexers and demultiplexers and possibly beam-steering or dispersion-control devices. We discuss four types of structure--periodic one-dimensional photonic crystal superprism structures, double-chirped structures exploiting wavelength-dependent penetration depth, coupled-cavity structures with dispersion that is due to stored energy, and numerically optimized nonperiodic structures utilizing a mixture of the other dispersion effects. We experimentally test the spatial dispersion of a 200-layer periodic structure and a 66-layer nonperiodic structure. Probably because of its greater design freedom, the nonperiodic structure can give both a linear shift with wavelength and a larger usable shift than the thicker periodic structure gives.

Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals

Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing effects for crystals of various shapes are examined. The dependence of the focusing length on the filling factor is also studied. It is observed that both the shape and filling factor play a crucial role in controlling the focusing. Furthermore, the robustness of the focusing against disorders is studied. The results show that the sensitivity of the focusing behavior depends on the strength of positional disorders. The theoretical results compare favorably with the experimental observations, reported by Cervera, et al. [Phys. Rev. Lett. 88, 023902 (2002)].

Extraordinary refraction and dispersion in two-dimensional photonic-crystal slabs

Studies of the refraction and dispersion properties of two-dimensional (2D) photonic-crystal (PC) slab waveguides are reported. The photonic band structure is strongly modified in a slab PC, and only a small number of bands satisfy the guiding conditions imposed by the lack of translation symmetry in the direction perpendicular to the slab; however, it was found that a significant number of the guided modes retain the giant refraction and strong dispersion properties discovered previously in pure 2D PCs. A small change in incident angle resulted in a dramatic change in refraction angle. Furthermore, the dispersion surface exhibited a strong dependence on the frequency, resulting in a superprism effect similar to what has been predicted for pure 2D PCs. In the silicon-based slab PC studied, refraction angles as high as nearly 70 degrees were predicted for incident angles of less than 7 degrees , and frequency components differing by 3% were separated by 15 degrees . The demonstration of giant refraction and superprism phenomena in slab waveguide PCs open the possibility of developing new classes of optical devices that can, for example, be used to develop 2D optical integrated circuits for communications and computing.

Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting

We demonstrate the use of a 30-period dielectric stack structure as a highly dispersive device to spatially separate two beams with a 4-nm wavelength difference by more than their beam width. Unlike previous devices, our structure is simple to fabricate and relatively compact. We discuss possible applications of our device within wavelength-division multiplexing systems.

Anomalous refractive properties of photonic crystals

We describe methods of investigating the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as When does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect and demonstrate the relevance of our approach.