Optical third-harmonic generation in one-dimensional photonic crystals and microcavities

The formalism of nonlinear transfer matrices is used to develop a phenomenological model of a cubic nonlinear-optical response of one-dimensional photonic crystals and microcavities. It is shown that third-harmonic generation can be resonantly enhanced by frequency-angular tuning of the fundamental wave to the photonic band-gap edges and the microcavity mode. The positions and amplitudes of third-harmonic resonances at the edges of a photonic band gap strongly depend on the value and sign of the dispersion of refractive indexes of the layers that constitute the photonic crystal. Model calculations elucidate the role played by phase matching and spatial localization of the fundamental and third-harmonic fields inside a photonic crystal as the main mechanisms of enhancement of third-harmonic generation. The experimental spectrum of third-harmonic intensity of a porous silicon microcavity agrees with the calculated results.     

Giant third-harmonic in porous silicon photonic crystals and microcavities

A giant enhancement (no less than by 10³) of the optical third-harmonic generation in one-dimensional porous silicon microcavities and photonic crystals was observed experimentally. The enhancement is due to the resonant enhancement of the fundamental field in the cavity mode and the fulfillment of the phase matching condition at the photonic band gap edges of the photonic crystal and in the vicinity of the microcavity mode.     

Resonant three-dimensional photonic crystals

The theory of the exciton-polariton band structure of a resonant three-dimensional photonic crystal is developed for an arbitrary dielectric contrast and an arbitrary effective mass of an exciton excited in a composite material. The calculation is performed for a periodic array of semiconductor balls embedded in a dielectric matrix. The position of the lower polariton dispersion branches is shown to depend monotonically on the exciton effective mass and to be governed by the interaction of light with the first several states of a mechanical exciton quantum-confined within each ball. The effect of excitonic states on the band gap of a photonic crystal in the [001] direction is considered analytically in terms of a two-wave approximation.     

Dramatic enhancement of high-order harmonic generation

We present a dramatic enhancement [Phys. Rev. Lett. 91, 043002 (2003)] of high-order harmonic generation by simultaneous irradiation of booster harmonics. A key feature of our experiment is the use of mixed gases (Xe and He) with different ionization energies. The harmonics from Xe atoms act as a booster to increase the harmonic yield from He by a factor of 4 x 10(3). The dominance of the dramatic enhancement effect is supported by simulation with the time-dependent Schr?dinger equation as well as the observed spatial characteristic of the generated harmonics and dependence on medium conditions.     

Broadband third-harmonic generation in two-dimensional short-range ordered nonlinear photonic structure

We study parametric frequency conversion in two-dimensional nonlinear photonic crystal with short-range ordered ferroelectric domains. We demonstrate that the short-range order enables broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We obtain conversion efficiencies that are much higher than those achieved from a randomized medium, owing to the unique distribution of reciprocal lattice vectors in the short-range ordered structure.     

Waveguide circuits in three-dimensional photonic crystals

Waveguide circuits in three-dimensional photonic crystals with complete photonic band gaps are simulated with finite difference time domain (FDTD) simulations, and compared with measurements on microwave scale photonic crystals. The transmission through waveguide bends critically depends on the photonic crystal architecture in the bend region. We have found experimentally and theoretically, a new waveguide bend configuration consisting of overlapping rods in the bend region, that performs better than the simple waveguide bend of terminated rods, especially in the higher frequency portion of the band. Efficient beam splitters with this junction geometry are also simulated.     

Engineering disorder in three-dimensional photonic crystals

We demonstrate the effect of introducing controlled disorder in self-assembled three-dimensional photonic crystals. Disorders are induced through controlling the self-assembling process using an electrolyte of specific concentrations. Structural characterization reveals increase in disorder with increase in concentrations of the electrolyte. Reflectivity and transmittance spectra are measured to probe the photonic stop gap at different levels of controlled disorder. With increase in disorder the stop gap is vanished and that results in a fully random photonic nanostructure where the diffuse scattered intensity reaches up to 100%. The estimated scattering mean free path shows significant reduction for photonic crystals with 100% controlled disorder as compared to those with 0% controlled disorder. Our random photonic nanostructure is unique in which all scatters have the same size and shape. Therefore, we observe the resonant characteristics in the multiple scattering of light.     

Layer-by-layer three-dimensional chiral photonic crystals

We fabricate and characterize polymeric three-dimensional layer-by-layer chiral photonic crystals. The obtained circular dichroism from polarization stop bands is comparable with that of recently demonstrated circular-spiral photonic crystals. Moreover, telecommunication wavelengths are easily accessible with the layer-by-layer approach; even visible wavelengths are in reach.     

Ultrafast optical switching in three-dimensional photonic crystals

We present the first experimental investigation of ultrafast optical switching in a three-dimensional photonic crystal made of a Si-opal composite. Ultrafast (30 fs) changes in reflectivity around the photonic stop band up to 1% were measured for moderate pump power (70 microJ/cm(2)). Short-lived photoexcited carriers in silicon induce changes in the dielectric constant of Si and diminish the constructive interference inside the photonic crystal. The results are analyzed within a model based on a two-band mixing formalism.     

Conditions for self-collimation in three-dimensional photonic crystals

We introduce the theoretical criterion for achieving three-dimensional self-collimation of light in a photonic crystal. Based on this criterion, we numerically demonstrate a body-center-cubic structure that supports wide-angle self-collimation and is directly compatible with the recently developed holographic fabrication technique. We further show that both bends and beam splitters can be introduced into this structure by the use of interfaces.     

Stimulated Raman scattering in three-dimensional photonic crystals

The results of experimental studies of stimulated Raman scattering of light (SRS) excited in three-dimensional photonic crystals — synthetic opal matrices infiltrated with Raman active media are presented. It is shown that the SRS threshold in such structures decreases with respect to the SRS threshold in Raman active bulk materials. The influence of the photonic-band structure of the active materials used on the SRS properties is estimated.     

Planar defects in three-dimensional chalcogenide glass photonic crystals

Here we report on the direct laser writing fabrication of Fabry-Perot-type planar microcavities in a three-dimensional (3D) photonic crystal (PhC) embedded within a high-refractive nonlinear chalcogenide glass (ChG) film. The fabricated planar microcavities in a nonlinear ChG 3D PhC facilitate the observation of resonant modes inside the stop gap. The experimental results show that the length of the planar cavity can be well controlled by the fabrication power and thus be used to tune the defect modes. The tunability of the observed defect modes is confirmed by the theoretical prediction.     

Imaging single quantum dots in three-dimensional photonic crystals

Performing fluorescence wide-field microscopy we have imaged single semiconductor quantum dots deep inside a 3-dimensional photonic crystal prepared from colloidal polymer beads. Exploring the emission diffraction patterns in defocused images of quantum dots we demonstrate that the direction-dependent photonic stop band imprints an anisotropy to the angular emission of a single quantum dot. Hence a single, quasi-point-like emitter is manipulated to radiate its photons only to certain well-defined directions by means of the anisotropic light propagation in photonic crystals. The experiments thus provide new routes to evaluate local, frequency selective optical properties in 3-dimensional photonic crystals employing single emitters.     

Enhanced photoluminescence from three-dimensional ZnO photonic crystals

We have fabricated optically active ZnO inverse opals by infiltrating polystyrene (PS) opal templates using an electrodeposition process. Compared with bare ZnO films also prepared by electrodeposition, the three-dimensional (3D) ordered ZnO structure exhibits markedly enhanced photoluminescence. The effect of photonic band gap on PL spectra is also clearly observed from the ZnO inverse opal structure.     

Fabrication of three-dimensional photonic crystals with tunable photonic properties by biotemplating

Photonic crystals with tunable D-surface structures for possible high-temperature gas- and temperature-sensing applications were prepared by a biotemplating method. This included infiltrating colored scales of the beetle Entimus imperialis with an organopolysiloxane mixture followed by simultaneous combustion of the template and calcination of the cured organopolysiloxane. A high-yield inorganic silica-based replica of the original structure was obtained, which is capable of withstanding temperatures up to 600 °C. Light- and scanning electron microscopy combined with focused ion beam milling showed a precise replication of the whole scales and their internal D-surface structure. Fourier-transform infrared spectroscopy and X-ray diffraction analysis confirmed the complete curing of the organopolysiloxanes and their transformation into amorphous silica during calcination. The dielectric constant of the manufactured materials determined by Abbé refractometry was ? = 2.3180 and used to perform band structure calculations utilizing the plane wave expansion method. By changing the chain length and degree of crosslinking of the organopolysiloxane precursor mixture, the lattice parameters and filling factors, and therefore the photonic properties of the replicas, could be tuned.     

Fabrication and annealing analysis of three-dimensional photonic crystals

Three-dimensional face-centered-cubic (fcc) photonic crystals (PhCs) are fabricated on quartz substrate using vertical deposition technique, and followed by annealing in a temperature range of 200-700 °C. The monodispersed SiO₂ microspheres with a diameter of 220 nm in colloidal solution are synthesized using tetraethylorthosilicate as a precursor material. The as grown opal structure exhibits a strong photonic band gap (PBG) around 450 nm in the transmission spectrum. We find that the position of PBG peak in the spectrum is relevant to incident angle of light. Moreover, it is very sensitive to annealing temperature. It quickly shifts to short wavelength direction with annealing temperature increasing. The effect results from the decrease in refraction index due to the moisture evaporation in silica microspheres.     

Enhanced second-harmonic generation from planar photonic crystals

Strongly enhanced second-harmonic generation is observed from a two-dimensional square lattice GaAs/AlGaAs photonic crystal waveguide when the fundamental beam, the second-harmonic beam, or both beams resonantly couple to a leaky eigenmode. P-polarized second-harmonic spectra are obtained for s-polarized, 150-fs pump pulses that are tuned from 5000 to 5600 cm(-1) and directed along the gamma-chi direction of the crystal for various angles of incidence. Compared with off-resonant conditions, enhancements of >1200x in the second-harmonic conversion are observed for resonant coupling of both the fundamental and the second-harmonic fields to leaky eigenmnodes. The angular and spectral positions of the peaks are in good agreement with simulations.     

Preconditioning bandgap eigenvalue problems in three-dimensional photonic crystals simulations

To explore band structures of three-dimensional photonic crystals numerically, we need to solve the eigenvalue problems derived from the governing Maxwell equations. The solutions of these eigenvalue problems cannot be computed effectively unless a suitable combination of eigenvalue solver and preconditioner is chosen. Taking eigenvalue problems due to Yee’s scheme as examples, we propose using Krylov–Schur method and Jacobi–Davidson method to solve the resulting eigenvalue problems. For preconditioning, we derive several novel preconditioning schemes based on various preconditioners, including a preconditioner that can be solved by Fast Fourier Transform efficiently. We then conduct intensive numerical experiments for various combinations of eigenvalue solvers and preconditioning schemes. We find that the Krylov–Schur method associated with the Fast Fourier Transform based preconditioner is very efficient. It remarkably outperforms all other eigenvalue solvers with common preconditioners like Jacobi, Symmetric Successive Over Relaxation, and incomplete factorizations. This promising solver can benefit applications like photonic crystal structure optimization.     

Introducing CdS into two- and three-dimensional photonic crystals

SiO₂/air three-dimensional (3D) periodic structures were fabricated by removing Si layers partially from Si/SiO₂ 3D photonic crystals (PhCs) formed by using autocloning. CdS/SiO₂ 3D periodic structures were formed by introducing CdS into the SiO₂/air structures by the TEA method and photoluminescence (PL) was observed from the introduced CdS. TiO₂/air/CdS two-dimensional (2D) PhCs were also fabricated by introducing CdS into the voids of TiO₂/air 2D periodic structures, in which SiO₂ layers were partially etched out from TiO₂/SiO₂ 2D PhCs fabricated by using autocloning. PL radiating normal to the surface was measured and large polarization dependence was observed.