Holographic Photonic Crystals Research Articles

Holography, Fourier Optics, and Beyond Photonic Crystals: Holographic Fabrications for Weyl Points, Bound States in the Continuum, and Exceptional Points

Since the 1990s, applications of holography and Fourier optics have been significantly expanded from the spatial modulation of light propagation to the nanofabrication of superlattices. Holographic mixing of multiple beams is found to be highly compatible with unprecedented engineering of 1D, 2D, and 3D superlattices, particularly at the nanoscales. This is essential for the development of champion photonic crystals working at optical frequencies. However, these extensive efforts toward holographic photonic crystals have declined with the failure to obtain a champion photonic crystal and the rapid rise of other important classes of optical modes in the 2010s such as Weyl points, bound state in continuum (BIC), and exceptional points (EPs). To obtain photonic crystals, the symmetric modulations of the sinusoidally distributed real part of permittivity (Re(ε)), that can be considered as waves of matter from the viewpoint of Fourier optics, are sufficient. However, Weyl points, BIC, and EPs demand more complicated and advanced modulation of such as asymmetrically distributed wave of Re(ε) and the coupled Re(ε) and imaginary ε (Im(ε)). It is, therefore, important to determine whether holographic fabrications can be an efficient solution to Weyl points, BIC, and EPs. In this review, a comprehensive overview of holography, Fourier optical surface/volume gratings, and their implementations for Weyl points, BIC, and EPs is presented.

Spectral characteristics of holographic photonic crystal models

A technique of calculating the spectral characteristics of model holographic photonic crystals (PhCs), including those with spatial structure defects, is presented. This technique is based on the model of a multilayer system of thin dielectric films and the calculated refractive index profile of the PhC structure along selected crystallographic directions. The calculation results of the studied characteristics for various examples of PhC structures are given.

Optimization design of holographic photonic crystal for improved light extraction efficiency of GaN LED

A study on improved light extraction efficiency (LEE) of LEDs with photonic crystals formed by holographic lithography (HL) was present. The propagation and extraction of light in LEDs were simulated using FDTD method for LED structures with top HL PC and embedded HL PC respectively. By optimizing the design parameters of the HL PC, the best value of 88.3% enhancement of LEE were obtained. Result also revealed that the scattering and diffraction of photonic lattices play a more important role in the increased light extraction of HL PC LEDs than photonic band gap effects.

Defect modes in silver-doped photonic crystals made by holography using dichromated gelatin

The defect mode in silver-doped photonic crystals is investigated. 1D and 3D photonic crystals were made by holography using dichromated gelatin mixed with silver nitrate. By controlling the concentration of the silver nitrate, the defect mode was observed in the bandgaps of the holographic photonic crystals. The numerical simulations were made, and the results showed the consistency with the experimental observations.

Label-free specific detection of immunoglobulin G antibody using nanoporous hydrogel photonic crystals

Photonic crystal (PC) based biosensors have been given attention because of their obvious advantages such as sensitivity, simple and low-cost realization. Many kinds of PC based biosensors have been reported, for example, holographic PCs, porous silicon PCs, PC fibers and colloidal crystal film. Among these PC based sensors, we have interested on an inverse opal structure film in order to apply to specific and label-free detection of proteins. This label-free PC bioassay is more attractive than labeling detection because target molecules can be detected in their nature forms, truly portable point-of-care testing is possible, and quantitative measurement of molecule interaction is allowable. In this study, we propose a specific and label-free detection method for immunoglobulin G (IgG) antibody using nanoporous hydrogel photonic crystals with simple process and cost-effective way. The hydrogels used as a backbone of PC in this study, which provide rather homogeneous water surrounding, are ideal substrates for biomolecular screening. Also, three-dimensional hydrogel structures show high capacity for biomolecule immobilization, greater probability of interacting with the target ligand, high S/N, and sensitivity. Finally, the film type biosensor was fabricated using photo-curable hydrogels with colloidal templating methods. The reflective color of the fabricated sample is changed from green to dark orange with the bandgap shift of 50nm, when the IgG concentration was 10mg/ml. Furthermore, our device showed different bandgap shifts according to the level of antibody concentration, so that it can be used to measure quantitative molecular interactions. This designed label free detection system has great potential for next generation of bioassay platform for diagnosis of pathogens such as virus, bacteria, and fungi.

Improvement of GaN light-emitting diodes with surface-treated Al-doped ZnO transparent Ohmic contacts by holographic photonic crystal

This letter presents a holographic photonic crystal (H-PhC) Al-doped ZnO (AZO) transparent Ohmic contact layer on p-GaN to increase the light output of GaN-based LEDs without destroying the p-GaN. The operating voltage of the PhC LEDs at 20 mA was almost the same as that of the typical planar AZO LEDs. While the resultant PhC LED devices exhibited significant improvements in light extraction, up to 1.22 times that of planar AZO LEDs without PhC integration. Temperature dependence of the integrated photoluminescence intensity indicates that this improvement can be attributed to the increased extraction efficiency due to the surface modification. These results demonstrate that the surface-treated AZO layer by H-PhCs is suitable for fabricating high-brightness GaN-based LEDs.

Defect mode of one-dimensional holographic photonic crystals modulated by the intensity ratio of two constructive beams

The effect of air impurity layer on the reflection spectrum of one-dimensional holographic photonic crystals was investigated in two forms. One form is the band-edge oscillation phenomenon when the air impurity layer is near the surface of the structure; the other form is the defect mode appearing in the band gap when the air impurity layer is near the center of the structure. For the defect mode, its central wavelength will nonlinearly change with some repeatability with the defect size, not as the result of the step-index photonic crystal. Moreover, the depth of the defect mode in the band gap can be modulated by the intensity ratio of the two construction beams. And the reflectance at the central wavelength of the defect mode can be almost zero with appropriate optical intensity ratio. The corresponding experimental results were also demonstrated.

Band-edge oscillations of the diffraction spectrum of a volume hologram investigated by the air-doping model

Oscillation exists at the high-frequency band edge in the diffraction spectrum of a volume hologram. An air-doping model of a volume hologram is proposed to explain the phenomenon. The numerical results show good agreement with the experimental results, which cannot be explained by the conventional models. The results show that the position of air impurity is the key factor to control the number and width of the oscillations. The present work gives a new approach to generate and control the defect mode in a holographic photonic crystal.

Transmission Properties of an Air Waveguide with Left-Handed Holographic Photonic Crystal Cladding

An air waveguide of left-handed photonic crystal (PhC) formed by holographic lithography is proposed. The symmetry mismatch between the incident wave and the Bloch modes of the holographic PhC is used to guide light efficiently. By properly designing the waveguide, backscattering loss can be significantly reduced. Due to the unique advantages of holographic photonic crystals, the serious problems of material loss and fabrication difficulty in left-handed material waveguides are also avoided. Furthermore it is shown that high transmission efficiency is easily achieved in the frequency region with effective refraction index near zero. These features may extend the possible guiding ability of holographic photonic crystal waveguide and its promising potential in the application of photonic integrated circuits.

Experimental study and modeling of holographic photonic crystals with defects of the spatial and band-gap structures

Results of experimental studies and modeling of holographic photonic crystals (PCs) with defects of their spatial and band-gap structures and also of studying quasi-crystals are presented. Thicklayer photopolymer materials with a hybrid matrix formed on the basis of the sol-gel technology are used for PC production. A method of obtaining delocalized defects is proposed and implemented. A code is written for computer modeling of the spatial PC structure, which offers a clear idea about the appearance of the synthesized crystal and the expected spectral characteristics.

Doping Defects in Two-Dimensional Holographic Photonic Crystals Using a Continuous-Wave Visible Laser

It is demonstrated that defects of any shape or size can be doped in holographic photonic crystals using a cw visible laser and spherical/cylindrical lens. Defects with different sizes at any depth in the material can be obtained by controlling the position of the focal point of the lens and exposure value. We facilitate the implementation of sub-wavelength arbitrary point or line defects in large-size 2D holographic photonic crystals.

Simulation of the spatial pattern and band-gap structure of holographic photonic crystals

Simulation software of the spatial pattern and band-gap structure of the holographic photonic crystals is developed for the research—education purposes. Friendly GUI and training technique elaborated. Examples of the 1D–3D model structures of photonic crystals and their transmission spectrums are given.

The effect of nonlinear exposure on bandgap of three-dimensional holographic photonic crystal

The effect of nonlinear exposure on the characteristics of photonic crystal fabricated by holography is investigated theoretically and experimentally. A kind of materials with low refractive index （n=152） is used to fabricate diamond structure. By controlling the exposure in strong nonlinear range, the property of photonic bandgap is improved. Also，some proposals are made to achieve complete band gaps by materials with low refractive index.

Improvement of transmission properties through two-bend resonance by holographic design for a two-dimemsional photonic crystal waveguide

We have investigated the transmission properties of a photonic crystal waveguide (PCW) formed by holographic lithography for the first time with a two-dimensional (2D) triangular holographic photonic crystal (PhC) including a line defect with two 60 masculine bends. Calculations have shown that for this PCW high transmission (>90%) through sharp corners can be obtained in a wide frequency range from 0.298 to 0.310 (omega alpha/2pi c) with the relative band gap of 4% when the dielectric contrast is 7.6:1. As far as we know, this result should be the widest frequency range with high transmission (>90%) in the waveguide of similar 2D triangular PhCs ever reported. We have also found that the specific holographic designs of PhC have strong influence on the resonance between the two waveguide bends, and thus this fact can be used as an effective means to improve the transmission property of 2D holographic PCW. In addition to the simplicity and low cost of holographic fabrication of PhCs, these features may reveal the possibly better guiding ability of holographic PCW than the conventional waveguide and the promising potential of the former in the application of photonic integrated circuits.

Fabrication of Two-Dimensional Photonic Crystals withTriangular Rods by Single-Exposure Holographic Lithography

We demonstrate a single-exposure holographic fabrication oftwo-dimensional photonic crystal with round-cornered triangular`atoms' arranged in a triangular lattice. Simulation results show thatdouble absolute photonic band gaps exist in this structure. Ourexperimental results show that holographic lithography can be usedto fabricate photonic crystals not only with various lattice structuresbut also with various kinds of structures of the atoms, to obtainabsolute band gaps or a particular band gap structure. Furthermore, thesingle-exposure holographic method not only makes the fabrication processsimple and convenient but also makes the structures of the atoms moreperfect.

Holographic three-dimensional polymeric photonic crystals operating in the 1550nm window

A polygonal prism based holographic fabrication method has been demonstrated for a three-dimensional face-centered-cubic-type submicron polymer photonic crystal using both positive and negative photoresists. Special fabrication treatments have been introduced to ensure the survivability of the fabricated large area (∼1cm2) nanostructures. Scanning electron microscopy and diffraction results proved the good uniformity of the fabricated structures. With the proper design of the refraction prism the authors have achieved the required band gap for S+C bands (1460–1565nm) in the [111] direction. The transmission and reflection spectra obtained by Fourier transform infrared spectroscopy are in good agreement with simulated band structure.

Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element

An electrically tunable two-dimensional holographic photonic crystal was fabricated in polymer-dispersed liquid crystal using a single diffraction element, which was a specially designed photomask consisting of three diffraction gratings, which had a period of 4μm, oriented 120° relative to one another. With the photomask subjected to a collimated Ar+ laser beam operating at 514.5nm, a two-dimensional spatial light intensity pattern was created by interference of the three first order diffracted beams produced by the mask. The spatial light intensity pattern was then recorded inside a cell filled with the liquid crystal/prepolymer mixture to create a photonic crystal. The photonic crystal structures were observed under an optical microscope. It showed triangular structures with a lattice constant of about 2.50μm. The diffraction properties and electro-optic tunability were also presented.

Design and fabrication of two-dimensional holographic photonic quasi crystals with high-order symmetries

From group theory, we have deduced the minimum number of laser beams to create corresponding two-dimensional photonic quasilattices with high-order symmetries. One case is that a quasi-periodicity with eightfold, tenfold, or twelvefold symmetry can be formed by only five linearly polarized beams, which can reduce fabrication complexity and considerably improve feasibility. Accordingly, we have fabricated large-area eightfold and twelvefold photonic quasi crystals by use of a minimum beam single-exposure holographic lithography technique. The high-order symmetries of the fabricated microstructures are confirmed by scanning electron microscopy images and diffraction patterns.

Phase-sensitive wave-packet dynamics caused by a breakdown of the rotating-wave approximation

The present thesis is devoted to theoretical studies of pulse propagation of light through linear and nonlinear media, and of light-induced nuclear dynamics. The first part of the thesis addresses propagation of light pulses in linear periodical media - photonic crystals. The main accent was put on studies of the angular properties of two qualitatively different types of photonic crystals: holographic photonic crystals, and impurity band based photonic crystals. The anisotropy of band structure, group velocity and pulse delay with respect to the light polarization are analyzed. In the second part of the thesis a strict theory of nonlinear propagation of a few strong interacting light beams is presented. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material. This technique is applied to studies of dynamics of cavityless lasing generated by ultra-fast multi-photon excitation. It is shown that interaction of co- and counter-propagating pulses of amplified spontaneous emission (ASE) affects the dynamics and efficiency of nonlinear conversion. Our dynamical theory allows to explain the asymmetric spectral properties of the forward and backward ASE pulses, which were observed in recent experiment with different dye molecules. It is shown that the ASE spectral profile changes drastically when the pump intensity approaches the threshold level. The effect of the temporal self-pulsation of ASE is studied in detail. The third part of the thesis is devoted to light-induced nuclear dynamics. Time- and frequency-resolved X-ray spectroscopy of molecules driven by strong and coherent infrared (IR) pulses shows that the phase of the IR field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. Such a dependence arises due to the interference of one (X-ray) and two-photon (X-ray + IR) excitation channels. The phase of the light influences the dynamics also when the Rabi frequency approaches the vibrational frequency, breaking down the rotating-wave approximation. The probe X-ray spectra are also sensitive to the delay time, the duration, and the shape of the pulses. The evolution of the nuclear wave packets in the dissociative core-excited state affects the dynamics of resonant Auger scattering from fixed-in-space molecules. One of the important dynamical effects is the atomic-like resonance which experiences electronic Doppler shift. We predict that the scattering of the Auger electrons by nearby atoms leads to new Doppler shifted resonances. These extra resonances show sharp maxima in the bond directions, which makes them very promising as probes for local molecular structure using energy and angular resolved electron-ion coincidence techniques. Our theory provides prediction of several new effects, but also results that are in good agreement with the available experimental data.

One-to-many laser fanout generated by single large-size two-dimensional holographic photonic crystal

The phenomenon of one-to-many laser fanout in large-size two-dimensional (2D) holographic photonic crystals (H-PhCs) is presented. Theoretical analysis demonstrates that the phenomenon is induced by multiple substrate waveguiding effect of 2D H-PhCs, and the orientations of the waveguided beams depend on the lattice structures of 2D H-PhCs. The fanout angle and separations between output spots are determined by λ∕d, light incident angle and thickness of glass substrate, therefore can be controlled via fabricating special lattice structures. The phenomenon has the potential to enable the application of 2D PhCs as interconnection devices in optical networks.