One-dimensional Photonic Band Gap Materials Research Articles

Variational Quantum Simulators Based on Waveguide QED.

Waveguide QED simulators are analog quantum simulators made by quantum emitters interacting with one-dimensional photonic band gap materials. One of their remarkable features is that they can be used to engineer tunable-range emitter interactions. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms for certain problems. In particular, we illustrate their power in creating wave function Ansätze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) with fewer gates and optimization parameters than other variational Ansätze based on nearest-neighbor or infinite-range entangling gates. Finally, we study the potential advantages of these waveguide Ansätze in the presence of noise. Overall, these results evidence the potential of using the interaction range as a variational parameter and place waveguide QED simulators as a promising platform for variational quantum algorithms.

Enhanced sensing in mixed porous–solid photonic stacks

A mix-and-match sol–gel deposition method allows fabrication of one-dimensional photonic bandgap materials with strategically placed porous layers.

A Computational Investigation of Third-harmonic Generation in One-dimensional Photonic Band-gap Materials with Multiple-Scale Method

In this paper, we present a numerical investigation of third-harmonic (TH) generation in a one-dimensional photonic band-gap material that is doped with a nonlinear χ(3)medium. For modeling harmonic generation phenomena, a multiple-scale method has been introduced to perturb the nonlinear wave equation by a small factor with appropriate scale. So, we obtain coupled-mode equations (CMEs) with different from the conventional CMEs for this phenomenon. Then, we have solved these CMEs numerically to obtain the output amplitudes of TH waves in both forward- and backward-directions, and the conversion efficiencies. Finally, the solutions show that this photonic band-gap material can generate the TH waves whose amplitudes and the conversion efficiencies may be larger than the TH wave and the efficiency produced by an equivalent length of a phase-matched, bulk medium.

Rapid Sol–Gel Fabrication of High-Quality Thin-Film Stacks on Planar and Curved Substrates

A versatile and rapid sol–gel technique for the fabrication of high quality one-dimensional photonic bandgap materials was developed. Silica/titania multilayer materials are fabricated by a sol–gel chemistry route combined with dip-coating onto planar or curved substrates. A shock-cooling step immediately following the thin-film heat-treatment process is introduced. This step was found crucial in the prevention of film crack formation—especially in silica/titania alternating stack materials with a high number of layers. The versatility of this sol–gel method is demonstrated by the fabrication of various Bragg stack-type materials with fine-tuned optical properties by tailoring the number and sequence of alternating layers, the film thickness and the effective refractive index of the deposited thin films. Measured optical properties show good agreement with theoretical simulations, confirming the high quality of these sol–gel fabricated optical materials.

Study on Z-Scan Characteristics for Light–Tunneling Heterostructures Composed Of One-Dimensional Photonic Band Gap Material and Metallic Film

The transmitted and reflected Z-scan characteristics for light-tunneling heterostructures composed of one-dimensional photonic bandgap material and metallic film are theoretically investigated. An apparent Z-scan signal will appear around the light-tunneling even if the incident peak intensity is very low. Both of the transmitted and reflected Z-scan signals from left incidence are much larger than those from right incidence, demonstrating the nonreciprocal for two incident directions. The variation of the reflected Z-scan curve shape is opposite to that of transmitted Z-scan curve shape as light wavelength increases. Moreover, the reflected Z-scan signals from left incidence will show a very sharp peak around the light-tunneling.

Optical limiting in one-dimensional photonic bandgap material with a bulk nonlineardefect

A composite optical limiting configuration is proposed, which consists of a one-dimensionalphotonic bandgap structure and a thick bulk material. Using the backward split-stepscheme, we studied the transmission and optical limiting properties of the compositestructure. Results show that the performance of the optical limiting of the compositestructure is better than that of the single bulk material and the optical limiting ability isimproved by almost two orders of magnitude. The effects of the number of periods and thethickness of the bulk material on the nonlinear transmittance of this structure are studied.The contribution of nonlinear refraction and absorption to the composite optical limiting isalso analyzed.

Tunable Chiral Photonic Defect Modes in Locally Polymerized Cholesteric Liquid Crystals

A structural defect is introduced in the helical periodic lattice of a cholesteric liquid crystal, a well-known pseudo one-dimensional photonic band-gap material. The method utilizes an ultra-fast pulse laser to induce two-photon polymerization in a photo-polymerizable cholesteric liquid crystal material to directly fabricate regions with different pitch lengths. Single or multiple defect modes were exhibited in the selective reflection band of the cholesteric liquid crystal, depending on the fabrication conditions of the defect structure. Optically pumped laser-action experiments showed that lasing from the single defect-mode had the smallest threshold compared to other lasing modes.

Geometric phases for a three-level Λ -type system in one-dimensional photonic band gaps

The geometric phase of a three-level atom interacting with single-mode in the presence of the one-dimensional photonic band gap material is studied. We consider dipole emitters situated in the thin slab region between two semi-infinite one-dimensionally periodic photonic crystals, a situation reminiscent of planar cavity laser structures. It shows that the Pancharatnam phase depends crucially on the presence of the photonic band gap. This feature is attributed to the fact that in the photonic band gap region electromagnetic modes are not allowed to propagate into the dielectric slab and hence no interaction can take place in this region. The outcomes are illustrated with numerical simulations applied to GaAs.

Enhancement of omnidirectional total-reflection wavelength range by using one-dimensional ternary photonic bandgap material

Here we demonstrate by theoretical analysis a novel way to enhance the omnidirectional total-reflection wavelength range in one-dimensional photonic bandgap material by using a ternary periodic structure (i.e., three material layers constituting a period of the lattice). The omnidirectional total reflection range using a binary (BaF2/PbS) periodic structure was enhanced by 108 nm when the structure was modified by sandwiching a thin layer of ZrO2 between every two layers, constituting a period of the lattice. A shift of the omnidirectional range toward higher wavelengths was also observed. When the sandwiched layer was CeF3, the enhancement in the range was 120 nm. As the sandwiched layer is very thin, there will not be any significant increase in the size of the reflector, contrary to the case of heterostructured photonic crystals (PCs) where two or more PCs are clubbed together to achieve enhancement.

Dynamic pattern of finite-pulsed beams inside one-dimensional photonic band gap materials

The dynamics of two-dimensional electromagnetic (EM) pulses through one-dimensional photonic crystals (1DPC) has been theoretically studied. Employing the time expectation integral over the Poynting vector as the arrival time [Phys. Rev. Lett. 84, 2370, (2000)], we show that the superluminal tunneling process of EM pulses is the propagation of the net forward-going Poynting vector through the 1DPC, and the Hartman effect is due to the saturation effect of the arrival time (smaller and smaller time accumulated) of the net forward energy flow caused by the interference effect of the forward and the backward field (from the interfaces of each layer) happened in the region before the 1DPC and in the front part of the 1DPC.

Coherent emission in one-dimensional photonic band gap materials

We study the properties of super-radiant coherent emission from a two-level system of atoms embedded in a one-dimensional photonic band gap (1D-PBG) structure. A reduced system of equations is derived that enables us to explore the role of the 1D-PBG band edge in the emission characteristics of coherent pulses. The effect of the emitters' spatial location in the PBG structures is also studied in a finite 1D-PBG, where the super-radiant emission characteristics are also presented.

Analytic, graphical, and geometric solutions for the band edges of one-dimensional photonic band gap materials

The conditions for the band gap edges of one-dimensional photonic band gap (PBG) materials are presented in forms that lead to alternate analytic, graphical, and geometric solutions and interpretations. Heretofore unavailable analytical conditions for the band edges of quarter wave∕half wave and eighth wave∕half wave PBG structures are derived. The graphical solution has the form of an intersection of an invariant (material dependent) figure with a straight (structure dependent) line, a convenient separation not possible with the Kronig-Penney (KP) equation. The geometric solution is represented by the sides and angles of simple triangles. The present formalism should help in visualizing the PBG band gap formation beyond the view offered by the KP equation.

One-dimensional photonic crystals in reflection geometry for optical applications

We investigate some properties of one-dimensional photonic band-gap materials that have the possibility of total internal reflection at one or more interfaces. The proposed structures have application for electro-optic modulation, sensing, and other optical devices. A specific example for electro-optic modulation is presented. Certain advantages of this arrangement may make it a desired geometry for specific applications like sensing.

Light propagation through birefringent, nonlinear media with deep gratings

We present a theory that includes birefringence in the description of one-dimensional photonic band-gap materials with a Kerr nonlinearity. The Bloch functions in the absence of nonlinearity completely characterize the linear problem, for deep as well as shallow gratings, and the method of multiple scales is used to include the effects of nonlinearity and finite optical pulse length. We derive two sets of equations appropriate in different frequency regimes, a set of coupled mode equations and a set of coupled nonlinear Schrodinger equations; we investigate the connections between these equations and where their regimes of validity overlap. Finally, we use our results to describe energy exchange between polarization modes in a birefringent medium.

Enhanced third-order nonlinear optical response of photonic bandgap materials

Abstract We calculate the nonlinear phase shift acquired by a laser beam in propagating through a one-dimensional photonic bandgap material, that is a material in which the linear refractive index is periodically modulated along the direction of propagation. We find that the nonlinear phase shift shows resonances for laser frequencies close to the edge of the stop band of the photonic bandgap structure. Enhancements of the nonlinear phase shift compared with that of a homogeneous nonlinear optical material by a factor of approximately five are predicted under realistic laboratory conditions. We find that similar enhancements of the two-photon absorption rate can occur for a material with an imaginary nonlinear susceptibility. We also treat the case of a photonic bandgap material containing a ′defect,' that is a central region somewhat too thick to conform to the periodicity of the system, and find that the nonlinear phase shift can be enhanced by a factor of approximately thirty.

Enhanced third-order nonlinear optical response of photonic bandgap materials

We calculate the nonlinear phase shift acquired by a laser beam in propagating through a one-dimensional photonic bandgap material, that is a material in which the linear refractive index is periodically modulated along the direction of propagation. We find that the nonlinear phase shift shows resonances for laser frequencies close to the edge of the stop band of the photonic bandgap structure. Enhancements of the nonlinear phase shift compared with that of a homogeneous nonlinear optical material by a factor of approximately five are predicted under realistic laboratory conditions. We find that similar enhancements of the two-photon absorption rate can occur for a material with an imaginary nonlinear susceptibility. We also treat the case of a photonic bandgap material containing a ′defect,' that is a central region somewhat too thick to conform to the periodicity of the system, and find that the nonlinear phase shift can be enhanced by a factor of approximately thirty.

The photonic band edge optical diode

Using numerical methods, we study pulse propagation near the band edge of a one-dimensional photonic band gap material with a spatial gradiation in the linear refractive index, together with a nonlinear medium response. We find that such a structure can result in unidirectional pulse propagation. That is, the field will be transmitted for, say, a left-to-right direction of propagation, while for right-to-left nearly complete reflection occurs. This behavior constitutes the operational mechanism for a passive optical diode.