Properties of defect modes in one-dimensional photonic crystals containing two nonlinear defects

Transmission properties of one-dimensional photonic crystal with two nonlinear defects were investigated based on the nonlinear transfer matrix method. From the inspection of the optical bistabilities around different defect modes, it was found that the threshold of bistability for the bonding mode is always lower than that for the anti-bonding mode. When intensity of the incident wave increases bistability could happen at any wavelength larger than the resonance wavelength of the linear anti-bonding mode in the gap. The threshold of bistability increases initially with the wavelength, then decreases sharply in reaching the resonance wavelength of the linear bonding mode. The coupling behavior of the two defects was also discussed, and it was found that the threshold of bistability increases with the distance between the two defects. A flat spectrum similar to that formed in the photonic crystal molecules was obtained under certain incident intensity.     

Properties of defect modes in one-dimensional symmetric defective photonic crystals

We theoretically investigate the properties of defect modes in one-dimensional symmetric defective photonic crystals. We consider three defective photonic crystal structures, air/[(AB)^NsA^α(BA)^Ns]^Np/air, air/[(AB)^NsAB^βA(BA)^Ns]^Np/air, and air/{[(AB)^NsAB^βA(BA)^Ns]B^γ}^Np−1[(AB)^NsAB^βA(BA)^Ns]/air, where A and B are respectively taken to be the high- and low-index dielectric materials. The first has a defect layer of A^α, the second has a composite defect, AB^βA, and the third has a interleaving defect B^γ. The effect of thickness on the defect mode is studied by varying the parameters α, β, and γ, respectively, for the above model structures. It is found that the positions and the number of defect modes can be significantly changed due to the change in the defect thickness. In addition, by increasing the repeated number N_p, we can have multiple defect modes, leading to a possible design of tunable multichannel filter.     

Near-infrared tunable narrow filter properties in a 1D photonic crystal containing semiconductor metamaterial photonic quantum-well defect

The near-infrared (NIR) narrow filter properties in the transmission spectra of a one-dimensional photonic crystal doped with semiconductor metamaterial photonic quantum-well defect (PQW) were theoretically studied. The behavior of the defect mode as a function of the stack number of the PQW defect structure, the filling factor of semiconductor metamaterial layer, the polarization and the angle of incidence were investigated for Al-doped ZnO (AZO) and ZnO as the semiconductor metamaterial layer. It is found that the frequency of the defect mode can be tuned by variation of the period of the defect structure, polarization, incidence angle, and the filling factor of the semiconductor metamaterial layer. It is also shown that the number of the defect mode is independent of the period of the PQW defect structure and is in sharp contrast with the case where a common dielectric or metamaterial defect are used. The results also show that for both polarizations the defect mode is red-shifted as the number of the defect period and filling factor increase. An opposite trend is observed as the angle of incidence increases. The proposed structure could provide useful information for designing new types of tuneable narrowband filters at NIR region.     

Controlled optical properties of a five-level atom embedded in photonic crystals with defect modes

The optical spectra of a five-level atom embedded in a photonic crystal are studied by considering the double-band photonic band gap reservoir with defect modes in the band gap. It is shown that some interesting phenomena such as absorption, transparency, normal or anomalous dispersion, and large amplification of a weak probe field can be observed by modulating system parameters.     

Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs

A theoretical model of disorder for the etched holes or pillars in a generic two-dimensional photonic crystal slab is presented. This model is employed to calculate the effects of size disorder on propagation losses in linear photonic crystal waveguides as well as on quality (Q)-factors in photonic crystal nano-cavities. The main results obtained by the present theory and shown in this work are: (a) large single-mode bandwidth and low-loss (<0.1 dB/mm) propagation of light is predicted for increased-width membrane-type photonic crystal waveguides, (b) pillar-based lattices show reduced sensitivity to size fluctuations than hole-based ones, (c) the effects of disorder on cavity Q-factors are quantitatively evaluated. An extension of the model is also introduced in order to take into account the side-wall micro-roughness of the perfectly vertical holes, and preliminary results of this more general approach are discussed.     

Analytical investigation of one-dimensional photonic crystals with a dielectric-superconducting pair defect

We have studied the dielectric-superconducting pair defect embedded into one-dimensional photonic crystals by an analytical method based on the Kronig-Penny model. The superconducting defect has been considered by using of two-fluid model whose permittivity depends on the frequency and superconductor parameters. We have showed that in contrast to the usual defect modes, superconducting defect modes are nearly invariant upon the change of defect size and with increasing defect sizes, the enhancement behavior is observed in the peak of electric field profiles. In addition, the physical parameters have less effect on the defect modes, which is placed under cutoff frequency of superconductor.     

Analysis of defect mode in a dielectric photonic crystal containing ITO defect

In this work, based on the use of ITO as a defect, we study the infrared defect mode in defective photonic crystal made of SiO₂ and InP. Due to the dispersion in the dielectric function of ITO, it is found that the defect mode is sensitive to the ITO thickness. The defect frequency is shown to be blue-shifted as the thickness of ITO decreases. In the angular dependence of defect mode, it is seen that the defect frequency is also blue-shifted when the angle of incidence increases for both TE and TM polarizations. However, the shifting feature is appeared to be nearly polarization-independent. The shift in the defect frequency enables us to employ ITO as a tunable agent in order to design a tunable photonic crystal filter in the infrared region.     

Temperature tunability of cavity-semiconducting waveguide coupling in a two-dimensional photonic crystal

We study the coupling efficiency between a cavity resonator and semiconducting waveguide in a two-dimensional photonic crystal by varying the temperature. We used the revised plane wave expansion and finite difference time domain methods to evaluate the coupling efficiency. The photonic crystal waveguide is composed of a row of InSb semiconducting materials, and the efficiency was calculated at various temperatures. The findings indicate that the temperature can be used as a useful efficiency controller.     

Gap maps, diffraction losses, and exciton–polaritons in photonic crystal slabs

A theory of photonic crystal (PhC) slabs is described, which relies on an expansion in the basis of guided modes of an effective homogeneous waveguide and on treating the coupling to radiative modes and the resulting losses by perturbation theory. The following applications are discussed for the case of a high-index membrane: gap maps for photonic lattices in a waveguide; exciton–polariton states, when the PhC slab contains a quantum well with an excitonic resonance; propagation losses of line-defect modes in W1 waveguides, also in the presence of disorder; the quality factors of photonic nanocavities. In particular, we predict that disorder-induced losses below 0.2 dB/mm can be achieved in state-of-the-art samples by increasing the channel width of W1 waveguides.     

Influence of defect mode displacement in photonic crystal band gap over light group velocity

The light group velocity of defect mode in photonic crystal is active controlled in order to gain controllable light delay by using thermo-optic effect to change the reflective index of material or changing the geometry structure of photonic crystal. From former research we know that the position of defect mode in band gap is changed with light group velocity. Our research further finds that the position of defect mode can be kept by changing more than one parameter correspondingly, and meanwhile the group velocity is not changed too. It comes to the relationship between position of defect mode in photonic band gap and light group velocity, and it is proved theoretically using the principle of plane wave expand method.     

多层介质的转移矩阵及其在声子晶体中的应用

引入四维波矢的概念,推导出弹性波斜入射到多层介质系统时的转移矩阵以及透射系数和反射系数。利用这些公式计算了纵波和横波正入射到一维掺杂声子晶体时纵波和横波的透射系数。得出:当纵波正入射时,透射波中纵波在一定频率范围内出现了禁带,并且在禁带的中心频率处出现了缺陷模。当横波正入射时也有相同的结果。     

Defect modes and wavelength tuning of one-dimensional photonic crystal with lithium niobate

The defect state of the one-dimensional photonic crystals consisting of lithium niobate and air is theoretically investigated. By applying an external voltage on the defect layer, remarkable wavelength tuning can be achieved. The relation between the wavelength peak and the external voltage is a straight line and the tuning rate is 1.358 nm/kV. The dependence of the wavelength peak on the angle of incidence was also observed at each applied voltage. This feature can be employed to fabricate tunable filters.     

Optimization of a 2D photonic crystal add/drop multiplexer based on contra-directional coupling

We present a highly integrated add/drop multiplexer, where the contra-directional coupling is realized by phase matching two photonic crystal waveguides. The device band structure, the corresponding transmission and drop spectra, and the coupling length are carefully analysed. Different device configurations are discussed and by tailoring the coupling factor, we optimize the frequency response of the filter, obtaining a -sized channel selector, characterized by a very high drop efficiency.     

Low threshold laser cavities of two-dimensional photonic crystal line defect mode

Two-dimensional (2D) rod-type photonic crystal (PC) line defect waveguide (LDW) laser cavities based on three types of line defect modes with zero group velocity are studied by using finite-difference time-domain (FDTD) method. These laser cavities have high quality (Q) factor, better localization of light, non-uniform gain distribution and small overlap between gain medium and light field. Therefore, they have the advantages over conventional and air-bridge PC cavities with uniform gain, such as low threshold, single mode lasing and effectively avoiding thermal effect. From their comparison, one can find the mode at middle Brillouin zones (BZ) is the best one to be used as lasing mode. Its dynamic lasing process and lasing features are demonstrated by the numerical experiment where the FDTD method coupling Maxwell's equations with the rate equations of electronic population is used.     

声子晶体材料的吸收对弹性波缺陷模的影响

为了研究声子晶体材料的吸收对缺陷模的影响,引入复波数,推导出一维掺杂声子晶体的转移矩阵,计算了衰减系数和周期数对透射波和反射波中缺陷模的影响。得出:当周期数一定时,衰减系数对一维掺杂声子晶体的透射波和反射波中的缺陷模都有显著的影响,缺陷模的峰值随衰减系数的增加而迅速减小,缺陷模的宽度随衰减系数的增加而增大。当衰减系数一定时,缺陷模的峰值和宽度都随周期数的增加而迅速减小。     

Optical transmission properties of an anisotropic defect cavity in one-dimensional photonic crystal

We investigate theoretically the possibility to control the optical transmission in the visible and infrared regions by a defective one dimensional photonic crystal formed by a combination of a finite isotropic superlattice and an anisotropic defect layer. The Green's function approach has been used to derive the reflection and the transmission coefficients, as well as the densities of states of the optical modes. We evaluate the delay times of the localized modes and we compare their behavior with the total densities of states. We show that the birefringence of an anisotropic defect layer has a significant impact on the behavior of the optical modes in the electromagnetic forbidden bands of the structure. The amplitudes of the defect modes in the transmission and the delay time spectrum, depend strongly on the position of the cavity layer within the photonic crystal. The anisotropic defect layer induces transmission zeros in one of the two components of the transmission as a consequence of a destructive interference of the two polarized waves within this layer, giving rise to negative delay times for some wavelengths in the visible and infrared light ranges. This property is a typical characteristic of the anisotropic photonic layer and is without analogue in their counterpart isotropic defect layers. This structure offers several possibilities for controlling the frequencies, transmitted intensities and the delay times of the optical modes in the visible and infrared regions. It can be a good candidate for realizing high-precision optical filters.     

Comparison of photonic bandgaps of two-dimensional periodic and quasi-periodic photonic crystals with different relative permittivity dielectric

Photonic bandgaps (PBGs) of two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) have been analyzed, with a given scatterer radius and dielectric relative permittivity changing from 1 to 30 within air-cylinders-in-dielectric and dielectric-cylinders-in-air constructions. The results have shown that 2D quasi-periodic PC is more likely to generate PBG and complete PBG than 2D periodic PC. For the given scatterer radius and two constructions, PBG widths of the two types of 2D PCs vary little, whereas the corresponding center frequencies decrease in smooth “hyperbola-like” curves with dielectric relative permittivity increasing monotonically. The present results will guide the design of PBG-type microstructure photonic devices.     

Optimization of prism coupling to high-Q modes in a microsphere resonator using a near-field probe

In this paper, we demonstrate a novel method for optimizing the in- and out-coupling of light confined in the fundamental high-Q whispering-gallery mode of a microsphere resonator via an external prism coupler. The technique relies on the use of a near-field probe to map the modes of the resonator and to obtain topographical information at the same time. We demonstrate the feasibility and efficiency of this technique by applying it to a sphere with a radius of 59 μm.