Slow light in photonic crystals

The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without losing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows the slowing of light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.     

Coupling into the slow light mode in slab-type photonic crystal waveguides

Coupling external light signals into a photonic crystal (PhC) waveguide becomes increasingly inefficient as the group velocity of the waveguiding mode slows down. We have systematically studied the efficiency of coupling in the slow light regime for samples with different truncations of the photonic lattice at the coupling interface between a strip waveguide and a PhC waveguide. An inverse power law dependence is found to best fit the experimental scaling of the coupling loss on the group index. Coupling efficiency is significantly improved up to group indices of 100 for a truncation of the lattice that favors the appearance of photonic surface states at the coupling interface in resonance with the slow light mode.     

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.     

Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals

Magnetic photonic crystals are periodic arrays of lossless materials, at least one of which being magnetically polarized. Magnetization, either spontaneous or induced, is associated with nonreciprocal effects, such as Faraday rotation. Magnetic photonic crystals of certain configuration can also display strong spectral asymmetry, implying that light propagates in one direction much faster or slower than in the opposite direction. This essentially nonreciprocal phenomenon can result in electromagnetic unidirectionality. A unidirectional medium, being perfectly transmissive for electromagnetic waves of certain frequency, freezes the radiation of the same frequency propagating in the opposite direction. The frozen mode has zero group velocity and drastically enhanced amplitude. The focus of our investigation is the frozen mode regime. Particular attention is given to the case of weak nonreciprocity, related to the infrared and optical frequencies. It appears that even if the nonreciprocal effects become vanishingly small, there is still a viable alternative to the frozen mode regime that can be very attractive for a variety of practical applications.     

Low group velocity in a photonic crystal coupled-cavity waveguide

A two-dimensional photonic crystal coupled-cavity waveguide is designed and optimized, the transmission spectrum is calculated by using the finite-difference time-domain method, and the group velocity of c/1856 is obtained. To our knowledge, this value of group velocity is the lowest group velocity in a photonic crystal waveguide calculated from its transmission spectrum so far. The result is confirmed by the photonic band structure calculated by using the plane wave expansion method, and it is found that the photonic crystal waveguide modes in a photonic band structure are in accordance with those in the transmission spectrum by using the finite-difference time-domain method. The mechanism of slow light in the coupled-cavity waveguide of photonic crystal is analysed.     

单光子晶体界面介质波导中的慢光效应

研究了单光子晶体界面介质波导中的慢光效应.芯层-空气层界面的全内反射效应以及光子晶体基底的禁带效应共同形成了对光场能量的横向约束.用基于超元胞的平面波展开法计算得到了导模色散曲线,并据此对其色散、群速以及群速色散性质做了详尽分析.由于利用了色散曲线慢光区域内拐点附近低群速色散的部分,该单光子晶体界面介质波导具有良好的慢光特性.对两个不同导模计算得到的平均群速分别为c/98和c/376,可用相对频带宽度分别达到2.1×10-3和4.1×10-4.另外,该慢光结构可以侧向耦合的方式克服光子晶体慢光波导耦合困难的缺点.     

Slow light in photonic crystals waveguide constructed with symmetrically perturbed structure

Symmetrically perturbed photonic crystal waveguide can be constructed by inserting perturbative dielectric rods into photonic crystal waveguide structure with whose rods’ radius distributed according to a certain proportion. Slow light properties in this new structure are studied by using the plane wave expansion method (PWM). In this paper, schemes of adjusting radius of perturbative dielectric rods and adjusting the dielectric constant of perturbative dielectric rods are proposed to optimize slow light properties. The result shows that the scheme for adjusting radius of perturbative rods can realize larger average slow light bandwidth and efficiently control the NDBP value of the waveguide, but it contributes little to obtain smaller group velocity. The scheme for adjusting dielectric constant of perturbative rods can realize smaller group velocity, but can only obtain smaller slow light bandwidth and cannot efficiently enlarge NDBP value of waveguide. Both optimization schemes proposed in this paper realize group velocity that is two magnitudes smaller than the vacuum speed of light meanwhile maintaining large NDBP and low GVD region. Our results provide important theoretical basis for the potential application offered by symmetrically perturbed photonic crystal in future optical networks.     

Dual-frequency division de-multiplexer based on cascaded photonic crystal waveguides

A dual-frequency division de-multiplexing mechanism is demonstrated using cascaded photonic crystal waveguides with unequal waveguide widths. The de-multiplexing mechanism is based on the frequency shift of the waveguide bands for the unequal widths of the photonic crystal waveguides. The modulation in the waveguide bands is used for providing frequency selectivity to the system. The slow light regime of the waveguide bands is utilized for extracting the desired frequency bands from a wider photonic crystal waveguide that has a relatively larger group velocity than the main waveguide for the de-multiplexed frequencies. In other words, the wider spatial distribution of the electric fields in the transverse direction of the waveguide for slow light modes is utilized in order to achieve the dropping of the modes to the output channels. The spectral and spatial de-multiplexing features are numerically verified. It can be stated that the presented mechanism can be used to de-multiplex more than two frequency intervals by cascading new photonic crystal waveguides with properly selected widths.     

Numerical demonstration of slow light tuning in slotted photonic crystal waveguide using microfluidic infiltration

Tuning of the operating wavelength of slow light in the slotted photonic crystal waveguide using microfluidic infiltration has been investigated. Using 2D plane wave expansion method, we numerically demonstrate that the operating wavelength can be shifted from the C to L band, simply by choosing the refractive index of the infiltrated fluid. It is also found that, as the refractive index of the infiltrated fluid changes, the group velocity dispersion has slight variation at different operating wavelength. This design opens the possibility for post-fabrication scheme of tuning the operating wavelength of slow light in slotted photonic crystal waveguide, and allows the device to be optimized for different applications.     

Slow light transmission in a photonic crystal power splitter with parallel outputs

In this paper, we investigate coupling of light to slow modes in a photonic crystal power splitter composed of a Y-junction and two 60° bends. First, a combination of two cascaded bends which is commonly used in integrated photonic crystal circuits is studied in slow light frequency regime. We propose a structure that its transmission spectrum covers the high group-index frequencies near the band edge. Also, by structural modifications, high transmission near to 95% is achieved in slow light bandwidth. Next, we study the complete structure of a photonic crystal power splitter with parallel outputs based on a Y-junction integrated with two 60° bends. Using modified bends and reducing sharpness of Y-junction, the efficiency of splitting increases in both high and low group-index frequency bands. The optimized structure has an average efficiency of 82% in slow mode regime. This structure can be used in photonic crystal based slow light devices, such as Mach-Zehnder interferometers.     

The slow light in the closed-packed face-centered cubic photonic crystal: characteristics and application design

Using the plane wave expansion method, we calculated the energy band distribution of face-centered cubic (FCC) photonic crystals in the reciprocal lattice space. The influences of various dielectric constant materials on the properties of slow light are discussed. The results show that, in the close-packed hollow spherical FCC photonic crystal, the group velocity of light can be slow down to the velocity about $10^{-4}c$ 10 - 4 c . And the slow light effect tends to occur more strongly in the hollow spherical structure in comparison with the dielectric spherical structure. The possible applications of the slow light effect in the 3D photonic crystal are proposed for solar cells and optical communication devices.     

二维正方光子晶体波导中的慢光传输

采用平面波展开法分析了正方晶格光子晶体线缺陷波导中的慢光传输.数值模拟结果表明,介质柱光子晶体线缺陷波导中,缺陷模的群速度与填充比、缺陷处介质柱半径及与波导相邻介质柱半径有关,其中缺陷处介质柱半径对缺陷模的群速度影响最大|随着填充比和缺陷处介质柱半径的增大及与波导相邻介质柱半径的减小,缺陷模的群速度逐渐减小且最小减至0.015c.进而对比研究空气柱光子晶体线缺陷波导,发现缺陷模的群速度随着缺陷处空气柱半径的减小而减小,最小减至0.008c.     

Intensity‐Enhanced Apodization Effect on an Axially Illuminated Circular‐Column Particle‐Lens

A particle can function as a refractive lens to focus a plane wave, generating a narrow, high intensive, weak‐diverging beam within a sub‐wavelength volume, known as the ‘photonic nanojet’. It is known that apodization method, in the form of an amplitude pupil‐mask centrally situated on a particle‐lens, can further reduce the waist of a photonic nanojet, however, it usually lowers the intensity at the focus due to blocking the incident light. In this paper, the anomalously intensity‐enhanced apodization effect was discovered for the first time via numerical simulation of focusing of the axially illuminated circular‐column particle‐lenses, and a greater than 100% peak intensity increase was realised for the produced photonic nanojets.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

级联三能级原子薄蒸汽膜的色散特性

从理论上讨论了囚禁于两电介质间的级联三能级系统薄原子蒸汽膜的色散特性.由于腔中慢速原子及泵浦-探测机制的速度选择贡献,色散谱线表现为Dicke窄化的亚多普勒结构及明显的慢光效应,当泵浦光和探测光异侧入射时这种现象更为突出.两个叠加的色散线型,一个对应光学泵浦,另一个对应可能出现的电磁诱致透明.     

光子晶体耦合腔光波导慢光结构特性研究

研究了用于光缓存的光子晶体耦合腔光波导的结构对慢光传输特性的影响.详细讨论了微腔间距关于波导禁带、导模带宽、导模传输群速度的具体关系.计算发现,随着微腔之间距离的增加导模显著平坦化,群速度急剧减小.当相邻微腔之间距离为7个晶格常数时,获得了小于2×10~(-4)c的超小群速度.通过长度为13.23 μm的7×7超胞构成的光子晶体耦合腔光波导,产生的最大光延迟超过了400 ps,这比相同长度传统光波导产生光延迟大四个数量级.     

Wideband and low dispersion slow light in slotted photonic crystal waveguide

We present a procedure to generate wideband and low dispersion slow light in slotted photonic crystal waveguide. By shifting the first and second rows of air holes of slotted photonic crystal waveguide, the bandwidth of slow light can be increased, with small group velocity dispersion. Using 2D plane wave expansion method, we numerically demonstrate slow light with the nearly constant group indices of 23, 42, and 54 over 17.6 nm, 6.7 nm and 3.3 nm bandwidth, respectively. The maximal normalized delay-bandwidth product is 0.26. From the fabrication's point of review, shifting the position of holes is easier to be controlled technically than changing the diameters of air holes. In addition, our simulations suggest this design is tolerant to deviation for positions of the first two rows of air holes. Therefore, the proposed approach decreases the dependence on the fabrication accuracy.     

Coupling loss minimization of slow light slotted photonic crystal waveguides using mode matching with continuous group index perturbation

We experimentally demonstrate highly efficient coupling into a slow light slotted photonic crystal waveguide. With optical mode converters and group index tapers that provide good optical mode matching and impedance matching, a nearly flat transmission over the entire guided mode spectrum of 68.8 nm range with 2.4 dB minimum insertion loss is demonstrated. Measurements also show up to 20 dB baseline enhancement and 30 dB enhancement in the slow light region, indicating that it is possible to design highly efficient and compact devices that benefit from the slow light enhancement without increasing the coupling loss.     

Temporally Correlated Narrowband Biphoton Interference Based on Mach–Zehnder Interferometer

Since early 1990s, Mach–Zehnder interferometer has been used to investigate the interference of biphoton wave packets. Due to subpicosecond time coherence of biphoton generated by spontaneous parametric downconversion process, some physical processes are ignored in the interferometer, most likely the biphoton time‐domain interference. Here, the two‐photon interference phenomenon based on the Mach–Zehnder interferometer is theoretically studied, where the correlated photon pairs are produced by the four‐wave mixing in atomic system. In particular, the quantum interference effect to effectively control the coherent time of two‐photon by adjusting the input delay is used. In the damped Rabi oscillation regime, two‐photon bunching and antibunching effects are observed. In addition, in the group‐delay regime, the interference between biphoton precursor, slow‐light wave packets and also in between the precursor and the slow‐light wave packets is observed, which had never been reported before. These results may have potential applications in the fields of biphoton shaping and quantum information processing.     

Tuning the flow of light in semiconductor-based photonic crystals by magnetic fields

Tuning the flow of light by external fields is a challenging task for scientific studies and optical applications, but it is important in many applications such as switches, modulators, and slow wave structures. Here, new results are presented which demonstrate that this effectively can be achieved by external magnetic fields in one-dimensional photonic crystals made from semiconducting material. The advantage of using semiconducting material is the magnetic-field dependent dielectric function of the free charge carriers particularly where the magnetic field causes large and strongly varying contributions – near the plasma frequency and the cyclotron resonance frequency. The results of simulations on the basis of a multiple scattering method at infrared and microwave frequencies and of experiments on Indium Antimonide in the latter frequency regime confirm the tunability up to the extreme case from full transparency to opaqueness and vice versa.