There were also given results of band structure computation for the Photoniccrystal with diamond lattice made of dielectric spheres placed in air where they found the complete Photonicbandgap between the second and third bands. In 1992, H.S. Sozuer and J.W. Haus  computed the band structure of the Photoniccrystal with inverted FCC lattice (also known as inverted opal). The term inverted opal means that instead of dielectric spheres placed in air, the inverted FCC lattice consists of a number of spherical cavities separated by baffles with higher refractive index. It appeared that such a Photoniccrystal has complete Photonicbandgap at relatively high refractive index of material. Investigated inverted opal had complete Photonicbandgap between the eighth and ninth bands. The appearance of the complete Photonicbandgap inside the Photoniccrystal with inverted FCC lattice attracts a special interest, because today inverted artificial opals provide possibility of mass photoniccrystal production.
These advantages have resulted in the development of a variety of opto-electronic devices, including multimode filters for wavelength division multiplexing (WDM) as well as opto-fluidic devices for biochemical and biomedical sensing. The desired characteristics for these devices are high quality factor (Q), large modulation depth, also known as extinction ratio (E.R), high selectivity, high out-of-band rejection, low power attenuation, low insertion losses and a small footprint, see, for example, Reed . The use of vertical 1D PhCs for sensing is particularly important for the near- and mid-infrared regions and may be extended in future to the far-infrared and even the THz regions [1–3, 7, 23]. Another attraction of these structures is that the delivery of chemical or biological substances into the air gaps can be performed via standard “flow-over” (see, for example ) and “flow-through” approaches. The latter method is achieved by pumping through the channels as well as by capillary action [25–27]. Simulations of three vertical silicon/air 1D PhC Fabry- Perot resonant cavities with different architectures and fluidic functionalities were discussed in Surdo and Barillaro . The impact of cavity order and 1D PhC micromirror reflectivity on their biosensing performance is analyzed. Results on the surface sensitivity, the limit of detection and the range of linearity of the devices are reported.
Abstract—We investigate the characterization of defect modes in one-dimensional ternary symmetric metallo-dielectric photoniccrystal (1DTSMDPC) band-gap structures. We consider the defect modes for symmetric model with respect to the defect layer. We demonstrate reflectance with respect to the wavelength and its dependence on different thicknesses and indices of refraction of dielectric defect layer, angle of incidence and number of periods for both transverse electric (TE ) and transverse magnetic (TM ) waves. Also, we investigate properties of the defect modes for different metals. Our findings show that the photoniccrystal (PC) with defect layer, made of two dielectrics and one metallic material, leads to different band-gap structures with respect to one dielectric and one metallic layer. There is at least one defect mode when we use dielectric or metallic defect layer in symmetric structure. And, the number of defect modes will be increased by the enhancement of refractive index and thickness of dielectric defect layer. 1. INTRODUCTION
In this case we consider a photonic structure with a high optical contrast of n1 / n2 = 3.42 / 1 and optimum filling frac- tion for the second component at 0.774 from formula 共 1 兲 . The refractive index of the media for incoming and outgoing light beams is 1. For BDs shown in Fig. 1 共 a 兲 , the blueshift 共to higher normalized frequencies兲 with increasing angle of incidence of PBGs for both polarizations is seen. The overlap of the lowest PBGs for the same condition is shown in Fig. 1共b兲. From the latter figure we can deduce that ODB in such PC cannot exist due to the fact that the short wavelength edge of the TM range for angles greater than 67° does not have a mutual overlapping range with PBGs with normal incidence of light.
over into the underlying layers when a multilayer structure is built. The epoxy is administered by putting down a tiny drop of epoxy using a stainless steel wire of ⬃ 0.5 mm. Using an epoxy hardened coated tip wire, we drag the tiny epoxy droplet across and up and down 共 one round trip 兲 the relief structure surface of the PDMS. Typically, about 20 round trips are needed to fill up the relief structure of the PDMS. The epoxy is applied in multistages with oven curing in- between. The number of applications depends on the dimen- sions of the structure. If we overdo the process an excess epoxy may result. Lastly, the epoxy filled PDMS is placed in contact with a substrate 关 Fig. 1 共 e 兲兴 , and cured at room tem- perature. A glass substrate of thickness 300 m has been used throughout the experiment. After the epoxy is hardened, the PDMS is peeled off, leaving a set of parallel epoxy rods on the substrate. As a result, one layer of the polymer tem- plate is created 关 Fig. 1 共 f 兲兴 . The second or subsequent layer is built in the same fashion except the epoxy-filled elastomeric mold is applied to the one-layer or multilayer structure on a substrate 关 Fig. 1 共 g 兲兴 . For a layer-by-layer photonic structure, the second layer is rotated 90° with respect to the first layer; the third layer is parallel to first layer but shifted laterally by half the periodicity with respect to the first layer. The fourth layer is also parallel to the second layer and shifted by half the periodicity with respect to the second layer. These four layers constitute a unit cell of the layer-by-layer photonic structure.
From Figure 8, it is clearly observed that the ODR range for γ = 1.2 is just double of ODR range for γ = 1. So, by choosing appropriate values of controlling parameters we can tune the ODR range. The ODR range for GSPC can be enhanced by increasing the value of γ. It is observed that in a GSPC structure, the ODR band gets enhanced without increasing the number of layers of the structure. It is found that the ODR range for GSPC structure is generally more than the ODR range of conventional PC. Also, it is more than the ODR bandwidth of simple graded PC structure .
One-dimensional (1D) periodic binary photonicbandgap (PBG) structures [1, 2] have been the subject of interest in recent years. These 1D periodic binary PBG structures are multilayer structures formed by using two materials. These periodic multilayer structures lead to formation of photonicband gaps or stop bands, in which propagation of electromagnetic waves of certain wavelengths are prohibited. These bands or ranges depend upon a number of parameters such as refractive indices of materials, thicknesses of material layers and angle of incidence etc. . If all these parameters are kept constant, then this 1D PBG structure will have fixed predetermined bands of wavelengths or frequencies which will be reflected or transmitted by the structure.
length L of upper patch (Fig.1 as 2) is 29.6 mm x 29.6 mm obtained by some equations [2-3] and coded by . The Lower patch (Fig.1 as 1) dimension is 46.78 mm x 29.6 mm due to adjusted similar of upper patch. The top view of the modified structure of the antenna is shown in Fig. 2. On the bottom side of the lower patch a 58.28 mm x58.28 mm square metallic ground plane has been constructed. Slots of 10 mm x10 mm square holes spaced 1.38 mm apart forming a 5x5 matrix have been made on this ground plane. The excitation for the antenna is given by a line feed at on the upper patch which dimension on 50 Ω is 17.18 mm x 3.16 mm (Fig.1 as 3). The three dimensional view of the structure is shown in the Fig.1.The main advantage of using PBG structure is elimination of surface wave currents which are responsible for low antenna efficiency and degraded pattern.
as a new optical material in recent years [1, 4–8]. Accordingly to the dimensionality of the stack, they can be classiﬁed into three main categories: one-dimensional (1-D), two-dimensional (2- D), and three-dimensional (3-D) crystals. Actually, 1-D PCs, traditionally called dielectric multilayers or superlattices, have been widely used as interference ﬁlter, high reﬂectors, etc before other PCs were invented [9, 10]. PCs have attracted extensive interest for their unique electromagnetic properties and potential applications in optoelectronics and optical communications .
Figure 8(c) suggests that a more obtuse slant in the lat- tice should result in a blue shift and should reduce the intensity. Previous findings suggest that rather a red shift should be experienced. As the lattice rotates relative to the centre of the photoniccrystal, the effective spacing and distance that the plane wave travels increases. How- ever, the response is the opposite. One possible reason for the blue shift can be that as the tilt angle increases the layers of nanoparticles no longer act as a photoniccrystal but rather act as a blazed grating. This grating may reflect the wavelengths according to title angles ra- ther than lattice spacings. The intensity decrease on the other hand, matches up to the theory that as the spacing grows the intensity decreases. It was anticipated that the slant angle would account for the slight discrepancy in the position of the bandgap from the expected in Fig. 8c. There was a consistent red shift of 20 nm from the pro- jected position of the bandgap. Figure 8(c) shows that
The artiﬁcial micro-structured materials with a periodically modulated dielectric functions are known as photonic crystals (PCs). Intensive investigations on PCs have been carried out since the idea of PCs was proposed [1,2]. Up to now, most calculations of the photonicband structures and the corresponding electric/magnetic ﬁeld distributions have been performed based on numerical methods,such as the plane wave expansion method and the ﬁnite diﬀerence time domain method [3,4]. Some qualitative conclusions have been derived from the related numerical analysis. It is well known that the exact analytical solutions are quite useful for us to understand the physics of PCs. In a sense,the simplest one-dimensional (1D) PC with Kronig-Penney periodic dielectric structure [5,6] is the only exactly solvable theoretical model. The purpose is to draw new physics out of the 1-D PC by means of the exact analytical solutions.
Fig 1. Schematic representation of GSPC structure In The edges of PBG will shift towards the higher frequency side as we increase the angle of incidence and at brewester angle TM mode do not reflects.these are the two important factor because of them there is no absolute photonicbandgap (PBG) but it does not mean that there is no Omni-directional reflection. The criterion for the existence of total Omni-directional reflection is that incident wave should no couple with any of propagating modes
For one-dimensional 共 1D 兲 PCs there is an alternative ap- proach available to generate the gap map. Using the transfer matrix method, 3,4 the set of reflection spectra for the f values in the range from 0 to 1 is calculated. The wavelengths 共 or wave numbers, ˜ 兲 for which R = 1 is determined and this information is then used to generate the gap map. 5 The PBG gap map allows an effective comparison of PC structures with various periods m, lattice constant A, refractive index contrast ⌬ n = n 1 / n 2 , angle of incidence and polarization of the incident light. 2,5,6 The gap map is a valuable tool for use during the specification of a PC for a particular application. In general, an extension or widening of the PBG can be achieved by increasing the optical contrast ⌬n and the num- ber of the lattice periods m. Recently a number of methods for the extension of the high reflection range 共HRR兲 for di- electric multilayer stack structures consisting of binary layers has been suggested based on a combination of experimental observation and theoretical considerations. 7–9 The theoretical framework for these methods was developed as a result of studies of light localization in 1D systems. 10–12 These theo- retical studies show that if disorder is introduced to a peri-
Now we analyze reﬂectance spectra of MQW at oblique incidence (at 20 ◦ , 30 ◦ and 50 ◦ ) for both polarizations (TE- and TM-polarizations). The range of reﬂection band or photonicbandgap common to both polarizations at all possible incidence angles (0 ◦ to 90 ◦ ) is called omnidirectional reﬂection (ODR) band. It is very diﬃcult to achieve broad ODR band in UV region by using a single MQW PC structure. One of the reasons behind this is narrower range of UV than other parts of EM spectrum (visible or infrared). Secondly, lower and higher band edges of TM-reﬂection band shift slowly towards lower and higher sides of the wavelength compared with TE-reﬂection band with the increase in incidence angle.
Theoretical analysis of Light propagation in periodic layered media solved by transfer matrix method The 1 D photonic crystals usually defined as media which are periodic in one spatial direction. Such structures are widely used in modern optoelectronics, ranging from Bragg mirrors for distributed-feedback lasers. A typical example of a one-dimensional periodic medium is a Bragg mirror which is a multilayer made of alternating transparent layers with different refractive indices. Assuming a laser beam is incident on a Bragg mirror; the light will be reflected and refracted at each interface. Constructive interference in reflection occurs when the condition
A comparative study is performed for calculating the photonicbandgap in photoniccrystal by using two numerical method , namely Plane Wave Expansion (PWE) and Finite Difference Time Domain Method (FDTD). A photoniccrystal (PC) is said to be an artificially periodic layered structure that is known to possess photonicband gaps (PBGs). Photonicbandgap is the range of frequency where the light can not propagate through the structure. In order to obtain most general idea of Phc’s characteristics as well as to effectively design it, it is convenient to use band structures which gives full information about radiation behavior when propagating within the specific direction inside the photoniccrystal using band structure.
gle. The analysis shows that 100 % reflectance range can be varied and enhanced by using the proposed structure for both (TE- and TM-) polarizations. The enhancement in reflection bands increases as the tilt angle increases for both the polarizations which cause the enlargement in the ODR bands. The reason for enhancement in the bandgap and hence in the ODR arises due to increase in the effec- tive optical path of the layer by tilting the structure. Fur- ther, the properties of defect modes in the bandgap re- gion have been studied. The results show that defect modes or tunneling modes can be tuned to different wavelengths by changing the tilt angle of the structure without changing other parameters. Moreover, the effect of variation of thickness of defect layers on the tunneling mode has been studied, also, for both TPC and conven- tional PC structure. From the study we can say that by tilting the PC structure, Q-factor of the structure may be varied without affecting the other material parameters of the structures. The proposed model might be used as a tunable broadband omnidirectional reflector as well as tunable transmission mode, which has a potential in the field of photonics and optoelectronics.
Abstract—The effect of temperature on the photonicbandgap has been investigated. One dimensionalphotoniccrystal in the form of Si/air multilayer system has been studied in this communication. The refractive index of silicon layers is taken as a function of temperature and wavelength both. Therefore, this study may be considered to be physically more realistic. It may be useful for computing the optical properties for wider range of wavelength as well as temperature. We can use the proposed structure as temperature sensing device, narrow band optical filter and in many optical systems.
In the recent years, the Photonic Crystals (PCs) which is also called PhotonicBandGap Materials (PBGMs) have received much attention and the large number of new type of PCs have been studied and fabricated [1-5]. The ability to confine and control the light has a wide range of applications in the area of optics and laser physics. The interactions of electromagnetic wave with plasma have ability to control the light because plasma in mi- crowave devices have modified the dispersion properties and enhances the efficiency of plasma lens , plasma antennas  and plasma stealth aircraft . Firstly, Kuo and Fatith  studied the propagation of electromagnetic wave in rapid created time varying periodic plasma. Hojo et al.  have studied the dispersion relation of elec- tromagnetic wave propagation in 1-D binary PPCs and they found that the bandgap can be controlled by the plasma density and plasma width. Prasad et al.  have theoretically studied the modal dispersion characteristics, group velocity, and effective group as well as phase in- dex of refraction of 1-D ternary PPCs structure having periodic multilayers of three different materials in one unit cell. They also found that such structure provide additional degree of freedom to control dispersion char- acteristic, group velocity and effective index of refraction
In our current work, we extended the study to traps which are arranged in a square lattice conﬁguration and observed strongly pronounced features of site-to-site coupling for small lattice constants and localized polariton modes for lattice constants exceeding the evanescent nearest neighbor coupling. The remarkable feature of our deep lattice is a complete gap between the M-point of the s-band and the X-point of the p-band of the energy spectrum. A complete gap in a two-dimensional periodic potential opens only above a certain depth threshold. The possibility of reaching this regime with our devices opens the way to investigations of topologically nontrivial states in more sophisticated lattice geometries. Polariton condensation in these lattice structures is observed in the full bandgap near the M-point of the s-band, indicating the presence of a spatially localized gap state. A combination of such a potential landscape with one induced by a structured optical pump [27, 28] may enable the engineering of tailored nontrivial potentials, such as bi-partite or deliberately non-Hermitian lattices, because the depth of potential wells produced by both techniques can be comparable. We believe that our work thus represents an important step toward the implementation of quantum emulators in polariton systems.