A **manufacturing** **method** of a **photonic** **crystal** is provided. In the **method**, a high-refractive-index material is conformally deposited on an exposed portion of a periodic template composed of a low-refractive-index material by an atomic layer deposition process so that a difference in refractive indices or dielectric constants between the template and adjacent air becomes greater, which makes it possible to form a three-dimensional **photonic** **crystal** having a superior **photonic** bandgap. Herein, the three-dimensional structure may be prepared by a layer-by-layer **method**.

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Since the concept of **photonic** **crystal** was proposed and theoretically discussed several decades ago [1,2], many novel **photonic** devices have been proposed aiming at controlling the propagation of electromagnetic waves. Practical applications of these results require the use of three-dimensional (3D) **photonic** **crystal** devices with 3D band gaps [3,4]. However, the fabrication of such struc- tures is not a simple task since they require a complex 3D connectivity and strict alignment requirements [5]. An alternative aiming at an easier fabrication process re- lies on the development of **photonic** **crystal** slabs. These are periodic two-dimensional dielectric structures which use index guiding to confine light in the third dimension [6-8]. **Photonic** **crystal** slabs share almost of the proper- ties with true 3D **photonic** crystals; however, new issues such as slab thickness or mirror symmetries are deter- minant in their optical behavior [9].

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waveguide (consisting of straight dielectric strip waveguide and bend **photonic** **crystal** waveguide) which offers minimum bending loss. Different bending angles (i.e. 60 o and 90 o ) along with their transmission efficiency through the bend at waveguide width of 0.5µm has been discussed and compared. The results show that the Hybrid configuration has a real potential for enhancing the efficiency. Well known Finite Difference Time Domain (FDTD) **method** has been used to optimize the efficiency and structure of Silicon-on-Insulator (SOI).

A second **method** for increasing the interaction strength is to minimize the mode area in Eq. (1.2) by more tightly confining the light into a waveguide, as shown in Fig. 1.2(c). This has been used in the nanophotonics community to achieve strong interactions between dielectrics and solid state emitters. While there have been many experiments with atoms coupled to dielectric systems [3, 25], most of them have relied on the high optical Q or large number of atoms rather than the reduce mode area to achieve strong interactions. In the early 2000’s, Hakuta’s group performed experiments coupling the fluorescence of a cloud of atoms to a nanofiber going through the cloud [26, 27]. In the pioneering work by Rauschenbeutal’s group [12], and now in many other groups [13–15], atoms are optically trapped around a sub-wavelength diameter nanofiber by the optical guided modes of the fiber. This system is convenient for its straightforward loading and cooling scheme, but is still restricted to small mode area since the atoms are trapped in the evanescent tail of the optical mode, resulting in Γ 1D /Γ 0 ≈ 0.03 or R 1.

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most remarkable geometries available for the optical communications community. PCFs consist of air holes running parallel to its axis over the whole length. The guidance of light through these fibers is governed by the type of these structures. PCF usually consists of pure silica with an array of air holes in the cladding region. This structure creates band-gaps where propagation at certain optical frequencies is forbidden. The core is usually made by a defect in the periodic structure of the PCF cross-section. In PCFs, light can be guided either by the modified total internal reflection (TIR) or by the **photonic** band gap (PBG) effect.

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We employ a full-vector finite-element **method** (FEM) [26] and anisotropic perfectly matched layers to investigate the guided modes of the proposed PCF. The confinement loss can be deduced from the imaginary part of the effective modal index. In what follows, the refractive indexes of fused silica and air are assumed to be 1.45 and 1, respectively. Calculated results are expressed in terms of the normalized frequency ν = Λ/λ, where λ is the operation wavelength in free space. The effective-circular-hole PCF with the structure shown in Fig. 1(a) has the parameters of Λ = 2.2 µm, Λ 0 = 0.5 µm, and d 0 = 0.4 µm. For comparison, the circular-hole PCF with the structure shown in Fig. 1(b) has the same lattice constant (Λ) and air- filling fraction as the effective-circular-hole PCF (air-filling fraction = 20.99%, d/Λ = 0.481).

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After testing the Glass Mechanix star line adhesive material and the results showed that it is suitable for making Bragg gating, a hollow core **photonic** **crystal** fiber is used. The fiber consists of core with diameter 10µm and surrounded by air holes which is separated by distance of 2.75 µm and cladding diameter of 123µm. It used to make fiber Bragg grating by injecting it in different liquid martials such as adhesive material and olive oil. The injection **method** used in this research is capillary action technique. The technique is one of the phenomenon of surface tension in which the can liquid to flow in narrow tubes without any help and in opposite direction of the external forces of gravity.

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equivalent index profile of a straight guide, R is the radius of the curvature and x is the distance from the centre of the waveguide. Subsequently, the straight waveguide with a transformed index profile can be analysed by a number of modal solution techniques, such as the eigenmode expansion [23], the methods of lines [24], the FDM [26], the variational **method** [28], the matrix **method** [29], the WKB analysis [30], and the FEM [32,33]. The FEM has also been employed by using cylindrical co-ordinate with E field [35] and the equivalent anisotropic refractive index approaches [36]. The beam propagation approach [37, 38] has been used successfully, but this approach makes the problem 3-dimensional with additional computational costs. Similarly the finite-difference time-domain (FDTD) [40] approach has also been used, which is more computer intensive than the modal solution or the BPM approaches.

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In this article, both the vector effect index **method** (VEIM) and finite element **method** (FEM) are exploited to calculate the effective index of FSM for the solid-and porous core PCF. For the solid-core, the EIM applies one time to estimate the equivalent cladding index. Then, the conventional characteristics’ equation will apply to construct the . For porous-core PCF, the EIM applies two times one for the core and other for cladding. Next, also the conventional characteristic equation will apply to explain the at the porous-core PCF.

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studied. The thickness of the two layers of the ﬁrst and second struc- ture is diﬀering from each other and the third **photonic** structure is the combination of ﬁrst and second structures. Using the Transfer Matrix **Method** (TMM) and the Bloch theorem, the reﬂectivity of one dimen- sional periodic structure for TE- and TM-modes at diﬀerent angles of incidence is calculated. From the analysis it is found that the proposed structure has very wide range of omnidirectional total frequency bands for both polarizations.

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Commonly, either oxygen plasma or a sonic bath in trichloroethylene is used to remove the electron beam resist after the plasma etching. In this case, oxygen plasma was ruled out because of its reaction with chalcogenide glasses and the blue light emission during the etching which can cause light induced changed in the chalcogenide thin film. The three chalcogenide glasses were immersed in trichloroethylene, where damage could be observed after 12 hours immersion and hence was ruled out for use as a solvent. The lack of available solvents for the resist removal was resolved by developing a new removal **method** and introducing dimethylformamide as solvent. This organic solvent did not provoke any observable damage to the thin films after 24 hours of immersion and was rated as suitable for resist removal. As a last solvent, MF-319 was tested. MF-319 is used as a developer for Shipley S1818 photo resist. Even after an immersion time of 45s, severe damage to the thin film could be observed, as can be seen in figure 2.9. This ruled S1818 out as masking material. The first **method** that was developed to remove the electron-beam resist involved heated Xylene. Since it is also used to develop ZEP, an artificial overdevelopment was created by immersing the **photonic** **crystal** samples in 138 ◦

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Abstract In this paper, optimization and management of dispersion of **photonic** **crystal** fibers (PCF) are presented, using 2D finite difference **method** in time domain based on an Intelligent Programming. In the analysis, for the proposed PCF structures, by evaluation of the effective refractive indices, the dispersions are calculated for 11 circular air-hole rings in the cladding. The effects of geometrical parameters of the PCFs, such as air-hole diameters, the pitch value, number of air rings on dispersion are investigated for the influence of the structural parameters of the PCFs on the obtained dispersions and the corresponding results are graphically compared. It is shown that when the air-hole diameter decreases, the slope of the negative dispersion would increase, while increase of the pitch would cause a decrease in the negative dispersion values. It is further shown that at pitches of higher than 5 µ m, irrespective of air-hole diameter, the variation of the dispersion is almost linear. The results presented can help in choosing the PCF parameters for appropriate applications.

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The Jacobi-Davidson **method** is another tool to compute eigenvalues for this problem. The style QR of the Jacobi-Davidson solver is based on the standard eigenproblem, the algorithm is based on the iterative construction of the (generalized) partial Schur form [12]. By this another script is used wherein the most important command is the jdqr, which refers to the script of JDQR by [12]. By use of [V,D,flag] = jdqr(A,I,struct('Disp',1,'Precond',A,'Tol', 1e- 4),10,'sm'), where A = Amatrix(Nx,Ny), I = speye(M), and M = Nx*Ny, and the same constants used by the eigs function earlier, we get find the ten lowest eigenvalues, from which we sort out the four smallest. The other parameters are used to get more information about the problem which is solved. Using this function and by use of contourf(x,y,Ez) it results in the next graphs in figure 6.

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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

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most important parameters in determining the perform- ance of inverted ZnO PhC in optical applications. The formation of point defects can have an enormous impact on the reflection properties. Figure 2a shows an image of the periodic arrangement of PSS structures with a diameter range of 15 mm formed on the substrate by the horizontal self-assembly **method**. The structures appear blue irides- cence. The detailed organization of the spheres is investi- gated by FE-SEM. Figure 2b is a top-view magnification of the FE-SEM image, which shows a relatively well-organized arrangement of the ordered close-packed face-centered cubic (fcc) structure along the (111) planes. The ordering is reasonably good, although point defects are observed in some areas, which may be produced by a variation in sphere size. A closer examination presented in Figure 2b shows perfectly ordered arrangement. The cross-section image of a larger magnification is tilted with an angle of 10°, as shown in Figure 2c. It was observed that the spheres were also organized as ordered close-packed fcc structure with the (111) planes parallel to the substrate surface. Optical characterization of the PhC could give the position of the stop band and its angle-dependent behavior. For op- tical characterization, reflectivity is recorded from the (111) plane of the crystals. Figure 3 shows the reflection spectra of the PSS PhC templates and inverted ZnO PhC measured in (111) direction at the incident angles of 10°, 20°, 30°, 40°, and 50°. The inset presents the measured conditions in this study. An inspection of this figure reveals that the spectrum of PSS PhC templates measured at the incident angle of 10° exhibits a maximum reflection of 34% at the wavelength of

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Having designed and fabricated devices, the next step is characterisation. There are two major measurement techniques used in this thesis. The first, analysis of the efficiency of surface grating couplers using the fibre to fibre coupling, is straightforward in principle, although the number of devices which must be fabricated successfully to complete this analysis is large, and hence demanding. The second is a more complex interferometric **method**, which yields useful data from a smaller set of devices. The end-to-end transmission spectrum is recorded at very high resolution, and then Fourier transformed to exploit the round-trip signature on the Fabry-Perot fringes. This allows us to calculate the loss due to the PhC, and also determine the points in the device where reflections occur, indicating impedance mismatches which must impair the device efficiency. Using these two methods, I have shown two separate cases - InP surface grating couplers and AlGaAs routing elements - that I have been involved in fabricating, operating very close to their designed levels, and thus validating the design.

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The Spectral Index (SI) **method** may be used to find quickly and easily the guided modes and propagation constants of semiconductor rib waveguides (Kendall et al. 1989; Stern et al. 1990). Here the true open structure is replaced by slightly larger, partially closed one, which is simpler to analyse, in order to model the penetration of the optical field into the cladding. The spectral index **method** can be expressed using steps in the region below the rib. First of all, the Fourier transform is applied in order to reduce the dimensionality of the problem to a one-dimensional structure and the field is expressed in spectral space using Fourier transform. Next, in the rib region the wave equation is exactly expressed using Fourier series in terms of cosine and sine functions then the two solutions are linked by employing a transfer relationship and consequently, giving a transcendental equation which can be solved for the propagation constant of the original rib structure. The presence of the strong discontinuities at the dielectric interfaces is dealt with by using an effective rib width and an effective outer slab depth. The spectral index **method** has been extended to include rib coupler problems (Burke 1989; Burke 1990) cases with loss and gain (Burke 1994) and also it has been used to analyse multiple rib waveguides (Pola et al. 1996).

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