OPTIMIZATION OF TWO DIMENSIONAL PHOTONIC CRYSTAL BAND GAP USING INDIUM PHOSPHIDE(InP)

A thesis submitted in partial fulfilment of the requirements of Staffordshire University for the degree of Master of Science in Electronics Engineering

Faculty of Computing, Engineering & Technology
DECEMBER 2010

ABSTRACT
Photonic crystals exhibit periodic structure and these are of many types such as one, two and three dimensional photonic crystals. Photonic crystal is a low loss periodic dielectric medium. In order to cover all periodic directions the gap must be extend to certain length which is equivalent to semiconductor band gap. The complete photonic band gap occurs in the three dimensional photonic crystals. The propagation of light which is confined to a particular direction can be analysed through Maxwell’s approach. The electromagnetic wave which contains both ‘E’ and ‘H’ fields can be calculated through these equations. These field vectors are more useful in calculating band structure of photonic crystal.
This report deals with the calculation of band structure in two-dimensional photonic crystal. There are many methods for calculating band structure and this thesis is mainly focused on the plane wave expansion method. This report contains the simulation procedure for calculating band structure for both TE and TM modes in the presence of dielectric medium using Computer Simulation Technology (CST) microwave studio. Results which are obtained during the simulation provide an overview of the two-dimensional photonic crystal behaviour in the presence of dielectric medium.

ACKNOWLEDGEMENT
This project could not be finished without the help and support of many people who are gratefully acknowledged here. At the very first, I’m honoured to express my deepest gratitude to my Project supervisor, Prof. Torfeh Sadat-Shafai, for his encouragement, guidance and supervision throughout the project, without whose support this work would have not ever been possible. I also extend my thankfulness to Prof. Dr. Ian Taylor, Head of the department of Electronic Engineering and all my academic tutors in Staffordshire University who have helped me throughout the academic career.
I would like to dedicate this dissertation to my family whose love and cherish and whose unconditional backing is the pillar of my strength.

CONTENTS

CHAPTER 1
1.1 INTRODUCTION:
The Photonic crystal is a solution to the optical manipulation and control. A photonic crystal is working as a dielectric medium with low - loss periodicity (Joannopoulos and Winn, 2008).
The study on Photonic crystals was started fifteen years ago. A new area in physics was developed through this photonic crystals investigation. Through the development of the concept of photonic crystals, Yablonovitch, a professor in California intended an application with name of crystal engineering technology. Now in optical electronics the photonic crystals have been predicted as a major field for its unique properties. The study of photonic crystals continues to improve in several other scientific fields like chemistry, acoustics, radio techniques, precision machinery and others.
The concept of photonic band gap is most important in development of photonic crystals. Band gap is the relation of optical dispersion between the frequency which is given and the corresponding wave vector in a photonic crystal. In 1979 the band of photons was proposed by Otaka. Then in 1987 Yablonovitch described that there is possibility to control the spontaneous release of photons in a Photonic Band Gap (PBG). After that researches and arguments on the structures and band gaps of photonic crystals developed rapidly. John elevates his argument on phonic crystals and says that, if in the arrangement of a photonic atom the randomness is initiated, then in a uniform photonic crystal the incident of light localization occurs. Overall, the Photonic Band Gap can be portrayed as a structure containing a general stop band for the light’s every occurrence angle.
There are three key points in progress of photonic crystals. First key point is the detection of new Photonic Band Gap structures in photonic crystals and the improvement of the rapidity and elasticity in calculations of PBG. The second key point is the disputes of improving crystals that perform in the optical frequency system. The final key point is the research of photonic crystals composed of metals that can perform in the range of microwave (Noda and Baba, 2003).
Photonic crystals are defined as, the crystals in which the molecules or atoms are arranged in a periodic fashion. Photonic crystals are available as one, two and three dimensional structures. Generally Photonic Crystals have photonic band gaps. A band gap is defined as the range of energy present in a solid where states of electron are absent. A crystal is formed from the perfect optical insulator. Usually PCs are complex, high index-contrast, vectorial systems and are 2, 3- dimensional. Photonic Crystals have opened new ways to control spontaneous emission. 3-D Photonic Crystals are the perfect compositions for light control. The Photonic Crystal applications have strongly limited in optical devices because of its intricate fabrication problems.
InP-based PCs are GaInAsP or InP 2-D PCs, which are formed from sub micrometer column arrays. The 2-D Photonic Crystals mirrors are used in InP-based short cavity lasers. Photonic crystals let the cavities and waveguides to be indiscriminate and balanced due to their useful properties to cover a larger range of frequencies. This feature makes photonic crystals to be very helpful in metallic waveguides and cavities in controlling microwave broadcast. The metallic waveguide lets the promulgation of electromagnetic waves along with its axis only and the metallic cavity walls forbid the promulgation with certain frequencies. Photonic crystals are typically “honeycomb” structures made of silicon. They can be classified into three different categories depending on what they will be used for: one-dimensional, two-dimensional, and three-dimensional builds. In photonic crystals the atoms are reinstated by macroscopic media with conflicting dielectric constants and as the same periodic dielectric function are replaced instead of periodic potential. Light reflections and refractions from all of different circumferences of crystal can generate several of the identical phenomena for photons when the materials of crystals are adequately diverse with its dielectric constants and when the materials absorb a minimal amount of light (Johnson and Joannopoulos, 2003).
1.2 MAXQWELLS EQUATIONS: * The electric and magnetic fields present in the electromagnetic waves is usually analysed through Maxwell’s equations. * In particular dielectric medium electric field is perpendicular to magnetic field. * These fields oscillate at higher frequencies in space and which exhibits harmonic variations. * For free space the Maxwell’s equations can be stated as
∇×E = - ∂B∂t ............................................................ 1

∇×H = J+ ∂D∂t .............................................................. 2

∇ ∙ D = ρ .............................................................. 3

∇ ∙ B = 0 ............................................................... 4 Whereas, t = time.

* The energy carried by the electromagnetic wave is usually reffered in terms of pointing vector and is given by

D = ε0E + P ................................................... ............ 5 B = µ0H + M ................................................................6

Where ε0= 8.854×10-12 F/m and

µ0=4×10-7

P = Electric polarization of medium.

M= Magnetic polarization of medium.

The product of ‘ε0’and ‘µ0’ is equal to

ε0. µ0= 1/c2 ...................................................................7

S = 1µ0 E×B ...................................................................8

Wave equation in Vacuum:

Here there is no polarization or current. And j= 0.

Then the reduction of Maxwell’s equation is

∇×E = - ∂B∂t ............................................................9

∇×H = ∂D∂t .................................................................10

∇ ∙ D = 0 ..............................................................11

∇ ∙ B = 0 ..............................................................12

By substituting the values in the above equations

Therefore the wave equation for the electric field in vacuum is zero i.e. in other words,

∇2E - 1c2∂2∂t2 E = 0 .........................................................13 |

1.3 LITERATURE REVIEW:
In photonic crystal, the atoms or molecules are arranged periodically. Our aim is to study, how does light propagate in photonic crystal? The properties of photonic crystals have increasing demand in the market year by year starting from one dimensional photonic crystal to the two and three dimensional structures. Next we have to think about which structures exhibit what properties and why?
One main approach to study the propagation of light in the photonic crystal is through the Maxwell equations. Using these equations we need to calculate the ‘E’ and ‘H’ field vectors. While calculating these fields there are some problems that occur like Eigen value problems. In order to overcome this problem, we make use of vector calculus by performing some linear operations. The properties of harmonic modes and the field vectors are useful in designing the photonic crystals with respect to their own applications. There are some symmetry properties in solid state physics such as continuous and discrete translational symmetries which can be applied to photonic crystals. These symmetries describe about the propagation of electrons in a periodic crystal potential and these can also be applicable in the study of light propagation in photonic crystal.
In order to implement the basic idea underlying photonic crystals, the primary approach is studying the properties of one dimensional photonic crystal. These crystals exhibit some major phenomena such as photonic band gaps, localized modes and surface states but the light in this crystal is confined to one direction. This crystal gives the basic approach to the complex structures like multi dimensional crystals.
In two-dimensional photonic crystals, the structure of the crystal is periodic in two directions and homogeneous in third direction. The field patterns are analysed through the electromagnetic modes such as TE and TM modes by reviewing the nature of band gaps in the presence of dielectric medium. In order to compute the photonic band gap in this crystal, there are different methods such as Plane wave expansion method, Finite difference time domain method and Finite element method. Here, I am dealing with the plane wave expansion method and this method yields some mathematical calculations to find out the modes and using these modes we analyse the band gap for the given dielectric medium. The CST microwave studio software tool is used to analyse the band gap in TE and TM modes and calculate the concentration factor for these modes. Some defects were found such as point defect, line defect and surface defect occur while localizing the modes in the plane.
There are many applications of photonic crystals such as beam splitters, optical power limiters, micro structured fibres and many other applications. The software tool we are dealing is not too fast even though it exhibit good results. Many tools are there to find band structure like MIT photonic band software which is fast compared to CST.

CHAPTER 2
2.1 PHOTONIC CRYSTALS:
Photonic crystals have periodic dielectric structure and they allow light for storage and wave-guiding via Bragg reflections. Generally photonic crystals are used for solid state crystals as an optical analog. In this optical analog of crystals the periodic arrangement of atoms increases the energy band gaps. The action of charge carriers is controlled by these energy bands through the crystal which can be changed by adding dopants. By using this method the semiconductor appliances such as diodes, semi conductor lasers and transistors were created. The cavities of photonic crystals also have energy band gaps. These prohibited the broadcast of light which has certain frequency range (Sahand, 2008).
In photonic crystals the molecules or atoms are restored by macroscopic media by conflicting dielectric constants and the same periodic dielectric function is replaced instead of periodic potential. Light reflections and refractions from all different circumferences of crystal can generate several identical phenomena for photons when the materials of crystals are adequately diverse with its dielectric constants and when the materials absorb a minimal of light. The photonic crystals can allow the broadcasting of light in a strange and useful mode. Photonic crystal is a low-loss periodic dielectric medium for ocular control and exploitation. Photonic crystals are very useful for preventing the light from broadcasting in certain directions with particular frequencies.
Photonic crystals let the cavities and waveguides to be indiscriminate and balanced due to their useful properties to cover a larger range of frequencies, due to which photonic crystals are very helpful for metallic waveguides and cavities in controlling microwave broadcast. The metallic waveguide lets the promulgation of electromagnetic waves along its axis only and the metallic cavity walls forbid the promulgation with certain frequencies.
Generally, a 3D structure is very complex, which has its complete control on the light emitted compared to 2d photonic crystal (Hecht, 2009).

Fig (1): 1-D, 2-D and 3-D photonic crystals (Joannopoulos, 2010).
The curiosity on 1D, 2D, 3D photonic crystal microstructures is growing tremendously in past time as their deep implication in both technological and fundamental view. By and large stunning new properties of photonic crystals are expected (Azonano. 2005).
Some different types of structures of photonic crystals in various dimensions are shown below to illustrate.

Fig (2): Various types of photonic crystals with different dimensions (Photonic-Lattice, 2010).
Wood pile photonic crystal is a three-dimensional photonic crystal which was one of the first proposed 3D photonic crystal structures. The opal photonic crystal is the second type, fabricating this type of photonic crystal required a lot of time. For fabrication of this type photonic crystal the self-assembly technique in which the particles of an optical material were used consigned in a liquid. These photonic crystals belong to opal type photonic crystal stack beads. Auto cloned is another type of photonic crystal which is an only multi-dimensional photonic crystal and unruffled of a moulded multilayer film. It was fabricated by predictable spluttering deposition (Photonic-Lattice, 2010).
2.1.1 ONE-DIMENSIONAL PHOTONIC CRYSTALS:
The one-dimensional photonic crystals are fabricated from polymeric materials like black co polymers and polymer–water colloidal crystal arrays by using layer-multiplying co extrusion. The matrix method is used to evaluate the quality of the 1D Photonic Crystals.
The one-dimensional PCs are widely used in thin film optics from low to high reflection coating ranges on mirrors and lenses (Kazmierczak, et al. 2007).

Fig (3): SEM image of an air bridge structure fabrication in 1D photonic crystal (Joannopoulos, 2010).
2.1.2 TWO-DIMENSIONAL PHOTONIC CRYSTALS:
A 2-D PC is periodic along its two axes, and homogeneous to third axis. The 2-D PCs are substantially extended structures with dielectric constant. The vertical cavities of 2-D PC are used to implement several nonlinear functions and these functions are useful for optical image processing. Today the two-dimensional technology is used in manufacturing of electronic integrated circuits because a two-dimensional crystal is supremely suitable to be integrated with existed integrated circuitry. The 2-D PCs have a potential to make integrated circuits. There are two kinds of two-dimensional PCs, one is hole type and other is rod type. First type two-dimensional PCs having cylinders that have low dielectric constant and other consisting of high dielectric constant rods which are encircled by a low dielectric (Kok et al, 2005).

Fig (4): Two-dimensional photonic crystals (Minghao et al, 2004).
2.1.3 THREE DIMENSIONAL PHOTONIC CRYSTALS:
3-D photonic crystals exhibit spontaneous emission. There are several techniques for 3-D Photonic Crystals fabrication some of them are silicon micromachining, angled-etching, auto cloning, wafer fusion bonding, and micromanipulation. 3-D PCs fabrication takes a novel layer-by-layer approach, where, in one process cycle two layers are fabricated. As a result, four process cycles seven functional layers can be achieved. A set of dielectric point defects can be viewed as micro cavities in 3-D Photonic Crystals. At first Nicolet Fourier transformed infrared microscope characterized the Photonic Crystals at room temperature. Fig (5): Schematic of the 3D Photonic Crystals (ideal 3D Photonic Crystal with three hole layers and three rod layer) (Minghao, et al, 2004).
The infrared light that passes through different holes, deviates in hyperbolic reflecting mirror, and is refocused on the sample. It gives a cone-shaped bundle of rays with angle of 350. For all tilt angles, a stop-band is observed from 1.15 µm to 1.6 µm (Minghao, et al, 2004).
2.2 APPLICATIONS OF PHOTONIC CRYSTALS: In next five years the bright LEDs and high efficient photonic crystal lasers are most expected to enter the marketplace. In the last decade the photonic crystal investigation had quickly spread over a wide range of photonics applications. Photonic crystals are used to make narrow-line width lasers for optical communications systems and were also used to create an LED that emits light at a specific wavelength and direction and thus helped to increase the efficiency of LEDs more than 50%. One dimensional photonic crystal is used from low to high level reflection coatings on mirrors and lenses in the form of thin film optics. The photonic crystal fibres are the first two-dimensional photonic crystal. They have more commercial applications. These are used in nonlinear devices and guiding exotic wavelengths. The semiconductor made with Photonic crystals is an excellent optical insulator while being a good electrical conductor. This unique feature of photonic crystals allows them for carrier injection. Photonic crystals can play an indispensable role in manufacturing of optoelectronic chips with mixed optical “circuits” and electronic circuits. The 3-D photonic crystals are still far from commercialization but it leads to a new devise concept e.g. optical computers. * To make highly efficient photonic crystal lasers. * For manufacturing optical computers. * High resolution spectral filters. * To make photonic clothes. * To manufacture photonic crystal diodes and transistors. * To make high efficiency light bulbs. * Highly used in telecommunication & computer networks (Li, 2008).

2.3 FUNDAMENTAL FEATURES OF PHOTONIC CRYSTALS:
By observing the Photonic Band Gap structures while calculating, there are many characteristic features of Band Structures that have been observed. These features are not only very common in one dimensional photonic crystal but also in two-dimensional and three dimensional Photonic crystals.
Some characteristic features of one dimensional photonic crystal: 1. First Band at K 0. Where K= Wave Number in the Band Structure of photonic crystal. 2. Photonic Bands for k near the Brillouin Zone (BZ) Boundary. 3. Propensity of Photon Localization. 4. Slow group velocity. 5. Density of States.
Some of the outstanding and unique features of 2D and 3D photonic crystals: 1. Photonic Band Gap existence. 2. Existence of local mode or defect. 3. Velocity of Anomalous group. 4. Dependence of Remarkable polarization 5. Peculiar Band manifestation 6. Other features.
For controlling light, which means the radiation field and propagation of light the photonic crystals are also very compatible. This potential of photonic crystals is based on the above features of Photonic Band Structure. These features of PBS are very useful in developing devices which are based on Photonic crystals (Inoue and Ohtaka, 2004).

2.4 OPTIMIZATION:
Optimization acts as a centre to the problems relating decision making in many regulations such as mathematics, computer science, statistics, economics and engineering. At present, it is more and more important to have a rigid grasp of the subject due to fast growth in computer technology, as well as the growth and availability of networks, user-friendly software and parallel processors.
In recent years considerable interest was attracted by the spread of waves in periodic media. Possibility of creating periodic structures to exhibit band gaps in their spectrum led to the interests decline. In many wave propagations band gap occurs with elastic, electromagnetic and acoustic waves. Periodic structures exhibiting photonic crystals have been proved very important as a device component for integrated optics together with switches, waveguides, frequency filters and optical buffers.
In 1887, the optimal conditions for the appearance of gaps were first studied for one-dimensional crystals by Lord Rayleigh. By increasing the contrasts in the refractive index and difference in width between the materials, band gap can be widened in one-dimensional array. By changing the periodic length of the crystal it is probable to create band gaps for any particular frequency. No exact principle was yet determined for the existence of a band gap in a periodic structure but one can suggest rule of thumb in two to three dimensions. This made the design for two or three dimensional crystals being far from optimal.
Photonic crystals explain a group of semiconductor structures. It is with a periodic variation of refractive index in 1, 2, or 3 dimensions. By this photonic crystals acquire a photonic band gap, frequencies in which the spread of light is forbidden. To control the light these characteristics of PCs are used. To change the spontaneous emission rate of emitters, designing highly efficient nanoscale lasers and slowing down the group velocity of light PCs are already used.
By observation of optical properties of two-dimensional photonic crystals in InP structures we came to know that the ILS experiment which investigates the combination between the structural analysis and optical characterization helps to appraise the needed improvements in the fabrication process of InP.

2.5 BAND GAP:
Band Gap in solid physics is also known as stop band or energy gap. This is the range of energy present in a solid where states of electron are absent. In electronic band structure’s graph of solids, band gap usually represents the difference in energy (measured in electron volts) in-between valence band of top and conduction band of bottom which can be seen in semiconductors and insulators. This is the energy needed to eliminate/free an electron of outer shell in orbit which is above the nucleus to form mobile charge carriers. This can move free in solid form of materials. Generally two bands overlap each other in conductors to avoid band gap (Streetman and Banerjee, 2000). * 2.6 PHOTONIC BAND GAP: * Photonic Band gap is an energy range for which a material neither allows light nor absorbs light propagation. The energy gap in PBG materials can be closed by inducing defects. Photonic Band gap materials hold potential ranging from optical communications to quantum computations. The Photonic Band Gap is a function of multi-variables which are related to the dielectric structure of Photonic Crystals (PCs).
Yablonovitch and John suggested that the face-centered-cubic (fcc) lattice appears to be favoured for photonic band gaps. Generally Nature gives us fcc crystals. The one-dimensional stop band idea is different from the idea of a photonic band gap as understood in electrical engineering. In 1914, Sir Lawrence Bragg proposed the dynamic theory of x-ray diffraction which is the earliest antecedent to photonic band structure. Because depending on their band gaps the photonic crystals reflect light of different wavelengths (Yablonovitch, 1992). * * * * * * * * DIFFERENCES AND SIMILARITIES BETWEEN ELECTRONIC AND PHOTONIC BAND STRUCTURES: * * S.No | * * Characteristic | * * EBS | * * PBS | * * 1 | * * Underlying | * * Parabolic | * * Linear | * * 2 | * * Angular | * * Spin ½ | * * Spin 1 | * * 3 | * * Momentum | * * Scalar Wave approximation | * * Vector wave character | * * 4 | * * Accuracy of band theory | * Approximate Owing to electron-electron interactions | * * Essentials Exact | * * Table 1: Differences and similarities between electronic and photonic band structures * 2.7 PHOTOIC BANDGAP MATERIALS:
Photonic Band Gap (PBG) Materials are similar to semiconductors, where the electrons are replaced by photons. In recent years there has been growing interest in the development of easily fabricated Photonic Band Gap materials. However, there is more recent work on PBG materials constructed from metals. The main reason for the interest on PBG materials arises from the possible applications several technical and scientific areas such as cavities, filters, more efficient lasers, optical switches etc. Recently Pendry and MacKinnon introduced the transfer-matrix method (TMM). The TMM has been previously used for identifying the defects in 2D PBG structures of PBG materials. The materials used in Photonic Band Gap are also called as Photonic crystals. In semiconductors the PBG materials make the process of rational localization of photons easy. Photonic Band gap materials hold potential ranging from optical communications to quantum computations. The PBG crystals work as electrons in crystalline semiconductors and they also control and affect the electromagnetic (EM) waves in different ways. By creating periodic structures, it is possible to guide the flow of light through the PBG material in a similar way to how electrons are directed through doped regions of semiconductors. These periodic structures are related to the wave length of light, for instance a few hundred nanometers for visible light (Sigalas, et al, 1995).
2.8 TWO-DIMENSIONAL PHOTONIC BAND GAP:
In semi conductors to restrain natural production the periodic dielectric structures have been anticipated. From this, many new concepts and periodic structures of PBGs have been introduced. Structure of Photonic Band Gap is a dielectric and/or metallic system in one, two and three dimensional periodic. For example these structures look like plates in one dimension, rods in two-dimension and like balls in three-dimension.
To get the materials of photonic band gap the two-dimensional periodic structures were investigated with hexagonal symmetry because the structure of band gap related to the properties and features of materials used. The 2D photonic crystals show band gap for the waves to travelling in crystal plane. One property of these two-dimensional photonic crystals is it improves the procedure of electronic appliances which optimize illustrating semiconductor lasers, frequency filters and light-emitting diodes.
To claim in photonic integrated circuits the two-dimensional photonic crystals have an enormous latent. To reduce the dimensions of existing components they are also used. For integration in optical circuits, many investigations have been done on 2D photonic crystals from the last two decades. By the photonic band gap the light is restricted in the side direction and in normal direction by total internal reflection in a 2D photonic crystal. Rod-type structures which contain rods of high dielectric constant bounded by a low dielectric and hole-type structures which contain cylinders of low dielectric constant fixed in an average of high dielectric constant are the illustrious two kinds of 2D photonic crystals (Kok et al, 2005). The crystals with multidimensional periodic structures with a lattice constant of optical wavelength order are called as photonic crystals (PCs). Their use to optoelectronics has become worldwide topics due to the strong control of light by the photonic band gap (PBG). From then two-dimensional photonic crystals can be made-up by the planar technology with lithography and a dry etching. Several groups have studied point-defect PC lasers, filters and line-defect PC waveguides (Inoshita and Baba, 2003).
Micro structured materials and photonic crystals in which the dielectric constant often varies on length scale in 1,2or 3 directions with periodicity similar to the wavelength of light, at different wavelengths the light reflects. A range of wavelengths that a photonic crystal exhibits strong reflection is called a photonic band gap.
Photonic band gap or photonic crystal materials are regularly viewed as an optical analog of semiconductors. These change the properties of light in the same way to a microscopic atomic lattice so as to create a band gap for electrons in semiconductors. Therefore, for handling of light on a micrometer scale they give a stimulating framework and it is necessary for the growth of devices that are now imagined for use in all optical networks. To control the optical properties of solids PCs facilitate band engineering in photonics. By creating defects light can be guided in photonic band gap structures. Photonic crystal waveguide that permit directed light transmission for the frequencies within the band gap can be made by creating a linear defect in a photonic crystal. Due to potential ability of tightly controlling the propagation of light with the possibility of the design and development of photonic band gap based directional couplers, the photonic band gap have been a topic of interest.
For understanding all optical networks the directional couplers are a necessary component in the design of integrated optic devices. Model fields overlap when two waveguides are brought sufficiently close to each other, between the two waveguides power can be moved periodically and this type of structure is known as directional coupler. In power polarization splitting, power splitting, so forth and in wavelength multiplexing/demultiplexing the directional couplers have many interesting functions. Exciting chance for designing compact wavelength-selective optical devices was offered by photonic band gap based waveguide couplers made of photonic band gap materials (Nagpal and Sinha, 2004).
Band-gap is the word to describe the properties of photonic crystals. The continuation of band structure is due to the spread of electromagnetic waves in media with a periodic spatial difference of properties that is refractive index. Single crystal solids are inherently anisotropic and this anisotropy is reflected by the equivalent electronic band structure. In the context of the electronic properties of solids the standard way to represent band structure is to generate a graph of energy vs. momentum.
Photonic crystal structures and its equivalent band structure are both significantly different from semiconductors. The scattering of light and other than the coherent scattering that leads to the survival of band structure and it is as small as probable if the structure being exploited is sufficiently regular. Strong frequency dependent behaviour was shown, typically, the propagation of optical frequency electromagnetic waves through a photonic crystal, although it is nevertheless essentially loss-less in the absence of absorption and deficiency. (Sibilia, Benson and Marciniak, 2008).

CHAPTER 3
3.1 PHOTONIC CRYSTAL STRUCTURE FABRICATION:
Photonic Crystal structures were carved in the GaInAsP/InP hetero structures by CAIBE and e-beam lithography. The A and B samples were fabricated, the intended ƒ values for sample A is 0.25 < ƒ <0.30 and for B 0.30< ƒ< 0.35. The chemically assisted ion beam etching process is used to fabricate the Photonic Crystals in the semiconductor hetero structure. After development of the polymethylmethacrylate in 1: 3 methylisobutylketone or in propanol the pattern of Photonic Crystals is transferred into SiO2. In mask patterning these two steps are high sensitive and for deep holes use thicker masks. The Photonic Crystals structures which are made of deep etched hetero structures air holes are depended on the hole morphology.

Figure (6): The cross section of photonic crystal

Figure (7): The top-view scanning of electron micrographs of a Photonic Crystals structure (Ferrini, et al, 2002).

3.2 PHOTONIC CRYSTAL STRUCTURE LAYOUT:
For both Γ M and Γ K samples oriented structures were fabricated with α =240–500 nm and Δα =20 nm. The 30- m-long Photonic Crystals slabs were fabricated with 3 different thicknesses: 4, 8, and 10 rows. Fig (8): Typical layout of simple Photonic Crystal structures along Γ M and Γ K orientations
Fig (8) shows the sketch of the typical layout of simple Photonic Crystal structures along Γ M and Γ K orientations. Each slab is 30 μm long, 4, 8, or 10 rows thick, and is differentiated by the period α value (Ferrini, et al, 2002).
One-dimensional Photonic Crystal cavities were fabricated by using Γ M-oriented PC-based mirrors separated by a spacer W varying from 500 to 1100 nm (Ferrini, et al, 2002).
3.2.1 NATURAL PHOTONIC CRYSTALS:
Generally Photonic Crystals are found naturally in gemstones and some living organisms like peacock, jelly fish, Morpho butterfly, sea mouse etc. The Morpho butterfly coloration involves in both interference and diffraction effects. Natural photonic crystals are 2D and 3D geometries, but these are not real Photonic Crystals because their dielectric differences are not large (Lipson and Lu, 2009).
In the world several organisms have photonic crystals in their body. The major factor of photonic crystals evaluation in nature is proportional genetic mutation, intracellular and molecular self-assembly combination. All PCs found in nature. Trans-Golgi vesicles manufacture the PCs of the single-celled phytoplankton. The cell organelles have literal control of photonic-crystal growth and packing. All these natural genitival phenomena’s are important for producing the optical devices.

3.2.2 NON-LINEAR PHOTONIC CRYSTALS:
The Nonlinear photonic crystals are also in the form of periodic structure like photonic crystals, but in the case of nonlinear photonic crystals (NLPCs), its structure’s optical response is based on the potency of its optical filed broadcasts into the crystal. As a result the structures obtain new optical properties with new or enhanced functionalities which cannot be got through the application of its linear counterpart. For example optical tunability that means the optical control of devices’ response depends on Photonic Crystal. The dielectric materials which are nonlinear have ultra-fast reaction to optical fields. Through altering the intensity of light in the Non-linear Photonic Crystals (NLPCs) it is possible to use the high level technology potential of photonic crystal. Owing to the change of refractive index of Non-linear Photonic Crystals (NLPCs) and its following shift of the edge of the band gap or the frequency of defect state resonant, the nonlinear photonic crystals have been employed to demonstrate the entire optical switching (Columbia, 2006).
3.3 OPTICS OF PHOTONIC CRYSTALS:
The Photonic Crystals optics is similar to that of anisotropic material crystal optics. The Photonic Crystals may observe as high range of anisotropic crystals which exemplify the crystal optics more prominent. The characteristics features of Photonic Crystals optics have their corresponding part in a uniform anisotropic crystal. For statistical expression, use the Photonic Crystal dielectric spheres of 3.2 reflexive index collections in fcc lattice. The spheres radius is taken as r=0.3α. The numerical results are shown by using Ζ (dimensionless frequency) and K (wave vector) balanced by 2πc/α and 2π/α respectively. Frequency of a CFS (constant frequency surface) is attained by sweeping K (Inoue and Ohtaka, 2004, pp112). 3.3.1 NANOFLUIDIC TUNING OF PHOTONIC CRYSTAL CIRCUITS:
The techniques used in photonic structures for refractive index modulation is limited to the utilization of relatively weak nonlinearities, but Nanofluidics offers high refractive index modulation. Generally PCs are striking for controlling optical propagation. The Nanofluidic tuning of PC circuits includes three levels, the nanophotonic level, the
Nanofluidic delivery level and micro fluidics control engine. Here the Photonic level consist of 30 identical PC structures are dry etching in a substrate of silicon-on-insulator, and had triangular holes constant a=434 nm, 140 nm of hole radius (r), and 207 nm of height (h).

Fig (9): Nanofluidically tunable photonic structures.
(a) The opto-fluidic assembly showing the photonic layer on bottom, fluidic layer in the middle, and control layer on top.
(b) Overview of device operation.
(c) overlay of nano-channels with photonic crystal (Erickson et al, 2006).
In this experiment the radius of holes increased within the photonic Crystal central row to 203 nm. This experiment is based on the series of mathematical experiments by changing the refractive index (Erickson et al, 2006).
3.3.2 OPTICAL PROPERTIES OF PHOTONIC CRYSTALS:
Depending on external illumination of Photonic Crystals by electromagnetic waves, the optical properties of Photonic Crystals are two types and the photonic crystals properties can be classified into two categories. In PBG structure certain frequency is exploited for controlling the electromagnetic radiation.
Photonic crystals solar cells: Germany and UK researchers have made solar cells having three- dimensional photonic crystals. This research can be helpful the design of complicated photovoltaics in the future. In photonic band gaps refractive index of visible light makes a band gap. This band gaps effects the flow of electrons by forbidden energy bands. Now a day’s silicon is used as active material in solar cells, but silicon has fewer converting photons into electricity. The unabsorbed photons are redirected by photonic crystals into silicon. When compare to Aluminium the photonic crystals reflect more light and also diffracts the light (Dume, 2010).
3.4 PHOTONC CRYSTAL SLABS:
Photonic crystals slabs are used to pass out-of-plane losses. The structure of a slab consists of a thin Two- dimensional PC core encircled by two layers that has low effective refractive index. Because of photonic crystal’s finite height the modes are not polarized purely. Different examples of photonic crystal slabs are shown below;

Fig (10): Photonic Crystal Slabs (Dume, 2010). (a) Air-bridge structure with high index contrast between core and cladding. (b) Low-index contrast hetero structure (c) Asymmetrical structure with two different claddings (d) Modulated-pores structure achieved (Dume, 2010)
The difference between Two-Dimensional PCs and PC slabs lies in the light line. If the thickness of the slab is not minute it forms a photonic gap beneath the light line, if it is larger it gives more modes lower the light line. 3D calculations are necessary for finite height structures to determine the band structure. If the thickness of the slab is increased it leads to decrease in the higher order modes cut off frequency (Dume, 2010).
3.5 PHOTONIC CRYSTAL FIBRE (PCF):
The Photonic crystal fibres are ultra-low loss transmission fibres of next generation. The applications of the photonic crystals are spread in nonlinear optics, sensors and power deliveries. According to their mechanism for confinement, the photonic crystals fibres are divided into two modes of operation. Most photonic crystal fibres have been fabricated in silica glass. Photonic crystal fibres can also be modified by coating the holes with sol-gels of similar material to enhance its transmittance of light. The method used to make the optical fibres is used in making the crystal fibres. First step is to construct a pre-form after that heat the pre-form and shrinking pre-form but maintaining the same features. The PCFs are made by stacking of silica rods and tubes into pre-form of the holes which are require for final fibre.
3.5.1 APPLICATIONS OF PHOTONIC CRYSTAL FIBRES:
The applications of photonic crystals fibres are widely spread in fibre-optic communications, high-power transmission, nonlinear devices, highly sensitive gas sensors and fibre lasers areas.
Photonic crystal fibre laser is one of the promising applications of photonic crystal fibres. A high-power fibre laser is one of the great applications of photonic crystals fibres. Photonic crystals fibres lasers act as thermal insulators. Photonic crystal fibre is used as dispersion tailoring devices. The solid-core PCF applications are more mature than that of hollow core applications. The Photonic crystal fibres made lasers play a significant role in many industrial and material processing applications, because it has advantages in efficiency, beam quality, scalability, and operating cost and also Photonic crystal fibres act as thermal insulator.
Solid core fibres are index guiding photonic crystal fibres with solid glass region. Highly bi-refringent fibres are used in optical devices and subsystems to maintain the polarization states. The photonic crystal fibres are successfully exploited to realize non linear fibre devices. Design the photonic crystal fibre with different properties is possible by changing the fibre cross section geometric characteristics (Poli, Cucinotta and Selleri, 2007).
3.6 PHOTONIC CRYSTAL MICRO CAVITIES:
The photonic crystal micro cavity is a form of surface emitter. In photonic crystal micro cavities the size of the photonic lattice defect cavity is few optical wavelengths. The photonic crystal micro cavities are made by AlGaAs-based planar waveguides patterned. The mixture of spontaneous emission with single-mode micro cavities at optical frequencies is basically a new regime in quantum electronics. Single-mode light-emitting diode is the example of this type of device. The micro cavities are formed by inserting defects into a dielectric slab patterned with hexagonal array of air holes. Changing the radius or index of refraction of a single hole is the simple method to forming a micro cavity. If a small defect is introduced in the photonic crystals, that defect behave like a micro cavity surrounded by reflecting walls. If the defect has suitable size to support a state in the band gap, the rate of spontaneous emission will be enhanced. Defect state is exited by increasing the single hole radius and a donor defect state is pulled into the band gap from the air band by decreasing the radius of an individual hole (Erickson et al, 2006). Fig (11): Cross section through the middle of the photonic crystal micro cavity (Theochem, 2010).
3.6.1 APPLICATIONS OF MICRO CAVITIES:
The applications of micro cavities range from telecommunications to nonlinear optics to chemical to biological sensing. Optical micro cavities structure control the optical emission properties, of materials placed inside them; they change the spectral width of the emitted light, modify the special distribution of radiation power and enhance the spontaneous emission rate. Optical micro cavities are used to constructing novel kinds of light-emitting devices. Threshold less lasing is the dramatic potential feature of Optical micro cavities. The micro cavities property, controlling the spontaneous emission plays an important role in generation of optical devices. To controlling the spontaneous emission also lead a remarkable change in oscillation properties of lasers. The attractive feature of micro cavity lasers is the response to speed in excess of 100 gigabits per second. The 2-D or 3-D confined micro cavity increase the response speed through increase the rate of spontaneous emission (Yakoyama, 1992).

CHAPTER 4
4.1 INDIUM PHOSPHIDE (InP):
Indium Phosphide (InP) is a binary semiconductor composed of indium and phosphorus. The structure of InP is zincblende (face-centered cubic crystal).The InP is also called as Indium Monophosphide. The InP belongs to the III-V family semi conductors. In periodic table the III-V elements have a structure like a cubic lattice. As a semi conductor InP has a great energy band gap and transparent. The most advantage of InP is the size of that device. Through its great potential it is very capable to create integrated devices. When compared with common semiconductors, silicon and gallium arsenide InP has high electron velocity.
It is a binary semiconductor composed of indium and phosphorus. Based on the electronic and physical properties InP is the important compound semiconductor for RF and microwave devices. High peak electronic velocity, high thermal conductivity and high electronic field break down are the important properties of indium phosphide. High amount of InP is used in the manufacture of photo electronic devices. It is also used in the fabrication of LEDs, laser diodes, solar cells and hetero junction bipolar transistors for optoelectronic integration and it is also used in high-performance ICs. When compare with common semiconductors silicon and gallium arsenide InP has high electron velocity. The key advantage of InP is its potential for the manufacture of very small devices (Golio, 2001).
At present, most InP-based circuits are made-up of metal-organic chemical vapour deposition or molecular beam epitaxial on Fe-doped semi insulating (SI) InP substrates. In the growth of hetero structures these materials properties are important. The industry standard is 4-inch diameter, but several manufacture companies are developing 6-inch diameter InP substrate capabilities. The manufacturers of integrated circuit required substrate specifications, but currently substrates are available to six different vendors only. Etch Pit Density (EPD) is a key metric for evaluating substrate quality for substrate manufacturers (Fastenau et al, 2005).

4.2 PROPERTIES OF INDIUM PHOSPHIDE:
GENERAL PROPERTIES:
Synonym : Indium Monophosphide
Chemical Formula : InP.
Chemical Family : Metal Phosphide.
Appearance and Odor : Brittle mass with metallic appearance, odorless.
Melting Point : 1070 oC
Crystal structure : Zinc Blende.
Density : 4.81 g/cm3.
Permittivity : 12.56

OPTICAL PROPERTIES:
Infrared refractive index: 3.1
Radioactive recombination coefficient: 1.2·10-10 cm3/s
Indium phosphide substrate:
It is used as a substrate to make cells with band gaps between 1.35eV and 0.74eV. InP has a band gap of 1.35eV.
Amorphous Indium phosphide (a-InP):
It is prepared by flash evaporating crystalline InP or by evaporating the InP components separately and also obtained by ion implantation. a-InP is used in photovoltaic, nuclear particle detector device applications.
4.3 TECHNICAL APPLICATIONS OF INDIUM PHOSPHIDE:
InP is an III-V binary compound semiconductor and it has tetrahedral unit cell structure of sphalerite with positive ‘In’ and negative ‘P’ atoms. Initially InP ingots were grown by Czochralski or Float Zone methods. InP is a direct semiconductor. In InP the photoluminescence is about 15 nm. InP has a good cleavage like other compound semiconductors and it is fabricated as Gunn diodes, laser diodes and solar cells (Walker and Tarn, 1991).
The applications of InP can be divided into two groups, one is optical devices and the other is electron devices. These two are strongly related to optical communication. At present almost all of Japanese InP markets are occupied by optical devices. The subsidiaries of big companies such as NEC, Hitachi, Fujitsu, Mitsubishi, Oki, Sumitomo, Furukawa, and NEL supplied the optical devices to Japan. Japan accounts for about 56% of the consumption of available indium phosphide wafers, and Europe and the USA for 22% each (Miyamoto and Tohmori, 2003).
4.4 STRUCTURE OF INP:
Indium Phosphide crystallizes under normal conditions in the Zinc blende structure. Under pressure the INP-I (Zinc blende) transforms to the InP-II (rock salt) structure and then to InP-III (-tin structure).
Crystal structure of InP: InP has Zinc blende structure. A face-centered cubic structure was formed from indium and phosphorous atoms. Both indium and phosphorous atoms make a tetrahedral binding structure in this indium atoms are surrounded by four phosphorous atoms and phosphorous atoms are surrounded by indium atoms. Tetrahedral binding makes InP as a semiconductor material. The Zinc blend cubic structure has a fourfold symmetric cleavage, so that it is convenient for producing laser devices. In InP crystal growth twinning is the main obstacle, but it is easier than GaAs and GaP because the energy faults of InP is similar than those of GaAs and GaP. InP has good lattice constant when matching with ternary and quaternary in GaAs alloys. This is the cause InP is an indispensable substrate material in fibre communications for laser and photo detectors and some of the electronic devices.

Fig (12): Indium (III) Phosphide
4.5 RAW MATERIALS FOR PRODUCTION OF INP:
InP does not occur naturally. Indium is present in the earth’s crust at concentrations of 50–200 μg/kg. Indium has been detected in air (43ng/m3), seawater (20 μg/L), rainwater (0.59 μg/L), and 10 μg/kg in pork and beef and up to 15 mg/kg in algae.
InP crystals are synthesized from pure indium and phosphorus. Indium combines with several non-metallic elements such as phosphorus and boric oxide. For producing high quality wafers, a huge amount of pure indium, boric oxide and phosphorous are needed and it is also obtained by thermal decomposition of a mixture of a tri-alkyl indium compound and Phosphine (PH3). In the beginning of InP production these material purity was not satisfactory, but now high purity material has produced due to use of advanced technology industries.
Indium: Pure raw indium is produced from fumes, dusts, slags, residues and alloys from Zinc and lead smelting. Indium is precipitated by adding AL or Zn to indium sulphate solution. Indium sulphate solution is abstained from hot sulphuric acid leaching.
Phosphorus: It is produced from phosphorus minerals. In this the main component is fluorine apatite. Yellow phosphorus is recovered from the reduction of cokes. It is flammable. So in thermal conversion process the stable red phosphorus is produced from yellow phosphorus (Manasreh, 2000).
4.6 INDIUM PHOSPHIDE PRODUCTION:
In earlier years liquid encapsulated Czochraski (LEC) method was used for InP crystal production. In this a single crystal is pulled through a boric oxide liquid encapsulant starting from a single crystal seed and a melt of polycrystalline indium phosphide. Before the extrusion of single crystal Fe, S, Sn or Zn is added to the melt, to prevent the indium phosphide decomposition high pressure is applied inside the chamber. In grinding process the single crystal is shaped into a cylinder of the appropriate diameter then it sliced in to wafers.
Uses of Indium Phosphide: * Used in the fabrication of laser diodes. * Used in manufacture LEDs. * Used in hetero junction bipolar transistors. * Used in solar cells. * Used in high-performance ICs. * Used in lasers and photodetectors. * Used to manufacture of devices with much sharper and smaller bends * Used in fabrication of optoelectronic devices.

4.7 INDIUM PHOSPHIDE BAND GAP:
A photoluminescence study is presented of the hydrostatic pressure and temperature dependence of the electronic band structure of InP. By using X-ray diffraction, electron probe microscopy and transmission electron microscopy methods 16 samples (0.0 < x < 0.67) structural and compositional analysis was made. It was determined that the X gap of InP to be 2.435 eV at ambient pressure. According to extrapolating the pressure dependence of the X gap to ambient pressure for the series of samples, it is confirmed that the compositional bowing of the X gap which can be described by E{rm g}^{ rm X}(x) = 2.435 - (0.478)x + (0.400)x^2. The InP energy band gap is also closer to light energy (Alten and Gregory, 1994).

CHAPTER 5 CST MICROWAVE STUDIO DESIGN 5.1 SOFTWARE SIMULATIONS: CST Microwave studio is a software tool which is fully characterized for electromagnetic analysis and design for frequency range, the important feature of CST design is the method on design tool which make using the mesh type or simulator which is the best match for a particular problem. All simulators supports hexahedral grids when they are combined with perfect boundary approximation(PBA) method. An advance method increases the accuracy of the simulations when compared with conventional simulator. The software consists of different simulation methods which are * Transient solver * Frequency domain solver * Integral equation solver * Eigen mode solver 5.1.1 Frequency domain solver: The frequency domain solver consists of highly qualified techniques for calculating the highly resonant structure like filters and also supports tetrahedral and hexahedral mesh types. 5.1.2 Transient solver: Transient solver can obtain the complete frequency behaviour of simulated device on single calculation run; the transient solver due to its flexible in nature is well organized for higher frequency applications like transmission lines, connectors, filter and antennae. For electrical small structures (which are much smaller than shortest wavelength), the transient solver is less competent. For this case instead of transient solver frequency solver domain is advantageous. 5.1.3 Integral equation solver: Integral equation based solver are best suited for electrically huge structures, volumetric discretization techniques basically bears from dispersion effects for which it need extremely fine meshes. 5.1.4 Eigen mode solver: Efficient filter design frequently needs the straight calculation of the operating mode in the filter than S parameter simulation, for this CST microwave studio has a feature called Eigen mode solver which calculates the finite number of modes in closed electromagnetic devices. CST microwave studio is able to analysis and design the electromagnetic devices. 5.2 CST Micro Studio Design a tool which is design for complex systems: CST Design Studio is a latest electromagnetic simulation tool that makes easy in designing the complex and high resonant structures. The electromagnetic field simulations of 3D complex structures arousing a competitive interest in terms of memory and simulation time. CST design allows the grouping of electromagnetic modules according to their scattering limits. The complex system is now divided into sub components and each of them was described by its S-matrix, the complete behaviour of the system can be analyzed very quickly and decreasing the system memory requirements. The interest of CST design capability is to think about higher order mode pairing between the sub components, and the structure can be partitioned into tiny parts without any loss of accuracy. 5.2.1 Functionality: CST design is developed as a complete platform to handle the numerical simulations as well as to design the complex structure. The electromagnetic device like perfect absorber and phase shifter the analytical models were previously implemented in CST Design and optimized the cost exactly within the level. CST design supports the structure of library of microwave components which are described by the results of CST MWS and also handles previously calculated data and ask new simulations runs if required. Being urbanized in the environment the CST design takes an advantage on complicated libraries. CST design allows a commanding visual basic application (VBA) compatible interface which includes editor and macro debugging. 5.3 APPLICATIONS OF CST MICROWAVE STUDIO: 1. CST microwave studio rapidly gives us insight behaviour of Electromagnetic for high frequency designs. 2. A typical microwave and radio frequency applications were included in mobile communications and wireless design which increases the signal integrity and Electromagnetic compatibility /interference. 3. The domain solver and frequency domain solver simulates on hexahedral and tetrahedral grids. Other types of software which are available in market and MIT Photonic bands. Software tool which computes definite frequency Eigen states of Maxwell’s equations in periodic dielectric structures. Periodic dielectric structure exhibits band gap in optical modes, forbidden the propagation of light in that frequency levels. MIT photonic band gaps is frequency domain which computes directly the Eigen values and Eigen states of Maxwell equations using plane wave. Each field of MIT photonic band gap computes a definite frequency. *

5.4 Designing of a Square lattice unit cell using CST Microwave studio:
5.4.1 Procedure for TM mode for Dielectric in Air (D in A): * To create a 2D square unit cell we need to define a brick according to the dimensions of X,Y,Z directions. Generally for square unit cell we take dimensions as (Xmin, Xmax) = (0,1), (Ymin, Ymax) = (0,0.1), (Zmin, Zmax )= (0,1)

Then brick will be obtained as follows

* Then we have to create a cylinder with the outer radius 0.2 with the material InP (Indium Phosphide), because we are creating Dielectric in Air for TE, TM and TETM modes.

Then cylinder will be obtained as follows

Transform the cylinder to all corners of crystal

Now we have to shape out the unit cell by cutting the outer edges using a brick Then the unit crystal cell will be appeared as follows

We can observe the material InP in Vacuum in the figure shown below

Before going to set the frequency we need to check the units and mesh shells.
Units should be Dimensions: µm, Frequency : GHz, Time: s

To increase mesh shells, set the lower mesh limit up to15 according to the outer radius.

Initially we don’t have exact frequency for our specifications, so to get the exact frequency we will just set the frequency from 0 to 1000.

To get the accurate frequency go to Eigenmode solve parameters and click on start without changing any parameters.

Then accurate frequency will be obtained and then we will set the frequency.

Then we have to set the boundary conditions as follows

Then click on phaseshift/Scan angles to set the phase shift. Initially we set the phaseshift from phase to 0

Normally we take the parameters with the range of 180

Now go to Eigenmode Solver and click on parameter sweep

Then click on New sequence, the window will be appeared as follows

In the same window now we have to click on the New parameter, to set the parameters. Generally we take the parameters in the intervals of 0-180, 180-360, 360-540 and we take 10 samples.

Now we have to click on the result watch and we take two frequency modes and the windows will be appeared as follows

Then we click on start, we will get the results from tables which appears in navigation tree

We have right click on the frequency modes from tables and copy the results and paste them in Excel sheet.

Then again we will goto boundary conditions and change the phaseshift form 180-phase and phase to phase for the parameters 180-360 and 360-540 in the eigenmode solver respectively which are shown in the following figures.

Then we will copy the results from tables and paste them in then same excel sheet which used above and we will get graph by scattering them.

TE mode:
For TE mode the process is same as above and only the thing we have to change in boundary conditions. The window will be appeared as follows.

And the remaining procedure will be same and repeated as above from boundary conditions.

5.4.2 Square lattice unit cell results using CST Microwave Studio:
Dielectric in Air:
TM Mode for outer radius 0.2:
Design of a Square Lattie:

Fig (13): 0.2 radius square unit cell

Simulation values: 0 | 143.1614 | 1.62E+05 | 20 | 1.06E+04 | 1.57E+05 | 40 | 2.11E+04 | 1.52E+05 | 60 | 3.13E+04 | 1.47E+05 | 80 | 4.10E+04 | 1.42E+05 | 100 | 5.01E+04 | 1.37E+05 | 120 | 5.82E+04 | 1.32E+05 | 140 | 6.49E+04 | 1.28E+05 | 160 | 6.94E+04 | 1.25E+05 | 180 | 7.10E+04 | 1.24E+05 | 200 | 7.13E+04 | 1.24E+05 | 220 | 7.23E+04 | 1.26E+05 | 240 | 7.37E+04 | 1.29E+05 | 260 | 7.55E+04 | 1.32E+05 | 280 | 7.74E+04 | 1.36E+05 | 300 | 7.94E+04 | 1.40E+05 | 320 | 8.10E+04 | 1.43E+05 | 340 | 8.21E+04 | 1.45E+05 | 360 | 8.25E+04 | 1.46E+05 | 380 | 8.17E+04 | 1.45E+05 | 400 | 7.90E+04 | 1.43E+05 | 420 | 7.39E+04 | 1.41E+05 | 440 | 6.61E+04 | 1.40E+05 | 460 | 5.57E+04 | 1.42E+05 | 480 | 4.33E+04 | 1.45E+05 | 500 | 2.96E+04 | 1.50E+05 | 520 | 1.50E+04 | 1.55E+05 | 540 | 1.43E+02 | 1.62E+05 |

Graph:

R/A (outer radius/unit cell) ratio = 0.2/1 = 0.2

Bandgap = Frequency mode 2 – Frequency mode = (12.4 E+ 04 ) – (8.25 E + 04) = 4.15 E + 04

Animation for 0.2 Dielectric (InP) in air:
Mode = 4
Degree= 0

Animation for Degrees: 180

Animation for Degrees: 360

TE Mode for outer radius 0.35:
Design of a Square Lattie:

Simulation values: 0 | 1156.786 | 2.753989 | 20 | 1.16E+04 | 1.06E+05 | 40 | 2.31E+04 | 1.06E+05 | 60 | 3.43E+04 | 1.05E+05 | 80 | 4.50E+04 | 1.04E+05 | 100 | 5.52E+04 | 1.02E+05 | 120 | 6.46E+04 | 9.95E+04 | 140 | 7.30E+04 | 9.63E+04 | 160 | 8.03E+04 | 9.23E+04 | 180 | 8.50E+04 | 8.87E+04 | 200 | 8.51E+04 | 8.97E+04 | 220 | 8.54E+04 | 9.25E+04 | 240 | 8.59E+04 | 9.69E+04 | 260 | 8.66E+04 | 1.02E+05 | 280 | 8.73E+04 | 1.09E+05 | 300 | 8.80E+04 | 1.15E+05 | 320 | 8.86E+04 | 1.21E+05 | 340 | 8.90E+04 | 1.26E+05 | 360 | 8.91E+04 | 1.27E+05 | 380 | 8.88E+04 | 1.24E+05 | 400 | 8.74E+04 | 1.17E+05 | 420 | 8.35E+04 | 1.10E+05 | 440 | 7.51E+04 | 1.06E+05 | 460 | 6.27E+04 | 1.04E+05 | 480 | 4.82E+04 | 1.05E+05 | 500 | 3.26E+04 | 1.05E+05 | 520 | 1.64E+04 | 1.06E+05 | 540 | 1.16E+03 | 2.75E+00 |

Graph:

R/A (outer radius/unit cell) ratio = 0.35/1 = 0.35

Bandgap = Frequency mode 2 – Frequency mode 1 = (8.87 E+ 04 ) – (8.91 E + 04) = -0.04 E + 04

TETM modes for Dielectric in air for outer radius 0.2:
Simulation values: 0 | 143.1614 | 1.62E+05 | 1913.165 | 0.329189 | 20 | 1.06E+04 | 1.57E+05 | 1.49E+04 | 1.61E+05 | 40 | 2.11E+04 | 1.52E+05 | 2.97E+04 | 1.61E+05 | 60 | 3.13E+04 | 1.47E+05 | 4.44E+04 | 1.60E+05 | 80 | 4.10E+04 | 1.42E+05 | 5.90E+04 | 1.59E+05 | 100 | 5.01E+04 | 1.37E+05 | 7.34E+04 | 1.56E+05 | 120 | 5.82E+04 | 1.32E+05 | 8.75E+04 | 1.52E+05 | 140 | 6.49E+04 | 1.28E+05 | 1.01E+05 | 1.46E+05 | 160 | 6.94E+04 | 1.25E+05 | 1.14E+05 | 1.38E+05 | 180 | 7.10E+04 | 1.24E+05 | 1.22E+05 | 1.31E+05 | 200 | 7.13E+04 | 1.24E+05 | 1.23E+05 | 1.31E+05 | 220 | 7.23E+04 | 1.26E+05 | 1.26E+05 | 1.32E+05 | 240 | 7.37E+04 | 1.29E+05 | 1.31E+05 | 1.34E+05 | 260 | 7.55E+04 | 1.32E+05 | 1.36E+05 | 1.38E+05 | 280 | 7.74E+04 | 1.36E+05 | 1.39E+05 | 1.45E+05 | 300 | 7.94E+04 | 1.40E+05 | 1.41E+05 | 1.54E+05 | 320 | 8.10E+04 | 1.43E+05 | 1.44E+05 | 1.63E+05 | 340 | 8.21E+04 | 1.45E+05 | 1.45E+05 | 1.72E+05 | 360 | 8.25E+04 | 1.46E+05 | 1.46E+05 | 1.76E+05 | 380 | 8.17E+04 | 1.45E+05 | 1.44E+05 | 1.69E+05 | 400 | 7.90E+04 | 1.43E+05 | 1.37E+05 | 1.60E+05 | 420 | 7.39E+04 | 1.41E+05 | 1.22E+05 | 1.57E+05 | 440 | 6.61E+04 | 1.40E+05 | 1.03E+05 | 1.57E+05 | 460 | 5.57E+04 | 1.42E+05 | 8.32E+04 | 1.58E+05 | 480 | 4.33E+04 | 1.45E+05 | 6.27E+04 | 1.60E+05 | 500 | 2.96E+04 | 1.50E+05 | 4.20E+04 | 1.61E+05 | 520 | 1.50E+04 | 1.55E+05 | 2.10E+04 | 1.61E+05 | 540 | 1.43E+02 | 1.62E+05 | 0 | 0 |

Graph:

Vacuum in Dielectric (A in D):
TM mode for outer radius 0.475:
Design of square lattice:

Simulation values: 0 | 36.09828 | 1.23E+05 | 20 | 7960.062 | 1.21E+05 | 40 | 1.59E+04 | 1.17E+05 | 60 | 2.36E+04 | 1.12E+05 | 80 | 3.12E+04 | 1.06E+05 | 100 | 3.84E+04 | 1.01E+05 | 120 | 4.51E+04 | 9.59E+04 | 140 | 5.10E+04 | 9.11E+04 | 160 | 5.54E+04 | 8.73E+04 | 180 | 5.72E+04 | 8.58E+04 | 200 | 5.75E+04 | 8.62E+04 | 220 | 5.83E+04 | 8.73E+04 | 240 | 5.97E+04 | 8.90E+04 | 260 | 6.16E+04 | 9.11E+04 | 280 | 6.37E+04 | 9.34E+04 | 300 | 6.59E+04 | 9.56E+04 | 320 | 6.79E+04 | 9.75E+04 | 340 | 6.93E+04 | 9.88E+04 | 360 | 6.99E+04 | 9.92E+04 | 380 | 6.88E+04 | 9.93E+04 | 400 | 6.53E+04 | 9.99E+04 | 420 | 5.96E+04 | 1.01E+05 | 440 | 5.20E+04 | 1.04E+05 | 460 | 4.30E+04 | 1.08E+05 | 480 | 3.30E+04 | 1.12E+05 | 500 | 2.23E+04 | 1.16E+05 | 520 | 1.12E+04 | 1.21E+05 | 540 | 36.09828 | 1.23E+05 |

Graph:

R/A (outer radius/unit cell) ratio = 0.475/1 = 0.475

Bandgap = Frequency mode 2 – Frequency mode 1 = (8.58 E+ 04 ) – (6.99 E + 04) = 1.59 E + 04

TE mode for outer radius 0.45:

Design of square lattice:

Simulation values:

0 | 440.0953 | 1.627147 | 20 | 8860.297 | 1.20E+05 | 40 | 1.76E+04 | 1.19E+05 | 60 | 2.63E+04 | 1.17E+05 | 80 | 3.46E+04 | 1.14E+05 | 100 | 4.25E+04 | 1.10E+05 | 120 | 4.97E+04 | 1.06E+05 | 140 | 5.59E+04 | 1.03E+05 | 160 | 6.03E+04 | 9.98E+04 | 180 | 6.19E+04 | 9.87E+04 | 200 | 6.27E+04 | 9.88E+04 | 220 | 6.48E+04 | 9.92E+04 | 240 | 6.82E+04 | 9.99E+04 | 260 | 7.25E+04 | 1.01E+05 | 280 | 7.72E+04 | 1.02E+05 | 300 | 8.21E+04 | 1.03E+05 | 320 | 8.65E+04 | 1.03E+05 | 340 | 8.96E+04 | 1.04E+05 | 360 | 9.08E+04 | 1.04E+05 | 380 | 8.84E+04 | 1.04E+05 | 400 | 8.16E+04 | 1.04E+05 | 420 | 7.21E+04 | 1.06E+05 | 440 | 6.11E+04 | 1.08E+05 | 460 | 4.94E+04 | 1.11E+05 | 480 | 3.73E+04 | 1.14E+05 | 500 | 2.50E+04 | 1.18E+05 | 520 | 1.25E+04 | 1.20E+05 | 540 | 4.40E+02 | 1.63E+00 |

Graph:

R/A (outer radius/unit cell) ratio = 0.45/1 = 0.45

Bandgap = Frequency mode 2 – Frequency mode 1 = (9.87 E+ 04 ) – ( 9.08 E + 04) = 0.79 E + 04

TETM modes for Dielectric in air for outer radius 0.475:

Simulation Values: 0 | 36.09828 | 1.23E+05 | 260.7442 | 0.400202 | 20 | 7960.062 | 1.21E+05 | 1.00E+04 | 1.30E+05 | 40 | 1.59E+04 | 1.17E+05 | 2.00E+04 | 1.29E+05 | 60 | 2.36E+04 | 1.12E+05 | 2.98E+04 | 1.27E+05 | 80 | 3.12E+04 | 1.06E+05 | 3.93E+04 | 1.24E+05 | 100 | 3.84E+04 | 1.01E+05 | 4.84E+04 | 1.21E+05 | 120 | 4.51E+04 | 9.59E+04 | 5.67E+04 | 1.17E+05 | 140 | 5.10E+04 | 9.11E+04 | 6.39E+04 | 1.13E+05 | 160 | 5.54E+04 | 8.73E+04 | 6.91E+04 | 1.09E+05 | 180 | 5.72E+04 | 8.58E+04 | 7.11E+04 | 1.08E+05 | 200 | 5.75E+04 | 8.62E+04 | 7.20E+04 | 1.08E+05 | 220 | 5.83E+04 | 8.73E+04 | 7.45E+04 | 1.08E+05 | 240 | 5.97E+04 | 8.90E+04 | 7.83E+04 | 1.09E+05 | 260 | 6.16E+04 | 9.11E+04 | 8.33E+04 | 1.10E+05 | 280 | 6.37E+04 | 9.34E+04 | 8.90E+04 | 1.11E+05 | 300 | 6.59E+04 | 9.56E+04 | 9.49E+04 | 1.13E+05 | 320 | 6.79E+04 | 9.75E+04 | 1.00E+05 | 1.14E+05 | 340 | 6.93E+04 | 9.88E+04 | 1.05E+05 | 1.14E+05 | 360 | 6.99E+04 | 9.92E+04 | 1.06E+05 | 1.15E+05 | 380 | 6.88E+04 | 9.93E+04 | 1.03E+05 | 1.14E+05 | 400 | 6.53E+04 | 9.99E+04 | 9.40E+04 | 1.15E+05 | 420 | 5.96E+04 | 1.01E+05 | 8.24E+04 | 1.17E+05 | 440 | 5.20E+04 | 1.04E+05 | 6.96E+04 | 7.29E+04 | 460 | 4.30E+04 | 1.08E+05 | 5.62E+04 | 1.22E+05 | 480 | 3.30E+04 | 1.12E+05 | 4.24E+04 | 1.25E+05 | 500 | 2.23E+04 | 1.16E+05 | 2.84E+04 | 1.28E+05 | 520 | 1.12E+04 | 1.21E+05 | 1.42E+04 | 1.30E+05 | 540 | 36.09828 | 1.23E+05 | 2.61E+02 | 4.00E-01 |

Graph:

Chapter 6
6.1 CONCLUSION:
The current study is based on basic structures and the patterns of 2 Dimensional photonic band gap of Indium Phosphide. The research was based on 2 D photonic band gap optimization for the further research on the Indium Phosphide. By using the CST microwave studio software 2D photonic crystals has been studied and band gaps are calculated and results are shown above. This approach is done in two modes i.e. TE and TM modes. Partial band gaps are created in 2D anisotropic photonic crystals in simple lattices. The quasi-independent adjustment of refractive indices for the E&H polarization modes can substantially improve the band gaps in 2D photonic crystals.
The groups are studied their applications to light sources including nano lasers, wave guide components and passive components.

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