Nanoelectronics Devices: Design, Materials, and Applications (Part II)

Design and Analysis of L-shape Defect-based 2D Photonic Crystal Waveguide for Optical Interconnect Application With Signal Amplification

Abinash Panda¹, *, Chandra Sekhar Mishra², Puspa Devi Pukhrambam¹, Malek Daher³

¹ Department of Electronics and Communication Engineering, National Institute of Technology Silchar, Assam, 788010, India

² Department of Electronics and Communication Engineering, Gandhi Institute for Technological Advancement (GITA), Bhubaneswar, Odisha, India

³ Department of Physics, Islamic University of Gaza, Gaza, Palestine

Abstract

Photonic crystal (PhC) has witnessed an unprecedented research interest since its discovery by Yablonovitch and John in 1987. PhC has undergone substantial theoretical and experimental study because of its periodic dielectric structure and ability to guide and manipulate light at the optical wavelength scale. The photonic band gap (PBG), one of the fundamental characteristics of PhC, prohibits the transmission of light inside a definite wavelength range. The PBG property of PhC opens up enormous opportunities for envisioning a wide range of applications like communication, filtering, bio-sensing, interconnector, modulator, polarizer, environmental safety, food processing etc. However, a peculiar property can be observed when defects are added to PhC, the periodicity of this dielectric structure is disrupted, allowing PC to exhibit high electromagnetic field confinement, a little more volume, and feeble confinement loss. The propagation of light can be altered and engineered by altering the structural characteristics of PhC or introducing appropriate materials into the rods of PC. Among the different applications, optical interconnect is the most escalating application in a photonic integrated circuit. This chapter addresses a novel 2D photonic crystal waveguide for optical amplifier application. The proposed structure comprises 9×9 circular rods of Si with air in the background. A sequence of Si rods is removed to create a defect in the 90o shape. The finite difference time domain method (FDTD) can be adjusted to envisage the electric field allocation along the 90o bend defective region. Several geometrical factors, such as the radius of the Si rods and the gap between lattices, are judiciously optimized in order to realize strong light confinement inside the defect region. The intensity of incident light and the transmitted light is evaluated through numerical analysis, where it is found that the transmitted intensity from the

waveguide is much higher than the intensity of incident light, which ensures that the projected construction can act as an optical amplifier. Apart from this, the bending loss close to the bending area of the photonic waveguide is investigated. A small bending loss of the order of 10-5 exists, which indicates efficient guidance of light along the 90o bend path. Lastly, the confinement loss along the defect region is studied, which is found to be in the order of 10-11. So, the light propagation with negligible loss indicates that the future PCW could be an appropriate applicant for optical interconnect applications.

Keywords: Bending loss, Confinement loss, FDTD, Nonlinearity, Optical interconnect, Photonic crystal waveguide.

* Corresponding author Abinash Panda: Department of Electronics and Communication Engineering, National Institute of Technology Silchar, Assam, 788010, India; E-mail: [email protected]

INTRODUCTION

In 1888, Lord Rayleigh initiated the era of photonics when he proposed a periodic multilayer dielectric stack to realize the mirror application [1]. However, at the time, scientists/researchers were unaware of the importance of photonics towards various societal applications. Almost a century later, in 1987, Eli Yablonovitch and Sajeev John [2, 3] came up with a revolutionary idea on photonic crystal, which completely changed the research perceptive of photonics, and the researchers began to explore the characteristics and applications of periodic structures in depth. Later, V.P. Bykov highlighted the high-dimensional photonic structures [4]. After 1987, nevertheless, the research on photonics has accelerated exponentially, and the fabrication constraints have come up as a hindrance in realizing high-dimensional photonic crystal structures. For the first time, Krauss [5], in 1996, presented the possible fabrication techniques to envisage two-dimensional photonic crystals using semiconductor materials. Besides this, works are also carried out on photonic crystal-based chips or components to communicate data between ON and OFF chips through optical signals. Afterwards, the researchers studied the impact of photonics in the healthcare sector, bioanalytics sensing, quantum computing, optical communications, the food industry, environmental hazards monitoring, display engineering, etc.

In earlier decades, a lot of significant steps were taken to manage the flow of electromagnetic rays in materials by regulating their optical characteristics. The introduction of optical fibers has revolutionized the optical and telecommunication industry, by allowing light guidance through the total internal reflection (TIR) effect [6]. Alternatively, the light can be controlled by using the Bragg diffraction technique, and the same has been the backbone of designing dielectric mirrors [7]. The principle of the dielectric mirror was further researched, and in 1987, scientists explored one-dimensional light reflection material, which led to the discovery of a new class of material called photonic crystal (PhC). The developments of photonic crystals were traced back to 1987, when two milestone publications were available in the journal of Physical Review Letters [8, 9], where the authors noticed the concept of the Photonic Band Gap (PBG). Even though the wave transmission in a periodic medium (containing even 2D optical lattices as well as gratings) had been identified for decades, these investigations opened up a novel avenue of experimental and theoretical inquiry. The fundamental goal of the year 1987 publications was to design the compactness of optical state in specific synthetic materials and remove natural light emanation, hence enhancing laser performance. The broadcast of electronic wave functions (i.e., electron mobility) in semiconductors and electronic lattices is paralleled by the transmission of optical frequencies in a material having a periodic structure.

PHOTONIC CRYSTAL WAVEGUIDE (PCW): CONCEPT AND GEOMETRY

Photonic crystal waveguides are typically generated by a linear defect, which is composed of a row of modified lattice unit cells printed onto a high-index dielectric membrane. Photonic crystals (PhCs) can be created by periodic arrangement of dielectric materials of the varied index of refraction in 1D, 2D and 3D. A plane wave is not an Eigen function of the Helmholtz equation in PCs since they are inhomogeneous materials. An overall field in a PhC is the aggregate of the transmitted and reflected fields from the entire scattering areas (distributed Bragg reflection). DBR and the incident field might add constructively or destructively depending on the structure's period and frequency of operation. When backward transmitting waves totally terminate out forward transmitting waves, the transmission coefficient disappears, resulting in a resonance condition. As a result, photonic crystals can have a certain gap (known as photonic bandgap or PBG [10-12] in the band diagrams, for example, in the figure of momentum vs. photon energy. Further, some frequencies of electromagnetic rays cannot propagate in certain structures. Photonic crystal waveguides (PCWGs) are basically constructed on a silicon-on-insulator (SOI) wafer. The spectral characteristics like communication spectra and reflection spectra are used to examine the whole photonic band gap, index-guided mode and band gap-directed mode. The PCWG's mini-stop bands can be simulated using various structural parameters. The coupling properties of PCWG are theoretically explored, while flaws during the manufacturing process were taken into account. Based on the complexity of their periodicities, PhCs are classified as follows.

ONE-DIMENSIONAL PHOTONIC CRYSTAL

1D PhCs are simple to design and analyse. These structures can be solved analytically with a few steps. 1D PhC is the alternate arrangement of dielectric materials along a single direction [13]. Upon incident light on this periodic structure, each dielectric interface reflects some of the light signals. When the reflected signals are in phase, a strong reflectance is realized due to constructive interference, which is known as Bragg reflection. It possesses many interesting properties like adjustable dispersion and birefringence, homogenous behavioural property, compatibility with existing photonic devices without much change in the fabrication process, etc. In this case, the layers of different dielectric slabs are arranged in such a way that the resulting bandgap performs in a particular direction.

TWO-DIMENSIONAL PHOTONIC CRYSTAL

In a 2D PhC structure, the alternate materials of different RI are implemented throughout the structure along the two directions [14]. The propagation of electromagnetic signals in the 2D PhC is also affected by the PBG mechanism, similar to the 1D PhC. The 2D photonic structure can be better understood by considering two polarizations like TE and TM modes. In TM mode, the magnetic field lies in ‘xy’ plane, whereas the electric field is in ‘z’, and in TE mode, the case is just the opposite, i.e., the magnetic field in ‘z’ plane and the electric field in ‘xy’ plane. Considering these polarizations, two basic topologies are involved in the 2D photonic structure [15]: (a) high refractive index material is enclosed by the material of lower refractive index, and (b) the lower index material is bounded by high refractive index materials. Apart from the traditional PBG mechanism in a regular lattice, light propagation in a 2D PhC could be controlled by inserting defects in the PhC, either point defect or line defect, such that localized defect states are formed inside the PBG. The defect can be created by removing cylinders at the centre or along a line, in order to form a waveguide to support different propagating modes.

THREE-DIMENSIONAL PHOTONIC CRYSTAL

The first 3D PhC was fabricated in the year 1991 by E. Yablonovitch and his research team by the drilling of cylindrical holes in the transparent material in the form of a triangular array. Later, in the year 1994, an innovative type of 3D photonic structure is suggested, which is specifically designed to be amenable for fabrication at the sub-micron scale. The research on the 3D photonic structure has progressed relatively slowly in comparison to other counterparts due to its fabrication constraints and trapping of photons in three directions [16]. Although many researchers have carried out theoretical investigations on the 3D PhC to explore its characteristics, no techniques have been developed in the semiconductor industry for market commercialization. Fig. (1) represents the structural arrangement of 1D, 2D, and 3D PhC.

Fig. (1))

Schematics of 1D/2D/3D PhC [3, 4].

CONTROLLING FACTORS OF PHOTONIC CRYSTALS

Photonic crystals (PhCs) are a relatively new type of optical device that employs a microscopic quarantine principle to regulate electromagnetic radiation [17]. PhC, like its electronic counterpart, has a photonic bandgap, which prevents the passage of an optical signal of a range of frequencies within itself due to the periodic nature of the arrangement of dielectric materials. The operating principle of photonic crystal is greatly influenced by the internal structure parameters. The parameters like dimensionality, symmetry, topology, lattice constant, filling fraction, effective refractive index, refractive index contrast, and scalability play a vital role in deciding the range of band gap and controlling the flow of electromagnetic signals in the structure [18].

Dimensionality: In order to comprehend the functioning mechanism of a PhC, it is necessary to grasp its dimensionality. The variability of the refractive index (RI) with respect to different directions is the basis for such dimensionality. A 1D PhC structure is one in which the RI of a material varies in a periodic fashion only in one direction. Similarly, for 2D and 3D photonic structures, the RI undergoes a periodic repetition along the two and three directions, respectively.

Symmetry: The symmetric property of the PhC can greatly influence the device outcomes. Such symmetric nature of the PhC depends on various types of lattice structures like SC (simple cubic), BCC (body centre cubic), and FCC (front centre cubic). Other than cubic structures, HCP (hexagonal close-packed) and diamond structures, can also be designed.

Topology: It is defined as the investigation of different properties of the PhCs through deformation, structuring, and twisting. If the PhC undergoes such features, the output characteristics of the PhC as well as its operational mechanism, will be altered.

Lattice parameter: The lattice parameter is the most basic variable in a photonic structure. It is explained as the spacing between the adjacent building blocks in the PhC. The value of the lattice parameter has a significant effect on the band gap characteristics, and thus can perform a vital role in monitoring the guidance of electromagnetic waves in the PhC.

Refractive index contrast: The contrast in the RI between the adjacent materials constituting the PhC, regulates the width of the band gap. Apart from this, the difference of RI between the column material and background material of the photonic structure affects the motion of the photons in the crystal. Hence, this parameter needs to be carefully selected by judiciously choosing the material in the design of the PhC.

Scalability: The outcomes which are computed from the theoretical investigation are absolutely scalable as there are no fundamental length scales or refractive index constants inherent in the photonic crystal structure. The explanation of the problematic assignment at one length of the photonic structure is appropriate to other lengths of the signal. The region of the spectrum pertaining to the optical properties of the photonic structure can be perceived by considering the RI of the crystal components, including their filling fraction, and it will be directly proportional to the lattice parameter. Therefore, frequency is usually normalized by the lattice constant.

MECHANISM OF PHOTONIC CRYSTAL

The principle behind the operation of PhC can be the index guiding technique or band gap mechanism.

Index Guiding Mechanism

The fundamental idea of index guiding PhC is identical to that of the conventional optical fibre, in which the core RI is always greater than the cladding RI. It can be developed by modifying some of the crystal parameters, particularly the lattice constant, the refractive index of holes, and filling factors. A consequential variation of the index is found by modifying the crystal parameters, which opens a new technology to control the propagation of electromagnetic waves through the structure. Correspondingly, many applications are designed to be associated with the same.

Band Gap Mechanism

The photonic structure with bandgap properties depends on its artificial fabrication, where the RI of the core is less than that of the cladding. In this case, the system is judiciously modelled such that the electromagnetic waves are opposed only at a certain range of frequencies [19], whereas other ranges of frequencies are allowed to pass through the structure. The prohibited frequency range is termed a bandgap. The bandgap characteristics are influenced by the geometrical parameters like the refractive index of core and cladding, a contrast in refractive index, effective refractive index, periodicity, direction, scalability, topology, and symmetric nature. Based on their geometrical configurations, the photonic bandgap of the aforementioned photonic structures are different. For example, the photonic bandgap of the 1D photonic structure is quite different from 2D as well as from 3D. Even though different computing methods are available for the detection of the photonic bandgap, the plane wave expansion (PWE) method is prevalent among the optical engineering fraternity. Fig. (2) represents the photonic bandgap of 1D, 2D, and 3D structure, which is accomplished with the help of the PWE method.

Fig. (2))

Representation of photonic bandgap of (a) 1D PhC (b) 2D PhC (c) 2D PhC [24].

Computational Methedology

Computational research for photonic crystal waveguides is roughly divided into two categories such as spectral analysis (transmission and reflection calculations) and band structure calculations. Transmission and reflection are determined by utilising the finite difference time domain (FDTD) approach, and band structure is computed utilising the plane wave expansion technique. These approaches are often implemented using formulae based on transmission, transfer, and reflection matrices. To execute the computational approach, the size along the vertical and horizontal directions must be limited, which benefits from the provision of

pseudo-periodicity qualities. In the following sections, the FDTD tool is described in depth.

FINITE DIFFERENCE TIME DOMAIN (FDTD)

In 1966, Yee initiated the FDTD technique, where he presented a discrete solution of Maxwell's equations, which depends on central difference approximation of the spatial as well as temporal derivatives of the curls equation [20]. Yee's technique is relatively effective compared to other methods as it staggered the electric as well as magnetic fields in both time and space to achieve second-order precision. Yee developed a complete three-dimensional formulation and confirmed it using two-dimensional situations. Yee's approach became popular in 1975, when Brodwin and Taflove used this technique to model scattering by biological heating and dielectric cylinders [21]. Holland used it in 1977 to forecast the currents caused on an airplane by an electromagnetic pulse.

The FDTD technique is a rigorous mathematical method that is deployed for computing, modelling, or finding the approximate solution of the electrodynamics differential equation. Being, it is a time-dependent technique, its elucidations can cover an extensive frequency or wavelength range in the solo execution of the program and treat non-linear material properties also. This technique associates with a common class of grid-centered differential time-domain mathematical tools. As far as intrinsic computation is concerned, it focuses with the Maxwell differential equation, which is discretized through the scheme of the center-difference method with respect to time and space, and this method is called FDTD. This particular method has been widely used by the researcher as the various applications have become feasible. As it is required for getting the modal solution of a complex structure, Chan et al. applied FDTD method to investigate the band structure related to complicated material for reliability testing. In this case, the required processing time and memory capacity are varied linearly with the number of grid points included for the computation, which depends upon the intrinsic mechanism of the crystal structure. Apart from this, the first-order differential equation is governed to take the exact initial field with respect to space and time. Further, various types of boundary conditions, including periodic structure, can be applied in particular in the grinding system. Moreover, the combination of the Fourier transform and Frequency domain method is used here to realize the different spectral content. Ward and Pendry further extended the same method to non-orthogonal meshes where the approximation of the equation conserves energy with the help of Green’s function. This method allows the solution of the governing equation inside a photonic structure. The field intensity using the FDTD algorithm is calculated from the Maxwell’s equations, which are written as,

Taking the derivative of the above equations and further simplifying, the fundamental FDTD equation can be stated as below [22],

Moreover, the transmitted and incident power is determined by a straightforward mathematical equation,

Where, ϵ0 indicates the permittivity, E is the electric field intensity, and c is the light velocity.

Next, we move on to calculate Aeff of the fundamental mode for the projected PCW, and the final expression can be written as [22]:

Where, I (x) = |EZ|² , denotes the intensity of electric field distribution.

We analyse the bending loss acquired by the incident signal through transmission. The bending loss (α) of PCW is given below [23],

Where,

In equation (6), VPCF is V parameter of the PCWG [22]. , whereas the term ‘a’ is the lattice constant, n indicates the RI of the circular rod, R denotes the bending radius, and β represents the propagation constant . Finally, the nonlinearity of the designed PCW is discussed as it is a significant parameter in determining the efficiency of the construction. The nonlinearity of the waveguide depends upon the effective area, and nonlinear coefficient (Γ). It can be calculated [24] using the following equations,

VARIOUS DEFECT-BASED PHOTONIC STRUCTURES

Inside the photonic crystals, defects are inserted to direct the desired wavelengths of light. Photonic crystals have the ability to generate localised modes that can arise within photonic band gaps, when the periodic is interrupted or changed locally by defects. There are two sorts of defects to introduce, such as point defects and line defects, which is appeared in Fig. (3).

Fig. (3))

Point defect (Yellow) and a line defect (Red) of photonic crystal waveguide.

The symmetry of the PhC is broken if a single rod is removed or its characteristics are changed in contrast to the remainder of the lattice. Basically, the symmetric or periodicity of a 2D photonic crystal can be destroyed by removing several rods. The effects of symmetry breaking in a 2D photonic crystal differ from those generated by the insertion of flaws in periodic tubes. As a result, breaking has two impacts. Light is trapped in photonic crystal waveguide point defects, and light propagation from one point to another is accomplished by forming a line defect. The photonic crystal waveguide, like the solid state crystal, contains two major defects: cavity defect and extended defect. Cavities are formed as a result of local disturbances. Extended defects are comparable to crystal dislocations, resulting in a spectral area with a transmission band. According to Fig. (2), the periodicity of the waveguide from its original construction is disrupted by deleting a single pillar or modifying the geometry of the pillar. This creates a cavity and confines light in the waveguide's centre.

A 2D photonic structure with a line defect [25] is demonstrated to examine human urine to find the glucose concentration by the principle of PBG variation with respect to different glucose concentrations. Similarly, the potassium chloride sensor is analyzed [26], where a 2D square photonic structure is implemented by using 8×8 rods on silicon. Typhoid-causing agent in the aqueous medium is detected by 2D photonic structure-based biosensor [27], where the FDTD method is used for validation. A 2D photonic crystal with line defect is suggested for cancer cell detection [28] by using PBG variation corresponding to the dielectric constant variation between a normal cell and a cancerous cell. A biosensor that can detect cervical cancer of human being is proposed [29]. The sensor is based on the 2D PhC, which can detect the RI variation between normal as well as cancerous cell. A naive Bayesian classifier of machine learning is also utilised to make the application automatic detection. A photonic crystal cavity sensor [30] which is based on the SOI platform, is presented where the design, fabrication, and other characteristics properties are discussed thoroughly. It is found that the sensitivity is significantly increased by reducing the width of the dielectric stack, and a high-quality factor of 1.3×10⁴ is also realized experimentally. Hemoglobin concentration [31] available in oxygenated as well as deoxygenated human blood is examined by utilising a 3D photonic configuration, where the principle of measurement lies in the photonic bandgap variation in accordance with the hemoglobin concentration. The investigation is carried out by PWE technique at input light wavelengths of 589 and 633 nm. Also, an experimental arrangement is discussed to examine the same. Pertaining to the input parameter for the simulation, the radius of rods in the 3D lattice is 432 nm and the spacing between two holes is 1 μm. A 2D PhC-based force/ pressure sensor [32] is fabricated through operating wavelength of 1300-1400 nm. The structure is based on GaAs/ AlGaAs material, where a high grade of compactness and decent resolution is achieved with sensitivity in the mN range. To achieve high sensing performance, a micro-cavity and a line defect are introduced in the 2D PhC. Using the same

technology and architecture, the design of a photonic-based actuator is also discussed.

Focusing on photonics-based communication, loss arises at the interface of transmitter-waveguide and waveguide-receiver is the major issue. In addition to coupling loss, another non-negligible loss known as bending loss also needs to be addressed. Bending loss arises during the passage of the signal along the bent waveguide [33]. So, a broad investigation needs to be undertaken to optimize the bend region in order to minimize the reflection loss in the bending corner. 2D PhCs with different shapes of defects have become a strong contenders to guide light along a predefined path without bending loss issues. A 120° shape defect is made in a 2D photonic crystal by Tokushima et al., where the authors accomplished a feeble bending loss at the bend region [34]. Similarly, the transmission properties of a 135° bend waveguide are investigated, which is designed on a square lattice 2D photonic crystal [35]. Y. Zhang et al. reported different configurations of defect, such as 90°, 135°, and 180°, where they attained a remarkable transmission of 98.5% [36]. M.K. Moghaddam et al. employed the FDTD technique to investigate the light propagation along the 60° bend PCW. Also, they completely optimized the geometrical parameters to envisage high transmittance over a broad range of wavelengths [37]. M. Danaie et al. reported a Y- shaped PCW for application as a power splitter, where they claimed only 2% of reflectance and 98% of transmittance to the output port. The authors validated the outcomes by simulating the structure by using PWE and FDTD [38]. Yang et al. succeeded in designing a Y junction power splitter with a feeble transmission loss at 162 nm wavelength. For the design, the authors used SOI structure based on photonic crystal slab waveguide [38]. V. Liu studied a 2D PCW, which is comprised of 7х7 rods, and further reported around 100% transmission along the 90° bending regime [39]. Andrey E. Miroshnichenko et al. derived the mathematical equations for 90° bend PCW, and found accurate solutions for reflection and transmission properties [40]. P. Sarkar and his team demonstrated an effective lo loss approach to guide light along an L-shaped PCW and evaluated the bending loss, nonlinearity, and confinement loss [41]. T. Zhang et al. proposed a 2D PCW containing a central elliptical defect to realize filtering applications based on the principle of matching of waveguide and defect modes. At a wavelength of 1.31 μm, the authors were able to attain a quality factor (Q) of 2017.00, and a transmission coefficient of 0.84 [42]. Gomyo et al. integrated a ring cavity with a parallel waveguide to find a filtering application with a transmission coefficient above 95%, and a remarkable quality factor of 4500 [43]. It investigated the optical Kerr effect as well as defective waveguides of the photonic crystal. It has also discussed ultrafast all-optical switches for the creation of two-photon absorption. Based on these findings, researchers were able to achieve the switching using an optical Mach-Zehnder interferometer (MZI) [44]. S. Schuler et al. proposed a graphene-based PCW for data communication applications. Due to improving the light-matter relations, the photonic structure confines the transmission light in a restricted area of the graphene sheet. In addition, a split gate electrode is used to form a p-n junction at the optical absorption zone. Owing to an extra silicon waveguide on both sides of the PhC, a defective waveguide permits for best photo thermoelectric conversion of the temperature outline in graphene into a photovoltage, thereby attracting the device reaction when evaluated to a conventional slot waveguide device [45, 46]. The authors are confident that the extensive analysis of the L-shaped bend PCW presented in this chapter can significantly contribute to this book.

SIMULATION METHODOLOGY

The mainstay of this work is to eliminate bending loss, confinement loss and nonlinearity problems in an L-shaped silicon-based PCWG in order to achieve towering transmission at wavelengths of 1.55 μm. The proposed structure is shown in Fig. (4), which is designed by creating 9×9 circular rods of Si with air in the background. However, sequences of Si rods are removed to create a defect in the 90o shape. The radius of the rods as well as the lattice constant, are selected as 400 nm and 1000 nm, respectively. With the help of the FDTD method computational technique, we studied the electric field distribution in the future 2D L-shaped bend PCWG structure. Fig. (5) illustrates the simulation upshot for the propagation of signal at wavelengths 1.55 μm along the L shape defective waveguide.

Fig. (4))

Crossectional view of the proposed L-shape defect PCW.

Fig. (5))

Signal propagation along the defect waveguide for a=400 nm.

Although the illustrations in the figure seem to be 2D photonic crystal structure, actually it is a 3D representation as illustrated in Fig. (6). In this diagram, the z-axis indicates the field intensity, whereas the x and y-axis indicate the length, and breadth of the PCW, respectively. The above illustration deduces that almost all light signals are contained within the waveguide. The principal reason behind such tight light confinement is the band gap effect. Due to the PBG, light is bounded in the defective region only and unable to escape into the cladding area, thereby reducing the bending loss next to the bend section. Apart from this, we propose that the configuration of 2D photonic waveguide can act as an optical amplifier. The application of optical amplifier is studied by changing the radius of the rods 400 nm, 500 nm and 600 nm. The field distribution along the L-shape defect region is indicated in Figs. (6-8), respectively.

By using the simple numerical equation, we evaluated the transmitted intensities and incident light at the two ports of the L-shaped waveguide. Table 1 shows the light intensities for each considered radius of the rods, where it is perceived that the transmitted light intensity is superior as a comparison of incident light intensity. Therefore, it can be asserted that the proposed 90-bend PCW can be a suitable candidate as an optical amplifier.

Fig. (6))

Electric field intensity at a=400 nm.

Fig. (7))

Electric field intensity at a=500 nm.

Fig. (8))

Electric field intensity at a=600 nm.

Table 1 Light intensities at a different radius of rods.

We explore further into bending loss that arises near the 90o bend area because they are crucial to the practical development of PCWG. The most crucial factor in determining the spectrum range within the waveguide can operate with a minimal bending loss. Furthermore, the propagating mode deviates from the bend zone due to bending, which results in a definite loss in the transmitted signal. Due to the significance of bending loss, we simulated the phenomenon for a number of the radius of the round Si rods (a = 400 nm, 500 nm, 600 nm) using numerical formulations, which is depicted in Fig. (9). In comparison to other choices of the radius of the rods, simulation findings revealed that the proposed 90° waveguide experiences extremely small bending loss at the operational value of 400 nm. It is also evident from this figure that bending loss rises as wavelengths grow, reaching values of 2.96x 10-7 dB/m for a=400 nm at a wavelength of 1.55 μm.

Fig. (9))

Bending loss analysis for various Si rod radius values.

The physics underlying the nonlinearity in photonic crystals is available because of a photon's interactions with atoms, despite the fact that the nonlinearity factor varies on the wavelength or frequency of the signal. Higher nonlinearities appear at lower wavelengths because lower wavelengths cause an atom's vibration to be more intense than at higher wavelengths. We examine the photonic waveguide's nonlinearity using a nonlinear coefficient in order to envisage the aforementioned statement. Fig. (10) illustrates the variation of nonlinearity at a=400 nm. This illustration clearly indicates that nonlinearity reduces as the wavelength rises. Additionally, it is clear that the proposed structure gives very minimal nonlinearity of 4.33 × 10-5w-1μm-1 at the wavelength of 1550 nm.

Finally, we consider confinement loss, which is caused primarily by the leaky character of the transmit mode. To do this, simulation is performed to examine confinement loss with relation to wavelength in case different values of radius of Si rods (a = 400 nm, 500 nm, and 600 nm), and the outcomes are displayed in Fig. (11). As noticed from this figure, at a=400 nm, the structure shows lowest confinement loss (10-11) than the other circular rod size. Also, it is claimed that the minimum confinement loss is found to be 1.26 x 10-11 for a=600 nm at 1.55 μm.

Fig. (10))

Analysis of nonlinearity in the proposed PCW.

Fig. (11))

Analysis of confinement loss for different values of radius of Si rods.

CONCLUSION

In conclusion, we designed a 90o shape defect on a photonic crystal slab to form a waveguide. The entire structure is realized by arranging 9×9 circular rods of Si with air in the background on a square lattice. FDTD simulation technique is employed to scrutinize the electric field distribution at the input and output end of the waveguide. It is revealed that the power at the output end is greater than the power at the input end, which makes the proposed structure a suitable power amplifier. Further, different losses like bending loss, confinement loss, and nonlinearity are studied for various values of radius of the Si rods. Finally, we concluded that the signal can propagate through the L-shaped waveguide with feeble losses. Thus, the proposed structure can be an apt optical interconnect with signal amplification in lightwave circuits.

Multiple Choice Questions

1. Which characteristics of PhC prohibits the transmission of light inside a definite wavelength range:

Photonic band gap

Semiconductor band gap

Insulator bandgap

Zero bandgap

2. When defects are added to PhC, the periodicity of this dielectric structure is disrupted, allowing PC to exhibit:

High electromagnetic field confinement.

A little mode volume.

Feeble confinement loss.

All of above

3. Optical interconnect is the most escalating application in:

Photonic integrated circuit

VLSI Design

Semiconductor Device

All of above

4. First time, who presented the possible fabrication techniques to envisage two-dimensional photonic crystal using the semiconductor materials in 1996?

Lord Rayleigh

V.P. Bykov

Krauss

Eli Yablonovitch and Sajeev John.

5. The operating principle of photonic crystal is greatly influenced by the internal structure parameters. The parameters like____________.

Dimensionality, symmetry, scalability.

Ropology, lattice constant, refractive index contrast.

Filling fraction, effective refractive index.

All of above

6. The fundamental idea of index guiding PhC is identical to that of the conventional optical fiber, in which the core RI is always ______than the cladding RI.

Lower

Zero

Equal

Greater

7. The first 3D PhC was fabricated in the year ______ by E. Yablonovitch and his research team by drill of cylindrical holes in the transparent material in the form of the triangular array.

1988

1990

2000

1991

8. Transmitted intensity from the waveguide is _____ the intensity of incident light, which ensures that the projected construction can act as optical amplifier.

Much higher than

Much Lower than

Equal

Zero

9. The type of absorption loss in an optical fiber are:

Intrinsic

Extrinsic

Both a and b

None of the above

10. The absorption losses is significantly increased due to an increase in ______.

Ionization Radiation

Reflection

Refraction

Scattering of light

11. In which of the following there is no distortion?

Single mode step index fiber.

Graded index fiber.

Multimode step index fiber.

Glass fiber.

12. In an optical fiber, micro-bending loss can be controlled by.

Refractive index of core/cladding.

Radius of core/cladding.

Light wavelength.

Polarization angle.

13. How the macro-bending loss can be minimized in case of multimode fiber?

By maintaining proper direction of propagation.

By designing the fiber with large relative refractive index difference.

By operating at larger wavelength.

By reducing the bend.

14. Maximum modal dispersion is realized in:

Step-index single mode fiber.

Graded-index single mode fiber.

Graded-index multimode fiber.

Step-index multimode fiber.

15. The phenomenon employed in the waveguide operation is:

Reflection

Refraction

Total internal reflection

Adsorption

Answer Key

1. (a)

2. (d)

3. (a)

4. (c)

5. (d)

6. (d)

7. (d)

8. (a)

9. (c)

10. (a)

11. (c)

12. (c)

13. (b)

14. (d)

15. (c)

REFERENCES