Governing Physics

Photonic crystal fibers (PCF) are a type of optical fibers that have a number of air holes arranged in a crystal that runs longitudinally in the structure. One of the designs is a highly birefringent photonic crystal fiber (PCF) with all round holes for transmission in the terahertz (THz) regime.

Background of Photonic Crystal Fiber

Conventional optical fibers can only direct light into a core with a high refractive index by total internal reflection. Using total internal reflections, it is not possible to direct light into an air core.

Initial Developments of PCF

Perfect cancellation in all directions for a narrow band of wavelengths is like the band gap for electrons in semiconductors: that band of light cannot propagate through the crystal. A photonic crystal is made primarily of an electronic semiconductor material, and thus the crystal has an electronic band gap and a photonic band gap.

Application of PCF…

Supercontinuum Generation

The major problem with replacement sources for incandescent lamps based on supercontinuum generation is the pump source. In the extreme case, a supercontinuum source requires a large femtosecond laser system worth hundreds of thousands of dollars, and it is therefore critical to develop more compact and cost-effective supercontinuum schemes.

PCF Laser

But this doubt has now been cleared because it has been found that there is no significant difference in heat dissipation for standard double-coated fiber lasers and properly designed double-coated PCF lasers. This is due to its increased flexibility in single-mode core sizes, increased numerical aperture of pump cores in double-clad fiber configurations, and high thermal stability of low-loss glass fiber structures in research and laser technology.

Sensing Application

In such an acoustic sensor, a photonic crystal mirror and a mirror at the end of the fiber form a FP interferometer [13]. The photonic crystal mirror provides a very thin mirror with high reflectance so that the Fabry-Perot is of low order and has high finesse.

THz Communication

THz Communication Background

The observed spectrum of this terahertz radiation exhibits a peak at 2 THz and a broader peak at 18 THz. In 2011, Japanese electronics maker Rohm and a research team at Osaka University produced a chip capable of transmitting 1.5 Gbit/s using terahertz radiation.

THz Communication Application

Sensing
Imaging
Spectroscopy
Information Showers…
Mobile Access
Security-Sensitive Communications
Fiber Equivalent Wireless Links
Connectivity with Miniature Devices
On-Chip and Chip-to-Chip Links
Safety Monitoring and Quality Control

THz pulsed imaging can actually be seen as an extension of the THz-TDS method. In this way, geometric images of the sample can be produced to reveal its inner structures [18].

Motivation for the Thesis

Objectives of the Thesis

Organization of the Thesis

Photonic crystal fibers (PCFs) characterized by a cladding of air capillaries arranged mostly in a triangular lattice have been a key topic of research in the field of optical fiber communication. The shape of the central defect core is responsible for the PCF's light conduction mechanism: index conduction in the case of a solid core, or bandgap conduction when low-index or hollow cores are used. Since this thesis is concentrated on index guidance of PCF, the methodology to simulate the different characteristics of PCF will be discussed here.

Governing Physics

In equation (2.3), 𝑘0 is the wave number in free space, 𝑛𝑒𝑓𝑓 is the mode index, 𝑛𝑥𝑥, 𝑛𝑦𝑦, 𝑛𝑧𝑧 the diagonal entries of the relative permittivity tensor, associated with the x, y, z components of the electric field.

Finite Element Method

This equation (2.4) can be solved by one of various standard subroutines to obtain various eigenvectors and eigenvalues. When the configuration and other details of the problem can be described in terms of two independent spatial coordinates, the two dimensional elements can be used. Each element is essentially a simple unit within which the unknown can be described in a simple way.

The basic and simplest element useful for two-dimensional analysis is the triangular element.

Applications of FEM

The eigenvalue of λ can be 𝑘02 or 𝛽2 depending on the variational formulation, and {x} are the eigenvectors representing the unknown values of the nodal fields. By dividing the cross-section of the waveguide into triangular elements, the unknown H is also treated as discretized into appropriate subregions. Here, 𝑤𝑥 & 𝑤𝑦 denote the weighting functions, Ω𝑒 is the area of each triangular element, 𝜏𝑖𝑛𝑡 is the line element at the interface between different materials and 𝜏𝑒 is the line element at the calculation boundaries.

Approximating the fields using node-based quadratic basis functions will lead to a generalized sparse eigenvalue matrix equation, which can be solved using an eigenvalue solver to obtain the eigenvalues associated with the modal indices (𝑛𝑒𝑓𝑓) and related to magnetic components. field [𝐻𝑥 𝐻𝑦]𝑇 of the corresponding nodes.

Boundary and Interface Conditions

Perfect Electric Conductor
Perfect Magnetic Conductor
Continuity
Perfectly Matched Layer

The PML is anisotropic and fabricated so that there is no loss in the direction tangential to the interface between the lossless region and the PML. However, in PML there is always a loss in the direction normal to the interface. Here, e is the thickness of the PML layer, which is ideally a multiple of the operating wavelength.

A stable value of the complex effective index can be obtained by varying the thickness of the PML and the distance of the PML from the center of the PCF.

Fig. 2.2 PML region surrounding the waveguide structure.

Dispersion in an optical fiber

Group velocity dispersion
Material Dispersion
Waveguide Dispersion
Polarization Mode Dispersion

The group velocity of a propagating wave is a measure of the wavelength dependence of the effective index in each waveguide. In an optical fiber of length L, a spectral component with frequency ω would arrive at the output end of the fiber after a time delay 𝑇=(L. vg). The frequency dependence of the group velocity leads to pulse broadening simply because different spectral components of the pulse spread out during propagation and do not arrive simultaneously at the fiber output.

If 𝛥ω is the spectral width of the pulse, the amount of pulse broadening for a fiber of length L is determined by -.

Fig. 3.2: Waveguide Dispersion in optical fiber.

Polarization & Birefringence of Light in Optical Fiber

Polarization Properties of Optical Fiber

Conventional circularly symmetric optical fibers do not maintain the polarization state of the guided mode along their length. Although nominally isotropic, small twists, bends and other stresses cause unknown and uncontrollable birefringence of the fiber, making the polarization of the fiber output unpredictable. These problems with random birefringence are solved in PMF by deliberately introducing a higher uniform birefringence throughout the fiber.

Where, and 𝛽𝑦 are the propagation constants of the two modes and 𝑛𝑥 and 𝑛𝑦 are the refractive index that each mode sees, with shorter L𝐵 corresponding to stronger birefringence.

Loss Mechanisms in Optical Fiber

Confinement Loss

Therefore, the loss of confinement is determined by the geometry of the PCF, in particular by the formation of air holes in the cladding. EML increases with increasing core diameter because more material is consumed as core size increases. One of the materials with the lowest material losses is dry air in the THz frequency range.

5.5, 5.6 presents the effective material loss (EML) as a function of frequency and core diameter.

Effective Material Loss (EML)

A Novel Design of Highly Birefringent Flattened Dispersion PCF

Design Approach

Since air holes in the core act as a low-index material and dry air is transparent in the THz frequency range, material absorption loss can be significantly reduced. The core diameter, Dcore= 2(Λ−d/2) was changed while AFF is fixed at 0.75 through all numerical calculations, where d denotes the diameter of the air holes at the cladding region and Λ the distance between two adjacent air holes. For a specific Dcore, the porosity at the core can be obtained by changing the diameter of the air holes.

Asymmetry is created in the core region by introducing rows of small holes with diameter Dcore.

A Novel Design of low loss PCF

Design Approach

Meanwhile, the core air filling fraction was variable and mostly determined by the porosity. The core diameter, Dcore= 2(Λ−d/2) has been changed while AFF is kept fixed at 0.76 throughout all numerical calculations, where d denotes the diameter of the air holes at the cladding region and Λ is the distance between two adjacent air holes. The core part is formed by a triangular lattice distribution of sub-wavelength sized air holes.

The one used in the core has six air holes in the first ring and six added air holes in each added ring.

Analysis for Highly Birefringent and Flattened Dispersion PCF

From Fig.5.3, 5.4, it can be estimated that single-mode exists when Dcore < 279 μm and f < 1.1 THz, which is implied in the following numerical analyses. 5.10, 5.11 show the power current distribution of the proposed PCF at optimal parameters, where it can be observed, especially using the enlarged view in the inset, that the light for a specific effective mode index is well confined around the porous core. To summarize this thesis, we have demonstrated an excellent technique to control the birefringence and loss properties of PCFs by introducing a pair of square holes and circular holes in the central ring of the proposed PCF model.

In the PML settings window, select the PML domain manually by clicking on the diagram. In the Model Builder window, expand the Model 1>Electromagnetic Waves, Frequency Domain node, and then click Wave Equation, Electrical 1. In the Model Builder window, under Model 1, right-click Mesh 1 and choose Physics Controlled Mesh.

Fig. 5.2: Effective refractive index vs. core diameter

Analysis for Low Loss Fiber

Summary

One of our proposed PCF models is significantly simpler than other structures proposed so far to control the birefringence, and dispersion compensating characteristics have been simultaneously achieved in the S-band (1460nm-1530nm), C-band (1530-1565nm) and L-band (1565 nm-1625 nm). Second model gives us low value of losses with a high power fraction in the air holes in the core. The main conclusion of this systematic approach is that with a modest number of design parameters, we could tune and optimize the birefringence and loss properties of the PCF.

Future Work

In the Mode Analysis window, type the desired number of modes as any number between 10 to 20. In the Arrow Surface window, find the Color and Style subsection and select the Arrow Length as normalized. Koucheryavy, "Applicability assessment of terahertz information showers for next-generation wireless networks," in 2016 IEEE International Conference on Communications (ICC), pp.

Koucheryavy, "Co-cooling and information transfer for board-to-board communications," in Proceedings of the Second Annual International Conference on Nanoscale Computing and Communications, NANOCOM' 15, (New York, NY, USA), pp.