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Developing the image quality of the two dimensional photonic crystal slab by modifying shape of the photonic crystal.

INTRODUCTION

Vaselago had introduced the concept of negative refractive index materials (left handed materials (LHM)) in 1968 [1] which exhibits a negative refractive index due to the simultaneous negative permeability and permittivity and these materials have electromagnetic properties such as negative refraction, reversed Doppler shift and reversed Cerenkov radiation. Since Pendry [2] suggested that flat slab of LHM can act as a perfect lens to break the limit of diffraction due to amplifying evanescent waves, many investigations have been demonstrated theoretically and experimentally [2-5]. PCs are periodic dielectric structure that affects the motion of photons in much the same way that ionic lattice lattices affect electrons in the solids and it has been shown that a dielectric two-dimensional PC can act as a LHM with a negative refractive index [4]. Recently it has been experimentally demonstrated at the microwave wavelengths, and at the optical communication wavelength. The sub-wavelength resolution of an imaging effects have been demonstrated experimentally [6-9] and theoretically [4, 10-16] for triangular lattice, square lattice and hexagon lattice PCs. There are two kinds of imaging based on negative refraction for PC, one is near field imaging and

another one is far field imaging.

The image quality of the PC have been improved many methods by reducing the reflectivity in the PC surface. In this paper, we improve the image quality of the PC by changing the actual shape of circular rod into elliptical rod of the PC and investigate the propagation of electromagnetic (EM) waves in the PC through the numerical simulation of field pattern.

2. Designing A Hexagon Lattice Of Two Dimensional Photonic Crystal:

We consider PC structures made from hexagon lattice of dielectric rods of permittivity [epsilon] = 12 (silicon) embedded in air background is taken into consideration. Fig. 1 shows the hexagon lattice of 2D PC structure consisting of dielectric rods with radius R=0.3a, where "a" is the lattice constant. The PC slab has 41 columns of dielectric rods in the x-direction and 7 columns of dielectric rods in the z-direction. Then, generally the shape of the dielectric rod is circular. To study EM wave beam propagation in the PC, so only the TE-polarized point source is considered. PC composed of dielectric columns in TE mode of negative refraction phenomenon is more obvious.

3.Numerical Simulation Of Field Patterns:

We employ the finite difference time domain (FDTD) method with the use of perfectly matched layer (PML) boundary condition. A continuous wave point source is placed at (41,-7.996) on the lower side of the PC slab (Fig. 2). The distance between the source and the PC slab is 2.8 and the working wavelength of the source is 1.55[micro]m. The simulated electric field map clearly demonstrates the superlensing effect in such a PC slab. Fig. 3 shows the propagation maps for this case.

An image is formed on the upper side of the PC slab and the phase difference between the source and image is zero. The distance between the source and image is 11.4.

In order to further develop the imaging quality of this hexagon lattice PC slab, we can change the circular shape into elliptical shape of the dielectric rods of the PC slab. The major radius of the elliptical dielectric rod is

0.3a and the minor radius of the dielectric rod is 0.2a. Fig. 4 shows the changed PC shape of the elliptical dielectric rods. For a changed PC slab, the source position remain unchanged.

For the changed PC slab, the distance between the source and image is no longer fixed, because it is not a good photonic crystal. The source and image have the same phases, which is the theoretical expectation of Pendry. The position of image must be the convergence direction of light and the image of the changed photonic crystal must appear near the image of the original photonic crystal. Fig. 5 shows the propagation maps of point source across the changed PC slab with wavelength 1.55[micro]m. In Fig. 5(b), (d), (f) we cannot find evident image, but Fig. 5(a), (c), (e), (g), a high quality of image above the slab is determined. It is founded the quality of image is optimal when the position of the

Fig. 6 shows the intensityof image across the original PC slab and the changed PC slab with the best structure when the wavelength of the source is 1.55[micro]m and the source position is (41, -3.996a). Fig. 7 shows the FWHM versus the object distance moves from (41, -6.996) to (41, -9.996). For the original slab, the FWHM vary with the postion of source changing, the maximum value of FWHM is 0.5 and minimum value is 0.33. For the changed slab with the best parameter the FWHM fluctuate between 0.21 to 0.26.

Conclusion:

In this Paper, we propose two dimensional photonic crystals with hexagon lattice and its imaging quality has been investigated. It has been demonstrated that image quality can be improved by changing the shape of the photonic crystal from circular dielectric rods into elliptical dielectric rods, the image quality improved at fixed wavelength of the source and the same lattice constant.

REFERENCES

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[5.] Xie, G.B., T.Geng, Y.Wang, 2013. Negative Refraction Properties of Anisotropic Magnetic Materials at Ferromagnetic Resonance, J.Univ.ShanghaiSci.Technol., 35: 440448.

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[7.] Berrier, A., M.Mulot, M.Swillo, M.Qiu, L.Thylen, A.Talneau, S.Anand, 2004. Negative refraction at infrared wavelengths in a two-dimensional photonic crystal, Phys. Rev. Lett. 93: 073902.

[8.] Martinez, A., H.Miguez, A.Griol, J.Marti, 2004. Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens, Phys. Rev. B 69: 165119.

[9.] Guven, K., K.Aydin, K.Alici, C.Soukoulis, E.Ozbay, 2004. Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens, Phys. Rev. B 70: 205125.

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[15.] Sun, J., Y. Shen, J. Chen, L. Wang, J. Zhou, Y. Zhang, K. Han, G. Tang, 2011. Improving unrestricted imaging quality of a triangular lattice photonic crystal slab by modifying surface configuration, Phys. B: Condens. Matter, 406: 461466.

(1) Arulkumar Y, (2) Sivanantharaja A, (3) Selvendran S

(1,2) A.C. College of Engineering and Technology, Karaikudi, Tamil Nadu, India -630 003.

(3) KL University, Green Fields, Vaddeswaram, Guntur, A.P, India-522 502

Received 28 February 2017; Accepted 29 April 2017; Available online 2 May 2017

Address For Correspondence:

Arulkumar Y,,A.C. College of Engineering and Technology, Karaikudi, Tamil Nadu, India -630 003.

E-mail: arul08kumar@gmail.com_

Caption: Fig. 1: Schematic diagram of the hexagon-lattice dielectric rods of permittivity [epsilon] = 12 embedded in air background.

Caption: Fig. 2: Schematic simulation diagram, the distance between the source and the PC slab is 1.2a.

Caption: Fig. 3: The propagation maps of a point source and its image against 2D PC slab.

Caption: Fig. 4:The position of the defect shape changes from bottom to top (a) modified first row (b) modified second row (c) modified third row (d) modified fourth row (e) modified fifth row (g) modified sixth row (h) modified seventh row.

Caption: Fig. 5: Propagation maps of point source across the changed slab for TE mode point source (a) the modified first row (b) the modified second row (c) the modified third row (d) the modified fourth row (e) the modified fifth row (f) the modified sixth row (7) the modified seventh row modified row is optimal when the position of the modified row is at the bottom layer.

Caption: Fig. 6: The intensity of image across the PC slab (a) original slab (b) changed slab.

Caption: Fig. 7: The FWHM of the image versus object position as the source move from (41,-3.996) to (41,-6.996).
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Author:Arulkumar, Y.; Sivanantharaja, A.; Selvendran, S.
Publication:Advances in Natural and Applied Sciences
Date:May 1, 2017
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