Department of Mathematics

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We analyze modal properties of dielectric optical bent slot waveguides by using the multilayer formulation of the well-known classical analytical model of bent waveguides based on the Bessel-Hankel functions. Unlike the previously studied approximate model based on the Airy functions, this model is valid for all values of bend radii. The present approach allows quick and accurate computations of propagation constants, mode profiles, and field-power densities for the 2D bent slot waveguides with very small radii. Using this model we characterize the optimal slot position inside the bent core to maximize the field enhancement in the slot. Such modal analysis is quite useful for the design of devices involving bent slot waveguides. Moreover the results obtained by the present 2D rigorous analytical model can also be used for benchmarking other numerical tools. © 2009 Optical Society of America.

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Analytical modal analysis of bent slot waveguides

In this chapter, a robust watermarking technique based on encryption in fractional wavelet Domain is presented to improve the protection and authentication of the images. The core idea of the proposed watermarking scheme is to encrypt an image via fractional wavelet transform and then watermark is embedded in encrypted image by modifying the singular values. After embedding, watermarked encrypted image is decrypted with the help fractional wavelet transform to get the watermarked image. First, watermarked image is encrypted by same algorithm at the receiver's end and then watermark is extracted by proposed watermark extraction algorithm. The feasibility of this method and its robustness against different kind of attacks are verified by computer simulations. © 2009 Springer-Verlag Berlin Heidelberg.

World University root node

Studies in Computational Intelligence

Encryption based robust watermarking in fractional wavelet domain

This paper presents a new robust reference watermarking scheme based on wavelet packet transform (WPT) and bidiagonal singular value decomposition (bSVD) for copyright protection and authenticity. A small gray scale logo is used as watermark instead of randomly generated Gaussian noise type watermark. A reference watermark is generated by original watermark and the process of embedding is done in wavelet packet domain by modifying the bidiagonal singular values. For the robustness and imperceptibly, watermark is embedded in the selected sub-bands, which are selected by taking into account the variance of the sub-bands, which serves as a measure of the watermark magnitude that could be imperceptibly embedded in each block. For this purpose, the variance is calculated in a small moving square window of size Sp × Sp (typically 3 × 3 or 5 × 5 window) centered at the pixel. A reliable watermark extraction is developed, in which the watermark bidiagonal singular values are extracted by considering the distortion caused by the attacks in neighboring bidiagonal singular values. Experimental evaluation demonstrates that the proposed scheme is able to withstand a variety of attacks and the superiority of the proposed method is carried out by the comparison which is made by us with the existing methods. © 2009 World Scientific Publishing Company.

International Journal of Image and Graphics

ROBUST REFERENCE-WATERMARKING SCHEME USING WAVELET PACKET TRANSFORM and BIDIAGONAL-SINGULAR VALUE DECOMPOSITION

In the recent years, Digital Watermarking is used for copyright protection and authentication. In this paper, a new Dual Watermarking Scheme based on DWT-SVD is presented to improve the robustness and protection. Both Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) have been used as a mathematical tool to embed watermark in the image. In the proposed technique, two watermarks are embedded in the host image. First watermark is called primary watermark, which is a gray scale digital image. Second watermark is called secondary watermark which is a gray scale meaningful logo instead of randomly generated Gaussian noise type watermark. The secondary watermark is embedded into primary watermark and the resultant watermarked image is used as watermark for the host image. A reliable watermark extraction scheme is developed for the extraction of the primary as well as secondary watermark from the distorted image. Experimental evaluation demonstrates that the proposed scheme is able to withstand a variety of attacks. The secondary watermark is easy to detect in all the cases but sometimes primary one is severely distorted. ©2008 IEEE.

1st International Conference on the Applications of Digital Information and Web Technologies, ICADIWT 2008

DWT-SVD based dual watermarking scheme

Collapsibility with respect to a measure of association implies that the measure of association can be obtained from the marginal model. We first discuss model collapsibility and collapsibility with respect to regression coefficients for linear regression models. For parallel regression models, we give simple and different proofs of some of the known results and obtain also certain new results. For random coefficient regression models, we define (average) A-collapsibility and obtain conditions under which it holds. We consider Poisson regression and logistic regression models also, and derive conditions for collapsibility and A-collapsibility, respectively. These results generalize some of the results available in the literature. Some suitable examples are also discussed. © 2007 Elsevier B.V. All rights reserved.

Journal of Statistical Planning and Inference

Collapsibility of regression coefficients and its extensions

In this paper, a dual watermarking scheme based on wavelet packet transform(WPT), singular value decomposition( SVD) and sub-sampling is presented. After dividing original image into four sub-sample images, two sub-images are selected by taking into consideration of block variance singular analysis(BVSA). Then two watermarks are embedded in the selected subimages. First watermark is embedded into one of the selected sub-image by modifying the singular values. For second watermark embedding, another sub-image is transformed into wavelet packet transform domain and embedding is again done by modifying the singular values of the selected sub-bands. After embedding, modified sub-bands are mapped to their original positions for constructing watermarked sub-image. After both embedding, watermarked image is constructed by inverse sub-sampling. Experimental results show good robustness and security of the proposed scheme. A new measure BVSA is presented, which gives an image block from a set of image blocks, whose mean, standard deviation, entropy, gradient and sum of singular values is greater. © 2008 IEEE.

Proceedings - 1st International Conference on Emerging Trends in Engineering and Technology, ICETET 2008

Dual watermarking scheme via sub-sampling in WPT-SVD domain

In this paper, a new robust watermarking scheme is proposed in multiresolution fractional Fourier transform domain using singular value decomposition. The watermark is embedded in the high frequency sub-band of the host image at coarsest level. Although the schemes based on SVD are robust but fail under ambiguity attacks. In this attack, both the owner and attacker can extract their watermark from the watermarked image. To prevent ambiguity, the normalized mass matrix is formed and embedded in the host image. In extraction, normalized mass matrix is extracted first and compared with original one. If the similarity is found then the singular values are extracted to construct the watermark. Experimental evaluation demonstrates that the proposed scheme is able to withstand a variety of attacks. © 2008 IEEE.

Proceedings - 6th Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2008

Robust watermarking scheme based on multiresolution fractional fourier transform

The effects of perturbations of whispering gallery modes (WGMs) in cylindrical microcavities by embedded particles are studied by FDTD modeling. The principal effects are: i) spectral shift of the WGM-related peaks caused by the variation of the average index, ii) broadening of the WGM peaks introduced by the scattering, and iii) splitting of the WGM peaks due to formation of symmetric (SSW) and antisymmetric (ASW) standing waves. The focus of this work is on the last effect. We show that it can be maximized by placing the nanoparticle inside the cavity at a position corresponding to the antinode of the radial distribution of intensity of WGM. It is demonstrated that in this case the magnitude of splitting reaches several angstroms for 5 μm cavities with index 1.59 supporting moderately high quality (Q≈105) WGMs. We show that for relatively small particles with radius &lt;70 nm and index contrasts &lt;0.2 the magnitude of SSW/ASW splitting is linearly dependent on the size and index of the nanoparticle. This allows developing biomolecular sensors based on measuring this splitting in porous cavities. It is predicted that a similar effect of splitting can occur in semiconductor microdisks and pillars where the role of embedded dielectric nanoparticles can be played by self-assembled quantum dots. © 2008 Optical Society of America.

Fulltext

Optics Express

Perturbations of whispering gallery modes by nanoparticles embedded in microcavities

Microresonator filters, which are realized by evanescent coupling of circular cavities with two parallel bus waveguides, are promising candidates for applications in dense wavelength-division multiplexing. Tunability of these filters is an essential feature for their successful deployment. In this paper, we present a framework for modeling of tuning of the microresonators by changes in their cavity core refractive index. Using a reciprocity theorem, a perturbational expression for changes in the cavity propagation constants due to slight modifications of the cavity core refractive index is derived. This expression permits us to analytically calculate shifts in the spectral response of the 2-D resonators. Comparisons of the resultant shifts and spectra with direct simulations based on a coupled mode theory show satisfactory agreement. © 2007 IEEE.

Journal of Lightwave Technology

Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts

For a multidimensional contingency table, we obtain several necessary and sufficient conditions for collapsibility and strict collapsibility, using the technique of Möbius inversion formula. As a consequence, the results of Whittemore (Journal of the Royal Statistical Society B, 40, 328-340, 1978) are stated in a form which is easy to understand and the proofs are much simpler and straightforward. Several new results on collapsibility and strict collapsibility with respect to more than one interaction parameter, are established, and their relationships to conditional independence are also pointed out. As applications of our results, several typical examples on collapsibility, strict collapsibility and conditional independence are discussed. It is also shown that Bishop et al. (Discrete Multivariate Analysis: Theory and Practice, MIT Press, Cambridge, 1975) conditions are necessary and sufficient for strict collapsibility with respect to a set of interaction factors. © 2007 The Institute of Statistical Mathematics, Tokyo.