Therefore, the filters can simultaneously exhibit constant passband group delay and high rejection asymmetrical slopes out of band. A systematic extraction procedure and the normalization expressions to accomplish the synthesis have been presented. To validate it, two different filters Žfourth and fifth orders. have been synthesized, calculating their circuital component values as well as their coupling matrices, and showing their theoretical responses. Likewise, a secondorder filter with two transmission zeros has been designed to illustrate the applicability of these kinds of responses. The filter has only one type of electromagnetic coupling Žcapacitive or inductive, depending on the structure., showing that an elliptic response can be obtained without changing the sign of the elements of the coupling matrix. Three different rectangular waveguide geometries have been designed using the mode-matching technique. The comparison with the theoretical response shows an excellent agreement.

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2001 John Wiley & Sons, Inc.

REFRACTIVE-INDEX PROFILE

OF FIBER OPTICS

Moataza A. Hindy1

1 Department of Electrical Engineering

University of Bahrain

Tsa-Town, State of Bahrain

Recei ed 4 December 2000

ABSTRACT: An optimized approach for obtaining the complex refrac- ti e-index profile of graded-index fiber optics is presented. The measured optical reflections from the sample are used to minimize the norm of the difference between measured and calculated data. An iterati e technique based on a one-dimensional search in the descent direction is applied for obtaining a new estimate of the refracti e-index profile. Numerical experiments are used to apply the gradient technique in sol ing optical in erse problems. 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 252 256, 2001.

Key words: optical fiber; refracti e index; index profile

I. INTRODUCTION

Graded-index fiber exhibits far less intermodal dispersion due to its refractive-index profile. The different group velocities of the modes tend to be normalized by index grading. Obtaining the actual refractive-index profile will lead to accurate modal analysis, determination of the acceptance angle, the numerical aperture and normalized frequency Ž -number., the number of modes propagating within the fiber core, the impulse response, and consequently, the information-carrying capacity of the fiber. In 1 , direct measurement of the refractive indexes of substrates and guiding layers in slab waveguides is presented. The method is based on the excitation of leaky waves in substrates and guided waves in guiding layers, owing to the etching of the grating coupler of the top of the substrates. Based on observations of diffracted or guided beams, the optical characteristics of materials are obtained. In the work of 2 , the authors present a nondestructive experimental method to measure the monotonically varying refractive-index profiles of planar waveguides using Lloyd’s setup, taking into account the multiple reflections inside the sample. In 3 , the authors obtained a functional form of the refractive-index profile of a planar microlens from total shearing interferometric measurements. In 4 and5 , the authors presented mathematical experimental methods to reconstruct the refractive-index profile of a planar optical waveguide. They used sets of measured effective refractive indexes, measured with TE and TM polarization, at different wavelengths. A simple interferometric technique for mapping the refractive-index profile of an optical fiber is presented in 6 . The WKB inverse method and reflectivity calculations are presented in 7 to obtain the refractive-index profile in a planar waveguide. Electromagnetic probing of an inhomogeneous stratified medium is presented in 8 9 . The inverse scattering problem of reconstructing the permittivity and conductivity profiles in an inhomogeneous isotropic lossy dielectric slab has been studied in the time and frequency domains in the literature 10 17 . These approaches need much smoothing, and the initially assumed profile must be close to the actual one. The electrical parameters cannot be evaluated at large depths, and the reconstruction process diverges. In 18 , the authors used the costate method in the time domain, through the knowledge Žmeasuring. of incident,