Weakly guiding analysis of elliptical core step index waveguides based on the characteristic numbers of Mathieu's equation

Shaw, J. K.; Henry, W.M.; Winfrey, W. R.

doi:10.1109/50.475576

Cited by 22 publications

(13 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These investigations started as a natural extension of those on the standard step-index optical fiber of circular cross section. The fibers of elliptical cross section exhibited a rich variety of modal characteristics and also shown the polarization of the modes [19,23] which have been studied both by analytical and numerical methods [3,24,25].…”

Section: Introductionmentioning

confidence: 99%

Modal analysis and dispersion curves of an elliptical W-type single mode fiber

et al. 2015

View full text Add to dashboard Cite

In this paper, the propagation of electromagnetic waves in W-type elliptical dielectric optical fiber having various cladding layers is presented. The presented fiber has concentric core and cladding which have elliptical cross section and the refractive index of one of the inner cladding (the cladding between first clad and last clad) maximum. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the fiber to be studied is determined by solving the Mathieu (q > 0) and the modified Mathieu functions (q < 0). In order to study the fundamental mode, the modal index m is put as m = 1. Finally, the cutoff frequencies for several lower order modes have been calculated and their dispersion characteristics are plotted. The effects of elliptical eccentricity e on the mode cutoff frequencies and mode transmissions are also addressed. The analysis shows that one can control the propagation property of optical fiber by increasing the number of inner claddings. These claddings provide additional degree of freedom to control the modes.

show abstract

Section: Introductionmentioning

confidence: 99%

Modal analysis and dispersion curves of an elliptical W-type single mode fiber

et al. 2015

View full text Add to dashboard Cite

show abstract

“…The concept of the proposed Bragg waveguide stems from some recent research articles on elliptical cored optical waveguides [17–20] and Mathieu functions [21, 22]. Shaw et al [17] developed a new analysis of weakly guiding mode in elliptical core step index optical fibers. An analysis of suspended strip of elliptical cross section by separation of variables was made by Rozzi et al [18].…”

Section: Introductionmentioning

confidence: 99%

Modal characteristic equation and dispersion characteristics for an elliptical Bragg waveguide with a small number of claddings

Prajapati¹,

Singh

Saini³

2011

Micro & Optical Tech Letters

View full text Add to dashboard Cite

This article presents a rigorous analytical treatment of electromagnetic wave propagation in a new type of Bragg waveguide having elliptical core cross‐section surrounded by Bragg cladding layers. Using Maxwell's equations in elliptical coordinates, the field components are obtained that specially incorporate Mathieu (q > 0) and the modified Mathieu functions (q < 0). Using this equation the modal dispersion curves for even guided modes are obtained and plotted for different cladding eccentricity e. It is found that the dispersion curves are discontinuous and modes can exist only in particular wavelength bands. Finally, the modal birefringence in the said waveguide is also estimated. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:932–938, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25863

show abstract

“…The solution of (1) in a medium with modulated density [4]. They have also long been applied on a broad scope of waveguide problems involving elliptical geometry, including: (i) analysis for weak guiding for step index elliptical core optical fibres [5], (ii) power transport of elliptical waveguides [6,7], (iii) evaluating radiated waves of elliptical horn antennas [8], (iv) elliptical annular microstrip antennas with arbitrary eccentricity [9], and (v) scattering by a coated strip [10].…”

Section: Introductionmentioning

confidence: 99%

Elliptic-Cylindrical Wavelets: The Mathieu Wavelets

Lira

Oliveira

Cintra³

2004

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and the smoothing filter is related to the solution of a Mathieu equation of odd characteristic exponent. The number of notches of these filters can be easily designed. Wavelets derived by this method have potential application in the fields of Optics and Electromagnetism.

show abstract

Weakly guiding analysis of elliptical core step index waveguides based on the characteristic numbers of Mathieu's equation

Cited by 22 publications

References 36 publications

Modal analysis and dispersion curves of an elliptical W-type single mode fiber

Modal analysis and dispersion curves of an elliptical W-type single mode fiber

Modal characteristic equation and dispersion characteristics for an elliptical Bragg waveguide with a small number of claddings

Elliptic-Cylindrical Wavelets: The Mathieu Wavelets

Contact Info

Product

Resources

About