Misalignment Consideration in Laser Diode to Circular Core Single-Mode Dispersion-Shifted/Dispersion-Flattened Fiber Excitation via Hemispherical Microlens on the Tip of the Fiber

Kiranmay Kamila; Tapas Ranjan Middya; Sankar Gangopadhyay

doi:10.1515/joc-2015-0027

Article

Misalignment Consideration in Laser Diode to Circular Core Single-Mode Dispersion-Shifted/Dispersion-Flattened Fiber Excitation via Hemispherical Microlens on the Tip of the Fiber

Kiranmay Kamila , Tapas Ranjan Middya and Sankar Gangopadhyay

Published/Copyright: October 16, 2015

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From the journal Journal of Optical Communications Volume 37 Issue 2

Abstract

We report the theoretical study of excitation efficiency in the presence of possible transverse and angular misalignments in the case of excitation of single-mode circular core dispersion-shifted and dispersion-flattened fiber by laser diode via hemispherical microlens on the tip of the fiber. The present study takes into consideration limited aperture allowed by the hemispherical microlens. Employing ABCD matrix technique involving refraction of paraxial rays by a hemispherical microlens on the fiber tip, we formulate analytical expressions for the coupling efficiencies in the presence of the said misalignments. The estimations of the concerned efficiencies as well as associated losses by using our formulations will require little computations. But the results found are sufficiently accurate and the execution of our formalism is simple. Thus the prescribed analytical expressions are useful and new in the sense that prediction of coupling optics can be made accurately but in a simple manner without requiring lengthy numerical integrations concerned with conventional phase model technique. Moreover, the present study, as per our knowledge till date, being the first theoretical investigation of excitation efficiency for the said type of coupling device, will benefit the experimentalists, designers and packagers who are working in the field of optimum launch optics involving such coupler.

Keywords: laser diode; hemispherical microlens; single-mode circular core dispersion-shifted and dispersion-flattened fiber; optical coupling; coupling losses in misalignments

PACS: 42.81.-i; 42.82.-m

Acknowledgment

The authors are indebted to the anonymous honorable reviewer for his critical comments and constructive suggestions.

Appendix A

The input parameter (q1) and output parameter (q2) of the light beam are related as follows [7]:

(20)q2=Aq1+BCq1+D

(21)where 1q1,2=1R1,2−jλ0πw1,22n1,2

Here, R, w, n and λ0 represent the radius of curvature of the wavefront, spot size, refractive index and the wavelength in free space, respectively.

The ABCD matrix involving refraction by the hemispherical microlens of radius R_L on fiber tip can be given by [7]

(22)M=ABCD=1d01101−nnRL1n1u01

This gives

(23)A=1+d1−nnRLB=u+ud1−nnRL+dnC=1−nnRLD=1n+1−nunRL

Here, u stands for the distance of separation between the laser diode and the hemispherical lens and the maximum depth (d) of the lens is incidentally equal to the radius of curvature (R_L) of the lens. The refractive index of the material of the lens with respect to incident medium is denoted by n where n=n2/n1.

The lens transformed spot sizes w_2x,2y and radii of curvature R_2x,2y are found by using eqs (23) (21) and (20) and those are given below:

(24)w2x,2y2=A12w1x,1y2+(λ12B2)/(π2w1x,1y2)nA1D−BC1

(25)1R2x,2y=A1C1w1x,1y2+λ12BD/(π2w1x,1y2)A12w1x,1y2+λ12B2/(π2w1x,1y2)

where λ1=λ0/n1, A1=A+B/R1 and C1=C+D/R1.

Appendix B

The refractive index profile of graded index optical fiber can be presented as

(26)n2(R)={nco2(1−2δf(R)), R≤1ncl2, R>1}

where R=r/a with “a” being the core radius, “r” the radial distance from the axis of the fiber and δ=(nco2−ncl2)/2nco2. Here, nco and ncl denote the refractive indices of the core and cladding, respectively, while f(R) determines the nature of refractive index profile of the fiber.

The different refractive index profile functions f(R) for the fibers used here are given by [21, 31–33]

(I) {f(R)=0, 0<R≤Sf(R)=R−S1−S , S<R≤1 }⇒dispersion-shifted trapezoidal fiber

(II) {f(R)=ρRq, R≤1Cf(R)=ρ, 1C<R≤1 }⇒ dispersion-flattened graded W fiber

(27)(III) {f(R)=0, R≤1Cf(R)=ρ, 1C<R≤1 } ⇒dispersion-flattened step W fiber

Here, the aspect ratio for trapezoidal fiber is represented by “S.” Further, q presents the profile exponent for W fiber and incidentally its value for step index profile is ∞ while ρ, which is a measure of the relative index depth of inner cladding of refractive index n_i, is given as ρ=(nco2−ni2)(nco2−ncl2).

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Received: 2015-3-26

Accepted: 2015-8-20

Published Online: 2015-10-16

Published in Print: 2016-6-1

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https://doi.org/10.1515/joc-2015-0027

Keywords for this article

laser diode; hemispherical microlens; single-mode circular core dispersion-shifted and dispersion-flattened fiber; optical coupling; coupling losses in misalignments