Simplified Loss Estimation of Splice to Photonic Crystal Fiber using New Model

Anup Karak; Dipankar Kundu; Somenath Sarkar

doi:10.1515/joc-2015-0043

Article

Simplified Loss Estimation of Splice to Photonic Crystal Fiber using New Model

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Published/Copyright: October 13, 2015

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From the journal Journal of Optical Communications Volume 37 Issue 2

Abstract

For a range of fiber parameters and wavelengths, the splice losses between photonic crystal fiber and a single mode fiber are calculated using our simplified and effective model of photonic crystal fiber following a recently developed elaborate method. Again, since the transverse offset and angular mismatch are the serious factors which contribute crucially to splice losses between two optical fibers, these losses between the same couple of fibers are also studied, using our formulation. The concerned results are seen to match fairly excellently with rigorous ones and consistently in comparison with earlier empirical results. Moreover, our formulation can be developed from theoretical framework over entire optogeometrical parameters of photonic crystal fiber within single mode region instead of using deeply involved full vectorial methods. This user-friendly simple approach of computing splice loss should find wide use by experimentalists and system users.

Keywords: photonic crystal fiber; spot size; splice loss; transverse offset; fundamental space-filling mode

PACS: 81.Bm; 42.81.Cn; 42.81.Dp; 42.81.Qb

Acknowledgment

The authors are grateful to the Centre for Research in Nanoscience and Nanotechnology (CRNN), University of Calcutta for infrastructural support. The first author gratefully acknowledges the financial support for award of senior research fellowship of UGC by CRNN, CU. The authors gratefully acknowledge anonymous reviewer for constructive suggestions.

Appendix

The normalized parameters v and u for the infinite cladding region of the chosen PCF are given by [1]:

(11)v=kΛ(nCO2−1)1/2

and

(12)u=kΛ(nCO2−β2k2)1/2

with

(13)u2+w2=v2

To obtain the nFSM, a basic air-hole at the center of a hexagonal unit cell is approximated to a circle in a regular photonic crystal [2]. Then, from relevant boundary conditions for the fields and their derivatives in terms of appropriate special functions, corresponding to a fixed value of v, obtained from eq. (11) for fixed λ and Λ-values, the value of concerned u is computed from the following equation [1]:

(14)wI1anwJ1buY0anu−J0anuY1bu+uI0anwJ1buY1anu−J1anuY1bu=0

where an=d2Λ, b=(32π)1/2

Using eq. (14), Russell has provided a polynomial fit to u, only for d/Λ = 0.4 and nCO = 1.444. However, for all d/Λ values of practical interest in the endlessly single mode region of a PCF, where d/Λ is less than or equal to 0.45, one should have a more general equation for wide applications.

Then the roots, that is, the u-values are obtained from eq. (14), for different d/Λ values at a particular λ, taking nCO = 1.45. The values of nFSM are determined by replacing β/k in eq. (12) with nFSM and this has enabled us to propose a modified simpler formulation of [8] as follows:

(15)nFSM=A+BdΛ+CdΛ2

where A, B and C are three different optimization parameters, dependent on both the relative hole-diameter or hole-size d/Λ and the hole-pitch Λ. Here we take up to quadratic term in eq. (15), which is providing tolerable accuracy at a less cumbersome computation.

Since, the operating wavelengths used in optical communication system are λ=1.55μm and 1.31μm, we only find the coefficients for these two wavelengths for different possible hole-size and hole-pitch. Such modification in the fitting is advantageous in the manner that, it will help us to reduce computation time, since only 9 coefficients are required to compute instead of 27 coefficients [8].

Now, for each value of Λ with the variations of d/Λ, we determine the nFSM values consequent to u values obtained from eq. (14). Applying least square fitting of nFSM in terms of d/Λ to eq. (15) for a particular Λ, we then estimate the values of A, B and C. The various values of A, B and C are then simulated for different Λ in the endlessly single mode region of the PCF, resulting in the empirical relations of A, B and C in eq. (15), in terms of Λ, as given in the following:

(16)A=A0+A1Λ+A2Λ2

(17)B=B0+B1Λ+B2Λ2

(18)C=C0+C1Λ+C2Λ2

where Ai, Bi and Ci (i = 0, 1, and 2) are the optimization parameters for A, B and C respectively. These A, B and C in eq. (15) are same as those in eqs (16)–(18). Computing A, B and C from eqs (16)–(18), one can find nFSM-s directly for any Λ and d/Λ value at any particular λ in the endlessly single mode region of the PCFs, using eq. (15).

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Received: 2015-5-1

Accepted: 2015-9-23

Published Online: 2015-10-13

Published in Print: 2016-6-1

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Articles in the same Issue

https://doi.org/10.1515/joc-2015-0043

Keywords for this article

photonic crystal fiber; spot size; splice loss; transverse offset; fundamental space-filling mode