Empirical relations for simple design of photonic crystal fibers

Kunimasa Saitoh; Masanori Koshiba

doi:10.1364/OPEX.13.000267

Optics Express
Vol. 13,
Issue 1,
pp. 267-274
(2005)
•https://doi.org/10.1364/OPEX.13.000267

Empirical relations for simple design of photonic crystal fibers

Kunimasa Saitoh and Masanori Koshiba

Open Access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Kunimasa Saitoh and Masanori Koshiba, "Empirical relations for simple design of photonic crystal fibers," Opt. Express 13, 267-274 (2005)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

In order to simply design a photonic crystal fiber (PCF), we provide numerically based empirical relations for V parameter and W parameter of PCFs only dependent on the two structural parameters — the air hole diameter and the hole pitch. We demonstrate the accuracy of these expressions by comparing the proposed empirical relations with the results of full-vector finite element method. Through the empirical relations we can easily evaluate the fundamental properties of PCFs without the need for numerical computations.

Full Article | PDF Article

More Like This

Approximate empirical relations for nonlinear photonic crystal fibers

Kunimasa Saitoh, Takeshi Fujisawa, Takahito Kirihara, and Masanori Koshiba
Opt. Express 14(14) 6572-6582 (2006)

Applicability of classical optical fiber theories to holey fibers

Masanori Koshiba and Kunimasa Saitoh
Opt. Lett. 29(15) 1739-1741 (2004)

Photonic crystal fiber design based on the V-parameter

Martin Dybendal Nielsen and Niels Asger Mortensen
Opt. Express 11(21) 2762-2768 (2003)

Previous Article Next Article

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.

Fig. 1. Index-guiding photonic crystal fiber.

Download Full Size | PDF

Fig. 2. Effective V parameter as a function of λ/Λ.

Download Full Size | PDF

Fig. 3. Effective cladding index as a function of λ/Λ.

Download Full Size | PDF

Fig. 4. Effective W parameter as a function of λ/Λ.

Download Full Size | PDF

Fig. 5. Effective index of the fundamental mode n_eff as a function of λ/Λ.

Download Full Size | PDF

Fig. 6. Chromatic dispersion as a function of wavelength for (a) Λ=2.0 µm, (b) Λ=2.5 µm, and (c) Λ=3.0 µm. Solid curves, results of empirical relations; dashed curves, results of vector FEM.

Download Full Size | PDF

Tables (2)

Table 1. Fitting coefficients in Eq. (6).

View Table | View all tables in this article

Table 2. Fitting coefficients in Eq. (8).

View Table | View all tables in this article

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

V = \frac{2 π}{λ} a_{eff} \sqrt{n_{co}^{2} - n_{FSM}^{2}} = \sqrt{U^{2} + W^{2}}

U = \frac{2 π}{λ} a_{eff} \sqrt{n_{co}^{2} - n_{eff}^{2}}

W = \frac{2 π}{λ} a_{eff} \sqrt{n_{eff}^{2} - n_{FSM}^{2}}

V_{eff} = \frac{2 π}{λ} Λ \sqrt{n_{eff}^{2} - n_{FSM}^{2}}

V (\frac{λ}{Λ}, \frac{d}{Λ}) = A_{1} + \frac{A_{2}}{1 + A_{3} \exp (A_{4} λ ⁄ Λ)}

A_{i} = a_{i 0} + a_{i 1} {(\frac{d}{Λ})}^{b_{i 1}} + a_{i 2} {(\frac{d}{Λ})}^{b_{i 2}} + a_{i 3} {(\frac{d}{Λ})}^{b_{i 3}}

W (\frac{λ}{Λ}, \frac{d}{Λ}) = B_{1} + \frac{B_{2}}{1 + B_{3} \exp (B_{4} λ ⁄ Λ)}

B_{i} = c_{i 0} + c_{i 1} {(\frac{d}{Λ})}^{d_{i 1}} + c_{i 2} {(\frac{d}{Λ})}^{d_{i 2}} + c_{i 3} {(\frac{d}{Λ})}^{d_{i 3}}

D = - \frac{λ}{c} \frac{d^{2} n_{eff}}{d λ^{2}} + D_{m}

	i=1	i=2	i=3	i=4
a _i0	0.54808	0.71041	0.16904	-1.52736
a _i1	5.00401	9.73491	1.85765	1.06745
a _i2	-10.43248	47.41496	18.96849	1.93229
a _i3	8.22992	-437.50962	-42.4318	3.89
b _i1	5	1.8	1.7	-0.84
b _i2	7	7.32	10	1.02
b _i3	9	22.8	14	13.4

	i=1	i=2	i=3	i=4
c _i0	-0.0973	0.53193	0.24876	5.29801
c _i1	-16.70566	6.70858	2.72423	0.05142
c _i2	67.13845	52.04855	13.28649	-5.18302
c _i3	-50.25518	-540.66947	-36.80372	2.7641
d _i1	7	1.49	3.85	-2
d _i2	9	6.58	10	0.41
d _i3	10	24.8	15	6

	i=1	i=2	i=3	i=4
a _i0	0.54808	0.71041	0.16904	-1.52736
a _i1	5.00401	9.73491	1.85765	1.06745
a _i2	-10.43248	47.41496	18.96849	1.93229
a _i3	8.22992	-437.50962	-42.4318	3.89
b _i1	5	1.8	1.7	-0.84
b _i2	7	7.32	10	1.02
b _i3	9	22.8	14	13.4

	i=1	i=2	i=3	i=4
c _i0	-0.0973	0.53193	0.24876	5.29801
c _i1	-16.70566	6.70858	2.72423	0.05142
c _i2	67.13845	52.04855	13.28649	-5.18302
c _i3	-50.25518	-540.66947	-36.80372	2.7641
d _i1	7	1.49	3.85	-2
d _i2	9	6.58	10	0.41
d _i3	10	24.8	15	6

Abstract

Cited By

Figures (6)

Tables (2)

Equations (9)

Optics Express