Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Dependence of mode characteristics on the central defect in elliptical hole photonic crystal fibers

Open Access Open Access

Abstract

Some mode characteristics are obtained by the full vector supercell overlap method that has been developed to model triangular lattice elliptical hole photonic crystal fibers regardless of whether the light is guided by total internal reflection or a photonic bandgap mechanism. When the central defect hole is large enough, the modes are disordered. Birefringence (Δn) dependence on the central defect is discussed in detail by numerical analysis.

©2003 Optical Society of America

Full Article  |  PDF Article
More Like This
Supercell lattice method for photonic crystal fibers

Wang Zhi, Ren Guobin, Lou Shuqin, and Jian Shuisheng
Opt. Express 11(9) 980-991 (2003)

Mode classification and degeneracy in photonic crystal fibers

Ren Guobin, Wang Zhi, Lou Shuqin, and Jian Shuisheng
Opt. Express 11(11) 1310-1321 (2003)

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.


Figures (13)

Fig. 1.
Fig. 1. Schematic of the way in which the transverse dielectric structure is constructed. PC1 is a perfect triangular lattice constructed by the blue elliptical holes, the dielectric constant is εair in the hole and εsi outside the hole. PC2 is another perfect triangular lattice constructed by the coaxial elliptical rings with which the inner major axis is dc and the outer major axis is d, the dielectric constant is 0 in dc or outside d and εsi -εair between dc and d.
Fig. 2.
Fig. 2. Simulation results of the dielectric constant profiles of the PCF and both virtually perfect PCs with parameters of D=2.3 µm, d=0.8D, dc =0.4D, η=2, and N=4.
Fig. 3.
Fig. 3. Minimum sectors for waveguides with C 2ν symmetry. The waveguide modes are classified into four classes (p=1,2,3,4). The solid lines indicate short-circuit boundary conditions, the dashed lines indicate open-circuit boundary conditions.
Fig. 4.
Fig. 4. Modal index of the first 12 modes of the triangular lattice EHPCF with the parameters D=2. 3 µm, d=0.8D, dc =D, η=2, λ=D/0.8.
Fig. 5.
Fig. 5. Electric field vector of the first six modes in the PCF with parameters as in Fig. 4.
Fig. 6.
Fig. 6. Modal index of the first 12 modes of the triangular lattice EHPCF with parameters D=2.3 µm, d=0.8D, dc =0.2D, η=2, λ=D/0.8.
Fig. 7.
Fig. 7. Electric field vector of the first three modes in the PCF with parameters as in Fig. 6.
Fig. 8.
Fig. 8. Mode order of HE11y and HE11x of an EHPCF. The parameters are shown at top right.
Fig. 9.
Fig. 9. (a) Mode orders of HE11y and HE11x of an EHPCF with the parameters shown at right. (b) Relationship between Δn and λ of fibers a, b, and c.
Fig. 10.
Fig. 10. Schematic of fibers a, b, and c, which is helpful to understand the mode disorder between the fundamental doublets.
Fig. 11.
Fig. 11. Relationship between Δn and central defect size dc /D at different wavelengths. The structure parameters of the PCF are D=2.3 µm, d=0.8D, and η=2.
Fig. 12.
Fig. 12. Relationship between Δn and normalized frequency D/λ in the PCFs with different central defect sizes. The parameters are D=2.3 µm, d=0.8D, and η=2.
Fig. 13.
Fig. 13. Relationship between Δn and normalized frequency D/λ in PCFs with different elliptical ratios. The parameters are D=2.3 µm and d=0.8D. The major axis of the elliptical hole is along the (a) y axis or (b) x axis. The major axis length is dc =0.4D.

Tables (1)

Tables Icon

Table 1. Parameters of Virtual PCs for Triangular Lattice PCFs

Equations (21)

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

L [ e x e y ] [ I abcd ( 1 ) + k 2 I abcd ( 2 ) + I abcd ( 3 ) x I abcd ( 4 ) x I abcd ( 4 ) y I abcd ( 1 ) + k 2 I abcd ( 2 ) + I abcd ( 3 ) y ] [ e x e y ] = β j 2 [ e x e y ] ,
I abcd ( 1 ) = + ψ a ( x ) ψ b ( y ) t 2 [ ψ c ( x ) ψ d ( y ) ] dx dy ,
I abcd ( 2 ) = + ε ψ a ( x ) ψ b ( y ) ψ c ( x ) ψ d ( y ) dx dy ,
I abcd ( 3 ) x = + ψ a ( x ) ψ b ( y ) x [ ψ c ( x ) ψ d ( y ) ln ε x ] dx dy ,
I abcd ( 3 ) y = + ψ a ( x ) ψ b ( y ) y [ ψ c ( x ) ψ d ( y ) ln ε y ] dx dy ,
I abcd ( 4 ) x = + ψ a ( x ) ψ b ( y ) x [ ψ c ( x ) ψ d ( y ) ln ε y ] dx dy ,
I abcd ( 4 ) y = + ψ a ( x ) ψ b ( y ) y [ ψ c ( x ) ψ d ( y ) ln ε x ] dx dy ,
ε ( x , y ) = ε | PC 1 + ε | PC 2 , ln ε = ( ln ε ) | PC 1 + ( ln ε ) | PC 2 ,
ε | PC 1 = a , b = 0 P 1 1 P 1 ab cos 2 π a x l 1 x cos 2 π b y l 1 y ,
ε PC 2 = a , b = 0 P 2 1 P 2 ab cos 2 π a x l 2 x cos 2 π b y l 2 y ,
( ln ε ) PC 1 = a , b = 0 P 1 1 P 1 ab ln cos 2 π a x l 1 x cos 2 π b y l 1 y ,
( ln ε ) PC 2 = a , b = 0 P 2 1 P 2 ab ln cos 2 π a x l 2 x cos 2 π b y l 2 y ,
f c = π d c 2 ( 2 η l 2 x l 2 y ) , f 2 = π d 2 ( 2 η l 2 x l 2 y ) ,
ε ( x , y ) PC 2 = m , n = ( P 2 1 ) P 2 1 F 2 ( K mn ) cos ( k 1 x ) cos ( k 2 y ) ,
F 2 ( K mn ) = 2 ( n si 2 n air 2 ) [ f . J 1 ( K mn d 2 ) K mn d 2 f c . J 1 ( K mn d c 2 ) K mn d c 2 ] , K mn 0 ,
F 2 ( 0 ) = ( f f c ) ( n si 2 n air 2 ) ,
K mn = ( m + n ) k x i ( m n ) k y , k x = 2 π l 2 x η , k y = 2 π l 2 y .
I abcd ( 4 ) x = f , g = 0 P 1 1 P 1 fg ln I fac ( 42 ) x I gbd ( 41 ) y f , g = 0 P 2 1 P 2 fg ln IN fac ( 42 ) x IN gbd ( 41 ) y ,
I abcd ( 4 ) y = f , g = 0 P 1 1 P 1 fg ln I fac ( 41 ) x I gbd ( 42 ) y f , g = 0 P 2 1 P 2 fg ln IN fac ( 41 ) x IN gbd ( 42 ) y ,
I i 1 i 2 i 3 ( 41 ) s = + cos ( 2 π i 1 s l 1 s ) s ψ i 2 ( s ) ψ i 3 ( s ) d s ,
I i 1 i 2 i 3 ( 42 ) s = + ψ i 3 ( s ) cos ( 2 π i 1 s l 1 s ) s ψ i 2 ( s ) d s .
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved