Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Reflection symmetry and mode transversality in microstructured fibers

Michael J. Steel

Open Access Open Access

Abstract

We investigate the influence of reflection symmetry on the properties of the modes of microstructured optical fibers. It is found that structures with reflection symmetry tend to support non-degenerate modes which are closer in nature to the analogous TE and TM modes of circular step-index fibers, as compared with fibers with only rotational symmetry. Reflection symmetry induces modes to exhibit smaller longitudinal components and transverse fields which are more strongly reminiscent of the radial and azimuthal modes of circular fibers. The tendency towards “transversality” can be viewed as a result of the interaction of group theoretical restrictions on the mode profiles and minimization of the Maxwell Hamiltonian.

©2004 Optical Society of America

Full Article  |  PDF Article
More Like This
Mode symmetry in microstructured fibres revisited

David Bird
Opt. Express 26(24) 31454-31463 (2018)

Improved symmetry analysis of many-moded microstructure optical fibers

John M. Fini
J. Opt. Soc. Am. B 21(8) 1431-1436 (2004)

Symmetry and degeneracy in microstructured optical fibers

M. J. Steel, T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten
Opt. Lett. 26(8) 488-490 (2001)

View More...

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 (10)
Fig. 1.
Fig. 1. Schematic of three “satellite” fibers with symmetry groups C 6v [(a) and (b)] and C 6 [(c)]. All three fibers support degenerate modes, but only (a) and (b) possess reflection symmetry. The fibers are referred to in the text as A6v , B6v and C 6.

Download Full Size | PDF

Fig. 2.
Fig. 2. (a) hz , (b) h t and (c) e t for the TE0 mode of a circular fiber. The fields of the TM0 mode are qualitatively similar with the roles of E and H reversed.

Download Full Size | PDF

Fig. 3.
Fig. 3. Mode spectra for (a) a glass-air circular step-index fiber (core diameter 5µm, nco =1.45), and (b) fiber A6v at l=1.55µm.

Download Full Size | PDF

Fig. 4.
Fig. 4. Mode profiles for the lowest p=1 mode of the fiber in Fig. 1b. (a) hz , (b) ez , (c) h t and (d) e t .

Download Full Size | PDF

Fig. 5.
Fig. 5. Boundary effects for the p=1 mode in fiber B6v: transverse curl of h t . For the p=2 mode, the profile looks similar with the roles of the fields swapped.

Download Full Size | PDF

Fig. 6.
Fig. 6. Mode profiles for the second lowest p=1 mode of the fiber in Fig. 1c. (a) hz , (b) ez , (c) h t and (d) e t .

Download Full Size | PDF

Fig. 7.
Fig. 7. Transversality of first 6 modes for the three fibers in Fig. 1. The two fibers with reflection symmetry exhibit larger contrast between the major and minor longitudinal components.

Download Full Size | PDF

Fig. 8.
Fig. 8. Examples of systematic fibers with C 3v and C 3 symmetry. (a) and (b) hz and ez for C 3v . (c) and (d) hz and ez for C 3.

Download Full Size | PDF

Fig. 9.
Fig. 9. Degree of transversality for TE and TM-like modes in matched C 4 and C 4v fibers. Crosses denote the C 4 results.

Download Full Size | PDF

Fig. 10.
Fig. 10. (a) Transversality µ TE=fz [E]/fz [H] and µ TM=fz [H]/fz [E] as a function of rotational order for single ring fibers. Small µ indicates strong transversality. Also profiles of H t for (b) n=3 and (c) n=9.

Download Full Size | PDF

Tables (1)

Tables Icon

Table 1. First two symmetry classes (all containing non-degenerate modes) for several symmetry groups.

View Table

Equations (16)

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

E ( r , t ) = [ e r , e ϕ , e z ] exp ( i [ β z − ω t ] ) = [ e t ( r t ) , e z ( r t ) ] exp ( i [ β z − ω t ] ) ,
H ( r , t ) = [ h r , h ϕ , h z ] exp ( i [ β z − ω t ] ) = [ h t ( r t ) , h z ( r t ) ] exp ( i [ β z − ω t ] ) ,
e t = i k 0 2 n ( r t ) 2 − β 2 [ β ∇ t e z − ( k 0 Z 0 ) z ̂ × ∇ t h z ] ,
h t = i k 0 2 n ( r t ) 2 − β 2 [ β ∇ t h z − ( k 0 ⁄ Z 0 ) z ̂ × ∇ t e z ] ,
∇ t · e t = i β k 0 2 n ( r t ) 2 − β 2 ∇ t 2 e z ,
∇ t × e t = − ik 0 Z 0 k 0 2 n ( r t ) 2 − β 2 ∇ t 2 h z ,
∇ t · h t = i β k 0 2 n ( r t ) 2 − β 2 ∇ t 2 h z ,
∇ t × h t = ik 0 ⁄ Z 0 k 0 2 n ( r t ) 2 − β 2 ∇ t 2 e z .
f z [ E ] = 〈 ∣ e z ∣ 2 〉 〈 ∣ E ∣ 2 〉
f z [ H ] = 〈 ∣ h z ∣ 2 〉 〈 ∣ H ∣ 2 〉
〈 g ( r t ) 〉 = ∫ − ∞ ∞ ∫ − ∞ ∞ d 2 r t g ( r t ) .
∇ f = ∇ t f + ∂ f ∂ z ,
∇ · F = ∇ t · F t + ∂ F z ∂ z ,
∇ × F = ∇ t × F t − z ̂ × ( ∇ t F z − ∂ F t ∂ z ) .
∇ t × ( ∇ t f ) = 0 ,
∇ t · z ̂ × ( ∇ t f ) = 0 ,

Metrics

Select as filters
Select Topics Cancel
Top
       
© Copyright 2023 | Optica Publishing Group. All Rights Reserved
Privacy | Terms of Use