Abstract

The coupling between optical fibers with left-handed materials is analyzed in this paper. First, we obtain new coupled-wave equations and define new relevant coupling coefficients by using Maxwell’s equations. Second, the coupling between two identical fibers with the same left-handed material as the core and the same right-handed material as the common cladding is discussed. The coupling coefficient for TE01 mode is calculated. The coupling coefficient versus distance of two fibers with different normalized frequencies is plotted. Through comparing these curves, some new coupling characteristics between fibers including left-handed materials are obtained.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. D. R. Smith and N. Kroll, "Negative refraction index in lefthanded materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  3. B. L. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
    [CrossRef]
  4. Z. Y. Xiao and Z. H. Wang, "Dispersion characteristics of asymmetric double-negative materials slab waveguides,"J. Opt. Soc. Am. B 23, 1757-1760 (2006).
    [CrossRef]
  5. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  6. H. Cory and T. Blum, "Surface-wave propagation along a metamaterial cylinder guide,"Microwave Opt. Technol. Lett. 44, 31-35 (2005).
    [CrossRef]
  7. J. L. He, L. F. Shen, S. L. He, and Z. C. Ruan, "Abnormal characteristics of guided modes in a fiber formed by a medium with negative-refractive index," Acta Photonica Sin. 33, 1327-1329 (2004) (in Chinese).
  8. D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, 1982).
  9. A. W. Snyder, "Coupled-mode theory for optical fibers," J. Opt. Soc. Am. 62, 1267-1277 (1972).
    [CrossRef]
  10. L. F. Shen and Z. H. Wang, "Guided mode characteristics in a fiber with left-handed material," Microwave Opt. Technol. Lett. 49, 1039-1041 (2007).
    [CrossRef]

2007

L. F. Shen and Z. H. Wang, "Guided mode characteristics in a fiber with left-handed material," Microwave Opt. Technol. Lett. 49, 1039-1041 (2007).
[CrossRef]

2006

2005

H. Cory and T. Blum, "Surface-wave propagation along a metamaterial cylinder guide,"Microwave Opt. Technol. Lett. 44, 31-35 (2005).
[CrossRef]

2004

J. L. He, L. F. Shen, S. L. He, and Z. C. Ruan, "Abnormal characteristics of guided modes in a fiber formed by a medium with negative-refractive index," Acta Photonica Sin. 33, 1327-1329 (2004) (in Chinese).

2003

B. L. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

2000

D. R. Smith and N. Kroll, "Negative refraction index in lefthanded materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

1972

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Acta Photonica Sin.

J. L. He, L. F. Shen, S. L. He, and Z. C. Ruan, "Abnormal characteristics of guided modes in a fiber formed by a medium with negative-refractive index," Acta Photonica Sin. 33, 1327-1329 (2004) (in Chinese).

J. Appl. Phys.

B. L. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Microwave Opt. Technol. Lett.

L. F. Shen and Z. H. Wang, "Guided mode characteristics in a fiber with left-handed material," Microwave Opt. Technol. Lett. 49, 1039-1041 (2007).
[CrossRef]

H. Cory and T. Blum, "Surface-wave propagation along a metamaterial cylinder guide,"Microwave Opt. Technol. Lett. 44, 31-35 (2005).
[CrossRef]

Phys. Rev. E

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith and N. Kroll, "Negative refraction index in lefthanded materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, 1982).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Geometry of two LHM fibers.

Fig. 2
Fig. 2

Coupling coefficient of T E 01 mode with different n 1 but the same V = 4 .

Equations (29)

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

E v = E ̂ v e i ( ω t β v z ) ( v = 1 , 2 ) ,
H v = H ̂ v e i ( ω t β v z ) ( v = 1 , 2 ) ,
t × H v i β v ( z × H v ) i ω ϵ v E v = 0 ,
t × E v i β v ( z × E v ) i ω μ v H v = 0 ,
E tot = A 1 ( z ) E 1 + A 2 ( z ) E 2 ,
H tot = A 1 ( z ) H 1 + A 2 ( z ) H 2 ,
× H tot = i ω ϵ E tot ,
× E tot = i ω μ H tot ,
A 1 z ( z × H 1 ) i ω ( ϵ 2 ϵ 3 ) A 1 E 1 + A 2 z ( z × H 2 ) i ω ( ϵ 1 ϵ 3 ) A 2 E 2 = 0 ,
A 1 z ( z × E 1 ) + i ω ( μ 2 μ 3 ) A 1 H 1 + A 2 z ( z × E 2 ) + i ω ( μ 1 μ 3 ) A 2 H 2 = 0 .
A 1 z = i c 1 A 2 e i ( β 1 β 2 ) z ,
c 1 = ω 0 0 [ ( ϵ 1 ϵ 3 ) E ̂ 2 × E ̂ 1 + ( μ 1 μ 3 ) H ̂ 2 × H ̂ 1 ] d x d y 0 0 [ z × ( E ̂ 1 × H ̂ 1 ) + z × ( E ̂ 1 × H ̂ 1 ) d x d y .
A 2 z = i c 2 A 1 e i ( β 2 β 1 ) z ,
c 2 = ω 0 0 [ ( ϵ 2 ϵ 3 ) E ̂ 2 × E ̂ 1 + ( μ 2 μ 3 ) H ̂ 1 × H ̂ 2 ] d x d y 0 0 [ z × ( E ̂ 2 × H ̂ 2 ) + z × ( E ̂ 2 × H ̂ 2 ) d x d y ,
c 1 = ω 4 P 0 0 [ ϵ 0 ( n 1 2 + n 2 2 ) E 2 ( 1 ) × E 1 ( 2 ) + 2 μ 0 H 2 ( 1 ) × H 1 ( 2 ) ] d x d y ,
E θ 1 ( i ) = j a ω A μ 0 J 1 ( U r i a ) U J 0 ( U ) r a ,
E θ 2 ( i ) = j a ω A μ 0 K 1 ( W r i a ) W K 0 ( W ) r a ,
H z 1 ( i ) = A J 0 ( U r i a ) J 0 ( U ) r a ,
H z 2 ( i ) = A K 0 ( W r i a ) K 0 ( W ) r a ,
H r 1 ( i ) = j a A β J 1 ( U r i a ) U J 0 ( U ) r a ,
H r 2 ( i ) = j a A β K 1 ( W r i a ) W K 0 ( W ) r a ,
U J 0 ( U ) J 1 ( U ) = W K 0 ( W ) K 1 ( W ) .
C = π ω μ 0 a 2 A 2 P J 0 ( U ) K 0 ( W ) { [ k 0 2 ( n 1 2 + n 2 2 ) + 2 β 2 ] M K 1 ( W d a ) 2 U W + N K 0 ( W d a ) a 2 } ,
M = 0 a I 0 ( W r 2 a ) J 1 ( U r 2 a ) r 2 d r 2 ,
N = 0 a I 0 ( W r 2 a ) J 0 ( U r 2 a ) r 2 d r 2 ,
P = 1 2 0 2 π 0 E θ H r r d r d θ = 1 2 0 2 π 0 a E θ 1 H r 1 r d r d θ 1 2 0 2 π a E θ 2 H r 2 r d r d θ = π a 2 ω β μ 0 A 2 ( R + S ) ,
R = 1 U 2 J 0 2 ( U ) 0 a J 1 2 ( U r 2 a ) r 2 d r 2 ,
S = 1 W 2 K 0 2 ( W ) 0 a K 1 2 ( W r 2 a ) r 2 d r 2 .
C = 1 β ( R + S ) J 0 ( U ) K 0 ( W ) { [ k 0 2 ( n 1 2 + n 2 2 ) + 2 β 2 ] M K 1 ( W d a ) 2 U W + N K 0 ( W d a ) a 2 } .

Metrics