Abstract

Using the full vectorial nonlinear Schrödinger equations that describe nonlinear processes in isotropic optical nanowires, we show that there exist structural anisotropic nonlinearities that lead to unstable polarization states that exhibit periodic bistable behavior. We analyze and solve the nonlinear equations for continuous waves by means of a Lagrangian formulation and show that the system has bistable states and also kink solitons that are limiting forms of the bistable states.

© 2011 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  2. S. Afshar V. and T. M. Monro, Opt. Express 17, 2298 (2009).
    [Crossref]
  3. S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, Opt. Lett. 34, 3577 (2009).
    [Crossref]
  4. F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
    [Crossref] [PubMed]
  5. B. A. Daniel and G. P. Agrawal, J. Opt. Soc. Am. B 27, 956 (2010).
    [Crossref]
  6. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1965).

2010 (2)

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

B. A. Daniel and G. P. Agrawal, J. Opt. Soc. Am. B 27, 956 (2010).
[Crossref]

2009 (2)

Agrawal, G. P.

B. A. Daniel and G. P. Agrawal, J. Opt. Soc. Am. B 27, 956 (2010).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Biancalana, F.

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

Daniel, B. A.

Ebendorff-Heidepriem, H.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1965).

Monro, T. M.

Russell, P. St. J.

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1965).

Schmidt, M. A.

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

Stark, S.

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

Tran, T. X.

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

V., S. Afshar

Zhang, W. Q.

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

F. Biancalana, T. X. Tran, S. Stark, M. A. Schmidt, and P. St. J. Russell, Phys. Rev. Lett. 105, 093904 (2010).
[Crossref] [PubMed]

Other (2)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1965).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

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Figures (2)

Fig. 1
Fig. 1

Contour plots of γ 1 , γ 2 , 3 γ c / 2 , 3 γ c in units of ( W · m ) 1 as functions of the major/minor diameters for elliptical waveguides.

Fig. 2
Fig. 2

The period T as a function of Δ P . The insets show the periodic variation of the two polarization powers P 1 , P 2 , and cos Δ ϕ , as the pulse (for Δ P = 100 W ) propagates along the fiber.

Equations (14)

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A j z + n = 1 i n 1 n ! β j n n A j t n = i ( γ j | A j | 2 + γ c | A k | 2 ) A j + i γ c A j * A k 2 exp ( 2 i z Δ β j k ) ,
γ 1 = γ 2 = 3 γ c / 2 = 3 γ c .
γ j = 2 π ε 0 3 μ 0 λ n 2 ( x , y ) n 2 ( x , y ) [ 2 | e ^ j | 4 + | e ^ j 2 | 2 ] d A , γ c = 4 π ε 0 3 μ 0 λ n 2 ( x , y ) n 2 ( x , y ) [ | e ^ 1 | 2 + | e ^ 2 | 2 ] d A , γ c = 2 π ε 0 3 μ 0 λ n 2 ( x , y ) n 2 ( x , y ) [ e ^ 1 2 + e ^ 2 2 ] d A .
v = P 1 P 0 , θ = 2 Δ ϕ , τ = 2 γ c P 0 z , a = Δ β 12 γ c P 0 γ c γ 2 γ c , b = γ 1 + γ 2 2 γ c 2 γ c ,
v ˙ d v d τ = v ( 1 v ) sin θ ,
θ ˙ d θ d τ = a + 2 b v + ( 1 2 v ) cos θ .
v min v d u Q ( u ) = τ τ 0 , T = 2 v min v max d u Q ( u ) ,
cos θ = 1 , v = a 1 2 ( b 1 ) , ( b 1 ) ,
cos θ = 1 , v = a + 1 2 ( b + 1 ) , ( b 1 ) ,
cos θ = a , v = 0 , ( | a | 1 ) ,
cos θ = a + 2 b , v = 1 , ( | a 2 b | 1 ) .
L = T V = 1 2 M ( θ ) θ ˙ 2 V ( θ ) ,
M ( θ ) = 2 | b cos θ | , V ( θ ) = | b cos θ | ( a b ) 2 | b cos θ | .
cos θ = 1 + 2 κ 1 ( κ + 1 ) cosh 2 κ ( τ c ) ,

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