Abstract

The main differences in nonlinear switching behavior between multicore versus multimode waveguide couplers are highlighted. By gradually decreasing the separation between the two cores of a dual-core waveguide and interpolating from a multicore to a multimode scenario, the role of the linear coupling, self-phase modulation, cross-phase modulation, and four-wave mixing terms are explored, and the key reasons are identified behind higher switching power requirements and lower switching quality in multimode nonlinear couplers.

© 2013 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. E. Nazemosadat and A. Mafi, “Nonlinear multimodal interference and saturable absorption using a short graded-index multimode optical fiber,” J. Opt. Soc. Am. B30, 1357–1367 (2013).
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    [CrossRef]

2013 (2)

2012 (2)

Q. Chao, D. D. Hudson, J. N. Kutz, and S. T. Cundiff, “Waveguide array fiber laser,” IEEE Photonics J.4, 1438–1442 (2012).
[CrossRef]

A. Mafi, “Pulse propagation in a short nonlinear graded-index multimode optical fiber,” J. Lightwave Technol.30, 2803–2811 (2012).
[CrossRef]

2008 (2)

2005 (1)

1992 (1)

1982 (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

Chao, Q.

Q. Chao, D. D. Hudson, J. N. Kutz, and S. T. Cundiff, “Waveguide array fiber laser,” IEEE Photonics J.4, 1438–1442 (2012).
[CrossRef]

Christodoulides, D. N.

Cundiff, S. T.

Horak, P.

Hudson, D. D.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

Kutz, J. N.

Mafi, A.

Morandotti, R.

Nazemosadat, E.

Poletti, F.

Proctor, J. L.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Schibli, T. R.

Shish, K.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Walton, D. T.

Winful, H. G.

IEEE J. Quantum Electron. (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron.18, 1580–1583 (1982).
[CrossRef]

IEEE Photonics J. (1)

Q. Chao, D. D. Hudson, J. N. Kutz, and S. T. Cundiff, “Waveguide array fiber laser,” IEEE Photonics J.4, 1438–1442 (2012).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Opt. Lett. (3)

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

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Figures (5)

Fig. 1
Fig. 1

(a) The refractive index profile of the double-waveguide nonlinear coupler is shown. (b) For weakly coupled waveguides (d = 10λ), the even and odd mode profiles Fe(x) and Fo(x) in Picture-�� are sketched above the index profile and F1(x) and F2(x) in Picture- are sketched below the index profile. (c) is similar to (b), except the waveguides are strongly coupled for d = 2λ. Results are shown for the TE polarization, where the transverse electric field vector is pointing in the vertical direction in these figures.

Fig. 2
Fig. 2

(a) The splitting between the propagation constants of the modes increases significantly as the waveguides are brought closer together. (b) The nonlinear coupling coefficients for the even and odd modes are shown as a function of the normalized separation, where their degeneracy is removed when the waveguides are strongly interacting.

Fig. 3
Fig. 3

The nonlinear coupling coefficients in Picture- are shown as a function of d/λ. The SPM coefficients in (a) are much stronger than the XPM/FWM coefficients in (b).

Fig. 4
Fig. 4

(a) A sketch of the NLS device. (b) The relative power transmission is plotted as a function of γ. The solid (black) curve corresponds to weakly coupled waveguides with d/λ = 10. The dashed (red) and dotted (blue) NLS curves correspond to the strongly interacting merged waveguide with d/λ = 0, where in case-1 the injected and collected beam profiles are F1(x), while in case-2, the injected and collected beam profiles are Fw(x).

Fig. 5
Fig. 5

The relative power transmission is plotted as a function of γ for (a) Lc = Lh versus Lc = 3Lh and (b) for Lc = 15Lh. The NLS quality for Lc = 3Lh and Lc = 15Lh are lower.

Equations (5)

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A μ z = i δ β μ A μ + i ( n 2 ω 0 c ) ν , κ , ρ = e , o f μ ν κ ρ A ν A κ A ρ , μ = e , o ,
f μ ν κ ρ = F μ F ν F κ F ρ d x ,
A ˜ j z = i δ β e A ˜ j + i ( n 2 ω 0 c ) k , l , m = 1 , 2 f j k l m A ˜ k A ˜ l A ˜ m , j = 1 , j = 2 , or j = 2 , j = 1 ,
f 1111 = f 2222 = ( f e e e e + f o o o o + 6 f e e o o ) / 4 , f 1122 = ( f e e e e + f o o o o 2 f e e o o ) / 4 , f 1112 = f 1222 = ( f e e e e f o o o o ) / 4 .
τ = 1 P ˜ 2 | i = 1 , 2 A ˜ i ( 0 ) A ˜ i ( L c ) | 2 = 1 P ˜ 2 | μ = e , o A μ ( 0 ) A μ ( L c ) | 2 ,

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