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Wavelength conversion bandwidth in fiber based optical parametric amplifiers

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We propose a systematic approach to evaluating and optimising the wavelength conversion bandwidth and gain ripple of four-wave mixing based fiber optical wavelength converters. Truly tunable wavelength conversion in these devices requires a highly tunable pump. For a given fiber dispersion slope, we find an optimum dispersion curvature that maximises the wavelength conversion bandwidth.

©2003 Optical Society of America

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Supplementary Material (1)

Media 1: GIF (32 KB)     

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Figures (4)

Fig. 1.
Fig. 1. Schematic of the operation of an ideal wavelength converter. a) Conversion from a fixed λ s to an arbitrary λ c , within a range Δλ. b) Conversion from a fixed λ c to an arbitrary λ s , within a range Δλ. c) Boundary for the region representing conversion from an arbitrary λ s to an arbitrary λ c , both within the same range Δλ.
Fig. 2.
Fig. 2. a) Theoretical gain spectra for a typical parametric amplifier at two different pump wavelengths. b) Ideal wavelength conversion spectra for two different pump wavelengths. Pump wavelengths are 1553 nm (black) and 1558 nm (red). G thresh (dotted) was chosen to be the gain at λ s p . Other parameters are in Table 1.
Fig. 3.
Fig. 3. Black contours show the intersection of gain curves for a PWC with G thresh=G 0. Fiber parameters are shown in Table 1. A square of maximum area (green) has been fitted and indicates the useful device wavelength coverage for a fixed band.
Fig. 4.
Fig. 4. a) Animation showing how G=G 0 contours (black) change with decreasing β4 and corresponding device bandwidth (green). The red square is the maximum bandwidth, for β4=β4opt≈4.11×10-54s4m-1. The blue square represents the bandwidth when β4=0. b) Plot of β4opt (black) and corresponding bandwidth maxima (red) for fibers with different β3 values. The dashed red line shows the worst effect of a 10% perturbation from β4opt. γ, Pp and L are as in Table 1. [Media 1]

Tables (1)

Tables Icon

Table 1. Table of parameters used in calculations [11]. λ0 is the dispersion zero wavelength of the fiber, γ is the fiber nonlinearity, L the fiber length, Pp the pump power, and β3 and β4 are the third and fourth order dispersion parameters at λ0.

Equations (11)

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2 ω p = ω s + ω c ,
Δ β = 2 β p β s β c .
G = ( γ P P g sinh ( g L ) ) 2 ,
g 2 = 1 4 [ Δ β ( 4 γ P P Δ β ) ] .
G max = sinh 2 ( γ P P L ) .
G 0 = ( γ P P L ) 2 .
Δ β = ( β 3 ( ω p ω 0 ) + β 4 2 [ ( ω p ω 0 ) 2 + 1 6 ( ω p ω s ) 2 ] ) ( ω p ω s ) 2 .
R = G max G 0 = ( sinh ( γ P P L ) γ P P L ) 2 .
ω S = ω p ± 12 Φ β 4 , ω s = ω p and
ω s = ω p ± 6 Φ ± Φ 2 ( 16 3 ) β 4 γ P p β 4 ,
Δ ω = 2 ( 48 γ P p β 4 ) 1 4 , and when β 4 = 0 , Δ ω = 2 ( 4 γ P p β 3 ) 1 3 .


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