Phase-sensitive amplification in a fiber

C. J. McKinstrie; S. Radic

doi:10.1364/OPEX.12.004973

Optics Express
Vol. 12,
Issue 20,
pp. 4973-4979
(2004)
•https://doi.org/10.1364/OPEX.12.004973

Phase-sensitive amplification in a fiber

C. J. McKinstrie and S. Radic

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C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004)

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About this Article
History
- Original Manuscript: September 9, 2004
- Revised Manuscript: September 27, 2004
- Manuscript Accepted: September 27, 2004
- Published: October 4, 2004

Abstract

Phase-sensitive amplification (PSA) has the potential to improve significantly the performance of optical communication systems. PSA is known to occur in χ ⁽²⁾ devices, and in a fiber interferometer, which is an example of a χ ⁽³⁾ device. In this report some four-wave mixing processes are described, which produce PSA directly in fibers.

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Fig. 1. Polarization diagram for degenerate scalar FWM.

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Fig. 2. Polarization diagram for degenerate vector FWM.

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Fig. 3. Polarization diagrams for cascaded scalar BS and PC. During BS pump 3 is on and pump 5 is off, whereas during PC pump 3 is off and pump 5 is on.

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Fig. 4. Polarization diagrams for cascaded vector BS and PC. During BS pump 3 is on and pump 5 is off, whereas during PC pump 3 is off and pump 5 is on.

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Equations (40)

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d_{z} A_{1} = i 2 \bar{γ} A_{2} A_{1}^{*} \exp (- iβz),

d_{z} A_{2} = i \bar{γ} A_{1}^{2} \exp (iβz),

A_{1} (z) = B_{1} (z) \exp (- \frac{iβz}{2}) .

(d_{z} - iδ) B_{1} = iγ B_{1}^{*},

B_{1} (z) = μ (z) B_{1} (0) + ν (z) B_{1} {(0)}^{*},

μ (z) = \cosh (κz) + i (\frac{δ}{κ}) \sinh (κz),

ν (z) = i (\frac{γ}{κ}) \sinh (κz)

d_{z} A_{1} = i \bar{γ} ({∣ A_{1} ∣}^{2} + 2 {∣ A_{2} ∣}^{2} + 2 {∣ A_{3} ∣}^{2}) A_{1} + i \bar{γ} A_{2}^{2} A_{3}^{*} \exp (iβz),

d_{z} A_{2} = i \bar{γ} ({2 ∣ A_{1} ∣}^{2} + {∣ A_{2} ∣}^{2} + 2 {∣ A_{3} ∣}^{2}) A_{2} + i 2 \bar{γ} A_{3} {A_{1} A}_{2}^{*} \exp (- iβz),

d_{z} A_{3} = i \bar{γ} ({2 ∣ A_{1} ∣}^{2} + 2 {∣ A_{2} ∣}^{2} + {∣ A_{3} ∣}^{2}) A_{3} + i \bar{γ} A_{1}^{*} A_{2}^{2} \exp (iβz),

A_{3} (z) = A_{3} (0) \exp [i \bar{γ} (2 P_{1} + P_{3}) z],

A_{1} (z) = A_{1} (0) \exp [i \bar{γ} (P_{1} + 2 P_{3}) z] .

A_{2} (z) = B_{2} (z) \exp [- \frac{iβz}{2} + \frac{i 3 \bar{γ} (P_{3} + P_{1}) z}{2}] .

(d_{z} - iδ) B_{2} = iγ B_{2}^{*},

d_{z} A_{1} = i \bar{γ} ({∣ A_{1} ∣}^{2} + 2 {∣ A_{2} ∣}^{2} + ε {∣ A_{3} ∣}^{2} + ε {∣ A_{4} ∣}^{2}) A_{1} + i \bar{γ} ε A_{2} A_{3} A_{4}^{*} \exp (iβz),

d_{z} A_{2} = i \bar{γ} ({2 ∣ A_{1} ∣}^{2} + {∣ A_{2} ∣}^{2} + ε {∣ A_{3} ∣}^{2} + ε {∣ A_{4} ∣}^{2}) A_{2} + i \bar{γ} ε A_{3}^{*} A_{4} A_{1} \exp (- iβz),

d_{z} A_{3} = i \bar{γ} ({ε ∣ A_{1} ∣}^{2} + {ε ∣ A_{2} ∣}^{2} + {∣ A_{3} ∣}^{2} + 2 {∣ A_{4} ∣}^{2}) A_{3} + i \bar{γ} ε A_{4} A_{1} A_{2}^{*} \exp (- iβz),

d_{z} A_{4} = i \bar{γ} ({ε ∣ A_{1} ∣}^{2} + {ε ∣ A_{2} ∣}^{2} + {2 ∣ A_{3} ∣}^{2} + {∣ A_{4} ∣}^{2}) A_{4} + i \bar{γ} ε A_{1}^{*} A_{2} A_{3} \exp (iβz),

A_{4} (z) = A_{4} (0) \exp [i \bar{γ} (ε P_{1} + P_{4}) z],

A_{1} (z) = A_{1} (0) \exp [i \bar{γ} (P_{1} + ε P_{4}) z] .

A_{2} (z) = B_{2} (z) \exp [- \frac{iβz}{2} + \frac{i \bar{γ} 3 P_{1} z}{2} + i \bar{γ} (ε - \frac{1}{2}) P_{4} z],

A_{3} (z) = B_{3} (z) \exp [- \frac{iβz}{2} + i \bar{γ} (ε - \frac{1}{2}) P_{1} z + \frac{i \bar{γ} 3 P_{4} z}{2}] .

(d_{z} - iδ) B_{2} = iγ B_{3}^{*},

(d_{z} + iδ) B_{3}^{*} = - i γ^{*} B_{2},

B_{2} (z) = μ (z) B_{2} (0) + ν (z) B_{3}^{*} (0),

B_{3}^{*} (z) = ν^{*} (z) B_{2} (0) + μ^{*} (z) B_{3}^{*} (0),

A_{1} (z) = A_{1} (0) \exp [i \bar{γ} (P_{1} + ε P_{3}) z],

A_{3} (z) = A_{3} (0) \exp [i \bar{γ} (ε P_{1} + P_{3}) z] .

A_{2} (z) = B_{2} (z) \exp [- \frac{iβz}{2} + \frac{i \bar{γ} 3 P_{1} z}{2} + i \bar{γ} (ε + \frac{1}{2}) P_{3} z],

A_{4} (z) = B_{4} (z) \exp [\frac{iβz}{2} + i \bar{γ} (ε + \frac{1}{2}) P_{1} z + \frac{i \bar{γ} 3 P_{3} z}{2}] .

(d_{z} - iδ) B_{2} = iγ B_{4},

(d_{z} + iδ) B_{4} = i γ^{*} B_{2},

B_{2} (z') = \bar{μ} (z') B_{2} (0) + \bar{ν} (z') B_{4} (0),

B_{4} (z') = - {\bar{ν}}^{*} (z') B_{2} (0) + {\bar{μ}}^{*} (z') B_{4} (0),

\bar{μ} (z) = \cos (kz) + i (\frac{δ}{k}) \sin (kz),

\bar{ν} (z) = i (\frac{γ}{k}) \sin (kz)

(d_{z} - iδ) B_{2} = iγ B_{4}^{*},

(d_{z} + iδ) B_{4}^{*} = - i γ^{*} B_{2},

B_{2} (z ″) = μ (z ″ - z') B_{2} (z') + ν (z ″ - z') B_{4}^{*} (z'),

B_{4}^{*} (z ″) = ν^{*} (z ″ - z') B_{2} (z') + μ^{*} (z ″ - z') B_{4}^{*} (z'),

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Equations (40)

Optics Express