Fiber Raman gain amplifier performance study using simple coupled-mode analysis
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"Fiber Raman gain amplifier performa..." refers background in this paper
...In Equation (6), β1 and β2 are the propagation constants of the inner and the outer cores, respectively....
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...Here, βs and βa are also calculated using the following relation: bs;a ¼ 1 2 b1 þ b2ð Þ 1 4 b1 b2ð Þ2þj2 1=2 (7) where j ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffij12j21p . κ12 and κ21 are written as j12 ¼ k 2 0 2b1 n21 n22 Za 0 w1w2rdr (8) j21 ¼ k 2 0 2b2 n23 n22 Zc b w1w2rdr (9) In writing the above Equations (8) and (9), the overlap integral of the modes is neglected assuming [15] Z Z1 1 w 1w2dxxy\\ Z Z1 1 w 1w1dxxy (10) which is valid for weak coupling between the waveguides....
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...In this connection, it may be relevant to recall that we have considered weak coupling of the two fiber waveguides following condition in Equation (10)....
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...Further, in terms of the effective area Aeff and the Raman gain coefficient gR, the effective Raman gain coefficient γR is defined as [8–10]: cR ¼ gR Aeff (12) We calculate the above γR from the following wellknown equation [8–10,16] given as: cR ¼ CSiSiðDmÞ 2p Z1 0 1 2xðrÞ½ IpðrÞISigðrÞrdr þ CGeSiðDmÞ 2p Z1 0 2xðrÞIpðrÞISigðrÞrdr (13) where in Equation (13), Δν represents the frequency shift from the pump frequency, whereas x(r) represents the Germania concentration....
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...bs 1⁄4 bs b1 j12 as 1⁄4 bs b2 j21 ba 1⁄4 ba b1 j12 aa 1⁄4 ba b2 j21 (9)>>>= >>; (6)...
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