Source: http://aoot.osa.org/josab/abstract.cfm?uri=josab-28-9-2301
Timestamp: 2019-04-22 08:46:10+00:00

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Using second-order coherence theory of nonstationary light we examine in detail the coherence properties of supercontinuum radiation generated in nonlinear fibers. We show that the supercontinuum can be divided into quasi-coherent and quasi-stationary parts and that the relative contributions depend on the dynamics involved in the spectral broadening process. We establish the correspondence between the quasi-coherent part of the two-frequency correlation function of the second-order theory and the usual Dudley–Coen degree of coherence used to characterize the shot-to-shot stability of supercontinuum sources. Experimental implementation for measuring separately the quasi-coherent and quasi-stationary contributions is further addressed. Our results open the route for complete characterization of supercontinuum coherence.
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Fig. 1 Overall degrees of spectral coherence μ ¯ (red diamonds) and | g 12 ( 1 ) | (black circles) versus input pulse peak power. A, B, and C mark the three cases of quasi-coherent, partially coherent, and quasi-incoherent SC light investigated in detail.
Fig. 2 Left: normalized cross-spectral density | μ ¯ ( ω , Δ ω ) | for (a) case A, (c) case B, and (e) case C. Right: normalized mutual coherence function | γ ( t ¯ , Δ t ) | for (b) case A, (d) case B, and (f) case C. For clarity, the absolute frequency and times axes are indicated. Note the different color scale in (a) and (b) compared to (c)–(f).
Fig. 3 Left: normalized cross-spectral density | μ ¯ ( ω , Δ ω ) | and right: normalized mutual coherence function | γ ( t ¯ , Δ t ) | for 960 nm input pulses with (a),(b) P P = 22 kW and (c),(d) P P = 88 kW .
Fig. 4 Left: normalized cross-spectral density | μ ¯ ( ω , Δ ω ) | and right: normalized mutual coherence function | γ ( t ¯ , Δ t ) | for (a),(b) 50 fs input pulses, (c),(d) 1 ps input pulses.
Fig. 5 Left: mean spectra (black lines), coherent (red lines) and quasi-stationary (blue lines) spectral contributions for (a) case A, (c) case B, and (e) case C. Right: mean temporal intensity (black lines), coherent (red lines) and quasi-stationary (blue lines) intensity contributions for (b) case A, (d) case B, and (f) case C.
Fig. 6 False color representation of the evolution of (a) mean spectrum, (b) quasi-coherent contribution, and (c) quasi- stationary contribution for case C ( P P = 22 kW ).
Fig. 7 Left: calculated cross-spectral density | W ( ω ¯ , Δ ω ) | for (a) case A, (c) case B, and (e) case C. Right: coherent part of the cross-spectral density | W ( ω ¯ , Δ ω ) | retrieved from g 12 ( 1 ) ( ω ) for (b) case A, (d) case B, and (f) case C.
Fig. 8 Schematic for complete experimental characterization of the SC coherence properties. OSA, optical spectrum analyzer; FROG, frequency-resolved optical gating; MZI, Mach– Zehnder interferometer.
Fig. 9 Reconstructed normalized CSD when measuring separately the quasi-coherent and quasi-stationary contributions for (b) case B and (d) case C. For comparison, the original CSD as directly numerically computed from the ensemble of simulation realizations is also shown for (a) case B and (c) case C.

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