• Photonics Research
  • Vol. 7, Issue 1, 1 (2019)
Jeff Demas1、2, Lars Rishøj1, Xiao Liu1, Gautam Prabhakar1, and Siddharth Ramachandran1、*
Author Affiliations
  • 1Department of Electrical Engineering, Boston University, Boston, Massachusetts 02115, USA
  • 2Currently with The Rockefeller University, New York, New York 10065, USA
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    DOI: 10.1364/PRJ.7.000001 Cite this Article Set citation alerts
    Jeff Demas, Lars Rishøj, Xiao Liu, Gautam Prabhakar, Siddharth Ramachandran. Intermodal group-velocity engineering for broadband nonlinear optics[J]. Photonics Research, 2019, 7(1): 1 Copy Citation Text show less
    (a) Intensity profiles of the pump modes LP0,4 and LP0,5. (b) Schematic representation of intermodal parametric frequency conversion of the pump (green pulse) to the anti-Stokes (blue pulse) and Stokes (red pulse) waves along the length of the fiber. Schematic representation of (c) energy conservation and (d) phase matching for four-wave mixing. (e) Phase matching in the effective refractive index picture: solutions exist where the straight, dashed lines intersect the neff curves for different modes (solid lines), where integer “m” denotes radial mode order. (f) Parametric gain for typical intermodal processes (black line) and a group-velocity-tailored process (purple line), offset for clarity; the purple line in (e) is tangent to the neff curves for an extended wavelength range leading to broadband parametric gain.
    Fig. 1. (a) Intensity profiles of the pump modes LP0,4 and LP0,5. (b) Schematic representation of intermodal parametric frequency conversion of the pump (green pulse) to the anti-Stokes (blue pulse) and Stokes (red pulse) waves along the length of the fiber. Schematic representation of (c) energy conservation and (d) phase matching for four-wave mixing. (e) Phase matching in the effective refractive index picture: solutions exist where the straight, dashed lines intersect the neff curves for different modes (solid lines), where integer “m” denotes radial mode order. (f) Parametric gain for typical intermodal processes (black line) and a group-velocity-tailored process (purple line), offset for clarity; the purple line in (e) is tangent to the neff curves for an extended wavelength range leading to broadband parametric gain.
    (a) Setup schematic for intermodal four-wave mixing experiments. SLM, spatial light modulator; OSA, optical spectrum analyzer. (b) Simulated electric field profiles of the LP0,4 (blue line) and LP0,5 (red line) modes plotted alongside the phase profile of a LP0,5 binary phase plate stretched by ∼12% (green line, right axis). (c) Simulations of the relative power coupled to each mode of the test fiber for a phase plate stretched by 12%. (d) Simulated group velocity for the LP0,4 and LP0,5 modes. (e) Simulated parametric gain for group-velocity-matched four-wave mixing pumped with LP0,4 and LP0,5.
    Fig. 2. (a) Setup schematic for intermodal four-wave mixing experiments. SLM, spatial light modulator; OSA, optical spectrum analyzer. (b) Simulated electric field profiles of the LP0,4 (blue line) and LP0,5 (red line) modes plotted alongside the phase profile of a LP0,5 binary phase plate stretched by 12% (green line, right axis). (c) Simulations of the relative power coupled to each mode of the test fiber for a phase plate stretched by 12%. (d) Simulated group velocity for the LP0,4 and LP0,5 modes. (e) Simulated parametric gain for group-velocity-matched four-wave mixing pumped with LP0,4 and LP0,5.
    (a) Spontaneous four-wave mixing spectra as a function of pump wavelength; each spectrum offset by 50 dB for clarity. (b) Zoom-in of the bandwidth-optimized spontaneous spectrum (λp=1047.6 nm) with mode images inset.
    Fig. 3. (a) Spontaneous four-wave mixing spectra as a function of pump wavelength; each spectrum offset by 50 dB for clarity. (b) Zoom-in of the bandwidth-optimized spontaneous spectrum (λp=1047.6  nm) with mode images inset.
    Full experimental spectra as a function of seed wavelength (1535–1570 nm) showing conversion to the Ti:sapphire band (786–795 nm) with representative experimental mode images shown as inset; each spectrum offset by 70 dB for clarity.
    Fig. 4. Full experimental spectra as a function of seed wavelength (1535–1570 nm) showing conversion to the Ti:sapphire band (786–795 nm) with representative experimental mode images shown as inset; each spectrum offset by 70 dB for clarity.
    Experimentally measured pump profiles for the (a) pump (pump alone shown as a solid black line; pump combined with seed shown as a dotted purple line), (b) anti-Stokes, and (c) Stokes wavelengths for a 1545 nm wavelength seed. (d) Peak pump depletion (purple markers, left axis) and peak Stokes gain (brown markers, right axis) as a function of seed wavelength. (e) Peak power (anti-Stokes shown with blue markers; Stokes shown with red markers).
    Fig. 5. Experimentally measured pump profiles for the (a) pump (pump alone shown as a solid black line; pump combined with seed shown as a dotted purple line), (b) anti-Stokes, and (c) Stokes wavelengths for a 1545 nm wavelength seed. (d) Peak pump depletion (purple markers, left axis) and peak Stokes gain (brown markers, right axis) as a function of seed wavelength. (e) Peak power (anti-Stokes shown with blue markers; Stokes shown with red markers).
    Pump ModesPump WavelengthStokes BandwidthAnti-Stokes Bandwidth
    LP0,1+LP0,21194 nm1519–1624 nm943–984 nm
    LP0,2+LP0,31142 nm1548–1644 nm874–904 nm
    LP0,3+LP0,41093 nm1533–1623 nm823–849 nm
    LP0,4+LP0,5a1048 nm1502–1586 nm779–801 nm
    LP0,5+LP0,61001 nm1469–1552 nm739–759 nm
    Table 1. Additional Simulated Broadband FWM Processes
    Jeff Demas, Lars Rishøj, Xiao Liu, Gautam Prabhakar, Siddharth Ramachandran. Intermodal group-velocity engineering for broadband nonlinear optics[J]. Photonics Research, 2019, 7(1): 1
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