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Four wave mixing in submicron waveguides Dragana Vukovic DTU Fotonik Department of Photonics Engineering Technical University of Denmark DK-2800 Kgs. Lyngby Denmark [email protected] Basis pump Material with 3rd order nonlinearity β Ο(3) Signal waveguide Pump Idler signal idler Energy from the pump is transferred to the signal and idler β’ Refractive index is dependent on the light intensity π = π0 + π2 πΌ π‘ nonlinear refractive index β’ Propagation constant is also dependent on light intensity (power) π½ = π½0 + πΎπ π‘ nonlinear coefficient Nonlinear phase shift is generated during propagation 2 Applications Wavelength conversion CW Pump Idler Nonlinear medium Signal Channel Possible to transfer data from signal to the idler wave at the new wavelength Optical filter Optical sampling Sampling of high speed signals beyond the limits of electronics Short samplings pulses act as the pump ο Idler pulse width comparable to pump pulses J. V. Erps et al., J. Lightwave Technol. 21 (2010) 209-15. 3 Different nonlinear media Waveguide Advantages Problems Extended length SiO2 highly nonlinear fiber Low losses n2 ~ 10-20 m2/W Stimulated Brillouin scattering n2 ~ 10-18 m2/W Silicon waveguides Two photon absorption Strong confinement Increased losses Length is shortened Photonic crystals waveguides Separate engineering of D and Ξ³ Fabrication Slow light regime III-V waveguides n2 ~ 10-17 m2/W Three photon absorption No two photon absorption 4 Outline β’ Motivation β’ Phase β matching β’ Characterization needs β’ Dispersion characterization β’ Nonlinear characterization β’ Conversion bandwidth 5 conversion efficiency (dB) phase mismatch οο’ L /ο° Phase matching pump 2 1 0 CE -1 -2 signal -3 idler -4 -5 1300 1400 1500 1600 1700 signal wavelength (nm) 1800 1900 Conversion efficiency: -20 ππ π§ = πΏ πΆπΈ = ππ π§ = 0 -40 -60 -80 1300 1400 1500 1600 1700 signal wavelength (nm) Linear phase mismatch: 1800 1900 Depends on phase matching parameter: π = Ξπ½ + 2πΎπππ’ππ Ξπ½ = π½π + π½π β 2π½π Therefore essential to be able to measure dispersion over a broad bandwidth as well the nonlinear coefficient ο§ 6 device under test fringe intensity (a.u.) broadband source 6 phase (radians) Dispersion characterisation 250 4 2 0 β’ Low coherence interferometer being implemented variable delay β’ Free space Mach-Zehnder interferometer structure β’ SOA used as broadband source β’ Good method to characterise dispersion over broad bandwidth β’ As required for phase matching evaluation dispersion (ps/nm/km) OSA 200 150 100 30 20 10 0 -10 1400 1500 1600 1700 wavelength (nm) 7 Nonlinear coefficient characterisation -10 OSA CW Att. PWM power (dBm) waveguide under test EDFA I0 -20 -30 I1 -40 -50 -60 -70 1554.5 CW 1555.0 1555.5 1556.0 1556.5 wavelength (nm) If the waveguide dispersion can be neglected (ο small wavelength separation between lasers) π π π½02 πππ + π½12 πππ πΌ0 2 2 = πΌ 1 π½2 ππππ + π½2 ππππ 1 2 2 2 with ππππ = πΎπΏπππ πππ Pin is the sum of the power of the 2 lasers at the waveguide input πΏπππ 1 β π βπΌπΏ = πΌ 2π π2 πΎ= π π΄πππ A. Boskovic et al., Opt. Lett. 21 (1996) 1966-8. β’ Measure I0 , I1 , versus Pin β’ Retrieve Ξ³ 8 Nonlinear coefficient measurement w Output of the chip h Power [dBm] Si SiO2 substrate h = 340 nm -20 -40 -60 w = 500 nm 1549 0.03 original data nonlinear-phase shift (rad) 0 linear fit 0.02 10 30 40 50 total input power (mW) 60 1551 7.82 (TE) 7.76 (TM) 2.66 1.95 Ξ³ [1/Wm] 151.56 145.91 π2 = 3.5 β 10 20 1550 1550.5 Wavelength [nm] Facet loss [dB] Propagation loss [dB/cm] Calculation: 0.01 1549.5 β18 π2 , π΄πππ = 0.097 ππ2 π π¦πππππ πΎ = 146.43 1 ππ Good agreement with theoretical calculation 9 Conversion efficiency Different models used by groups working in the field πΎπππ’ππ πΆπΈ = sinh ππΏ π π= πΎπππ’ππ 2 2 π βπΌπΏ 2 Ξπ β 2 πΆπΈ = πΎπΏπππ πππ’ππ R.H. Stolen et al., J. Quantum Electron.18 (1982) 1062-71 πΎπππ’ππ πΆπΈ = sinh ππΏ π πΏπππ πππ’ππ = πππ’ππ πΏ π₯π ππΏ = 2πΎπππ’ππ M.E. Heidari et al., Opt. Express 17 (2009) 1834053. 2 π βπΌπΏ Modified pump power No pump depletion π π Ξπ½πΏ 4π βπΌπΏ π ππ2 πΌ2 2 π= 2 1+ 2 βπΌπΏ 2 πΌ + Ξπ½ 1βπ No nonlinear phase matching No loss No pump depletion 2 βπΌπΏ N. Shibata et al., J. Quantum Electron. 23 (1987) 1205-10. No pump depletion πΎπππ’ππ πΆπΈ = sinh ππΏπππ π 2 π βπΌπΏ Losses taken into account No pump depletion K. Wang et al., Opt. Lett. 37 (2012) 1331-3. 10 Conversion efficiency bandwidth 500 Example: w Si w = 900 nm h SiO2 substrate Dispersion (ps/nm/km) h = 205 nm 0 -500 -1000 -1500 -2000 -2500 1200 -20 1400 1500 1600 1700 Stolen L Stolen L -30 Conversion efficiency [dB] 1300 Wavelength (nm) Shibata -25 194.544 THz 1541.000 nm β’ Exact solution obtained using numerical method eff Modified Stolen -35 β’ Bandwidth for Stolen Leff is overestimated Numerical -40 β’ Maximum conversion efficiency for Stolen model is overestimated β model does not include loses -45 -50 -55 β’ Bandwidth for Shibata model and Modified Stolen model are very close -60 -65 1540 1560 1580 1600 1620 Wavelength [nm] 1640 1660 1680 11 Conclusions β’ Conversion efficiency and the FWM bandwidth can be further increased in waveguides. β’ Phase matched nonlinear processes like FWM benefit from the use of engineered waveguides through dispersion engineering, which ensures phase matching over a large bandwidth. β’ Using FWM in new materials photonic waveguides should continue to provide unique nonlinear optical functionality at even lower power levels. Thank you ο 12
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