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Plenary 2: S Coen

Plenary 2: S Coen

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11.15 k6 s coen Presentation Transcript

  • 1. Temporal 1D Kerr cavity solitons a new passive optical buffer technology Stéphane Coen Physics Department, The University of Auckland, Auckland, New Zealand Work performed while on Research & Study Leave at Special thanks to François Leo and to Pascal Kockaert The Université Libre Simon-Pierre Gorza de Bruxelles (ULB), Philippe Emplit Brussels, Belgium Marc Haelterman1. What are cavity solitons? 4. Experimental setup2. Temporal cavity solitons 5. Results3. Theory & Historical background 6. Conclusion
  • 2. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavityfilled with a nonlinear material
  • 3. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavityfilled with a Intracavity soliton nonlinear superimposed on material a low level background
  • 4. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavityfilled with a Intracavity soliton nonlinear superimposed on material a low level background The cavity solitons are independent from each other and from the boundaries They can be manipulated by external beams They exist for a wide range of nonlinearities L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003) W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)
  • 5. 1. What are cavity solitons? Traditionally described in passive planar cavities In semiconductor µ-cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavityfilled with a Intracavity soliton nonlinear superimposed on material a low level background The cavity solitons are independent from each other and from the boundaries They can be manipulated by external beams They exist for a wide range of nonlinearities L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003) S. Barland et al W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) Nature 419, 699 (2002)
  • 6. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Planar cavity Diffraction Nonlinearityfilled with a Intracavity soliton nonlinear superimposed on material a low level background
  • 7. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearityfilled with a Intracavity soliton nonlinear superimposed on Losses material a low level background ... but also cavity solitons
  • 8. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearityfilled with a Intracavity soliton nonlinear superimposed on Losses material a low level background ... but also cavity solitons They are not solitons in a box W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) 2D Kerr cavity solitons are stable while 2D Kerr nonlinear Schrödinger solitons collapse
  • 9. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearityfilled with a Intracavity soliton nonlinear superimposed on Losses material a low level background ... but also cavity solitons They are not solitons in a box W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) Cavity solitons form a subset of dissipative solitons 2D Kerr cavity solitons are stable while 2D Kerr nonlinear for coherently-driven Schrödinger solitons collapse optical cavities
  • 10. 2. Temporal cavity solitons Spatial versus Temporal cavity solitons We extend the terminology External plane wave to the temporal case coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearityfilled with a Intracavity soliton Dispersion nonlinear superimposed on Losses material a low level background cw driving beam Input coupler Input Temporal cavity solitons are naturally immune to longitudinal variations or imperfections along the cavity length Output
  • 11. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer Coherent driving Dispersion Nonlinearity Losses cw driving beam Input Output
  • 12. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving Dispersion Nonlinearity Losses cw driving beam Input Output
  • 13. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE cw driving beam Input Output
  • 14. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE The double balance makes temporal cw driving CSs unique attractive states beam Input Output
  • 15. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE The double balance makes temporal address pulses cw driving CSs unique attractive states beam ALL-OPTICAL RESHAPING Input They can be excited incoherently with address pulses at a different wavelength WAVELENGTH CONVERTER Output
  • 16. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE The double balance makes temporal address pulses cw driving CSs unique attractive states beam ALL-OPTICAL RESHAPING Input They can be excited incoherently with address pulses at a different wavelength WAVELENGTH CONVERTER A periodic modulation of the driving beam can trap the CSs in specific timeslots ALL-OPTICAL RETIMING Output
  • 17. 2. Temporal cavity solitonsTemporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly An optical buffer Coherent driving The driving power is independent of the based on Nonlinearity Dispersion number of bits stored temporal cavity solitons Losses would seamlessly combine ALL-OPTICAL STORAGE all these important address pulses The double balance makes temporal cw driving CSs unique attractive states telecommunications beam functions ALL-OPTICAL RESHAPING Input They can be excited incoherently with Here we report, address pulses at a different wavelength with a Kerr fiber cavity, WAVELENGTH CONVERTER the first experimental A periodic modulation of the driving beam observation can trap the CSs in specific timeslots of these objects ALL-OPTICAL RETIMING Output
  • 18. 3. Theory & Historical backgroundThe Kerr cavity“Hydrogen atom” of nonlinear cavity Input coupler Input Interferences Feedback Nonlinearity & Dispersion OutputCombination of a simplenonlinearity with feedback anddispersion in a 1D geometry
  • 19. 3. Theory & Historical backgroundThe Kerr cavity Linear regime: Fabry-Perot type response“Hydrogen atom” of nonlinear cavity Constructive Input coupler interferences Input Interferences P Feedback 2p Nonlinearity Pin = n0L f f0 = & Dispersion l 0 2(m–1)p 2mp 2(m +1)p f Output Destructive interferencesCombination of a simplenonlinearity with feedback anddispersion in a 1D geometry
  • 20. 3. Theory & Historical backgroundThe Kerr cavity: Nonlinear regimeNonlinear resonances and Bistability Instantaneous pure Kerr nonlinearity When approaching the resonance ... ... the intracavity power P increases ... fLP NL =g ... the nonlinear phase-shift increases ... ... the cavity round-trip phase shift increases ... P Pin 0 f 2(m–1)p 2mp 2(m +1)p fg = f LP 0+
  • 21. 3. Theory & Historical backgroundThe Kerr cavity: Nonlinear regimeNonlinear resonances and Bistability Instantaneous pure Kerr nonlinearity When approaching the resonance ... ... the intracavity power P increases ... fLP NL =g Positive ... the nonlinear phase-shift increases ... feedback ... the cavity round-trip phase shift increases ... Accelerated approach of the resonance P Pin 0 f 2(m–1)p 2mp 2(m +1)p fg = f LP 0+
  • 22. 3. Theory & Historical backgroundThe Kerr cavity: Nonlinear regimeNonlinear resonances and Bistability Instantaneous pure Kerr nonlinearity When approaching the resonance ... ... the intracavity power P increases ... fLP NL =g Positive ... the nonlinear phase-shift increases ... feedback ... the cavity round-trip phase shift increases ... Incident power Accelerated approach of the resonance PP PinPin 0 f 2(m–1)p 2mp 2(m +1)p Tilting of the cavity fg = f LP 0+ 0 f 0 resonance and bistability 2mp
  • 23. 3. Theory & Historical backgroundThe Kerr cavity: Nonlinear regimeNonlinear resonances and Bistability Bistability for various d0 Linear cavity detuning constant detunings D parameter (normalized = a respect to the losses) with P D =4 Bistability for various Incident power constant driving powers D =0PPin Pin 0 Onset of bistability: D =3 dp 0 =f 2m - 0 Tilting of the cavity 0 f 0 resonance and bistability 2mp
  • 24. 3. Theory & Historical backgroundThe intracavity field can be in the lower state in one part of the cavity andin the upper state in another part. The two parts can co-exist and be connected. Diffractive autosolitons Connecting the upper and lower bistable states with locked switching waves N. N. Rosanov and G. V. Khodova, J. Opt. Soc. Am. B 7, 1057 (1990) P P 0 Pin t
  • 25. 3. Theory & Historical backgroundThe intracavity field can be in the lower state in one part of the cavity andin the upper state in another part. The two parts can co-exist and be connected. Diffractive autosolitons Connecting the upper and lower bistable states with locked switching waves N. N. Rosanov and G. V. Khodova, J. Opt. Soc. Am. B 7, 1057 (1990) P PThe domain ofexistence is limitedas the switching wavescannot always lockand the upper statemay be unstable 0 Pin t Not the type of localized structures we are concerned with in this work
  • 26. 3. Theory & Historical backgroundIntracavity modulation instabilityStudied through a linear stability analysis Anomalous dispersion 5The homogeneous D = 4 L. A. Lugiato and R. Lefever 4upper state is Y? Phys. Rev. Lett. 58, D = 2.5unstable in favor of 3 P 2209 (1987)a modulated solution 2 D = 1 M. Haelterman, S. Trillo, and S. Wabnitz 1 Opt. Lett. 17, 745 (1992) 0 0 4 8 12 X? Pin P Frequency domain P t 0
  • 27. 3. Theory & Historical backgroundIntracavity modulation instabilityStudied through a linear stability analysis Anomalous dispersion 5The homogeneous D = 4 L. A. Lugiato and R. Lefever 4upper state is Y? Phys. Rev. Lett. 58, D = 2.5unstable in favor of 3 P 2209 (1987)a modulated solution 2 D = 1 M. Haelterman, S. Trillo, and S. Wabnitz 1It can coexist in Opt. Lett. 17, 745 (1992)different parts of 0 0 4 8 12the cavity with the X? Pinhomogeneous lowerstate P Localized dissipative structure t
  • 28. 3. Theory & Historical backgroundIntracavity modulation instabilityStudied through a linear stability analysis Anomalous dispersion 5The homogeneous D = 4 L. A. Lugiato and R. Lefever 4upper state is Y? Phys. Rev. Lett. 58, D = 2.5unstable in favor of 3 P 2209 (1987)a modulated solution 2 D = 1 M. Haelterman, S. Trillo, and S. Wabnitz 1It can coexist in Opt. Lett. 17, 745 (1992)different parts of 0 0 4 8 12the cavity with the X? Pinhomogeneous lowerstate P Cavity soliton G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990) S. Wabnitz, Opt. Lett. 18, 601 (1993) M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 73, 640 (1994) tW. J. Firth and A. J. 1623 (1996) Phys. Rev. Lett. 76, Scroggie,
  • 29. 3. Theory & Historical background Driving power (mW)Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300Turing bifurcation 9 8 7 6 5 4 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 30. 3. Theory & Historical background Driving power (mW)Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300Turing bifurcation 9 8 7 6 5 4 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 31. 3. Theory & Historical background Driving power (mW)Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300Turing bifurcation 9 8 7 6 5 4 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 ? = 3.8 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 32. 3. Theory & Historical background Driving power (mW)Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300Turing bifurcation 9 2 8 E é ¶ 2 ¶ ù 7 =( E êi - D E (S ih t ) 1 +- 2 ú,t )- + t ë ¶ ¶ t 6 û 5 L. A. Lugiato and R. Lefever 4h(= 2)sign b Phys. Rev. Lett. 58, 2209 (1987) 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 ? = 3.8 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 33. 3. Theory & Historical background Driving power (mW)Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300Turing bifurcation 9 2 8 E é ¶ 2 ¶ ù 7 =( E êi - D E (S ih t ) 1 +- 2 ú,t )- + t ë ¶ ¶ t 6 û 5 L. A. Lugiato and R. Lefever 4h(= 2)sign b Phys. Rev. Lett. 58, 2209 (1987) 3 10 1.9Similar to reaction P [W] 1.8diffusion systems 1.6 1.6 8 1.4Cavity solitons 1.2 1.2are localized 6dissipative ? = 3.8 1 Ystructures 0.8 4.4 ps 0.8 4“à la” Prigogine 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 34. 3. Theory & Historical background Driving power (mW)Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300Turing bifurcation 9 2 8 E é ¶ 2 ¶ ù 7 =( E êi - D E (S ih t ) 1 +- 2 ú,t )- + t ë ¶ ¶ t 6 û 5 L. A. Lugiato and R. Lefever 4h(= 2)sign b Phys. Rev. Lett. 58, 2209 (1987) 3 10 1.9Similar to reaction P [W] 1.8diffusion systems 1.6 1.6 8 1.4Cavity solitons 1.2 1.2are localized 6dissipative ? = 3.8 1 Ystructures 0.8 4.4 ps 0.8 4“à la” Prigogine 0.6 0.4 ? = 3.3 0.4 Fundamental 2 example of 0.2 self-organization phenomena in 0 0 nonlinear optics 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 35. 4. Experimental setupExperimental demonstration of temporal Kerr cavity solitons Input Fiber Coupler Output 90/10Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator To avoid Brillouin scattering
  • 36. 4. Experimental setupExperimental demonstration of temporal Kerr cavity solitons DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Output 90/10Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator To avoid Brillouin scattering
  • 37. 4. Experimental setupExperimental demonstration of temporal Kerr cavity solitons DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator Piezoelectric Fiber Stretcher To avoid Brillouin Controller scattering
  • 38. 4. Experimental setupExperimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator Piezoelectric Fiber Stretcher To avoid Brillouin Controller scattering
  • 39. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m Excited F = 24via XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric Fiber Stretcher To avoid Brillouin Controller scattering
  • 40. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m Excited F = 24 WDMvia XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric WDM Fiber Stretcher To avoid Brillouin Controller scattering
  • 41. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m Excited F = 24 WDMvia XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric WDM Fiber Stretcher To avoid Brillouin Controller scattering
  • 42. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM 1 nm BPF EDFA 1 kHz linewidth DFB 1551 nm CW pump Remove ASE 5 GSa/s Fiber Coupler Fiber Coupler oscilloscope 90/10 95/5 BPF Polarization Controller t R =s 1.85 m Remove driving beam 90m Excited F = 24 WDM Fiber Coupler 50/50via XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric WDM Fiber Stretcher Optical To avoid Brillouin Controller spectrum scattering analyzer
  • 43. 5. ResultsA single soliton in the cavityAddressing pulse: Off - CS only sustained by the cw driving beam The intracavity pulse persists in the cavity for more than 1 s (> 550,000 round-trips) Coherent driving Losses
  • 44. 5. ResultsA single soliton in the cavityAddressing pulse: Off - CS only sustained by the cw driving beam Experiment Simulations The intracavity pulse persists in the cavity for more than 1 s (> 550,000 round-trips) Coherent driving Dispersion Nonlinearity Losses Autocorrelation reveals it is 4 ps long, Dispersion matching simulations length: 230 m
  • 45. 5. ResultsA single soliton in the cavityAddressing pulse: Off - CS only sustained by the cw driving beam Experiment Simulations The intracavity pulse persists in the cavity for more than 1 s (> 550,000 round-trips) Coherent driving Dispersion Nonlinearity Losses Autocorrelation reveals it is 4 ps long, Dispersion matching simulations length: 230 m
  • 46. 5. ResultsStoring data as binary patterns with cavity solitons
  • 47. 5. ResultsInteractions of temporal cavity solitonsSending two close addressing pulses andobserving the CSs within the next 1 sAddressing pulses closer than 25 ps Only one CS present at the output
  • 48. 5. ResultsInteractions of temporal cavity solitonsSending two close addressing pulses andobserving the CSs within the next 1 sAddressing pulses closer than 25 ps Only one CS present at the outputWith a larger separation betweenthe addressing pulses ... The two excited CSs repel
  • 49. 5. ResultsInteractions of temporal cavity solitonsSending two close addressing pulses andobserving the CSs within the next 1 sAddressing pulses closer than 25 ps Only one CS present at the outputWith a larger separation betweenthe addressing pulses ... The two excited CSs repel ... but repulsion gets progressively weaker
  • 50. 5. ResultsInteractions of temporal cavity solitonsSending two close addressing pulses andobserving the CSs within the next 1 sAddressing pulses closer than 25 ps Only one CS present at the outputWith a larger separation betweenthe addressing pulses ... The two excited CSs repel ... but repulsion gets progressively weakerThe CSs could be easilytrapped by modulating thedriving powerPotential buffer capacity: 45 kbit @ 25 Gbit/s
  • 51. 5. ResultsWriting dynamics of temporal cavity solitons Experiment Simulation Time (100 µs/div)
  • 52. 5. ResultsWriting dynamics of temporal cavity solitons Output with off-center filter Experiment Inside the cavity Simulation Time (100 µs/div) Time (100 µs/div)
  • 53. 5. ResultsErasing of temporalcavity solitonsComplete erasing of thecavity can be obtainedby switching off thedriving beam for about4 round-trips
  • 54. 5. ResultsErasing of temporalcavity solitonsComplete erasing of thecavity can be obtainedby switching off thedriving beam for about4 round-tripsDriving beam switchedback on after4 round-trips
  • 55. 5. ResultsErasing of temporalcavity solitonsComplete erasing of thecavity can be obtainedby switching off thedriving beam for about4 round-tripsDriving beam switchedback on after4 round-tripsFrom there on, new CSscan be written withoutaffecting the erasureof neighboring CSs
  • 56. 5. ResultsErasing of temporalcavity solitonsSelective erasing ofone CS can be obtainedby overwriting it withan addressing pulseabout 50% morepowerfulThis realizes anall-optical XORlogic gate
  • 57. 5. Results Driving power (mW)Breathing temporal cavity solitons 0 50 100 150 200 250 300Above a certain driving power, 9the cavity solitons become breathers 8 7 6 5 4 Hopf 3 10 bifurcation 1.9 1.8 1.6 8 1.4 1.2 6 ? = 3.8 1 Y 4 0.8 0.6 ? = 3.3 0.4 2 0.2 0 0 0 2 4 6 8 10 X
  • 58. 5. Results Driving power (mW)Breathing temporal cavity solitons 0 50 100 150 200 250 300Above a certain driving power, 9the cavity solitons become breathers 8 7 6 5 4 Hopf 3 10 bifurcation 1.9 1.8 1.6 8 1.4 1.2 6 ? = 3.8 1 Y 4 0.8 0.6 ? = 3.3 0.4 2 0.2 0 0 Time (50 µs/div) 0 2 4 6 8 10 X
  • 59. 6. Conclusion We have reported the first direct experimental observation of temporal cavity solitons as well as Kerr cavity solitons Temporal cavity solitons could be used as bits in an all-optical buffer, combining all-optical storage with wavelength conversion, all-optical reshaping, and re-timing Our experiments have been performed in a purely 1-dimensional system with an instantaneous Kerr nonlinearity Due to this simplicity, our experiments may constitute the most fundamental example of self-organization in nonlinear optics Kerr frequency combs generated in microresonators may be the spectral signature of a temporal cavity soliton P. Del’Haye et al,Nature 450, 1214 (2007)