y y x x 3µm Hz 2µm z -30 NW 0.9µm y db 0-15 In 20 µm Out 20 µm GaAs Membrane PhC Hole Al2O3 ALD Course 7: Use of photonic nanostructures for all-optical signal processing. Part B Alfredo De Rossi Processing Radar Signals key operation is to go move the signal to the base band [down-conversion] the detection chain need to be simplified RF LO S/H ADC Bande de base DSP Thales Research and Technology 1 av. Augustin Fresnel, 91767 Palaiseau IF LO Brique tec hno. c ritique LO DSP DSP Fréquence Fréquence H z Sampling (Nyquist band) sub-sampling Signal (V) Sampling instant 5µm Time removing one conversion stage 1 / 80 10 / 80 All-photonic sampling All-photonic sampling Photonic Assisted Sampling: use optical clock to control an electronic gate Photonic Assisted Sampling: use optical clock to control an electronic gate Other advantages of light: transport of the signal Bandwidth, immunity to EM disturbances, lightweight Simplified radar receiver architecture Simplified radar receiver architecture RF Filter S/H ADC DSP RF Filter S/H ADC DSP clock (Mode-Locked Laser) Photonic assisted sampling clock (Mode-Locked Laser) Photonic assisted sampling 11 / 80 11 / 80
All-photonic sampling Photonic Assisted Sampling: use optical clock to control an electronic gate Other advantages of light: transport of the signal Bandwidth, immunity to EM disturbances, lightweight Implication: All-Photonic Sampling: light to control light, which combines the benefits above All-photonic sampling Photonic Assisted Sampling: use optical clock to control an electronic gate Other advantages of light: transport of the signal Bandwidth, immunity to EM disturbances, lightweight Implication: All-Photonic Sampling: light to control light, which combines the benefits above Still, this requires an All-Optical (nonlinear) gate. Signal on optical carrier Full-photonic link S EDFA Photo diode ADC DSP Signal on optical carrier Full-photonic link S EDFA Photo diode ADC DSP clock All-optical sampling front-end (Mode-Locked Laser) clock All-optical sampling front-end (Mode-Locked Laser) 11 / 80 11 / 80 Dynamical response of a NL PhC cavity Contents Pump Probe delay Spectra Summary of part A All-optical signal processing Transmission Time Resonance wavelength Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices excitation Application of PhC waveguides Nonlinear PhC waveguides Free carrier index change n 4<0 Blue shift Parametric effects in PhC 12 / 80 13 / 80
Using optics to process the signal Optically-assisted processing no need to act on every individual bit, as transistors do. e.g. : the EDFA, nonlinear wavelength conversion, MEMS switch optically-assisted processing e.g. : all-optical correlation and routing A. Wilner, IEEE-JLT, v.32, p.660 (2014) Routing a signal using a optical correlation. Use of an optical flip-flop 14 / 80 Contents Summary of part A All-optical signal processing Generation of new colors 15 / 80 out λ 1 out λ 2 time (us) 0 1 2 time (ns) Dorren, JLT 2003 An optical flip flop is a bistable laser controlled all-optically by the input header of the data signal. It decides which wavelength channel the output will go. Eventually a memory is necessary. Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC 16 / 80 17 / 80
Prism adapted from V. Torres-Company LPR. 8,368 (2014) Nonlinear Optics Green Nonlinear or non-stationary device weak optical field large optical field Linear time-independent response: f(cos(ωt)) g(cos(ωt)), no new frequencies. e.g. EDFA Linear time-dependent response: f(cos(ωt)) g(cos(ωt),t), new frequencies (EO modulator) Nonlinear response: f(cos(ωt)) g(cos(ωt),cos(2ωt),...), new frequencies. e.g. basically any optical material at large enough field intensity Weak oscillations harmonic potential linear permittivity Large oscillations Anharmonic potential Permittivity reveals nonlinear terms Nonlinear Optics: historical notes First experiment: Second harmonic generation Franken, Hill, Peters and Weinreich, Phys. Rev. Lett., v.7 p. 118 (1961)...One year later the Laser... 18 / 80 Some applications of Nonlinear Optics The selective generation of new wavelengths in biological tissues is exploited for medical imaging. 19 / 80 Figure: Generation of the optical harmonic of the radiation emitted by the ruby laser (λ=694 nm) The theoretical framework is set up just afterwards Armstrong, J. A. and Bloembergen, N. and Ducuing, J. and Pershan, P. S. Interactions between Light Waves in a Nonlinear Dielectric, Phys. Rev., v. 127, p. 1918 (1962). 20 / 80 More generally, NLO has a variety of applications. Some other examples: metrology, instruments, optical sources, and signal processing. R. Boyd, Nonlinear Optics G. Agrawal, Nonlinear Fiber Optics 21 / 80
Nonlinear optical processes Parametric Interaction Nonlinear dielectric polarizability Second Harmonic (sum-frequency) Generation Nonlinear Phase Accumulation Cross-Phase modulation Four-wave mixing Third harmonic generation (a) (b) adapted from Wilner, IEEE JLT v.32, p.660 (2014) Four Wave Mixing non-resonant, nonlinear response of the electronic polarizability 3 rd order, Four Wave Mixing: P4 = χ (3) ε0e1e2e3 Similar to Three Wave Mixing [χ (2) ], phase-matching is easier, particularly in isotropic materials. Gain spectrum after ~ 500 m of Higly NL Fiber Amplifica on Conversion and phase conjuga on 22 / 80 Four Wave Mixing Resonant process Conservation of the energy: ω1 +ω2 = ω3 +ω4 In waveguides, conservation of the momentum: κ1 +κ2 = κ3 +κ4 case of degenerate process: ω2 = ω3 23 / 80 (linear) phase mismatch κl = κ1 +κ4 2κ2 = 2 ωκ ω 2 +O( ω 4 ) [ depends on the dispersion] with nonlinear contribution: κ = κl +2γP this term governs the conversion efficiency: e.g. pump ω2, signal ω1, idler ω4 P4(out) P1(in) = (γ 2 P 2 κ2 4 )L2 < (γpl) 2 Hansryd et al, 2002 spontaneous and stimulated emission parametric 24 / 80 25 / 80
All-Optical Processing with FWM Flexible format encoder N-fold multi-casting adapted from Wilner, IEEE JLT v.32, p.660 (2014) Wilner, IEEE JLT v.32, p.660 (2014) Ultra-fast communications 26 / 80 Ultra-fast communications 27 / 80 640 Gbit/s 1.28 Tbit/s Oxenlowe, IEEE JSTQE 18, 996 (2012) 28 / 80 Wilner, IEEE JLT v.32, p.660 (2014) 29 / 80
Contents Summary of part A All-optical signal processing Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC 30 / 80 31 / 80 Optical Combs Generation of Optical Combs More advanced schemes V. Torres-Company LPR. 8,368 (2014) comb generator Using opto-electronic techniques (modulators and RF generators) is very simple V. Torres-Company LPR. 8,368 (2014) 32 / 80 33 / 80
exemple of Comb Application to the telecommunications Using Multiple Lasers One Laser + comb generator Fourier transforms connects time and frequency! V. Torres-Company LPR. 8,368 (2014) Particularly useful for OFDM and other novel formats 34 / 80 35 / 80 Optical Combs using laser and nonlinear optics Optical Combs in Microcavities Time domain Tunable cw-laser Optical amplifier Microresonator Photodiode E( ƒ) 2 ƒ o ƒ r E (t) φ 1 φ 2 t FWM: Degenerate (1) Non-degenerate (2) (1) Microwave beat note Energy 0 ML Laser Pump Gain medium ν n Saturable absorber = n ƒ r + ƒ o Energy ƒ Pump χ(3) 1/ƒ r Parametric Oscillator medium Adapted from: Kippenberg, Science,v332,555,2011 Power (a.u.) (a.u.) Energy f r f 0 ν pump Frequency ν n-2 WGM ν n-2 κ 2π WGM WGM WGM ν n-1 ν n ν n ν n+1 ν n-1 ν n+1 (2) ν n+2 WGM ν n+2 Microresonator modes Equidistant comb modes n-2 < n-1 < n < n+1 Frequency Kippenberg, Science,v332,555,2011 36 / 80 37 / 80
SiO 2 Input Through Drop Add 10 µm 20 µm Optical Combs in Microcavities Contents 20 Wavelength (nm) 2300 2000 1750 1550 1350 1200 1100 1000 Summary of part A Power (dbm) 0-20 -40 850 GHz 160 THz All-optical signal processing Generation of new colors -60 140 160 180 200 220 Frequency (THz) 240 260 280 300 Optical Combs and Metrology Signal (dbm) 0-10 25 GHz -20-30 -40-50 -60-70 1500 1520 1540 1560 1580 1600 Wavelength (nm) Signal (dbm) 0-10 -20-30 -40-50 1350 1450 1550 204 GHz 1650 1750 1850 Wavelength (nm) 75 THz 1950 2050 2150 Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices Hydex R=135µm Silica Silicon Nitride Silica CaF 2 (Crystalline) Adapted from: Kippenberg, Science,v332,555,2011 Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC 38 / 80 39 / 80 Enhancement of the light-matter interaction Simple case of the nonlinear phase accumulation: φ = γpl Parametric Interactions Can be extremely broadband because the Kerr effect is ultra-fast Coherent process: generation of correlated pairs, squeezed states, phase conjugation However Kerr effect requires optical intensity in the GW/cm 2 range in common optical materials Example: φ = γpl in an optical fiber: for φ π, and the power 1W then L is 100 m to 1 km Low propagation loss are crucial: L < 1/α Nonlinear Integrated Photonic circuits Increasing γ will reduce the size L and the power P 40 / 80 41 / 80
Nonlinear Silicon Photonics Strong field confinement nonlinear coupling parameter γ 100m 1 M 1 [e.g. 10 5 standard fiber] control of the dispersion β2 Photonic wire λ Contents Summary of part A All-optical signal processing Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides M. Foster, Nature 441, 960 (2006) IBM nonlinear absorption in Silicon in the telecom spectra (Eg(Si) = 1.1eV < 2 ω = 1.6eV) novel materials: Chalcogenides, Hydrogenated Silicon, III-V materials Linear slow waves and compact devices Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC 42 / 80 43 / 80 2D photonic crystals Accessing Photonic Crystal waveguides Optical mode with sub-λ confinement Alfredo De Rossi, THALES R&T 2D PhC pattern ~ 500 nm SiO 2 λ Silicon (Substrate) Waveguide input First demonstration : T. Krauss et al, Nature 1996 Much easier to fabricate : use of planar etching process of Silicon technology Breakthrough in the technology : Viable photonic devices based on PhC are feasible Strong magnification and large numerical aperture optics required! 44 / 80
1µm Low loss PhC chip Packaged PhC chip electric control P(in) 3 db 2dB 3 db P(out) P(in)/P(out) ~8 db α=5 db/cm PhC cavity Photonic Crystal Waveguide impedance converter Use lensed fiber enables compact package. Quynh Vy Tran et al. In: Appl. Phys. Lett. 95.6 (2009), p. 061105 Nozaky 2012 45 / 80 46 / 80 Dispersion of waveguides Dispersion effective index n eff Dispersion diagram (waveguide community) n g guided mode n c cut-off Frequency Dispersion diagram (solid state physics) n c n g cut-off guided mode frequency wavevector n c n g n c guided mode Dispersion diagram relates the wavevector and the frequency of a mode. propagation delay pulse broadening asymmetry Agrawal, Nonlinear Fiber Optics Meaningful parameters (truncated Taylor s expansion) 47 / 80 48 / 80
Dispersion in photonic crystals dispersion in Photonic crystals waveguides Alfredo De Rossi, THALES R&T Phase velocityv p: traveling speed of any given phase of the wave Group velocityv g: velocity of wave packets k dω c d v g = n 0 ω Effective group index g= = c0 dk vg dk band structure of a photonic crystal. Frequency (f c/a) Wavevector (k/k') Slow light propagation 49 / 80 Dispersion engineering via mode hybridisation 50 / 80 Alfredo De Rossi, THALES R&T Frequency (f*a/c) Perturbation with symmetry A2 Wavevector (k*a) very large change of the group velocity! Perturbation with symmetry A2 -> Even and odd mode hybridized Inflection point in the lower even-like band. Colman et al, Opt. Expr. 2012 51 / 80
Contents Structural disorder Summary of part A All-optical signal processing Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC Holes are not perfect! Roughness size fluctuations Fabrication is not perfect. Consequences of the disorder 52 / 80 Measurement of dispersion and transmission 53 / 80 measurement of the reflectance Reflection at the input facet R After 1 round trip 2 3 transmitted signal (a kind of OCT) Slowlight: Disorder Backscatter! (c) Signal is backreflected and strongly dispersed in time as ng grows Time (ps) Transmission (db) Backscattering (hence attenuation) is n 2 g! The extraction of the disorder-induced attenuation is not trivial! 54 / 80 55 / 80
Attenuation vs group velocity Contents Slotted photonic crystal waveguides [IEF-E. Cassan] Extraction of the propagation loss from a single WG Summary of part A All-optical signal processing Attenuation (db/cm) 400 300 200 100 leaky modes L=1mm 0.5 0.1 Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides 0 5 10 15 20 Group Index (n g) Linear slow waves and compact devices Application of PhC waveguides Attenuation is well correlated to the group index Propagation loss are still OK for a 100µm-long sensor. Charles Caër et al. In: Appl. Phys. Lett. 105.12 (2014), p. 121111 Nonlinear PhC waveguides Parametric effects in PhC 56 / 80 57 / 80 Enhancement of the field below the diffraction limit Optical delay line 80 8 500 nm Group Indexng 40 20 10 5 2...5 FOM ng = nslot φ Slot WG A eff = 0.019μm 2 Loss = -3dB 1540 1550 1560 1570 1580 1590 1600 Wavelength (nm) Slot WG Effective focusing area is 0.02 µm 2, tenfold below the diffraction limit ( λ 2nslot )2 = 0.25µm 2 without plasmonics! Can be used for sensing small objects, e.g. molecules. Caer et al., 2014, work with IEF, E. Cassan team 4 2 1 0.5 0.25 Confinement FOM (A slot /A eff ) 1.5 mm*n g/c delay = 25 ps = 100 ps 50 db/cm >150 db/cm tune laser to change the delay! PhC waveguide is fine, however, tuneable laser is expensive! 58 / 80 59 / 80
Tuneable delay line Filtering of microwave signals localized thermo-electric control of the delay Heating power Lattice-shifted PhC Wavelength (um) frequency J. Bourderionnet Hishikura 2012 benefits of Silicon Photonics radar signal has to be analyzed over a wide band. reconfigurable filters working over a wide frequency span are crucial 60 / 80 61 / 80 Finite impulse response filter Tuneable Interferometer Integrated Interferometer with tuneable elements Fixed delay line this architecture comes from digital signal processing. It can be implemented in an optical circuit. Tuneable coupler tuneable delay line This is a two-way finite impulse response filter. Just a first step... 62 / 80 63 / 80
Tuneable Interferometer: key device miniaturized directional coupler Transmission 1 0.1 0.01 S 12 S 13 Total S 14 P4 1490 1500 1510 1520 1530 1540 1550 1560 1570 Wavelength[nm] lambda=1478.57nm P3 lambda=1526.60nm P1 lambda=1532.72nm P2 lambda=1538.46nm lambda=1552.31nm lambda=1558.15nm PhC waveguide here! Compensation of fiber dispersion M. Gay et al., FOTON, Projet ANR Symphonie 64 / 80 Combrié et al, Opt. Expr. 2015 Used to control the weight of the filter Contents Summary of part A All-optical signal processing Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC 65 / 80 66 / 80 67 / 80
Slow light enhancement Simple case of the nonlinear phase accumulation: φ = γpl slow light as a spatial compression waveguide v ~ c/3 photonic crytsal waveguide v ~ c/20 spatial compression increase of the density of the electromagnetic energy Huge effect: γ depends on n 2 g Structural slow-light 68 / 80 Slow light enhancement of interactions 69 / 80 normalized Stored energy and Group delay propagation modified by a spatial modulation of the optical properties "slow light" "fast light" exemple: fiber bragg grating (FBG) dwell time τd = U/Pi coincides with group delay τg = dφ dω but not necessarily a transit time! spatially averaged energy U τg Detuning (normalized) H. G. Winful. In: New J. Phys 8 (2006), p. 101 R. W. Boyd. In: J. Opt. Soc. Am. B 28.12 (2011), A38 A44 Nonlinearindex change: I =Irradiance trueonlyif group velocity~phase velocity A more general equation: Nonlinear susceptibility energy Connection with the irradiance: Energy velocity Thus: as energy and group velocity coincide (absorption/gain are negligible) This effect adds up to the increase of the effective interaction lenght 2 hence the scaling as 1/v g P. Yeh, J.Opt. S. 1979 Bath and Sipe, Phys. Rev. B, 2001 M. Santagiustinaet al., Opt. Expr. 2010 70 / 80 71 / 80
Nonlinear PhC waveguide Spectral broadening due to the intensity dependent phase δφ δz = γp(t) Waveguide length 1.3 mm Input peak power 3.5 W Nonlinear phase shift ϕ~1.5π Nonlinear parameter γ 1/W/mm theory S. Combrié et al. Appl. Phys. Lett v.95 p. 221108 (2009) Almost ideal behavior as in optical fibres γ is about 10 6 fold larger than a SM fibre Nonlinear absorption (3PA) still negligible, TPA suppressed because Eg > 3 ω Contents Summary of part A All-optical signal processing Generation of new colors Optical Combs and Metrology Semiconductor nonlinear integrated circuits Governing the propagation in optical waveguides Linear slow waves and compact devices Application of PhC waveguides Nonlinear PhC waveguides Parametric effects in PhC 72 / 80 73 / 80 Four-wave-mixing in one PhC FWM in a 1 mm-long GaInP PhC. On-chip All-optical signal processing FWM in a 200 µm-long Silicon PhC. Spectral Power Density Tunable laser Probe λ 2 Tunable laser Pump λ 1 50:50 XOR gate for differential phase shift keying (DPSK) non-degenerate FWM 1530 1534 1538 1542 1546 Wavelength (nm) V. Eckouse et al, Opt. Lett. v35, p1440 (2010) J. McMillian et al., Opt. Express 18, 15484 (2010) C. Monat et al., Opt. Express 18, 22915 (2010) K. Suzuki and T. Baba, Opt. Express 18, 26675 (2010) Off-chip parametric gain demonstrated afterwards. collab. Technion, G. Eisenstein power ~ 40 mw (1 pj/bit @ 40 Gb/s) at CUDOS, C Husko et al. In: Optics express 19.21 (2011), pp. 20681 20690 74 / 80 75 / 80
Wavelength conversion and sampling Second harmonic generation GaInP is a non centro-symmetric crystal: χ (2) is non-zero! CCD Objective Fibre Tunable laser + Modulator PhC 1540 nm OSA Time resolution 6 ps. collab. K. Lenglé M. Gay L. Bramerie, FOTON Non-phase matched SHG (broadband). Normalized efficiency 2 10 4 W 1. Max SHG generated: 100µW Collab. FOTON, Lenglé et al., APL 2013. Autocorrelator based on harmonic generation SHG is used for autocorrelation. In silicon, only THG cross Third Harm gen 76 / 80 Nonlinear waves 77 / 80 100um PhC waveguide Alfredo De Rossi, THALES R&T time offset no time offset Monat, Nature Comm 2014 Need external delay line, but that exists. Nonlinear wave going against the stream (Abel Tasman Park, Nouvelle Zelande) 78 / 80
4 2 1 0.6 0.4 0 5 10 15 20 Coupled pulse energy (pj) λ = 1551 nm E = 22 pj Soliton-Effect Compression Compression from 3.2 ps to 580 fs 22 pj/pulse. Application in compact sub-ps optical sources. Autocorrelation Spectra 0.9 ps 22 pj 19 pj 17 pj 15 pj 12 pj 9.8 pj 7.4 pj 4.9 pj 2.5 pj 4.9 ps Input -10-5 0 5 10 1547 1551 1555 Delay (ps) Wavelength (nm) Pulse width (ps) Autocorrelation (a.u.) Phase (π) 1 0.8 0.6 NLSE T=580 fs Input soliton number N > 4 NLSE deconvolu on T=580 fs 0.4 0.2 0 0! 4! 2 0 2 4-1 -4-2 0 2 4 Delay (ps) P. Colman et al. Nat. Phot. 4, 862 (2010) Collab. with C.W. Wong. Soliton-Effect Compression Compression from 3.2 ps to 580 fs 22 pj/pulse. Application in compact sub-ps optical sources. could be associated to a Mode Locked Laser Diode for on-chip compression QD ML LASER (ps) Chirped ps pulse mm Si chip PhC WG compressor fs pulse Supercontinuum generation 79 / 80 79 / 80 combining compression, FWM, SFG, XPM, etc. etc. in photonic crystal fibres, now also in semiconductor waveguides Dudley, RMP, 78 1135 (2006) J. Dudley [SPIE Newsroom 2009] ultimate tool to generate colors... 80 / 80