Nonlinear optical effects in ordered and disordered photonic crystals, and applications

Transcription

1 Nonlinear optical effects in ordered and disordered photonic crystals, and applications Ramon Vilaseca, José F. Trull,, Crina M. Cojocaru, V. Roppo, K. Staliunas Universitat Politècnica de Catalunya, Dept. de Física i Enginyeria Nuclear Terrassa (Barcelona), Spain Collaboration (in part of the work) with: S. M. Saltiel, Faculty of Physics, University of Sofia, Bulgaria W. Krolikowski,, D. Neshev, Y.Kivshar Centre for Ultrahigh Bandwidth Devices for Optical Systems (CUDOS), Nonlinear Physics Centre, Australian National University, Canberra, Australia 1.- Loooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the random nonlinear domain distrib. 5.- Conclusions Menu for today:

2 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions Menu for today: Research activities of the Group on Nonlinear Dynamics & Optics and Lasers (DONLL) Universitat Politècnica de Catalunya (Campus de Terrassa) Photonics Biology

3 Research lines: Photonics: Nonlinear Optics, Nonlinear Dynamics Biology: Nonlinear dynamics Kestutis Staliunas José F. Trull Cristina Masoller Crina Cojocaru Ramon Herrero Josep Lluís Font Juanjo Fernández (Muriel Botey) Ramon Vilaseca Jordi Tiana Jordi Zamora Cristian Nistor Vito Roppo Jordi García-Ojalvo M. Carme Torrent Antoni Pons Núria Domedel Lorena Espinar Belén Sancristóbal Pau Rué Marta Dies Research lines: Photonics Linear & nonlinear light propagation in spatially modulated materials Kestutis Staliunas José F. Trull Crina Cojocaru Ramon Herrero Ramon Vilaseca Cristian Nistor Vito Roppo Nonlinear light dynamics, in semiconductor lasers Jordi García Ojalvo Cristina Masoller M. Carme Torrent (Cristina Martínez) Jordi Tiana Jordi Zamora Nonlinear light dynamics, in other structures and systems Kestutis Staliunas Ramon Herrero Ramon Vilaseca Josep Lluís Font Juanjo Fernández

4 Research lines: Linear & nonlinear light propagation in spatially modulated materials Kestutis Staliunas José F. Trull Crina Cojocaru Ramon Herrero Ramon Vilaseca Cristian Nistor Vito Roppo Subdiffraction & spatial filtering in linear materials: - Spatial dispersion in PC materials (index-modulated), and PC resonators. cw case Short-pulse case Extention to BEC systems. - In linear gain-modulated materials Subdiffraction in NL PC materials and resonators: - Modified phase-matching (broad & narrow angular spectrum). - Nonlinear wave mixing: SHG and parametric amplific. with narrow beams. - Spatial solitons (Bloch cavity solitons in Kerr PC resonators) Ultrafast all-optical tuning of NL PC response: - PC waveguide. Control of a pulse by a 2 pulse Materials with random spatial distribution of χ (2) : -StudyofSHG - Application: femtosecond pulse measurement. Phase-locked SHG and THG in resonators and PC s - Study of the resonant growth of SHG Menu for today: 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions

5 Nonlinear Optics: r E( r, t) r P( r, t) E(t) y ATOM x z P r (t) Material response: r r r r r r r P = ε 0 χ E (1) (2) (3) ( χ E + χ EE + EE + L) (1) P r (2) Linear P r (3) P r P r NL Nonlinear P E Nonlinear Optics Example: SECOND HARMONIC GENERATION (SHG) r r r r r r r P = ε 0 χ E (1) (2) (3) ( χ E + χ EE + EE + L) E e it E2 ei 2t Ε E(t) y ATOM x 2 z 2 Ε 1 P r (t)

6 NONLINEAR OPTICS: Generalizing Generalizing: examples of nonlinear processes: electron E 4 E 3 E h E 1 E 1 Variety of features: non-resonant resonant; without with energy exchange with the atom; spontaneous stimulated; effects over diffraction, effects over light pulses, NONLINEAR OPTICS: Generalizing Generalizing: examples of nonlinear processes: electron h E 4 E 3 E h E 1 Variety of features: non-resonant resonant; without with energy exchange with the atom; spontaneous stimulated; effects over diffraction, effects over light pulses,

7 Nonlinear Optics: SHG Problem with SHG: Phase matching condition! Classical description: In general, dispersion n() n(2) λ 2λ 2 λ 2 Destructive interference! Back conversion!: 2 λ 2 z To have 2λ 2 = λ n(2) = n() Phase-matching condition Quantum description: Photon momentum conservation: r r h k + 2 = hk1 hk1 k 2 = 2k 1 r k 1 k 1 k 2 Nonlinear Optics: SHG I 2 Phase matching ( k = 0) Non phase matching ( k k 2 -k 0) 0 L c = π k Coherence length z (penetration distance within the crystal) Ways to achieve phase matching?: Crystal birefringence Temperature Quasi-phase matching Photonic crystals

8 Menu for today: 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions Photonic crystals: structures with a built-in periodic distribution of dielectric material, with lattice dimensions comparable to the wavelength of the light. (E. Yablonovitch, Phys. Rev. Lett. 58 (1987) and S. John, Phys. Rev. Lett. 58 (1987)) 1D multilayer film Photonic crystals 2D square lattice of dielectric columns surrounded by air 3D spheres in a FCC configuration AlGaAs/air waveguide AlOx/GaAs AlGaAs/air inverted opals

9 Photonic crystals: regular structures Joannopoulos et al. (MIT) (proposed theoretically, on Si) A. Blanco et al., Nature (2000) - Opal Colloidal crystal AlGaAs /air E. Yablonovitch et al., PRL (1991) Yablonovite Soukoulis et al. (Ames Lab., Iowa State Univ.) (proposed theoretically) Photonic-crystal fiber Photonic crystals: with defects 18 x L z Light confinement (to make micro-lasers, etc.)

10 Photonic circuits: the dream.. These optical circuits should provide active functions for all-optical information processing. use of nonlinear optics sub-λ structures: photonic crystals laser µ-sources Tunable filters, amplification, frequency conversion.. change the propagation direction resonators 1µm waveguides Photonic crystals Extended zone scheme Reduced zone scheme n=3 n=3 Forbidden band n=2 n=2 Forbidden band n=1 n=1 0 π/a g 2π/a k x 0 1st Brillouin zone π/a k x

11 DISPERSION CURVES, CALCULATED, FOR PHOTONIC CRYSTALS 21 Reduced-zone scheme (J.F. Trull, Tesis doctoral, UPC, 1999). 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions Menu for today:

12 Nonlinear optics & Photonic crystals Advantages of photonic crystals for nonlinear effects? 1) To achieve the phase matching condition n() = n(2) 2) Slower light propagation (and/or lower diffraction) larger intensity (it occurs near the photonic band gaps) 3) Take advantage of narrow resonances (it occurs near the photonic band gaps or in defect states) 4) Interesting multifunctions for all-optical processing: tunable PC, switch, amplification, laser effect, ANALYSIS IF THE DISPERSION CURVES, FOR PHOTONIC CRYSTALS 24 (real part)

13 inside a 1, PHOTONIC CRYSTAL (the light is incident from the left) 4.00 a 1-D PHOTONIC CRYSTAL E ^ E ^ distance into the crystal (period units) air band E ^ n distance into the crystal (period units) n= E ^ n= distance into the crystal (period units) n= distance into the crystal (period units) E ^ ª zona Brillouin π/a k x E ^ Dielectric band distance into the crystal (period units) J. Trull, C. Cojocaru, J. Martorell, R. Vilaseca distance into the crystal (period units) PHOTONIC CRYSTAL WITH A DEFECT 26 x y L z 500 Field amplitude within the structure, for two different input fields (cases A and B) B 400 Field amplitude (arb. units) A J. Trull, C. Cojocaru, J. Martorell, R. Vilaseca z ( µ m)

14 k Research line: Linear & Nonlinear light propagation in spatially modulated materials Sub-diffraction (or self-collimation collimation) ( k r ) k k k k II k 1,0 k y 0,5 M Input output Diffractive Non diffractive 0,0 Γ 0,0 X k 1,0 x K. Staliunas, R. Herrero (UPC) DONOR and ACCEPTOR DEFECTS 28 x Regular-period value: L=137.7 nm y L z periodic structure L=275 nm L=325 nm L=350 nm 1 (c) Donor defect periodic structure L=100 nm L=50 nm L=10 nm 1 (b) Acceptor defect Transmissivity Transmissivity / ο / ο J. Trull, C. Cojocaru, J. Martorell, R. Vilaseca

15 Nonlinear Optics Menu for in random today: nonlinear crystals Menu for today: Our past contributions Photonic crystals First experiment on SHG in a photonic crystal (Martorell, Vilaseca, Corbalán, APL + PRA, 2007) Nonlinear slab First experiment on modification of SHG from a localized source inside a photonic crystal (Trull, Martorell, Vilaseca, Corbalán, OL 1995) M. botey 2 (a) Truncated 1-dimensional photonic crystal

16 Time division demultiplexing Reflected signal at Multiplexed signal at transmitted signal at control signal at 2 [110] C. Cojocaru, J. Trull, J. Martorell, R. Vilaseca CONFIGURATIONS for the MATERIAL STRUCTURE Microcavity NL material 2 2 AlGaAs/air 1D structure in guided configuration C. Cojocaru, J. Trull, J. Martorell, R. Vilaseca

17 Measurements of the induced transmission and reflection in microcavities Experimental set-up in Terrassa, with Nd:YAG and Ti:Sapphire pulsed lasers F(RG610) M SH M FF F(KG5) F(RG610) Translation stage Corner cube Nd:YAG LASER 1064 nm 35 ps SHG KDP crystal M SH P 1 Translation stage λ/2 waveplate M FF M FF Corner cube P2 λ/4 waveplate L M FF M FF F(KG5) FD 1 (trigger) Crystal plate F(RG610) F(RG610) Microcavity FD 2 (transmission) D M FF 400 x 0 0 Spatial filtering z/zr Sub-diffraction 18 In a photonic crystal with modulation of the gain and losses (instead of modulationn fo the refractive index) 400 x GLM 0.84Z R Homogeneus a) m=0.1 and Q = % of energy 0 0 d z/zr 10 K. Staliunas, R. Herrero, R. Vilaseca, PRA, 2009

18 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions Menu for today: NonlinearOptics Menu opticsfor in in today: random nonlinear crystals The spatial modulation, can affect: The linear properties: χ (1), n() (Most photonic crystals) Phase-matching condition: k 2 = 2k 1 n(2) = n() k 1 k 1 k 2 The nonlinear properties: χ (2) ( Nonlinear photonic crystals) k 2 = 2k 1 + G k 1 k 1 G k 1 k 1 G k 2 k 2

19 Nonlinear optics in random nonlinear crystals χ (2) periodic 1-D : Quasi-phase matching (PPLN) k 2 = 2k 1 + G χ (2) spatial Fourier components (Refractive index uniform) Problem of all these phase-matching techniques: G k 1 k 2 Narrow frequency bandwidth Do not work for different frequencies Do not work for several NL processes simultaneously Power 2 Phase-matched L c = π k not phase-matched Distance (z/l c ) Λ=2L c QPM Nonlinear optics in random nonlinear crystals Generalizing Quasi - Phase matching: 1-D Multiple channel wavelength conversion by use of engineered quasi phase matching structures in LiNbO3 waveguides. Opt.Lett, 24, 1157 (1999) Fibonacci distribution Zhu et al., Science 278, 843 (1997) Generalized Q-P structure Fradkin-Kashi et al., PRL 88 (2002) <<<< Tranversed-pattern PPLN Kurtz et al., IEEE JSPQE 8 (2002)

20 Nonlinear optics in random nonlinear crystals χ (2) periodic k 2 = 2k 1 + G 2-D Berger, PRL 81, 4136 (1998) G Phys.Rev.Lett, 84, 4346 (2000) Momentum space, and Reciprocal lattice Nonlinear optics in random nonlinear crystals χ (2) periodic, with some degree of aperiodicity or randomness k 2 = 2k 1 + G 2-D 2-D Quasi-crystal (Penrose pattern) Bratfalean et al., OL 30, 424 (2005)

21 Nonlinear optics in random nonlinear crystals χ (2) random distribution?? k 2 = 2k 1 + G 2-D z y G Continuous set of reciprocal-lattice vectors, in x-y plane x c-axis ( ) 2 > 0 χ ( ) 2 < 0 χ Random quasi Phase matching Does it exist? χ (2) random distribution k 2 = 2k 1 + G Nonlinear optics in random nonlinear crystals Tetragonal 4mm point symmetry It appears naturally in unpoled (as-grown) ferroelectric (relaxor-type) crystals: Strontium Barium Niobate (SBN): Sr x Ba 1-x Nb 2 O 6, with 0.25<x<0.75 (standard x=0.61) [P. Molina et al. Adv. Funct. Mat. 18, 709 (2008)] V.V. Shvartsman et. Al., Ferroelectrics 376,1 (2008) Quenched Electric random fields χ ( 2 ) > 0 χ ( 2 ) < 0 c-axis z y x

22 Nonlinear optics in random nonlinear crystals SBN CBN LiNbO 3 Coercive field (E c ) < 500 V/mm 20 kv/mm Curie Temperature (T c ) 70 ºC 260 ºC 1210 ºC Maximum χ (2) coefficient d 33 = 200pm/V d 33 = 55 pm/v d 15 =70 pm/v z y x ( 2 ) χ > 0 G ( 2 ) χ < 0 c-axis Results so far? References G. Dolino. Phys.Rev.B, 6, 4025 (1972) M. Horowitz et al. Appl.Phys.Lett. 62, 2619 (1992) A.R. Tunyagi et al. Phys.Rev.Lett. 90, (2003) M. Baudrier-Raybaut et al; Nature, 432, 374 (2004) S.E. Skipetrov; Nature,432, 285 (2004) R. Fischer et al. Appl. Phys.Lett., 89, , (2006) X. Vidal, J., Phys.Rev.Lett. 97, (2006) P. Molina et al. Adv.Funct. Mater.18, 709 (2008) J. Trull et al. Optics Express, 15, (2007) Nonlinear optics in random nonlinear crystals SHG for propagation perpendicular to c-axis Avalilable grating vectors in the plane allow the phase matching in different directions Planar SHG k 1 c-axis [M. Horowitz, et al. APL 62, 2619 (1993)] r k r k 2 = r G ee e [P. Molina et al. Adv. Funct. Mat. 18, 709 (2008)]

23 Random quasi Phase matching Advantages: Phase matching for any second order parametric process Extremely large spectrum range (limited only by the transparency window of the crystal: from λ =0.4 to λ =6 µm!) and broad angular bandwith. Full bandwith conversion, without need of alignment or temperature control (SHG of short pulses, ) Multiple directions converter. (Simultaneous phase-matching of different processes) Limitations/Drawbacks Drawbacks: Nonlinear optics in random nonlinear crystals Lower efficiency (good for pulse characterization: no pulse depletion) Intensity grows linearly with distance Radiation emitted in broad directions (Simultaneous phase-matching of different processes) Nonlinear optics in random nonlinear crystals SHG of short pulses Top view low power Front view Also: Self- and cross- correlations functions (seen in space) R. Fischer et al, Broadband fs frequency doubling in random media, Appl. Phys. Lett. 89, (2006). R. Fischer et al. Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media, Appl. Phys. Lett. 91, (2007).

24 SHG for propagation along c-axis Nonlinear optics in random nonlinear crystals k 2 Z G G 2k α 1 k 2 2k cos( α ) = k 2 1 c-axis Applications: Super prism effect: X < 2 1, 2 Z 1, 2 A.R. Tunyagi et al. Phys.Rev.Lett. 90, (2003) Radial polarization Better focusing SHG with two fundamental beams Configuration with counter- propagating pulses: Application: Autocorrelation measurements of fs pulses Image of the background and of the autocorrelation trace (visible in the center). R. Fischer, D.N. Neshev, S.M. Saltiel, A.A. Sukhorukov, W. Krolikowski and Yu S. Kivshar, Appl. Phys. Lett. 91, (3) (2007)

25 3.- SHG with two non-colinear fundamental beams Configuration with non- collinear pulses: 800 nm y z x Application: Autocorrelation measurements of fs pulses V. Roppo, J. Trull, S. Saltiel, C. Cojocaru, D. Dumay, W. Krolikowski, D. Neshev, R. Vilaseca, K. Staliunas and Y.S. Kivshar, Optics Express 18, (2008) J. Trull, S. Saltiel, V. Roppo, C. Cojocaru, D. Dumay, W. Krolikowski, D. Neshev, R. Vilaseca, K. Staliunas and Y.S. Kivshar, Appl.Phys.B 95, 609 (2009) 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions Menu for today:

26 3.- SHG with two non-colinear fundamental beams Application: Autocorrelation measurements of fs pulses z k 1 +k 1 Noncollinear planar SHG in SBN 3.- SHG with two non-colinear fundamental beams: Application to pulse measurements Long pulse Short pulse τ >> 2ρ tanα u τ <<2ρ tanα u z 10 ns pulse 190 fs pulse AUTOCORRELATION

27 Noncollinear autocorrelation in SBN 3.- SHG with two non-colinear fundamental beams: Application to pulse measurements E = e I 1 SH = e 2 X 1 2 t Z1 u 2 2 2ρ 0 2T Model E = e 2 2 X 2 2 t Z2 u 2 2 2ρ 0 2T Z cos ( α ) + X sin ( α ) ( Tu X cos( α )) + Z sin ( α ) ρ0 u T e τ <<2ρ tanα u I ( Z ) I Z sin ( α ) exp 2 u T = o,2 2 τ = 2 Z fwhm sin ( α ext ) c z 190 fs pulse τ = 2 AUTOCORRELATION z FWHM sinα c Noncollinear autocorrelation in SBN 3.- SHG with two non-colinear fundamental beams: Application to pulse measurements Femtosecond pulses from a Ti:saphire laser at 810 nm τ = z sinα 2 = 193 fs c 2α ext =22º V. Roppo et al. Optics Express 18, (2008)

28 3.- SHG with two non-colinear fundamental beams: Application to pulse measurements z Calibration of the measurement technique? By changing the delay between the pulses an amount δ t, the autocorrelation line is displaced a distance δ z =c δ t /2sin(α ext ) in z direction: α α δt δz z Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Real time monitoring of pulse duration for large frequency bandwith without any tuning parameter (we are planning to try with pulses below 30 fs, in collab. with Salamanca).

29 Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Real time monitoring of pulse duration for large frequency bandwith without any tuning parameter (we are planning to try with pulses below 30 fs, in collab. with Salamanca). Background-free autocorrelation measurement (a) (b) (c) (a) (b) (c) X 2 1 Z Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Real time monitoring of pulse duration for large frequency bandwith without any tuning parameter Background free autocorrelation measurement Pulse changes its duration during propagation: pulse initial chirp measurement C: chirp parameter

30 Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Real time monitoring of pulse duration for large frequency bandwith without any tuning parameter Background free autocorrelation measurement Pulse changes its duration during propagation: pulse initial chirp measurement Recording of a train of pulses as parallel traces in the crystal Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Real time monitoring of pulse duration for large frequency bandwith without any tuning parameter. Background free autocorrelation measurement Pulse changes its duration during propagation: pulse initial chirp measurement Recording of a train of pulses as parallel traces in the crystal Pulse tilting can be observed

31 Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Pulse tilting can be observed V. Roppo et al. Optics Express,18, (2008) Noncollinear autocorrelation in SBN Properties of noncollinear autocorrelation measurements in SBN: Real time monitoring of pulse duration for large frequency bandwith without any tuning parameter Background free autocorrelation measurement Pulse changes its duration during propagation: pulse initial chirp measurement Recording of a train of pulses as parallel traces in the crystal Pulse tilting can be observed The autocorrelation trace can be observed for any polarization of the incident fields

32 1.- Looooong Introduction: Research Group DONLL in Terrassa Nonlinear Optics Photonic crystals 2.- Nonlinear optics in photonic crystals 3.- Nonlinear Optics in random nonlinear crystals - Application to short-pulse measurement 4.- Influence of the nonlinear domain distribution. 5.- Conclusions Menu for today: Influence of domain size, shape and distribution? 5.- Modelling of SHG in these materials, sample characterization y z x Φ Homogeneous emission Angular emission with maxima Is SH light actually emitted uniformly in all directions? (as it is usually assumed ) 10x5x5 mm 20x5x5 mm

33 3.- Influence of light polarization Influence of light polarization? beam A beam B eo o This is in contrast to previous claims [Horowitz et al. APL 62, 2619 (1993)] that in SBN crystals only e-pol SH could be generated J.Trull et al, Opt. Express 15, (2007) 3.- Influence of light polarization e-pol o-pol e-pol SH signal detected o-pol SH signal detected The NL coefficient ratio: d 32 /d 33 =0.44 This allowed us to determine: The domain average size and variance: a=3.25µm, σ=1.15µm

34 Angular distribution of transverse SHG Influence of domain size, shape and distribution? A. R. Tunyagi PhD thesis : Noncollinear SHG in SBN Universität Osnabrück (2004) x=0.75 [M. Ramirez et al., JAP SBN as a multifunctional 95,6185 (2004)] 2D nonlineal photonic glass P. Molina, M. Ramirez, L. Bausá Domain observation by chemical etching + optical microscopy Domain observation by PFM (Piezoelectric Force Microscopy) Strontium Barium Niobate (SBN): Sr x Ba 1-x Nb 2 O 6, with 0.25<x<0.75 (standard x=0.61) x = 0.40 x = 0.75 Domain observation by PFM (Piezoelectric Force Microscopy)

35 MODELLING of Angular distribution of transverse SHG The role of ferroelectric domain structure in second harmonic generation in random quadratic media V.Roppo, W.Wang, K.Kalinowski, Y.Kong, C.Cojocaru, J.Trull, R.Vilaseca, M.Scalora, W.Krolikowski, Yu.Kivshar (Optics Express, 2010) Angular distribution of transverse SHG The role of ferroelectric domain structure in second harmonic generation in random quadratic media V.Roppo, W.Wang, K.Kalinowski, Y.Kong, C.Cojocaru, J.Trull, R.Vilaseca, M.Scalora, W.Krolikowski, Yu.Kivshar (Optics Express, 2010)

36 Angular distribution of transverse SHG nm distance (μm) spatial spectrum (μm 1 ) 25 λ=790nm 350 nm ~17 ~ nm λ=790nm λ=1064 nm λ=790nm Angular distribution of transverse SHG Incident wavelength: 1064 nm 950 nm

37 Angular distribution of transverse SHG Beam propagation method The time dynamics of both the fundamental and second harmonic pulses is simulated using a fast fourier transform beam propagation method Complete control of the nonlinear terms Complete management of the dispersion Not any kind of approximations on the field shape or behaviour 5.- Modelling of SHG in these materials, sample characterization Other factors that could contribute to the wide angular emission? : Linear scattering? (is n actually uniform?) (does it affect the FF or SH field?) Refraction (and total reflection) of the SH light at the sample surfaces?

38 Angular distribution of transverse SHG Linear scattering: Small, but it exists (due to some inhomogeneities of n at the domain walls). It is larger for the sample with broader (and more uniform) angular emission (i.e., for the sample with smaller of domains). It affects more the SH than the FF ( the model of Molina et al., Adv. Func. Mater. 18, 709 (2008) does not seem to apply here). λ=790nm No scattering linear scattering Angular distribution of transverse SHG Refraction and total reflection: c-axis c-axis SH FF Radiation emitted between 23.5º and 66.5º is not leaving the crystal due to the large index contrast!. Eventually it will be scattered

39 5.- Modelling of SHG in these materials, sample characterization Controlling the aperture of the angular emission (through the domain size and distribution) ) can be useful: Wide angular emission: Makes it easier applications in short-pulse measurements, etc. Smaller angular emission: Larger peak intensity can be generated significant THG observed! [ 2 3] (more than in Molina et al., Adv. Funct. Mat. 18, 709 (2008)) W.Wang, V. Roppo,, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski,, Optics Express 17, (2009). Third-harmonic harmonic generation (THG): W.Wang, V. Roppo,, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski,, Optics Express 17, (2009). VIDEO!

40 Conclusions (about about the random NL materials): Random quasi-phase matching in SBN and similar crystals, with non-collinear dual fundamental beam,, can be used for short-pulse measurements. Random quasi-phase matching occurs for any light polarization, and allows to get information about the nonlinear coefficients and the domain distribution of the sample. The angular distribution of SHG is sensitive to the domain distribution and can have maxima. Modelling allows to interpret these results. Linear light scattering can play a certain role. Different experimentalists seem to grow samples with quite different domain distributions. Control of domain distributions would be important for progress in the field. Gràcies per la vostra atenció!!