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Non-linear photonic crystals

Non-linear photonic crystals. Resumed by: D. Simeonov PO-014 Photonic crystals. Definition. Nonlinear photonic crystals (NPC) are periodic structures whose optical response depends on the intensity of the optical field that propagates into the crystal. At low light densities:.

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Non-linear photonic crystals

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  1. Non-linear photonic crystals Resumed by: D. Simeonov PO-014 Photonic crystals

  2. Definition Nonlinear photonic crystals (NPC) are periodic structures whose optical response depends on the intensity of the optical field that propagates into the crystal. At low light densities: At high light densities:

  3. Types of non-linear response in PC With periodic modulation of the non-linear material properties Modulated c(2) for quasi-phase matching (QPM) Applications: harmonic generation, wave mixing, optical parametric amplifiers etc Without periodic modulation of the non-linear material properties Non linear response due to optical Kerr effect

  4. c(2) modulated NPC • Second harmonic generation (SHG) and phase matching • Quasi phase matching (QPM) • Phenomenological approach • Analytical approach • Fabrication techniques • Some devices and applications • 2D QPM-NPC • Natural QPM-NPC

  5. SHG Non-linear polarization: Second harmonic polarization: Where 2deff = c(2) Second harmonic polarization (vectorial representation):

  6. SHG SHG gained over the traveled distance (l): Dk=0 Coherence length:

  7. QPM for SHG Proposed by N. Bloembergen in 1962

  8. QPM for SHG Maximal efficiency for 50/50 duty cycle and: The effective efficiency is reduced by factor of p/2

  9. QPM for SHG Second harmonic of the electric field: c(2) susceptibility in Fourier representation: Where

  10. QPM for SHG After integration: QPM when Dk’=0 The lattice reciprocal vectors can help for momentum conservation

  11. QPM generalized For any frequency conversion process in media with periodic c(2) it can be generalized: Energy conservation law: Momentum conservation law: Such formalism can be derived for both 1D, 2D or 3D QPM-NPC crystals

  12. Theory details

  13. Some benefits of QPM

  14. Methods and materials • Periodic E field (via segmented electrode) + field-induced c(2) • ‘Frozen-in' field-induced c(2), in optical fibers • Periodic destruction/reduction of nonlinearity via ion-implantation through a mask • Overgrowth on a template having periodic modulation of substrate orientation c(2)→-c(2): semiconductor materials: GaAs, GaN • Periodic modulation of pump intensity (corrugated capillary waveguide for High Harmonic Generation) • Periodic-poling of ferroelectrics, switching c(2) →-c(2): LiBaNO3, etc… • Many more…

  15. Fabrication of PPLN ~30 mm References: • Easy to fabricate • The change could be either temporary or permanent

  16. Fabrication of PPLN SEM top view of PPLN grating 100 mm

  17. PPLN tuning

  18. Some results PPLN

  19. Some results PPLN Review for different techniques:

  20. Some results PPLN

  21. Some results PPLN

  22. Some results PPLN

  23. Some results PPLN

  24. Some results PPLN

  25. Fabrication of GaAs QPM NPC Why GaAs? ●Large nonlinearity, d14~ 100pm /V ●Extensive transparency, 0.9 μm -17 μm ●Mature technology 1st proposition – stacking thin plates (wafers): A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi-phase matching technique for efficient optical mixing and frequency doubling,” J.Appl. Phys., vol. 47, pp. 2025-2032, (1976) (2-5 plates, m = 3). 2nd proposition – growth inversion: Ex: O. Levi et al Optics Lett. 27, 2091, (2002)

  26. Fabrication of GaAs QPM NPC

  27. Some results on GaAs QPM NPC

  28. GaN QPM NPC • Very large transparency window • Low efficiency

  29. 2D QPM NPC • Interesting for : • Compensation of very large phase mismatches • Simultaneous phase matching of several parametric processes • Very broad band OPO Pioneering papers: Theory Experiment

  30. 2D QPM NPC • Constant linear dielectric constant • Periodically modulated c(2) constant Where ris an in-plane vector

  31. 2D QPM NPC ~ Parametric process (SHG) in 2D: The periodically modulated c(2) constant can be represented as a Fourier series: Where G are the available vectors from the reciprocal lattice (RL), and kG is its corresponding Fourier coefficient

  32. 2D QPM NPC Reciprocal lattice (RL) representation Phase matching condition (momentum conservation law): While deff ~ kG

  33. 2D QPM NPC Nonlinear Ewald construction • In the RL space: • Draw 2.kw in the right direction finishing at an origin; • Draw a circle with center Ce.s.; • Where the circle passes trough an origin – successful phase matching is possible. Gmn In 2D basis: Gmn = m Gx + n Gy Can be generalized for of plane incident light.

  34. Observation of SHG in 2D QPM NPC Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal k2w - 2kw - Gmn = 0

  35. Natural 2D QPM NPC Existence of natural structures 2D QPM NPC At a Currie temperature the SBN crystal exhibit a phase transition to form random size (given distribution) of needle like domains with opposite sign c(2) Sr0.61Ba0.39Nb2O6 (SBN) Such crystals are natural 2D QPM NPC and for: Where p(L) is the probability of existence of domain size L=G/p

  36. SHG in natural 2D QPM NPC

  37. SHG in natural 2D QPM NPC Interesting but complicated analytically: Out of plane incident light • Central symmetry due to the random size distribution: • The G (kG) vector magnitudes are given by the domain size distribution • All possible G vectors exist in all directions perpendicular to the domains

  38. Conical SHG

  39. c(3) NPC • Definition • Analytical considerations • Photonic crystals with Kerr type defects • Kerr effect super-prism • Kerr type PC - optical response • Non-linear modes, spatial optical solitons • Analytical description

  40. c(2) NPC conclusion • Used for assure the momentum conservation law for various non-linear parametric processes • Experimental techniques demonstrated it utility • Widely used and commercially available • A Fourier representation of c(2) gives both the available vectors in the reciprocal space and the efficiency coeficients

  41. c(3) NPC Periodic modulation of the linear part of the refractive index as standard PC The optical response is based on that of a linear PC Dynamical switching of the optical response based on AC Kerr effect: Types: Insertion of defects exhibiting Kerr type non-linearity The material exhibits high Kerr non-linearity Studied phenomena: Switching of the properties of photonic crystal using high intensity control beam Mode self generated changes of the optical properties: soliton waves High order harmonic generation

  42. Some literature • Photonic Crystals with Kerr nonlinear effects: • Existence of stable nonlinear localized modes in 2D & 3D PC • S.Johnet al.,PRL, 71 1168 (1993) • Controlling transmission in 1D PC • M.Scalora et al., PRL, 73 1368 (1994), P.Tran , Opt. Lett, 21 1138 (1996) • Nonlinear guiding modes in 2D PC • A.R. McGurn, Phys. Lett. A,251 322 (1999) • Tunable microcavity for fast switching • P.R. Villeneuve, Opt. Lett.,21 2017 (1996)

  43. Analytical considerations One of the materials is considered non-linear: Kerr non-linearity is small: Kerr non-linearity can be considered in perturbation theory

  44. Diversity of Kerr type defects A – Symmetric optical filter B – Asymmetric optical filter C – Optical bend D – Channel drop filter E – Waveguide branch In absence of high power excitation – standard defect response In presence of high power excitation – switched defect response due to changed refractive index

  45. Some literature Theoretical proposals and descriptions: S. F. Mingaleev and Yu.S.Kivshar Effective equations for photonic-crystal waveguides and circuits Opt. Lett. 27, 231 (2002) M Soljacic, M Ibanescu, S G Johnson, Y Fink, and J. D. Joannopoulos Optimal bistable switching in nonlinear photonic crystals Phys. Rev. E 66, 055601R (2002) M Soljacic, C Luo, S Fan, and J. D. Joannopoulos Nonlinear photonic crystal microdevices for optical integration Opt. Lett. 28, 637 (2003) Experimental observations: Somebody should do them …

  46. Linear Drop-off filter 2 waveguides 2 high Q factor microcavities High index rods Filing factor - 0.2 In – Out symmetric transmission given by: No power dependence

  47. Bistable Drop-off filter Rods from Non-linear Kerr material For carrier frequency: Expected bistability of the carrier transmission due to « resonance shift » 1-4 Transmission for high intensity signal 4-3 Transmission for the reflected weak signal

  48. Bistable Drop-off filter Non-linear transmission: Where P0 is a characteristic power of the process

  49. Feasibility of Bistable Drop-off filter Design parameters: n2 = 1.5x10-17 m2/W (for GaAs n2 = 3x10-16 m2/W) Q = 4000 (compatible with 10 Gbit/s) l0 = 1.55 mm Required conditions: P0 = 15 mW Working power 25 mW

  50. Kerr effect super-prism GaAs-based PC slab: Kerr coefficient n2 = 3x10-16 m2/W. r/a 0.33 Dependence of the diffraction angle on the signal power Controllable diffraction angle via pump pulse “Optically tunable superprism effect in nonlinear photonic crystals”, N. - C. Panoiu, M. Bahl, and R. M. Osgood, Jr., Opt. Lett. 28, 2503 (2003).

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