Quadratic nonlinear interaction

Transcription

1 Nonlinear second order χ () interactions in III-V semiconductors 1. Generalities : III-V semiconductors & nd ordre nonlinear optics. The strategies for phase-matching 3. Photonic crystals for nd ordre nonlinear optics 1 Quadratic nonlinear interaction Second Harmonic Generation χ () Parametric generation 1 χ () Conservation requirements : Energy 1 + = Phase velocity k = k -k 1 k = 0 Group velocity v g = v g, - v g,ι = 0 ι

2 Key parameters for SHG I Conversion efficiency ( z) = π 0 ε cλ Characteristic of the NL material Intensity dependence Phase mismatch : k=k -k Coherence length : L c =π/ k Ex. : III-V 1,5µm high d eff but too small L c ~ µm [ d ] n eff 1 n [ I ] SH intensity 1,00 0,75 0,50 0,5 sin k ( ) kz z at best Interferential phasematching term 0, z/l kl=π kl=π/ kl=0 Les semiconducteurs III-V et l ONL du nd ordre Advantages High second order susceptibility : for example GaAs : d µm. - Possibility of integration Problems Highly dispersive material L c 1.55µm! - Symmetry 43m : III-V are isotropic Birefringent phasematching is impossible - Difficulties imposed by usual [001] epitaxy z=[001] k E θ y=[010] φ x=[100] d eff (u. a.) 1,0 0,8 0,6 0,4 0, TM φ=π/4 TM φ=0 TE 0, θ en degrès

3 Semiconductors : some important parameters 5 Semiconductors : some important parameters 6

4 Semiconductors : advantages and drawbacks Take benefit from high semiconductor NL susceptibility at 1.55 µm Take benefit from semiconductor technologies Compatibility with vertical or waveguide devices compatibility with VCSELS and other vertical devices Problem! Semiconductor are very dispersive and non-birefringent materials No phase matching : k=k -k L c =π/ k ~ µm 7 Solutions with periodic media, also an «old» history Periodically poled χ () : the Quasi-Phase-Matching was proposed in the seminal nonlinear paper of NLO in 196 J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, Phys. Rev. 17, (196) +χ() -χ() Periodicity dielectric constant : k E e E o n o k n e Form birefringence J. P. van der Ziel, Appl. Phys. Lett. 6, 60 (1975). Anomalous dispersion N. Bloembergen and J. Sievers, APL 17, 483 (1970). J. P. van der Ziel, Appl. Phys. Lett. 8, 437 (1976). A. Yariv, and P. Yeh, J. Opt. Soc. Am. 67, 438 (1977). 8 Needs strong refraction index contrast!

5 k The Quasi Phase Matching First proposition : to inverse the component of the NL tensor each L c, Armstrong et al. Phys. Rev. 17, 1918 (196). Generalization : Fejer et al. IEEE J. Quantum Electron. 8, 631 (199). d 1 d l 1 l SHG equation : k k dz K p Λ p= dξ + j = ξ n c p= z j( K p k ) z d e p j ξ = n c ( L) d L pξ The NL periodicity allows to conservate the momentum χ () periodical Intensité du SH (u.a) 10 5 K p π = p Λ d eff p ( ) = + z = p= +χ () -χ () +χ () -χ () +χ () -χ () +χ () 0 +χ () 0 +χ () Distance de propagation (L c ) d p e jk p z 9 Quasi Pase Matching at long wavelength Difficult or Impossible at wavelengths < 8µm 10

6 Experimental demonstrations of QPM in III-Vs (1/) 1/ Epitaxial re-growth on a oriented substrate Al 50% Ga 50% As 1µm Al 60% Ga 40% As µm Al 60% Ga 40% As µm S. J. B. Yoo et al., Appl. Phys. Lett. 66, 3410 (1995) Al Ga O 3 SiO MPQA 44% GaAs 50Å 14Å 5Å 0% 44% 0% 44% χ () MPQA Massif J. S. Aitchison et al., IEEE J. Sel. Top. Quantum Electron. 4, 695 (1998). 11 II-VI Semiconductor Waveguide ZnTe <100>CdTe GaAs <100> GaAs <100> GaAs <100> GaAs <100> <111>CdTe <100>CdTe ZnTe <100>CdTe ZnTe GaAs <100> GaAs <100>

7 III-V Semiconductor Waveguide In 0.5 Ga 0.5 P GaAs <001> Bonding GaAs <001> Al 0.8 Ga 0. As GaAs GaAs <001> In 0.5 Ga 0.5 P GaAs Al 0.8 Ga 0. As GaAs <001> <001> <001> <110> <110> Compromise between losses and efficiency

8 Parametric generation and Optical Parametric Oscillator pump χ () idler signal Seed pump χ () idler signal pump χ () idler signal 15 Parametric generation and Optical Parametric Oscillator 16

9 First semiconductor OPO GaAs L=11 mm QPM : alternance of [110] et [-110] orientations (period : 61, µm) Mirors of OPO : external - PM between1,8 et,01 µm - Excellent agreement theorie/exp - Tunability :,4 to 3,1 µm for signal and 5,8 to 9,1 µm for idler 17 Experimental demonstrations of QPM in III-Vs : microcavity / QPM in a microcavity résonante FF SH L c C. Simonneau et al., Opt. Lett., 1775 (1997). QPM condition SH power (µw) Fundamental power (mw) 18

10 Experimental demonstrations of QPM in III-Vs : microcavity Reflectivity 1,0 0,5 0,0 1,0 0, Fabry-Pérot resonance 0, Wavelength (nm) C. Simonneau et al., Opt. Lett., 1775 (1997). SH power (µw) Fundamental power (mw) Experimental demonstrations of QPM in III-Vs : microcavity 0