• Chinese Optics Letters
  • Vol. 14, Issue 12, 121902 (2016)
Ruma Debnath, Digvijay Singh Hada, Susheel Kumar Beda, and Ardhendu Saha*
Author Affiliations
  • Department of Electrical Engineering, National Institute of Technology, Agartala 799046, India
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    DOI: 10.3788/COL201614.121902 Cite this Article Set citation alerts
    Ruma Debnath, Digvijay Singh Hada, Susheel Kumar Beda, Ardhendu Saha. Electro-optically tunable self-focusing and self-defocusing in KTP crystals by a cascaded second-order process[J]. Chinese Optics Letters, 2016, 14(12): 121902 Copy Citation Text show less

    Abstract

    We report the transformation of a linear electro-optically tunable non-phase-matched second-order nonlinear process into a cascaded second-order nonlinear process in a bulk KTP crystal to generate the effect of electro-optically tunable Kerr-type nonlinearity. By applying an electric field on the xy plane, parallel to the z-axis of the crystal, phase mismatch is created, which introduces a nonlinear phase shift between the launched and reconverted fundamental waves from the generated second harmonic wave. Due to the nonuniform radial intensity distribution of a Gaussian beam, a curvature will be introduced into the fundamental wavefront, which focuses or defocuses the incident beam while propagating through the crystal.
    [(1/nx2)+r13Ez]x2+[(1/ny2)+r23Ez]y2+[(1/nz2)+r33Ez]z2=1,(1)

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    nx=nx[11/(2nx2r13Ez)];ny=ny1[1/(2ny2r23Ez)];nz=nz[11/(2nz2r33Ez)],(2)

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    dE1/dy=(iωχ(2)(ω;2ω:ω)E2*E3eiΔky)/2n1c,(3)

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    dE2/dy=(iωχ(2)(ω;2ω:ω)E1*E3eiΔky)/2n2c,(4)

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    dE3/dy=(2iωχ(2)(2ω;ω:ω)E1E2eiΔky)/2n3c,(5)

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    n(ωi)=[2/{Bi±(Bi4Ci)1/2}]1/2,(6)

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    ΔkL=L(k1+k2k3)=(2πL/λ)(nω1+nω2nω3),(7)

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    dE1/dy=(iAE2*E3eiΔky)/nω1,(8)

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    E1=E0ei(Δk/2)y[cos(sy)+iΔksin(sy)/(2s)],(9)

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    Γ=[(ωdeff)/(cnω1nω2nω3)][(2Io)/(cεo)]1/2,(10)

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    Ω={(4I1/I0)(I/I0)}.(11)

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    ΔϕNL=ΔKL2tan1[Δk2stan(sL)].(12)

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    ΔϕNL[(Γ2L2)/ΔkL]Ω.(13)

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    ΔϕNL[(Γ2L2)/ΔkL]=(2πLn2effIo)/λ,(14)

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    n2eff=4πcε0×Lλ×deff2nω1nω2nω3×1ΔkL.(15)

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    n2effdeff2/n3.(16)

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    f=a2/(4In2effL),(17)

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    f=(a2π)/(2ΔϕNLλ).(18)

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    Ruma Debnath, Digvijay Singh Hada, Susheel Kumar Beda, Ardhendu Saha. Electro-optically tunable self-focusing and self-defocusing in KTP crystals by a cascaded second-order process[J]. Chinese Optics Letters, 2016, 14(12): 121902
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