Abstract

An experimental analysis technique is described for accurate extraction of the coherence length and the complex third-order nonlinear susceptibility χ(3) in films or bulk optical glasses from the Maker fringes obtained by third-harmonic generation measurements. This method permits calculation of the third-order susceptibility of a sample without the need for assumptions as to the magnitude or the phase of the nonlinearity relative to a reference material such as the substrate. To illustrate the utility of the method we study spin-coated films of copper 2,3,9,10,16,17,23,24-octa(1,4,7,10-tetraoxaundecyl)phthalocyanine.

[Optical Society of America ]

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  1. F. Kajzar , J. Messier , and C. Rosilio , Nonlinear optical properties of thin films of polysilane , J. Appl. Phys. JAPIAU 60 , 3040 3044 ( 1986
    [CrossRef]
  2. J. B. Van Beek , F. Kajzar , and A. C. Albrecht , Third-harmonic generation from all- trans -carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance , Chem. Phys. CMPHC2 161 , 299 311 ( 1992
    [CrossRef]
  3. N. Bloembergen and P. S. Pershan , Light waves at the boundary of nonlinear media , Phys. Rev. PHRVAO 128 , 606 622 ( 1962
    [CrossRef]
  4. F. Kajzar and J. Messier , Third-harmonic generation in liquids , Phys. Rev. A PLRAAN 32 , 2352 2363 ( 1985
    [CrossRef] [PubMed]
  5. M. M. Fejer , G. A. Magel , D. H. Jundt , and R. L. Byer , Quasi-phase-matched second harmonic generation: tuning and tolerances , IEEE J. Quantum Electron. IEJQA7 28 , 2631 2654 ( 1992
    [CrossRef]
  6. Zhong Hua Zhou , H. Nasu , T. Hashimoto , and K. Kamiya , Non-linear optical properties and structure of Na 2 S GeS 2 glasses , J. Non-Cryst. Solids JNCSBJ 215 , 61 67 ( 1997
    [CrossRef]
  7. G. R. Meredith , Cascading in optical third-harmonic generation by crystalline quartz , Phys. Rev. B PRBMDO 24 , 5522 5532 ( 1981
    [CrossRef]
  8. K. Kubodera and H. Kobayashi , Determination of third-order nonlinear optical susceptibilities for organic materials by third harmonic generation , Mol. Cryst. Liq. Cryst. MCLCA5 182A , 103 113 ( 1990
  9. G. R. Meredith , B. Buchalter , and C. Hanzlik , Third-order optical susceptibility determination by third harmonic generation. I , J. Chem. Phys. JCPSA6 78 , 1533 1551 ( 1983
    [CrossRef]
  10. F. Kajzar and J. Messier , Resonance enhancement in cubic susceptibility of Langmuir Blodgett multilayers of polydiacetylene , Thin Solid Films THSFAP 132 , 11 19 ( 1985
    [CrossRef]
  11. G. J. Clarkson , N. B. McKeown , and K. E. Treacher , Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens , J. Chem. Soc. Perkin Trans. JCFTAR 1 , 1817 1823 ( 1995
    [CrossRef]
  12. T. Wada , T. Masuda , and H. Sasabe , Third-order nonlinear optical properties of substituted polyphenylacetylenes , Mol. Cryst. Liq. Cryst. MCLCA5 247 , 139 147 ( 1994
    [CrossRef]
  13. H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
    [CrossRef]
  14. J.-I. Lee , D.-H. Hwang , and H.-K. Shim , Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene) s , Mol. Cryst. Liq. Cryst. MCLCA5 247 , 121 128 ( 1994
    [CrossRef]
  15. F. Kajzar and M. Zagorska , Third-order nonlinear optical properties of functionalized polymers , Nonlin. Opt. NOPDEP 6 , 181 192 ( 1993

Buchalter, B

G. R. Meredith , B. Buchalter , and C. Hanzlik , Third-order optical susceptibility determination by third harmonic generation. I , J. Chem. Phys. JCPSA6 78 , 1533 1551 ( 1983
[CrossRef]

Clarkson, G. J

G. J. Clarkson , N. B. McKeown , and K. E. Treacher , Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens , J. Chem. Soc. Perkin Trans. JCFTAR 1 , 1817 1823 ( 1995
[CrossRef]

Hanzlik, C

G. R. Meredith , B. Buchalter , and C. Hanzlik , Third-order optical susceptibility determination by third harmonic generation. I , J. Chem. Phys. JCPSA6 78 , 1533 1551 ( 1983
[CrossRef]

Hashimoto, T

Zhong Hua Zhou , H. Nasu , T. Hashimoto , and K. Kamiya , Non-linear optical properties and structure of Na 2 S GeS 2 glasses , J. Non-Cryst. Solids JNCSBJ 215 , 61 67 ( 1997
[CrossRef]

Hayashi, T

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

Hwang, D.-H

J.-I. Lee , D.-H. Hwang , and H.-K. Shim , Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene) s , Mol. Cryst. Liq. Cryst. MCLCA5 247 , 121 128 ( 1994
[CrossRef]

Kanbara, H

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

Konami, H

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

Lee, J.-I

J.-I. Lee , D.-H. Hwang , and H.-K. Shim , Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene) s , Mol. Cryst. Liq. Cryst. MCLCA5 247 , 121 128 ( 1994
[CrossRef]

Maruno, T

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

McKeown, N. B

G. J. Clarkson , N. B. McKeown , and K. E. Treacher , Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens , J. Chem. Soc. Perkin Trans. JCFTAR 1 , 1817 1823 ( 1995
[CrossRef]

Tanaka, N

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

Treacher, K. E

G. J. Clarkson , N. B. McKeown , and K. E. Treacher , Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens , J. Chem. Soc. Perkin Trans. JCFTAR 1 , 1817 1823 ( 1995
[CrossRef]

Van Beek, J. B

J. B. Van Beek , F. Kajzar , and A. C. Albrecht , Third-harmonic generation from all- trans -carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance , Chem. Phys. CMPHC2 161 , 299 311 ( 1992
[CrossRef]

Yamashita, A

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

Zagorska, M

F. Kajzar and M. Zagorska , Third-order nonlinear optical properties of functionalized polymers , Nonlin. Opt. NOPDEP 6 , 181 192 ( 1993

Zhou, Zhong Hua

Zhong Hua Zhou , H. Nasu , T. Hashimoto , and K. Kamiya , Non-linear optical properties and structure of Na 2 S GeS 2 glasses , J. Non-Cryst. Solids JNCSBJ 215 , 61 67 ( 1997
[CrossRef]

Other (15)

F. Kajzar , J. Messier , and C. Rosilio , Nonlinear optical properties of thin films of polysilane , J. Appl. Phys. JAPIAU 60 , 3040 3044 ( 1986
[CrossRef]

J. B. Van Beek , F. Kajzar , and A. C. Albrecht , Third-harmonic generation from all- trans -carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance , Chem. Phys. CMPHC2 161 , 299 311 ( 1992
[CrossRef]

N. Bloembergen and P. S. Pershan , Light waves at the boundary of nonlinear media , Phys. Rev. PHRVAO 128 , 606 622 ( 1962
[CrossRef]

F. Kajzar and J. Messier , Third-harmonic generation in liquids , Phys. Rev. A PLRAAN 32 , 2352 2363 ( 1985
[CrossRef] [PubMed]

M. M. Fejer , G. A. Magel , D. H. Jundt , and R. L. Byer , Quasi-phase-matched second harmonic generation: tuning and tolerances , IEEE J. Quantum Electron. IEJQA7 28 , 2631 2654 ( 1992
[CrossRef]

Zhong Hua Zhou , H. Nasu , T. Hashimoto , and K. Kamiya , Non-linear optical properties and structure of Na 2 S GeS 2 glasses , J. Non-Cryst. Solids JNCSBJ 215 , 61 67 ( 1997
[CrossRef]

G. R. Meredith , Cascading in optical third-harmonic generation by crystalline quartz , Phys. Rev. B PRBMDO 24 , 5522 5532 ( 1981
[CrossRef]

K. Kubodera and H. Kobayashi , Determination of third-order nonlinear optical susceptibilities for organic materials by third harmonic generation , Mol. Cryst. Liq. Cryst. MCLCA5 182A , 103 113 ( 1990

G. R. Meredith , B. Buchalter , and C. Hanzlik , Third-order optical susceptibility determination by third harmonic generation. I , J. Chem. Phys. JCPSA6 78 , 1533 1551 ( 1983
[CrossRef]

F. Kajzar and J. Messier , Resonance enhancement in cubic susceptibility of Langmuir Blodgett multilayers of polydiacetylene , Thin Solid Films THSFAP 132 , 11 19 ( 1985
[CrossRef]

G. J. Clarkson , N. B. McKeown , and K. E. Treacher , Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens , J. Chem. Soc. Perkin Trans. JCFTAR 1 , 1817 1823 ( 1995
[CrossRef]

T. Wada , T. Masuda , and H. Sasabe , Third-order nonlinear optical properties of substituted polyphenylacetylenes , Mol. Cryst. Liq. Cryst. MCLCA5 247 , 139 147 ( 1994
[CrossRef]

H. Kanbara , T. Maruno , A. Yamashita , S. Matsumoto , T. Hayashi , H. Konami , and N. Tanaka , Third-order nonlinear optical properties of phthalocyanine and fullerene , J. Appl. Phys. JAPIAU 80 , 3674 3682 ( 1996
[CrossRef]

J.-I. Lee , D.-H. Hwang , and H.-K. Shim , Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene) s , Mol. Cryst. Liq. Cryst. MCLCA5 247 , 121 128 ( 1994
[CrossRef]

F. Kajzar and M. Zagorska , Third-order nonlinear optical properties of functionalized polymers , Nonlin. Opt. NOPDEP 6 , 181 192 ( 1993

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Figures (5)

Fig. 1
Fig. 1

Experimental Maker fringes of the third-harmonic generated, an analysis of the positions of the minima for (a) a fused-silica substrate in vacuum and (b) a microscope slide in vacuum.

Fig. 2
Fig. 2

Experimental configuration for the measurement of Maker fringes in THG. HP, high-pass filter; OPO, optical parametric oscillator; ND, neutral density, PMT, photomultiplier tube.

Fig. 3
Fig. 3

Effect of air on THG: top, Maker fringe pattern and residuals to the model from a fused-silica sample in vacuum; bottom, corresponding pattern and residuals from the same sample immersed in air.

Fig. 4
Fig. 4

Harmonic signal from top, a bare substrate and bottom, a substrate coated on one side with a spin-coated film of (TOU)CuPc.

Fig. 5
Fig. 5

Orientation of a sample comprising a substrate coated on one side with a nonlinear film. PMT, photomultiplier tube.

Tables (2)

Tables Icon

Table 1 Comparison of Coherence-Length Values Calculated from Dispersion Data and from Maker Fringe Experiments

Tables Icon

Table 2 Parameters of the (TOU)CuPc Film a

Equations (46)

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E3t3ω=E2b3ωA exp(ik2t3ωl){exp[i(k2b3ω-k2t3ω)l]-1},
E2b3ω=4πP2NLΔε
P2NL=¼χ(3)(-3ω; ω, ω, ω)(E2ω)3,
E2b3ω=πχ(3)Δε (E2ω)=πχ(3)Δε (t12ωEω)3,
A=N23ω+N2ωN23ω+N33ω,Njω,3ω=njω,3ω cos θjω, 3ω,
j=2, 3,
t12ω=2n1 cos θ1n1 cos θ1+n2ω cos θ2ω,
I3ωχ(3)Δε2(Iω)3A2(t12ω)6×expi 6πλ (nω cos θω-n3ω cos θ3ω)l-12χ(3)Δε2(Iω)3A2(t12ω)6×sin26πλ (nω cos θω-n3ω cos θ3ω)l2.
(3π/λ)(n3ω cos θ3ω-nω cos θω)L=mπ,
L=(mλ/3)(n3ω cos θ3ω-nω cos θω)-1.
nω sin θω=n3ω sin θ3ω,
L=mλ3n3ω 1-nωn3ω sin θω21/2-nωn3ω cos θω-1.
L=L0 cos θω1+n3ω-nω2n3ω tan2 θω,
L0=mλ3(n3ω-nω)=2mlC.
lC=λ6(n3ω-nω).
y=cos θω1+n3ω-nω2n3ω tan2 θω-1
y=kx+b,
k=dydx=2lCL
lC=d2(j-i) 1(1-sin2 θj/nω2)1/2-1(1-sin2 θi/nω2)1/2.
E3ω(r, t)=jTjEj3ω(r, t),
I3ω=cε(ω)8π jTjEj3ω(r, t)2.
I3ω|ES3ω+C(χ(3)/Δε)A{T3ω exp[i(ψ+α)]-Tω3 exp[-i(ψ+β)]}(Eω)3|2,
Tω=t12ωt23ω,
T3ω=t233ω,
t12ω=2n1 cos θ1n1 cos θ1+n2ω cos θ2ω,
t23ω=2n2ω cos θ2ωn2ω cos θ2ω+n3 cos θ3,
t233ω=2n23ω cos θ23ωn23ω cos θ23ω+n3 cos θ3.
I3ω=Bχ(3)ΔεS2 f(λ3ω)(Iω)3|A(t12ω)3 exp(iψS3ω)×{exp[i(ψSω-ψS3ω)]-1}|2,
ψS3ω=kS3ωl=3ω/cnS3ωl cos θS3ω,
ψSω=3kSωl=3ω/cnSωl cos θSω,
θ3ω=arcsinsin θvacuumn3ω,
θω=arcsinsin θvacuumnω.
I3ω=Bf(λ3ω)χ(3)ΔεS2(Iω)3|A(t12ω)3× exp(iψS3ω){exp[i(ψSω-ψS3ω)]-1}+C{t233ω exp[i(ψ+α)]-(t12ωt23ω)3 exp[-i(ψ+β)]}|2,
C=χ(3)ΔεA/χ(3)ΔεSC
I3ω|ES3ω(t12ω)3 exp(iψPω)+EP3ωt343ω exp(iψS3ω)|2|[χ(3)/Δε]SESω(t12ω)3 exp(iψPω)exp(iψS3ω)A1×[exp(iΔψS)-1]+(χ(3)/Δε)PEPωt343ω exp(iψS3ω)×exp(iψP3ω)A2[exp(iΔψP)-1]|2|exp[i(ψS3ω+ψPω)](χ(3)/Δε)S(Eω)3×{T1[exp(iΔψS)-1]+ρ exp(iϕ)T2[1-exp(-iΔψP)]}|2,
I3ω=Bχ(3)ΔεS2 f(λ3ω)(Iω)3|exp[i(ψS3ω+ψPω)]×{T1[exp(iΔψS)-1]+ρ exp(iϕ)T2[1-exp(-iΔψP)]}|2
T1=(t12ωt23ω)3 N23ω+N2ωN23ω+N33ω,
T2=(t12ω)3t343ω N33ω+N3ωN33ω+N43ω;
Njω,3ω=njω,3ω cos θjω,3ω.
I3ω=Bf(λ3ω)χ(3)ΔεS2(Iω)3|exp[i(ψS3ω+ψPω)]×{T1[exp(iΔψS)-1]+ρ exp(iϕ)T2[1-exp(-iΔψP)]}+C{t233ωt343ω exp[i(ψ+α)]-(t12ωt23ωt34ω)3 exp[-i(ψ+β)]}|2,
ρeiϕ=χ(3)Δεfilm/χ(3)ΔεS,
C=χ(3)Δεair/χ(3)ΔεS.
I3ω=(64π4/c2)[Aχ(3)]2(Iω)3fa,
fa={[1-exp(-α3ωd/2)]2+(Δψ)2 exp(-α3ωd/2)}[(n3ω2-nω2-k3ω2)2+(2n3ωk3ω)2],
χ(3)=χS(3)2πlC,SlI3ωIS3ω1/2
χ(3)=χS(3)2πlC,S α/21-exp(-αl/2) I3ωIS3ω1/2.

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