Abstract

We model the relationship between the microscopic and macroscopic second-order nonlinear optical susceptibilities of axially ordered and poled dye-doped polymers. The bulk polarization is derived under the assumptions of addibility of the microscopic polarizations of the nonlinear moieties and the dipole approximation. The calculations provide correction terms to the model by Singer, Kuzyk, and Sohn [J. Opt. Soc. Am. B 4, 968 (1987) ].

© 1998 Optical Society of America

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References

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  1. K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
    [CrossRef]
  2. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, London, 1990).
  3. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  4. J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
    [CrossRef]
  5. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1990).
  6. A. L. Tsykalo and A. D. Bagmet, Mol. Cryst. Liq. Cryst. 46, 111 (1978).
    [CrossRef]
  7. J. D. Le Grange, M. G. Kuzyk, and K. D. Singer, Mol. Cryst. Liq. Cryst. 150b, 567 (1987).
  8. J. F. Nye, Physical Properties of Crystals (Oxford University, London, 1967).
  9. C. P. J. M. van der Vorst and S. J. Picken, J. Opt. Soc. Am. B 7, 320 (1990).
    [CrossRef]
  10. S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, London, 1977).

1990 (1)

1987 (2)

J. D. Le Grange, M. G. Kuzyk, and K. D. Singer, Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

1982 (1)

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[CrossRef]

1978 (1)

A. L. Tsykalo and A. D. Bagmet, Mol. Cryst. Liq. Cryst. 46, 111 (1978).
[CrossRef]

Bagmet, A. D.

A. L. Tsykalo and A. D. Bagmet, Mol. Cryst. Liq. Cryst. 46, 111 (1978).
[CrossRef]

Kuzyk, M. G.

J. D. Le Grange, M. G. Kuzyk, and K. D. Singer, Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

Le Grange, J. D.

J. D. Le Grange, M. G. Kuzyk, and K. D. Singer, Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

Oudar, J. L.

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[CrossRef]

Picken, S. J.

Singer, K. D.

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

J. D. Le Grange, M. G. Kuzyk, and K. D. Singer, Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

Sohn, J. E.

Tsykalo, A. L.

A. L. Tsykalo and A. D. Bagmet, Mol. Cryst. Liq. Cryst. 46, 111 (1978).
[CrossRef]

van der Vorst, C. P. J. M.

Zyss, J.

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[CrossRef]

J. Opt. Soc. Am. B (2)

Mol. Cryst. Liq. Cryst. (2)

A. L. Tsykalo and A. D. Bagmet, Mol. Cryst. Liq. Cryst. 46, 111 (1978).
[CrossRef]

J. D. Le Grange, M. G. Kuzyk, and K. D. Singer, Mol. Cryst. Liq. Cryst. 150b, 567 (1987).

Phys. Rev. A (1)

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[CrossRef]

Other (5)

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1990).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, London, 1990).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

J. F. Nye, Physical Properties of Crystals (Oxford University, London, 1967).

S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, London, 1977).

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Equations (36)

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Pi=χi(0)+χij(1)(-ω; ω)Ej(ω)+χijk(2)(-ω; ω1, ω2)Ej(ω1)Ek(ω2)+ ,
pI=mI*+αIJ*(-ω; ω)EJ(ω)+βIJK*(-ω; ω1, ω2)EJ(ω1)EK(ω2)+ ,
P=1V nnpn,
Pi=NpIi,
pIi=aiIpIG(Ω, ξ)dΩ,
a=cos θ cos φ cos ψ-sin φ sin ψcos θ sin σ cos ψ+cos φ sin ψ-sin θ cos ψ-cos θ cos φ sin ψ-sin φ cos ψ-cos θ sin φ sin ψ+cos φ cos ψsin θ sin ψsin θ cos φsin θ sin φcos θ.
G(Ω, ξ)=exp[-H(Ω, ξ)/kBT] exp[-H(Ω, ξ)/kBT]dΩ,
H=-m*Ep+U(Ω, ξ),
Gexp(-U/kBT)1+m*EpkBT exp(-U/kBT)dΩ.
m*Ep=a3LmL*Ep,
G(Ω, Ep)exp(-U/kBT)1+a3LmL*EpkBT exp(-U/kBT)dΩ.
χijk(2)=NβIJK*ijk.
βIJK*ijk=βIJK*aiIajJakKG(Ω, ξ)dΩ.
βIJK*ijk=βIJK*aiIajJakKa3LG(Ep)d(cos θ),
Pn=-1+1Pn(cos θ)exp(-U/kBT)d(cos θ)-1+1 exp(-U/kBT)d(cos θ),
χijk(2)=NEpkBT [uijk(0)+uijk(2)P2+uijk(4)P4],
γ0=βxxx*000βyyy*000βzzz*,
γ1=0βxyy*βxzz*βyxx*0βyzz*βzxx*βzyy*0,
γ2=0βyxy*βzxz*βxyx*0βzyz*βxzx*βyzy*0,
γ3=0βyyx*βzzx*βxxy*0βzzy*βxxz*βyyz*0,
M=mx*my*mz*mx*my*mz*mx*my*mz*.
γ=γ1+γ2+γ3,
(AB)zz=AzkBkz,
(AB)ii=Trace{AB}=i=13k=13AikBki.
u333(0)=115 [M(3γ0+γ)]ii,
u333(2)=27 [3(Mγ0)zz-(Mγ0)ii]-121 [2(Mγ)ii-3(Mγ+γM)zz],
u333(4)=135 [5(Mγ0)zz+3(Mγ0)ii+(Mγ)ii-5(Mγ+γM)zz].
u113(0)=130 (2Mγ0-γM+5γ3M)ii,
u113(2)=142 [3(Mγ0)zz-(Mγ0)ii+2(γM)ii-3(Mγ+γM)zz-3(Mγ3)ii-4(γ3M)ii+21(γ3M)zz],
u113(4)=-170 [3(Mγ0)ii+5(Mγ0)zz+(γM)ii-5(Mγ+γM)zz].
u131(0)=130 (2Mγ0-γM+5γ2M)ii,
u131(2)=142 [3(Mγ0)zz-(Mγ0)ii+2(γM)ii-3(Mγ+γM)zz-3(Mγ2)ii-4(γ2M)ii+21(γ2M)zz],
u131(4)=-170 [3(Mγ0)ii+5(Mγ0)zz+(γM)ii-5(Mγ+γM)zz].
u311(0)=130 (2Mγ0-γM+5γ1M)ii,
u311(2)=142 [3(Mγ0)zz-(Mγ0)ii+2(γM)ii-3(Mγ+γM)zz-3(Mγ1)ii-4(γ1M)ii+21(γ1M)zz],
u311(4)=-170 [3(Mγ0)ii+5(Mγ0)zz+(γM)ii-5(Mγ+γM)zz].

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