M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, "Mechanisms of quadratic electro-optic modulation of dye-doped polymer systems," J. Opt. Soc. Am. B 7, 842-858 (1990)
We present the experimental and theoretical considerations needed to determine the mechanisms of quadratic electro-optic modulation in dye-doped polymer systems. The modulation is observed in thin dye-doped polymer films and the quadratic Kerr coefficient is determined by using a modified Mach–Zehnder interferometric technique. The theory of several nonlinear mechanisms is developed and applied to representative systems to determine the various contributions. The fast, virtual electronic mechanism is shown to be the largest contribution, as inferred from the measured frequency dispersion of the quadratic electro-optic effect. This quick interferometric method is also shown to be useful for determining nonlinear-optical structure–property relationships.
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Some Physical Properties of PMMA at Room Temperaturea
Thermal refractive-index coefficient
1.1 × 10−4 K−1
Thermal-expansion coefficient
7 × 10−5 K−1
Density
ρ
1.19 × 103 kg/m2
Specific heat
c
1.42 × 103 J/kg-K
Dielectric constant
∊(ω = 1kHz)
3.0
Sound velocity
ν(2 MHz)
2700 m/sec
Elastic modulus
E′
6.6 × 1010 dyn/cm2
Shear modulus
G′
2.0 × 1010 dyn/cm2
Thermal conductivity
σ
0.193 W/m-K
See Ref. 71. The elastic moduli at 4 kHz were extrapolated from lower-frequency measurements.55
Table 2
Heating Contribution to the Third-Order Susceptibility in PMMAa
n
d (μm)
Ω (kHz)
R (Ohms)
s1133(m2/V2)
1.5
3.0
4.0
>20 × 106
1 × 10−4
<0.3 × 10−23
Typical experimental values of refractive index n, sample thickness d, modulating frequency Ω, resistance R, and coefficient of expansion (1/n)/(∂n/∂T).
Table 3
Molecular Values Used to Calculate Orientational Contributions in DRl/PMMAa
Laser wavelength of λ = 633 nm and modulating frequency of Ω.62 Ref. 54. Ref. 52.
Table 4
Orientational Contributions and Quadratic Electro-Optic Coefficienta
−1.8 (± 0.9)
2.2 (± 1.1)
1.0 (± 0.1)
Calculated orientational contribution
, second-order induced orientational contribution
and measured quadratic electro-optic coefficient
for isotropic DR1/PMMA with N = 1.8 × 1020 cm−3 and n11 = 1.53. Note that the doped sample had a refractive index of ∼1.52.
Table 5
Third-Order Susceptibility Comparison between Electro-Optic Measurement and Third-Harmonic Measurementa
0.6 (± 0.2)
11 (± 3)
9.9
Note that the electro-optic measurement was at λ = 633 nm with a number density of N = 1.8 × 1020 cm−3 and that the third-harmonic was at a fundamental wavelength of λ = 2050 with number density N = 1.9 × 1021 cm−3.
Table 6
Third-Order Susceptibility of a Series of Molecules as Determined with Quadratic Electro-Optic Modulationa
All measurements are at λ = 633 nm except for ISQ, which was measured at 799 nm. Orientational effects are not subtracted. DNBA, a diaminonitrobenzaniline dye; DNTA, a diaminonitrothiophene aniline dye; NFAI, a nitrofuran-substituted dye; NPCV, a nitrophenylcyanovinylazo dye.
The refractive index n was purposely overestimated owing to resonance enhancement, yielding as upper limits values of 〈γzzzz*〉 and χ(3). Also, the orientational effects have not been taken into account, so the dressed molecular third-order susceptibility could be systematically high by ∼30% for the noncentrosymmetric molecules.
Table 7
Experimental and Theoretical Isotropic Averages of Molecular Nonlinear-Optical Susceptibilities of Small Moleculesa
Molecule
N (1021 cm−3)
〈γ〉exp (10−35 esu)
〈γ〉the (10−35 esu)
m-Dinitrobenzene
1.24
0.6(± 0.3)
1.0
m-Dicyanobenzene
1.09
0.8 (±0.4)
1.0–3.0
The range in calculated values represents the range of results over several parameter sets.
Tables (7)
Table 1
Some Physical Properties of PMMA at Room Temperaturea
Thermal refractive-index coefficient
1.1 × 10−4 K−1
Thermal-expansion coefficient
7 × 10−5 K−1
Density
ρ
1.19 × 103 kg/m2
Specific heat
c
1.42 × 103 J/kg-K
Dielectric constant
∊(ω = 1kHz)
3.0
Sound velocity
ν(2 MHz)
2700 m/sec
Elastic modulus
E′
6.6 × 1010 dyn/cm2
Shear modulus
G′
2.0 × 1010 dyn/cm2
Thermal conductivity
σ
0.193 W/m-K
See Ref. 71. The elastic moduli at 4 kHz were extrapolated from lower-frequency measurements.55
Table 2
Heating Contribution to the Third-Order Susceptibility in PMMAa
n
d (μm)
Ω (kHz)
R (Ohms)
s1133(m2/V2)
1.5
3.0
4.0
>20 × 106
1 × 10−4
<0.3 × 10−23
Typical experimental values of refractive index n, sample thickness d, modulating frequency Ω, resistance R, and coefficient of expansion (1/n)/(∂n/∂T).
Table 3
Molecular Values Used to Calculate Orientational Contributions in DRl/PMMAa
Laser wavelength of λ = 633 nm and modulating frequency of Ω.62 Ref. 54. Ref. 52.
Table 4
Orientational Contributions and Quadratic Electro-Optic Coefficienta
−1.8 (± 0.9)
2.2 (± 1.1)
1.0 (± 0.1)
Calculated orientational contribution
, second-order induced orientational contribution
and measured quadratic electro-optic coefficient
for isotropic DR1/PMMA with N = 1.8 × 1020 cm−3 and n11 = 1.53. Note that the doped sample had a refractive index of ∼1.52.
Table 5
Third-Order Susceptibility Comparison between Electro-Optic Measurement and Third-Harmonic Measurementa
0.6 (± 0.2)
11 (± 3)
9.9
Note that the electro-optic measurement was at λ = 633 nm with a number density of N = 1.8 × 1020 cm−3 and that the third-harmonic was at a fundamental wavelength of λ = 2050 with number density N = 1.9 × 1021 cm−3.
Table 6
Third-Order Susceptibility of a Series of Molecules as Determined with Quadratic Electro-Optic Modulationa
All measurements are at λ = 633 nm except for ISQ, which was measured at 799 nm. Orientational effects are not subtracted. DNBA, a diaminonitrobenzaniline dye; DNTA, a diaminonitrothiophene aniline dye; NFAI, a nitrofuran-substituted dye; NPCV, a nitrophenylcyanovinylazo dye.
The refractive index n was purposely overestimated owing to resonance enhancement, yielding as upper limits values of 〈γzzzz*〉 and χ(3). Also, the orientational effects have not been taken into account, so the dressed molecular third-order susceptibility could be systematically high by ∼30% for the noncentrosymmetric molecules.
Table 7
Experimental and Theoretical Isotropic Averages of Molecular Nonlinear-Optical Susceptibilities of Small Moleculesa
Molecule
N (1021 cm−3)
〈γ〉exp (10−35 esu)
〈γ〉the (10−35 esu)
m-Dinitrobenzene
1.24
0.6(± 0.3)
1.0
m-Dicyanobenzene
1.09
0.8 (±0.4)
1.0–3.0
The range in calculated values represents the range of results over several parameter sets.