Attenuated total reflectance measurements of the complex refractive index of polystyrene latex at CO<sub>2</sub> laser wavelengths

S. G. Jennings

doi:10.1364/JOSA.71.000923

Journal of the Optical Society of America
Vol. 71,
Issue 8,
pp. 923-927
(1981)
•https://doi.org/10.1364/JOSA.71.000923

Attenuated total reflectance measurements of the complex refractive index of polystyrene latex at CO₂ laser wavelengths

S. G. Jennings

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S. G. Jennings, "Attenuated total reflectance measurements of the complex refractive index of polystyrene latex at CO₂ laser wavelengths," J. Opt. Soc. Am. 71, 923-927 (1981)

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Abstract

Attenuated total reflectance (ATR) measurements of the complex refractive index m of 5, 10, 15, 20, and 30% water suspensions of polystyrene latex are presented for CO₂ laser wavelengths (measurements for the 30% suspension are for λ = 10.591 μm only). The use of the Maxwell Garnet mixture rule for the real index and the imaginary index (at λ = 9.305 μm) and an extrapolation scheme for the remaining values of imaginary index yield the values m = 1.709 − 0.07i (λ = 9.305 μm); m = 1.887 − 0.06i (λ = 9.504 μm); m = 1.705 − 0.04i (λ = 9.694 μm); m = 1.764 − 0.045i (λ = 10.591 μm). ATR measurements of the complex index of water and water–ammonium sulfate solutions are in reasonably good agreement with those previously published.

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		ATR (Present Work)		Interpolated from Hale and Quarry^a

Wavelength (μm)	Incident Angles	Real Index (n)	Imaginary Index (k)	Real Index (n)	Imaginary Index (k)
9.603	27°30′, 30°, 32°30′, 35°, 40°	1.230 ± 0.002	0.054 ± 0.001	1.239	0.045
10.195	27°30′, 30°, 32°30′	1.193 ± 0.008	0.059 ± 0.007	1.202	0.059
10.494	27°30′, 30°, 32°30′, 35°	1.196 ± 0.014	0.075 ± 0.007	1.185	0.066

			ATR (Present Work)		Interpolated Values from Downing et al.^a

(NH₄)₂SO₄ Solution	Wavelength (μm)	Incident Angles	Real Index (n)	Imaginary Index (k)	Real Index (n)	Imaginary Index (k)
1.6 M (NH₄)₂SO₄	9.519	32°30′, 35°, 37°30′, 40°	1.411 ± 0.003	0.084 ± 0.002	–	–
2.4 M (NH₄)₂SO₄	9.519	42°30′, 45°, 47°30′, 50°	1.472 ± 0.003	0.126 ± 0.003	1.541	0.153
3.2 M (NH₄)₂SO₄	9.519	42°30′, 45°, 47°30′, 50°	1.545 ± 0.002	0.129 ± 0.002	1.642	0.164
1.6 M (NH₄)₂SO₄	9.317	35°, 37.30′, 42°30′	1.500 ± 0.002	0.139 ± 0.003	–	–
2.4 M (NH₄)₂SO₄	9.317	35°, 40°, 45°, 50°	1.560 ± 0.005	0.229 ± 0.007	1.543	0.317
3.2 M (NH₄)₂SO₄	9.317	40°, 45°, 47°30′, 50°	1.605 ± 0.012	0.268 ± 0.015	1.65	0.38

Wavelength (μm)	Index of Refraction^a	Percent by Weight					Incident Angles

		30	20	15	10	5
9.305	n	–	1.326 ± 0.009	1.311 ± 0.009	1.291 ± C.003	1.275 ± 0.003	25°35′, 30°
	k	–	0.041 ± 0.005	0.047 ± 0.001	0.044 ± 0.003	0.037 ± 0.001	33°24′ 35°
9.504	n	–	1.321 ± 0.004	1.320 ± 0.003	1.304 ± 0.001	1.282 ± 0.003	25°35′, 30°
	k	–	0.038 ± 0.004	0.035 ± 0.001	0.031 ± 0.002	0.033 ± 0.002	33°24′, 35°
9.694	n	–	1.317 ± 0.002	1.296 ± 0.003	1.278 ± 0.006	1.253 ± 0.004	25°35′, 30°
	k	–	0.035 ± 0.001	0.037 ± 0.002	0.043 ± 0.004	0.043 ± 0.006	33°24′, 35°
10.591	n	1.326 ± 0.004	1.282 ± 0.003 (5)^b	1.266 ± 0.004 (3)^b	1.228 ± 0.003 (4)^b	1.212 ± 0.004 (2)^b	22°, 26°45′
	k	0.051 ± 0.002	0.048 ± 0.001	0.047 ± 0.002	0.051 ± 0.003	0.051 ± 0.009	30°30′, 32°30′, 35°

Wavelength (μm)	Real Index (n) from Use of Maxwell Garnet Mixture Rule [Eq. (4)]	Imaginary Index (k) from Use of Maxwell Garnet Mixture Rule [Eq. (4)]
9.305	1.709 ± 0.017	0.070 ± 0.012
9.504	1.887 ± 0.017	0.060 ± 0.012^b
9.694	1.705 ± 0.011	0.0400 ± 0.005^b
10.591	1.764 ± 0.021	0.045 ± 0.019^b

		ATR (Present Work)		Interpolated from Hale and Quarry^a

Wavelength (μm)	Incident Angles	Real Index (n)	Imaginary Index (k)	Real Index (n)	Imaginary Index (k)
9.603	27°30′, 30°, 32°30′, 35°, 40°	1.230 ± 0.002	0.054 ± 0.001	1.239	0.045
10.195	27°30′, 30°, 32°30′	1.193 ± 0.008	0.059 ± 0.007	1.202	0.059
10.494	27°30′, 30°, 32°30′, 35°	1.196 ± 0.014	0.075 ± 0.007	1.185	0.066

Abstract

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Equations (10)

Journal of the Optical Society of America