Refractive-Index Interpolation for Fused Silica*

Berlyn Brixner

doi:10.1364/JOSA.57.000674

Journal of the Optical Society of America
Vol. 57,
Issue 5,
pp. 674-676
(1967)
•https://doi.org/10.1364/JOSA.57.000674

Refractive-Index Interpolation for Fused Silica

Berlyn Brixner

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Berlyn Brixner, "Refractive-Index Interpolation for Fused Silica*," J. Opt. Soc. Am. 57, 674-676 (1967)

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Abstract

The advantages of a four-term Sellmeier-equation fit to refractive indexes of recently produced fused silica are described. The four-term fit gives more accurate smoothing and interpolation of data than the three-term fit used previously and also indicates data of questionable accuracy. After the suspect data had been eliminated, fits with an average deviation of 4.3 · 10⁻⁶ were obtained with both three- and four-term equations over the range 0.21–2.32 μ.

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Wavelength in microns	Spectral source	Four-term fit to 180 data points				Four-term fit to 123 data points
Wavelength in microns	Spectral source	Computed	Corning	Dynasil	G. E.	Computed	Corning	Dynasil	G. E.
0.213856	Zn	1.534289	−11	−24	−13	1.534281	−3	−16	−5
0.214438	Cd	1.533706	+5	−5	−6	1.533698	+13	+3	+2
0.226747	Cd	1.522755	+67	+64	+69	1.522750	(+71)^c	(+68)	(+73)
0.230209	Hg	1.520088	−35	−38	−30	1.520083	(−30)	(−32)	(−25)
0.237833	Hg	1.514739	+3	+13	+9	1.514736	+6	+16	+12
0.239938	Hg	1.513377	−4	−8	−1	1.513374	−1	−5	+2
0.248272	Hg	1.508408	−4	−11	−3	1.508407	−3	−10	−2
0.265204	Hg	1.500036	−39	−32	−20	1.500036	(−39)	(−32)	(−20)
0.269885	Hg	1.498052	+2	−9	+6	1.498053	+1	−10	+5
0.275278	Hg	1.495917	−2	+4	+8	1.495918	−3	+3	+7
0.280347	Hg	1.494042	−6	−11	−13	1.494043	(−8)	(−13)	(−15)
0.289360	Hg	1.490990	+18	+22	+20	1.490992	(+16)	(+20)	(+18)
0.296728	Hg	1.488732	−5	−10	−2	1.488730	−8	−13	−5
0.302150	Hg	1.487192	−7	+0	+6	1.487195	−10	−2	+4
0.330259	Zn	1.480534	+6	+15	+8	1.480537	+3	+12	+5
0.334148	Hg	1.479758	−3	+4	+14	1.479761	−6	+1	+11
0.340365	Cd	1.478578	+15	+8	−2	1.478582	+12	+5	−5
0.346620	Cd	1.477462	−11	−6	−8	1.477465	−14	−9	−11
0.361051	Cd	1.475123	+9	−3	−2	1.475126	+6	−6	−5
0.365015	Hg	1.474533	−5	−9	−15	1.474536	(−8)	(−12)	(−18)
0.404656	Hg	1.469613	+5	+3	+6	1.469615	+3	+1	+4
0.435835	Hg	1.466690	+8	+4	+6	1.466692	+7	+3	+5
0.467816	Cd	1.464292	+5	+3	+6	1.464293	+4	+2	+5
0.486133	H	1.463127	+5	+4	+6	1.463127	+5	+4	+6
0.508582	Cd	1.461865	+2	−1	+3	1.461865	+2	−1	+3
0.546074	Hg	1.460082	+0	−3	−9	1.460082	+1	−2	−8
0.576959	Hg	1.458851	−0	−2	−1	1.458851	+0	−2	−1
0.579065	Hg	1.458774	+1	+1	+1	1.458773	+2	+2	+2
0.587561	He	1.458469	−2	−7	−4	1.458469	−2	−7	−4
0.589262	Na	1.458410	+0	−3	+1	1.458409	+1	−2	+2
0.643847	Cd	1.456711	+2	−3	−0	1.456710	+3	−2	+1
0.656272	H	1.456374	−0	−2	−0	1.456373	+1	−1	+1
0.667815	He	1.456075	+0	−2	−5	1.456074	+1	−1	−4
0.706519	He	1.455154	+1	+3	−2	1.455153	+2	+4	−1
0.852111	Cs	1.452475	−2	−7	−5	1.452474	−1	−6	−4
0.894350	Cs	1.451845	+2	−4	+1	1.451844	+2	−4	+1
1.01398	Hg	1.450250	−2	−5	−2	1.450250	−2	−5	−2
1.08297	He	1.449412	+1	−6	+2	1.449412	+1	−6	+2
1.12866	Hg	1.448875	+1	+2	+3	1.448876	−0	+1	+2
1.3622	Hg	1.446213	−7	−15	−13	1.446216	(−10)	(−18)	(−16)
1.39506	Hg	1.445837	−2	+3	−4	1.445840	−5	+0	−7
1.4695	Cs	1.444974	+4	+10	+11	1.444978	−0	+6	+7
1.52952	Hg	1.444266	+10	+8	+2	1.444270	+6	+4	−2
1.6606	TCB^a	1.442666	−10	−15	−7	1.442670	(−14)	(−19)	(−11)
1.681	Poly^b	1.442409	+3	−5	+13	1.442414	(−2)	(−10)	(+8)
1.6932	Hg	1.442255	+12	−1	+6	1.442259	+8	−5	+2
1.70913	Hg	1.442052	+5	+8	+4	1.442056	+1	+4	−0
1.81307	Hg	1.440692	−0	−0	+13	1.440697	−5	−5	+8
1.97009	Hg	1.438512	+14	+20	+20	1.438516	(+9)	(+15)	(+15)
2.0581	He	1.437216	+5	−1	−3	1.437219	+2	−4	−6
2.1526	TCB	1.435762	−15	−18	−17	1.435764	(−17)	(−20)	(−19)
2.32542	Hg	1.432922	−4	+3	−0	1.432921	−3	+4	+1
2.4374	TCB	1.430951	−20	−18	−11	1.430946	(−15)	(−13)	(−6)
3.2439	Poly	1.413138	+1	+9	+5	1.413087	(+53)	(+61)	(+57)
3.2668	Poly	1.412525	−0	+10	+5	1.412472	(+53)	(+63)	(+58)
3.3026	Poly	1.411554	+13	+11	+9	1.411498	(+69)	(+67)	(+65)
3.422	Poly	1.408194	+26	+28	+23	1.408129	(+91)	(+93)	(+88)
3.5070	Poly	1.405683	−33	−27	−17	1.405611	(+39)	(+45)	(+55)
3.5564	TCB	1.404175	−28	−30	−19	1.404100	(+47)	(+45)	(+56)
3.7067	TCB	1.399360	+7	+15	+20	1.399278	(+89)	(+97)	(+102)

Code		NBS	LASL	LASL	LASL	LASL
Data points		180	180	180	123	123
∑ (Deviations)2		(5.164 · 10⁻⁸)	4.906 · 10⁻⁸	3.731 · 10⁻⁸	3.752 · 10⁻⁹	3.739 · 10⁻⁹
Avg. deviation		11.9 · 10⁻⁶	11.3 · 10⁻⁶	9.3 · 10⁻⁶	4.3 · 10⁻⁶	4.3 · 10⁻⁶
Parameter	max.	(1.2 · 10⁻³)	2.6 · 10⁻¹²	9.8 · 10⁻⁶	2.4 · 10⁻⁹	4.8 · 10⁻⁹
slopes	min.	(1.3 · 10⁻⁵)	1.8 · 10⁻¹⁴	6.6 · 10⁻⁸	5.2 · 10⁻¹³	1.9 · 10⁻¹²

i = 1	a = 1	0.6961663	0.61145816	0.53186932	0.55105619	0.54788469
1	2	0.0684043	0.063264820	0.056857781	0.058686335	0.058408579
2	3	0.4079426	0.49267859	0.57234217	0.55312773	0.55630387
2	4	0.1162414	0.11318188	0.11075886	0.11128041	0.11118795
3	5	0.8974794	0.90213984	0.066425330	0.92922006	0.47527267
3	6	9.896161	9.9180201	6.6776876	10.052067	8.5964707
4	7			1.1524322		6.7025334
4	8			12.206844		49.173434

Wavelength in microns	Spectral source	Four-term fit to 180 data points				Four-term fit to 123 data points
Wavelength in microns	Spectral source	Computed	Corning	Dynasil	G. E.	Computed	Corning	Dynasil	G. E.
0.213856	Zn	1.534289	−11	−24	−13	1.534281	−3	−16	−5
0.214438	Cd	1.533706	+5	−5	−6	1.533698	+13	+3	+2
0.226747	Cd	1.522755	+67	+64	+69	1.522750	(+71)^c	(+68)	(+73)
0.230209	Hg	1.520088	−35	−38	−30	1.520083	(−30)	(−32)	(−25)
0.237833	Hg	1.514739	+3	+13	+9	1.514736	+6	+16	+12
0.239938	Hg	1.513377	−4	−8	−1	1.513374	−1	−5	+2
0.248272	Hg	1.508408	−4	−11	−3	1.508407	−3	−10	−2
0.265204	Hg	1.500036	−39	−32	−20	1.500036	(−39)	(−32)	(−20)
0.269885	Hg	1.498052	+2	−9	+6	1.498053	+1	−10	+5
0.275278	Hg	1.495917	−2	+4	+8	1.495918	−3	+3	+7
0.280347	Hg	1.494042	−6	−11	−13	1.494043	(−8)	(−13)	(−15)
0.289360	Hg	1.490990	+18	+22	+20	1.490992	(+16)	(+20)	(+18)
0.296728	Hg	1.488732	−5	−10	−2	1.488730	−8	−13	−5
0.302150	Hg	1.487192	−7	+0	+6	1.487195	−10	−2	+4
0.330259	Zn	1.480534	+6	+15	+8	1.480537	+3	+12	+5
0.334148	Hg	1.479758	−3	+4	+14	1.479761	−6	+1	+11
0.340365	Cd	1.478578	+15	+8	−2	1.478582	+12	+5	−5
0.346620	Cd	1.477462	−11	−6	−8	1.477465	−14	−9	−11
0.361051	Cd	1.475123	+9	−3	−2	1.475126	+6	−6	−5
0.365015	Hg	1.474533	−5	−9	−15	1.474536	(−8)	(−12)	(−18)
0.404656	Hg	1.469613	+5	+3	+6	1.469615	+3	+1	+4
0.435835	Hg	1.466690	+8	+4	+6	1.466692	+7	+3	+5
0.467816	Cd	1.464292	+5	+3	+6	1.464293	+4	+2	+5
0.486133	H	1.463127	+5	+4	+6	1.463127	+5	+4	+6
0.508582	Cd	1.461865	+2	−1	+3	1.461865	+2	−1	+3
0.546074	Hg	1.460082	+0	−3	−9	1.460082	+1	−2	−8
0.576959	Hg	1.458851	−0	−2	−1	1.458851	+0	−2	−1
0.579065	Hg	1.458774	+1	+1	+1	1.458773	+2	+2	+2
0.587561	He	1.458469	−2	−7	−4	1.458469	−2	−7	−4
0.589262	Na	1.458410	+0	−3	+1	1.458409	+1	−2	+2
0.643847	Cd	1.456711	+2	−3	−0	1.456710	+3	−2	+1
0.656272	H	1.456374	−0	−2	−0	1.456373	+1	−1	+1
0.667815	He	1.456075	+0	−2	−5	1.456074	+1	−1	−4
0.706519	He	1.455154	+1	+3	−2	1.455153	+2	+4	−1
0.852111	Cs	1.452475	−2	−7	−5	1.452474	−1	−6	−4
0.894350	Cs	1.451845	+2	−4	+1	1.451844	+2	−4	+1
1.01398	Hg	1.450250	−2	−5	−2	1.450250	−2	−5	−2
1.08297	He	1.449412	+1	−6	+2	1.449412	+1	−6	+2
1.12866	Hg	1.448875	+1	+2	+3	1.448876	−0	+1	+2
1.3622	Hg	1.446213	−7	−15	−13	1.446216	(−10)	(−18)	(−16)
1.39506	Hg	1.445837	−2	+3	−4	1.445840	−5	+0	−7
1.4695	Cs	1.444974	+4	+10	+11	1.444978	−0	+6	+7
1.52952	Hg	1.444266	+10	+8	+2	1.444270	+6	+4	−2
1.6606	TCB^a	1.442666	−10	−15	−7	1.442670	(−14)	(−19)	(−11)
1.681	Poly^b	1.442409	+3	−5	+13	1.442414	(−2)	(−10)	(+8)
1.6932	Hg	1.442255	+12	−1	+6	1.442259	+8	−5	+2
1.70913	Hg	1.442052	+5	+8	+4	1.442056	+1	+4	−0
1.81307	Hg	1.440692	−0	−0	+13	1.440697	−5	−5	+8
1.97009	Hg	1.438512	+14	+20	+20	1.438516	(+9)	(+15)	(+15)
2.0581	He	1.437216	+5	−1	−3	1.437219	+2	−4	−6
2.1526	TCB	1.435762	−15	−18	−17	1.435764	(−17)	(−20)	(−19)
2.32542	Hg	1.432922	−4	+3	−0	1.432921	−3	+4	+1
2.4374	TCB	1.430951	−20	−18	−11	1.430946	(−15)	(−13)	(−6)
3.2439	Poly	1.413138	+1	+9	+5	1.413087	(+53)	(+61)	(+57)
3.2668	Poly	1.412525	−0	+10	+5	1.412472	(+53)	(+63)	(+58)
3.3026	Poly	1.411554	+13	+11	+9	1.411498	(+69)	(+67)	(+65)
3.422	Poly	1.408194	+26	+28	+23	1.408129	(+91)	(+93)	(+88)
3.5070	Poly	1.405683	−33	−27	−17	1.405611	(+39)	(+45)	(+55)
3.5564	TCB	1.404175	−28	−30	−19	1.404100	(+47)	(+45)	(+56)
3.7067	TCB	1.399360	+7	+15	+20	1.399278	(+89)	(+97)	(+102)

Code		NBS	LASL	LASL	LASL	LASL
Data points		180	180	180	123	123
∑ (Deviations)2		(5.164 · 10⁻⁸)	4.906 · 10⁻⁸	3.731 · 10⁻⁸	3.752 · 10⁻⁹	3.739 · 10⁻⁹
Avg. deviation		11.9 · 10⁻⁶	11.3 · 10⁻⁶	9.3 · 10⁻⁶	4.3 · 10⁻⁶	4.3 · 10⁻⁶
Parameter	max.	(1.2 · 10⁻³)	2.6 · 10⁻¹²	9.8 · 10⁻⁶	2.4 · 10⁻⁹	4.8 · 10⁻⁹
slopes	min.	(1.3 · 10⁻⁵)	1.8 · 10⁻¹⁴	6.6 · 10⁻⁸	5.2 · 10⁻¹³	1.9 · 10⁻¹²

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Tables (2)

Journal of the Optical Society of America