2.11.3 Faraday Rotator Glasses
Diamagnetic Glasses
The Verdet constant of diamagnetic glasses is proportional to the dispersion of the refractive index, dn/dλ. Thus high index, large dispersion glasses are generally used for Faraday rotation applications. Data for representative diamagnetic glasses are given below.*
|
|
Wavelength (nm) |
|
|
|
Schott BK 7 |
435.8 |
480.0 |
546.1 |
632.8 |
1060 |
Verdet constant, V(rad/T m) |
9.6 |
7.6 |
5.8 |
4.1 |
1.7 |
Loss coefficient, α (cm–1) |
0.0017 |
— |
0.0016 |
— |
— |
Index of refraction, n |
1.5267 |
1.5228 |
1.5187 |
1.5151 |
1.5067 |
|
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
|
Schott SF 6 |
435.8 |
480.0 |
546.1 |
632.8 |
1060 |
Verdet constant, V(rad/T m) |
48.1 |
34.9 |
25 |
18 |
6.1 |
Loss coefficient, α (cm–1) |
0.024 |
0.008 |
0.002 |
— |
— |
Index of refraction, n |
1.8470 |
1.8297 |
1.8126 |
1.7988 |
1.7738 |
|
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
|
Schott SF 57 |
435.8 |
480.0 |
546.1 |
632.8 |
1060 |
Verdet constant, V(rad/T m) |
52.4 |
39.6 |
29 |
20 |
6.7 |
Loss coefficient, (cm–1) |
0.0205 |
— |
0.002 |
0.002 |
0.002 |
Index of refraction, n |
1.8939 |
1.8742 |
1.8550 |
1.8396 |
1.8118 |
|
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
|
Schott SF 59 |
435.8 |
480.0 |
546.1 |
632.8 |
1060 |
Verdet constant, V(rad/T m) |
69.8 |
— |
37.2 |
25.9 |
8.1 |
Loss coefficient, α (cm–1) |
— |
— |
— |
— |
— |
Index of refraction, n |
2.0156 |
1.9890 |
1.9635 |
1.9432 |
1.9078 |
|
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
|
As2S3 |
435.8 |
480.0 |
546.1 |
632.8 |
1060 |
Verdet constant, V(rad/T m) |
86.7 |
56.4 |
38.7 |
19 |
13 |
Loss coefficient, α (cm–1) |
— |
— |
— |
— |
— |
Index of refraction, n |
2.636 |
2.562 |
2.521 |
2.465 |
2.448 |
* Schott glass designations. Similar glasses are available from other sources.
© 2003 by CRC Press LLC
Paramagnetic Glasses
Data from manufacturer’s data sheets.
|
|
Wavelength (nm) |
|
|
Hoya FR 4 (discontinued) |
325 |
442 |
632.8 |
1064 |
Verdet constant, V(rad/T m) |
— |
–82.6 |
–30.5 |
–8.4 |
Loss coefficient, α (cm–1) |
— |
|
0.00597 |
0.0054 |
Index of refraction, n |
— |
1.584 |
1.570 |
1.561 |
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
Hoya FR 5 |
325 |
442 |
632.8 |
1064 |
Verdet constant, V(rad/T m) |
–444 |
–174 |
–71.0 |
–20.6 |
Loss coefficient, α (cm–1) |
— |
— |
0.0291 |
0.0086 |
Index of refraction, n |
1.731 |
1.701 |
1.684 |
1.673 |
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
Hoya FR 7 |
325 |
442 |
632.8 |
1064 |
Verdet constant, V(rad/T m) |
— |
–82.3 |
–34.9 |
–9.6 |
Loss coefficient, α (cm–1) |
— |
— |
— |
— |
Index of refraction, n |
— |
1.540 |
1.530 |
1.524 |
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
Kigre M-18 |
543.1 |
632.8 |
830.0 |
1064 |
Verdet constant, V(rad/T m) |
–103 |
–70.9 |
–37.9 |
–21.3 |
Loss coefficient, α (cm–1) |
— |
— |
— |
— |
Index of refraction, n |
— |
1.6845 (nD) |
— |
1.664 |
|
|
|
||
Verdet constant relative to FR 5 measured at 21.7 rad/T m. |
|
|
||
|
Wavelength (nm) |
|
Kigre M-24 |
532 |
1064 |
Verdet constant, V(rad/T m) |
–87 |
–26 |
Loss coefficient, α (cm–1) |
— |
— |
Index of refraction, n |
1.701 (nD) |
1.687 |
|
|
|
|
Wavelength (nm) |
|
Kigre M-32 |
532 |
1064 |
Verdet constant, V(rad/T m) |
–98 |
–29 |
Loss coefficient, α (cm–1) |
— |
— |
Index of refraction, n |
1.727 (nD) |
1.713 |
|
|
|
© 2003 by CRC Press LLC
|
|
Wavelength (nm |
|
|
O-I EY-1 (discontinued) |
325 |
442 |
632.8 |
1064 |
Verdet constant, V(rad/T m) |
–273 |
–98.0 |
–41.9 |
–11.9 |
Loss coefficient, α (cm–1) |
— |
— |
— |
<0.005 |
Index of refraction, n |
1.665 |
1.639 |
1.624 |
1.615 |
|
|
|
|
|
|
|
Wavelength (nm) |
|
|
O-I EY-2 (discontinued) |
325 |
442 |
632.8 |
1064 |
Verdet constant, V(rad/T m) |
— |
— |
— |
–11 |
|
|
|
||
Loss coefficient, α (cm–1) |
— |
— |
— |
<0.010 |
Index of refraction, n |
— |
— |
— |
1.607 |
|
|
|
|
|
Optical Properties of Paramagnetic Faraday Rotator Glasses
|
Transmission |
Refractive |
Abbe |
|
Nonlinear |
Glass |
range |
index |
number |
dn/dT |
index n2 |
type |
(µm) |
nD |
νD |
(10-6/K) |
calc. (10--13esu) |
FR-4 |
~0.4–2.0 |
1.5732 |
58.0 |
2.8 |
1.59 |
FR-5 |
~0.4–1.5* |
1.6864 |
53.5 |
7.5 |
2.45 |
FR-7 |
~0.4–1.5* |
1.5316 |
74.9 |
– |
0.95 |
M-18 |
~0.4–1.5* |
1.682 |
48.8 |
7.5 |
2.7 |
M-24 |
~0.4–1.5* |
1.701 |
52.0 |
– |
2.6 |
M-32 |
~0.4–1.5* |
1.727 |
51.1 |
– |
2.9 |
* Tb3+ absorption line at ~0.54 µm.
Mechanical and Thermal Properties of Paramagnetic Faraday Rotator Glasses
|
|
Young’s |
Poisson’s |
Knoop |
Thermal |
Transform. |
Glass |
Density |
modulus E |
ratio |
hardness |
expansion |
temp |
type |
(g/cm3) |
(103 N/mm2) |
µ |
(N/mm2) |
( 10-6/°C) |
(°C) |
FR-4 |
3.10 |
65.2 |
0.244 |
6020 |
98 |
625 |
FR-5 |
4.28 |
108 |
0.22 |
7310 |
47 |
756 |
FR-7 |
4.32 |
– |
– |
5070 |
17.1 |
398 |
M-18 |
4.33 |
113 |
0.339 |
7380 |
5.63 |
757 |
M-24 |
4.45 |
121 |
0.326 |
7500 |
5.59 |
775 |
M-32 |
4.85 |
120 |
0.306 |
7930 |
6.00 |
774 |
Data from manufactures’ sheets.
© 2003 by CRC Press LLC
2.11.4 Gradient-Index Glasses
Gradient-index (GRIN) glasses are ones in which the index of refraction varies spatially within the glass. A radial gradient is one that is symmetric about a line; therefore the surfaces of constant index of refraction are cylinders. There are two commonly used mathematical representations for such gradients. The first, used to specify products manufactured by Nippon Sheet Glass, is N(r)= N0(1 – Ar2/2 + h4r4 + h6r6 + . . . ); the second is N(r)= N00 + N10r2 + N20r4 + . . . ). In both cases, the quadratic coefficient determines the focal length, numerical aperture, and other first-order properties of the lens. The higherorder coefficients determine the image quality.
The tables below present catalog data for Nippon Sheet Glass (NSG) materials and those of Gradient Lens Corporation(GLC) together with calculated maximum numerical aperture (NA) and quarter-pitch length. Other diameters and numerical apertures may be available; the reader should contact the appropriate vendor for current data.
NSG Radial Gradient Lenses (Selfoc)
|
SLS |
SLS |
SLW |
SLW |
SLW |
SLW |
SLH |
Numerical aperture |
0.37 |
0.37 |
0.46 |
0.46 |
0.46 |
0.46 |
0.6 |
Diameter (mm) |
1 |
2 |
1 |
1.8 |
2 |
31.8 |
|
Wavelength ( m) |
0.63 |
0.63 |
0.63 |
0.63 |
0.63 |
0.63 |
0.634 |
|
2.49E–1 |
6.10E–2 |
3.70E–1 |
1.15E–1 |
9.24E–2 |
4.24E–2 |
1.85E–1 |
Square root A |
0.499 |
0.247 |
0.608 |
0.339 |
0.304 |
0.206 |
0.43 |
N00 |
1.5637 |
1.5637 |
1.6075 |
1.6075 |
1.6075 |
1.6075 |
1.6576 |
N10 |
–1.95E–1 |
–4.77E–2 |
–2.97E–1 |
–9.24E–2 |
–7.43E–2 |
–3.41E–2 |
–1.53E–1 |
∆ N |
–4.87E–2 |
–4.77E–2 –7.43E–2 –7.48E–2 –7.43E–2 –7.67E–2 |
–1.24E–1 |
||||
Index at edge |
1.515 |
1.516 |
1.5332 |
1.5326 |
1.5332 |
1.5307 |
1.5334 |
Quarter-pitch length |
3.15 |
6.36 |
2.58 |
4.63 |
5.17 |
7.63 |
3.65 |
Data from SELFOC Product Guide, NSG America, Inc., Somerset, NJ 08873.
GLC Radial Gradient Lenses (BIG GRINS)
|
BG 30 |
BG 40 |
BG 50 |
Numerical aperture |
0.19 |
0.19 |
0.19 |
Diameter (mm) |
3 |
4 |
5 |
Wavelength ( m) |
0.63 |
0.63 |
0.63 |
A |
5.78E–3 |
3.25E–3 |
2.12E–3 |
Square root A |
0.076 |
0.057 |
0.046 |
N00 |
1.643 |
1.643 |
1.643 |
N10 |
–4.74E–3 |
–2.67E–3 |
–1.74E–3 |
∆ N |
–1.07E–2 |
–1.07E–2 |
–1.09E–2 |
Index at edge |
1.6323 |
1.6323 |
1.6321 |
Quarter-pitch length |
20.67 |
27.56 |
34.15 |
Data from Gradient Lens Corporation Data Sheets, Rochester, NY 14608.
Tables from Moore, D. T., Gradient-index materials, Handbook of Laser Science and Technology, Suppl. 2: Optical Materials (CRC Press, Boca Raton, 1995), p. 499.
© 2003 by CRC Press LLC