ОПТИКА И СПЕКТРОСКОПИЯ, 2014, том 116, № 2, с. 336-339
ФИЗИЧЕСКАЯ ОПТИКА
y%K 535.32
THE TEMPERATURE EFFECT ON THE TRANSMISSION SPECTRUM OF THE QUARTZ OPTICAL ROTATION FILTER
© 2014 n Fei Gao, Yong Kong, XiaoLi Zhao, Keke Song, Xiangkai Zhao, and Mingming Shen
Shanghai University of Engineering Science, College of Electrical and Electronic Engineering, 201620 Shanghai, China E-mail: kkyy7757@yahoo.com.cn, ky7757@163.com, hi4455707@163.com Received April 4, 2013; in final form, July 8, 2013
In this paper the temperature effect on the transmission spectrum of the quartz optical rotation filter is investigated theoretically and experimentally in detail, which shows that the output center wavelength of filter will shift towards the long wavelength with the temperature increasing and the output center wavelength of filter will shift towards the short wavelength with the temperature decreasing. The simulation and the experiment results are the same basically. According to this conclusion, a new type quartz optical rotation filter that is insensitive to the changing temperature is proposed.
DOI: 10.7868/S0030403414020068
INTRODUCTION
There are usually two kinds of traditional birefringence filter: Lyot [1, 2] and Solc optical filter [3, 4]. Compared with other optical filters, the unique advantages offered by this birefringence filter are the tenabil-ity to a desired wavelength, low insertion loss and wide field of view. Therefore birefringence filter is widely used in the fields of laser tuning [5, 6], astronomy [7—9], dense wavelength division multiplexing [10, 11] and so on. Recently a novel polarization coherent spectral filter based on optical dispersion effect has been demonstrated by C. Ye [12—14]. Compared with traditional Lyot and Solc filter, it can be adjusted not only by mechanical structure but also by the applied voltage (if it have an active device, such as LC polarization rotator), and it does not require additional achromatic retarder.
For the optical filter, working in fixed transmission spectra is very important. For example, the variation of output central wavelength caused by temperature fluctuation is unacceptable in the sunlight observation instrument [7—9]. The temperature effect on the output spectrum characteristic of the quartz birefringence filter has been widely investigated [15, 16], but the temperature effect on output spectrum characteristic of the quartz optical rotation filter has not been published yet to our best knowledge.
In this paper, a relative research is demonstrated in detail. The experimental and theoretical results show that the output central wavelength of filter will shift towards the long wavelength with the temperature increasing and the output central wavelength will shift towards the short wavelength with the temperature decreasing, which is opposite to the output central wavelength of the quartz birefringence filter with the temperature change. According to this conclusion, we
propose a new type quartz filter composed of three polarizers, a quartz birefringent crystal and a quartz rotation crystal. The analysis shows that this structure may eliminate the center wavelength fluctuation of the quartz birefringence filter caused by the temperature change in a certain extent.
NUMERICAL SIMULATION
As shown in Fig. 1, a rotation dispersion polarization filter is composed of two polarizers P1, P2 and a quartz rotation crystal L1. The azimuth angle of two polarizer prisms is parallel to the azimuth angle of Z-axis, the quartz optical axis is perpendicular to its own surface, and T is the temperature applied to the quartz optical rotation filter.
The natural light will become a linear polarization light after it pass through P1, and the linear polarization light transmitting in L1 will rotate with a different angle varying as a function of optical wavelength, at last the output light intensity will change with optical wavelength after the light pass through P2.
SZ
X
Li
P2
Fig. 1. The schematic diagram of quartz optical rotation filter.
1
T
0.9
0.6 0.3
0L
400
- f" / \
- /.' /■'■ /• \ 9 2
- 1
/ 1 1 1
D = -1.57039 x 10-4 - 3.42124 x 10-6T -
460
520 580 WL, nm
Fig. 2. The output spectrum of the quartz rotation filter at 20°C as 1 line and 60°C as 2 line.
The Muller matrix of Pb P2, and L1 [17] can be expressed as follows:
Mpi = Mp2 =
1100" 1100 0000 0000
(1)
Ml =
11 0 0" 0 cos 20 sin 200 0 - sin 20 cos 20 0 0 0 0 1
(2)
a = A + B/(X2 - C) - DX2,
(4)
where A, B, C, and D are the temperature coefficients, X is the wavelength of the incident light, its unit is mm. A, B, C, and D can be obtained by the following expressions [19]:
A = -311.87457 - 2.75492T - 0.35441T2 +
+ 0.01061T3 - 7.99432 x 10-5T4,
B = 1.76092 x 108 + 5.31675 x 105T +
+ 7.1668 x 104T2 - 2.090 x 103T3 + 15.35985T4,
C = 1.04049 x 105 - 130.6369T - 22.26345T2 +
+ 0.62473T3 - 0.00442T4,
- 4.1859 x 10-7T2 + 1.2732 x 10- 9.75758 x 10-11T4.
T 3 _
At the range of — 10~60°C and range of 470~600 nm of wavelength, calculating by the formulas (3), (4), we can easily obtain the specific rotation of quartz crystal of each wavelength at any temperature in the above ranges.
Linear expansion coefficient of the quartz crystal along the optical axis direction is y = 7.97 x 10-6 (°C)-1, when the quartz rotation crystal is heated or cooled, the thickness variation should be also taken into account, namely:
d1 = d + y AT, (5)
d ' is the quartz thickness at 20°C, if the incident light is the nature light I'0, its Stokes parameters is:
"1 "
S0 - h)
(6)
Then, Stokes parameters of light passing through a single-stage quartz rotation filter is:
where 0 is the angle of rotation for the quartz crystal [18], and can be described as:
0 = ad1. (3)
Here, d1 is the thickness along the optical axis direction of the quartz crystal, and its unit is mm; a is the optical rotation coefficient of the quartz crystal, its unit is (°)/mm. The value of a is related to the wavelength, properties of the material, temperature, [19] and so on.
With the changing temperature, the relationship between optical rotation coefficient of quartz crystal and the wavelength is given by the following formula [19]:
= M1M2L1S0
10 cos2 [a
(7)
Here 10 is incident nature light intensity. Ignoring the inserting loss of light of each element, considering the output intensity I0(I0 = To/2) of P1, then the transmitted intensity of the quartz rotation filter is I = = I0cos2[a(^, T)d1], and the normalized transmit-tance is:
T = cos2 [a (X,T)d1].
(8)
Thickness of the quartz rotation crystal, namely, parallel to the direction of the optical axis, is 5 mm. Seen from Fig. 2, the 1 and 2 curves respectively are the output spectrum curves of quartz rotation filter at 20°C and 60°C.
The transmittance is 100% as shown in Fig. 2, which is due to not considering the inserting loss of quartz rotation filter such as the light absorption, inflection scattering of quartz rotation filter, etc. It can be seen from Fig. 2 that the output center wavelength shifts towards the long wavelength with the temperature increasing, and it shifts toward the short wavelength with the temperature decreasing. The changing trend for short wavelength is not obvious because the adopting formula is a fitting formula for the 470~600 nm, however, the numerical simulation for short wavelength filtering is beyond this range. The
2
11 OOTHKA H CnEKTPOCKOnHa tom 116 № 2 2014
338
FEI GAO et al.
T, % 100
50
1 2
1
400
500
600 WL, nm
Fig. 3. The spectrum curves of quartz rotation filter with changing temperature.
T, % 100
50
400
500
600 WL, nm
Fig. 4. The spectrum curves of quartz birefringence filter with changing temperature.
X
Li
P2
L2
Fig. 5. The schematic diagram of new type temperature insensitive quartz optical filter.
simulation result is not in good agreement with the actual value, which will be further discussed in the experiment.
Variation of quartz specific rotation with the changing temperature caused by the quartz crystal thermal expansion and the increasing of internal atomic distance caused by the higher temperature will result in larger pitch of quartz crystal molecules. Based on the helix theory, larger the pitch, larger the specific rotation, which will lead to the change of the output spectrum of the quartz rotation filter in different temperature.
EXPERIMENTAL RESULTS AND DISCUSSION
In order to compare with the output spectrum of quartz birefringence filter with the changing temperature the experiment for the output spectrum of quartz birefringence filter with the changing of temperature is also investigated. The thickness of the quartz rotation crystal perpendicular to the optical axis direction is 5 mm, and the thickness of the quartz birefringence crystal parallelled to the optical axis direction is 0.6 mm. Seen from Figs. 3 and 4, the curves 1 and 2are respectively the output spectrum curve at 20°C and 60°C for two kinds of quartz filter. Spectrophotometer used is homemade and the model number is V-1600, the scanning range of wavelength is from 350 to 1100 nm, and the scanning wavelength resolution is 1 nm.
As shown in Fig. 3 the center wavelength indeed shifts towards the long wavelength with the increasing temperature and the center wavelength indeed shifts towards the short wavelength with the reducing temperature. The changing trends are opposite for the two quartz filters in Figs. 3 and 4, which is a good agreement with the above analysis results. It is noted that considering the quartz filter insertion loss, transmit-tance is less than 100%. Whether the quartz rotation filter or quartz birefringence filter, with the increasing temperature, their transmittance will decrease, which is mainly caused by the increasing of the absorption coefficient of the filter with increasing temperature. In addition, with the changing temperature, the changing trend for short wavelength output of the quartz rotat
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.