Stokes polarimeters are most commonly used to measure the state of polarization of optical wave. Dependence of Stokes parameters, degree of polarization on external magnetic field are presented for garnet and groove films on garnet in the transmission and reflection modes. The Stokes parameters S1, S2, S3 of different modes show different tendency and asymmetrically change when the external magnetic field change, while the degree of polarization basically unchange.
© 2014 Optical Society of America
In recent years, a lot of research has shown that the degree of polarization (DOP) may change on propagation of an electromagnetic Gaussian Schell model beam in free space [1–3]. The state of polarization is one very important parameter of optical field. Many practical situations make the light polarization properties depend on the spatial location . The polarization properties of electromagnetic beams are important in a great variety of optical phenomena . Polarization properties are commonly used rigonometric method, Jones vector method, Stokes vector method and Poincare sphere method (see Fig. 1) [6,7]. The standard description of optical polarization employs the Stokes parameters, and it is more useful for describing fully polarized light and non-depolarizing optical devices, so Stokes vector method is a major representation to research polarization.
Garnet film is widely used in data storage , optical isolator , spectral domain technique to compute the dispersion characteristics and the transverse field distributions of micro-strip lines  and optical magnetic field (current) sensors [11–16]. In order to satisfy these various applications, the polarization properties of garnet are researched. In this letter, we report the polarization properties of garnet and Ta/Nd2Fe14B/Ta groove films, which are researched by 1550nm optical fiber and Thorlabs PAX5710 IR3 polarimeter. The Ta/Nd2Fe14B/Ta groove films have been grown on garnet substrate by magnetron sputtering method. We observe for the first time the asymmetrically change of Stokes parameters in orientation angle with the external magnetic field (Hext).
The use of the Stokes parameters is a standard method to characterize the state of polarization of an optical field . And any state of paraxial, elliptic polarization can be described completely using the Stokes parameters . The Stokes parameters (S1, S2, S3) and DOP characterize the randomness of a polarization state. The DOP in terms of the Stokes vector S = (S0, S1, S2, S3) is given by
The relationship of the Stokes parameters to intensity and polarization ellipse and the figures are shown below.
Here DOP, Ip, 2Ψ and 2χ are the spherical coordinates of the three-dimensional vector of cartesian coordinates (S1, S2, S3). The parameter S0 is the total light intensity; S1 is the intensity difference between horizontally and vertically polarized components; S2 is the intensity difference between + 45° and −45° polarized components; and S3 is the intensity difference between right- and left- circularly polarized components. DOP is the degree of polarization, I is the total intensity of the beam and Ψ is the orientation angle, the angle between the major semi-axis of the ellipse and x-axis. The factor of two before Ψ represents the fact that any polarization ellipse is indistinguishable from one rotated by 180°.
Any state of polarization can be represented on the surface of a sphere, with coordiates Si/S0 (i = 1,2,3).
In order to evaluate the polarization properties of garnet and the groove films, the samples are illuminated with a single mode linearly polarized 1550nm optical fiber laser. Garnet film (Granopt Co., Ltd) with a thickness of 0.39 mm and 3 mm × 3 mm square and Ta(50nm)/Nd2Fe14B(xnm)/Ta(50nm)(x = 100, 500, 1000, 2000, 4000, 5000) groove films on garnet film prepared by magnetron sputtering method are used as samples. The width of groove film is 200µm, and the width between groove films is 200µm in Fig. 2.
The experimental set-up is shown schematically in Fig. 3. On the left side, a 1550nm optical fiber laser and Thorlabs PAX5710IR3 polarimeter are used as light source and detector, respectively, the laser beam is divided into two parts with the help of a 50:50 beamsplitter, and the laser beam goes through the beamsplitter in the transmission mode. While on the right, the laser beam reflects from the beamsplitter in the reflection mode. Then the laser beam passes through the polarizer, sample and reflect from the mirror. Afterwards, the beam is focused on the polarimeter. The polarizer can be oriented to transmit the components along the x-axis, or y-axis, initially the laser intensity is the maximum in this experiment, so that it allows us to measure the Stokes parameters S1, S2, S3. The Hext is generated by high current generator, the maximum current is 3000A, then the magnetic field from 0 Oe to 178 Oe is applied in the thickness direction and the light propagates along the same direction. The Stokes parameters S1, S2, S3 and DOP are measured using Thorlabs PAX5710IR3 polarimeter and the optical unit of Thorlabs PAX5710IR3 measurement sensor consists of a rotating quarter waveplate, a fixed polarizer and a photodetector. The waveplate transforms the input polarization. The polarizer only transmits the portion of light which is parallel to the transmission axis. The photodetector acts as powermeter .
4. Results and discussion
The polarization properties of garnet on Stokes parameter are shown in Fig. 4. The sampling rate of polarimeter used in the present experiments of measuring the output Stokes parameters is 333 samples per second. There, we use 666 data points to calculate the average data in experiments. The Stokes parameter S1 is calculated by
Figure 4 illustrates the relationship between the Stokes parameter S1 of garnet in transmission mode and time when the external magnetic field changes from 0Oe 178Oe. The average Stokes parameters decrease from S1(Hext = 0Oe) = −0.6227 to S1 (Hext = 178Oe) = −0.8137 and the change is −30.67% when the Hext changes from 0Oe to 178Oe, and the S12 increases from 0.3876 to 0.6621. In Fig. 4, we see that the amplitudes of Stokes parameter S1 are small and their magnitudes remain essentially constant at fixed magnetic field.
The polarization properties of garnet in transmission mode are also measured using polarimeter and are shown in Fig. 5 (dark). The Stokes parameter S1 decreases from −0.6227 (Hext = 0Oe) to −0.8137 (Hext = 178Oe). The Stokes parameter S2 increases from −0.6363 (Hext = 0Oe) to −0.4468 (Hext = 178Oe), the Stokes parameter S3 increases from −0.4547 (Hext = 0Oe) to −0.3724 (Hext = 178Oe). However the DOP oscillates around 96.5% when the Hext changes from 0Oe to 178Oe. The absolute value of parameter S1 shows an upward trend, in that case the intensity of light transmitting between horizontally and vertically polarized components increases; while the absolute value of parameter S2 shows a downward trend, in that case the intensity of light transmitting between + 45° and −45° polarized components decreases. Figure 6 (dark) shows the relationship between 2Ψ angle and Hext in transmission mode using Eq. (3). The 2Ψ angle shows a downward trend and decreases from 1.0218 to 0.5491 when the Hext changes from 0 to 178Oe.
The polarization properties of garnet in reflection mode are shown in Fig. 7 (dark). The Stokes parameter S1 increases from −0.978 (Hext = 0Oe) to −0.909 (Hext = 178Oe), the Stokes parameter S2 increases from 0.0543 (Hext = 0Oe) to 0.318 (Hext = 178Oe), the Stokes parameter S3 increases from 0.1998 (Hext = 0Oe) to 0.278 (Hext = 178Oe), when the Hext changes from 0 to 178Oe. The DOP increases from 90.99% to 92.00%. The absolute value of parameter S1 shows a downward trend, in that case the intensity of light transmitting between horizontally and vertically polarized components decreases; while the absolute value of parameter S2 shows an upward trend, in that case the intensity of light transmitting between + 45° and −45° polarized components increases. Figure 8 (dark) shows the relationship between 2Ψ and Hext in reflection mode using Eq. (3). The 2Ψ angle shows a downward trend decreases from −0.0555 to −0.3498, however the absolute value of 2Ψ angle increases from 0.0555 to 0.3498, when the Hext changes from 0 to 178Oe.
The effect of Ta(50 nm)/Nd2Fe14B(xnm)/Ta(50 nm) groove films on garnet is also researched. Figure 5 shows their polarization properties of groove films on garnet when the Hext changes from 0 to 178Oe in transmission mode. It can be noticed that the S1 shows a downward trend and decreases from −0.612 (Hext = 0Oe) to −0.9006 (Hext = 178Oe), while the S2 and S3 show an upward trend and increases from −0.6363 (Hext = 0Oe) to −0.3244 (Hext = 178Oe) and −0.4788 (Hext = 0Oe) to −0.3197 (Hext = 178Oe), respectively. However, the DOP oscillates around the equilibrium value, when the Hext changes from 0 to 178Oe. Figure 6 shows the relationship between 2Ψ and Hext in transmission mode using Eq. (3). The 2Ψ angle shows a downward trend and decreases from 1.055 to 0.3602.
Figure 7 also shows the polarization properties of groove films on garnet when the Hext changes from 0Oe to 178Oe in reflection mode. It can be noticed that the S1, S2, S3 show an upward trend and increases from −0.8085 (Hext = 0Oe) to −0.5947 (Hext = 178Oe), 0.2438 (Hext = 0Oe) to 0.4865 (Hext = 178Oe) and 0.6421 (Hext = 0Oe) to 0.6117 (Hext = 178Oe), respectively, when the Hext increases from 0Oe to 178Oe. However, the DOP also unchanges and oscillates around the equilibrium value, when the Hext changes from 0 to 178Oe shown in Fig. 7. The 2Ψ angle shows a downward trend and decreases from −0.3159 (Hext = 0Oe) to 0.9349 (Hext = 178Oe) in Fig. 8, while the absolute value of 2Ψ angle increases from 0.3159 to 0.9349.
When comparing the Stokes parameters of S1, S2, S3, DOP and 2Ψ in different modes from Figs. 5 and 7 and Figs. 6 and 8, it can be seen that the Ta/Nd2Fe14B/Ta groove films could affect the polarization properties of garnet such as the Stokes parameters value S1, S2, S3, DOP, as the scattering effect of groove films , but they do not change the trends of the Stokes parameters. The absolute value of Stokes parameter S1 in transmission and reflection mode show different trends, one upward other downward, in that case the different modes induce the different change in the intensity between horizontally and vertically polarized components. And the absolute value of Stokes S2 in different mode also show different changes, in that case the intensity between + 45° and −45° polarized components give different changes when the Hext changes from 0Oe to 178Oe. The 2Ψ in the transmission and reflection modes show asymmetrically change when the Hext changes. Although the all the Stokes parameters vary with the application of external magnetic field on the sample, the value of S12 + S22 + S32 basically unchanges, from Eq. (1), we can get that the DOP remains essentially constant.
In conclusion, we have researched the polarization properties of garnet and groove films. The Stokes parameters results indicate that the groove films affect the value of the garnet polarization, but do not change their trends. The transmission and reflection modes lead to different azimuth angle trends. The measuring modes are proposed to change the polarization. And this is very important for the sensor manufacturing and optics design.
This work was supported by the Project of National Natural Science Foundation of China (NSFC) (Grant No. 61205076) and The Innovation Fund Project For Graduate Student of Shanghai (JWCXSL1302).
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