International Journal of Advances in Electrical and Electronics Engineering 362 Available online at www.ijaeee.com& www.sestindia.org/volume-ijaeee ISSN: 2319-1112 Verdet Constant Measurement of Olive Oil for Magnetic Field Sensor Ali Adnan Shakir 1, Reiam D. AL-Mudhafa 2, Anwaar A. Al-Dergazly 3 1 Ministry of Science and Technology Baghdad, Iraq 2,3 Laser and Optoelectronics Department Nahrain University Baghdad, Iraq 1 aldergazly@gmail.com 2 reiam_dhiaa@yahoo.com Abstract- Most of the liquid crystal devices are driven by the electric field due to their relatively large dielectric permittivity. Also they have good nonlinear optical properties candidate to be used in photonic applications. Due to these properties olive oil one of these liquid crystal has been used. Simple experiment is designed to measure the Verdet constant of Olive oil by using Faraday Effect. Five laser wavelengths are used to determined the Verdet constant 405 nm, 532 nm, 632.8nm, 650nm, and 804.3 nm. The experimental values show a large Verdet constant for Olive oil at 650 nm laser wavelength equal to 98.68 rad /T. m. Key-Words Verdet constant, faraday effect, magnetic field, olive oil. I. INTRODUCTION The Verdet constant is an optical constant that describes the strength of the Faraday effect for a particular material. The phenomenon of the Faraday effect was first observed by Michael Faraday in 1845. He discovered the concrete evidence for the relationship between the major branches of optics, magnetism and atomic physics [4]. He found out that when a block of glass is subjected to a strong magnetic field, it becomes optically active. The effect occurs when the rotation of a linearly polarized wave passes through a thickness of a transparent medium. However, rotations of polarized light are not only limited to optically active materials, but also including some optically inactive materials exposed to high magnetic field. In magnetized medium the refractive indices for right-and lefthanded circularly polarized light are different. This effect manifests itself in a rotation of the plane of polarization of linearly polarized light. This observable fact is called magneto optic effect. Magneto optic effects are those effects in which the optical properties of certain materials are affected by applied magnetic fields or the material's own magnetization. Magneto optic effects occur in gases, liquids, and solids. The goal of this paper was to determine the Verdet constant of Olive oil by using faraday effect. And a simple experimental setup suitable is designed for this purpose using an DC magnetic field parallel with light propagation. II. PROPOSED ALGORITHM The faraday effect can be defined as the rotation of the plane of polarization of light due to magnetic-fieldinduced circular birefringence in a material. The angle of rotation is proportional to the product of magnetic field, path length through the sample and the Verdet constant. The relation between the angle of rotation of the polarization and the magnetic field in the transparent material is given by [4]: = (1) where is the angle of rotation, l is the length of the path where the light and magnetic field interact, B is the magnetic field component in the direction of the light propagation and is a proportional factor called the Verdet constant. To analyze the process as shown in Figure 1 the electric field of the output linearly polarized light beam propagating in the z direction and polarized along the x-axis (after the polarizer) can be expressed in Jones matrix as [1]
Verdet Constant Measurement of Olive Oil for Magnetic Field Sensor 363 = exp ( + ) (2) where is the amplitude of the electric field of incident light beam, k is the wave vector, ω is the angular frequency, and t is the time. After passing through the sample, the polarization direction of the light is changed by an angle,, which is the Faraday rotation of the sample. Then the electric field of the transmitted light beam becomes[1] = exp ( + ) (3) Then the light traverses through an analyzer which is set at an angle,, with respect to the first polarizer. Then the electric field of the light beam after transmitting analyzer is[1] = ( ) ( ) exp ( + ) (4) Figure1. faraday effect[3]. Then the light beam reaches to the detector, the intensity of light beam at the detector is given by[1] = ( ) (5) The polarizer needs to be fixed in an optimal angle to get the maximum modulation of light beam. By taking the first derivative of I with respect to angle,, the condition can be obtained and is[1] = 2( ) (6) Here, the angle of rotation, φ, is very small (<< 1º), so when = 45º, the maximum modulation of light beam will be obtained. Thus when the analyzer is set at 45º, the intensity of light beam that reaches to the detector photodiode is given by[1] = (1+2 ) (7) So that, the transmitted light,which is passed through transparent medium( gas, solid or liquid) placed in a uniform magnetic field in the direction parallel to the magnetic lines of force, is still plane polarized but that the plane of polarization is rotated by an angle proportional to the field intensity. In this experiment, we determine by measuring the polarization angle,, as a function of the applied B-field. Therefore, we need to determine The rotation angle, for each applied B-field, By using malus`s law[3]
IJAEEE, Volume2, Number 3 Ali Adnan Shakir et al. = ( ) (8) light intensity after polarizer, light intensity before polarizer, represents the angle between the plane of polarization, i.e., the plane of vibration, in light beam and the axis of the optical polarizer. Since the rotation due to the Faraday Effect is usually very small, let s express as the sum of two terms where represents the polarization axis of the incident light beam and represents the small rotation due the Faraday Effect[3]: = + (9) Though can be adjusted arbitrarily when setting up the experiment, during the experiment it will remain constant. The change in intensity due to the Faraday Effect, then becomes[3]: = ( + ) (10) III. EXPERIMENT AND RESULT The experiment setup system is shown in Figure 2. Five laser wavelengths had been used to measured the verdet`s constant of olive oil. The laser sources that had been used are shown in the Table 1. The light from laser source first passed through polarizer, which was set at 45. Then the light will pass through the medium ( in our experiment the olive oil) contained in cuvette made from glass. This cuvette was placed in a hole, which has the cuvette`s shape and size( 1.2cm x 1.2cm), made in the top-center of a pipe surface. The pipe, in which the cuvette was placed, with U-shaped iron core completed square-shaped as it is shown in Figure 2. Our experiment designed to make light passing through the medium parallel to magnetic field. Figure 2. The experimental set up to measure the verdet constant. The magnetic field was generated from current produced by connecting two 250-turn coils to high current DC power supply. These two coils placed on the U-shaped iron core to allow the field to flow through the medium in closed cycle. Mounted lens of f = 15 cm was fixed on the optical bench behind the analyzer to focus the laser beam to the power meter. In addition, the sensitivity of light intensity depends on analyzer angle. For example, for =0 or =90, light intensity is not very sensitive with respect to ( the rotation angle). The best sensitivity can be obtained by setting =45. Therefore, Both the analyzer and polarizer were set at the same angle but with opposite sign. When they are crossed, the intensity will have its smallest value approach to zero. And this value would be increased or decreased when the coils current was switched on and a longitudinal magnetic field was generated through the pipe.
Verdet Constant Measurement of Olive Oil for Magnetic Field Sensor 365 Table -1 The five laser source that are used to determined the verdet constant of olive oil. laser source laser power 405 nm diode laser 114mW 532 nm diode laser 135mW 632.8 nm He-Ne laser 5mW 650 nm diode laser 114mW 804.3 nm diode laser 36mW In the absence of the cuvette, the distribution of the magnetic flux density was determined through the hole in the center of the surface top of the pipe. By using the axial probe of digital gauss-meter (DGM-202), which can easily moved through the hole in universal clamp on a slide mount, the flux-density for different coil currents ( the maximum current under permanent use is 5A) was measured along the whole gap in steps of 3mm. After the flux density distribution had been measured, the 1.2 cm long cuvette was inserted in the hole. The laser light was passed through the cuvette and the laser output power had been measured, by using power meter, in the absent and present of the magnetic field and for each coil currents (from 1 A to 5A). when the current flowed through the coils, a magnetic field is produced, permeating the cuvette in the direction of irradiation. When the power supply was switched off (the magnetic field would be zero), there is no change in polarization of light, i.e. the rotation angle is zero. After the power supply had been switched on, the output power would be decreased due to polarization rotation that had been happened to the polarized light in the present of magnetic field according to Faraday effect. Each flux value has its output power and this power decreased as the magnetic field was increased. Five laser wavelength were used in this experiment ( 405nm, 532nm, 632.8 nm, 650nm, and 804.3nm ) and each output power had been measured for different flux- density value. The mean flux-density was calculated by taking the average value of the flux along the pipe hole as seen in Figure 3. The mean flux density as function of coil currents also determined (see Figure 3). After measuring the output power, for each flux value and laser wavelength, the rotation angle was calculated by using equation 10. Because of good output power for 532 nm, 650 nm and 804.3nm laser light it would be have observable angle rotation of light polarization (for virgin olive oil) for each flux density value is shown in Figure 4, 5 & 6. (a) (b) Figure 3. (a) the flux density distribution along the pipe hole for different coil currents (from 1A to 5A), (b) the mean flux density as function of coil currents.
IJAEEE, Volume2, Number 3 Ali Adnan Shakir et al. Figure 4. polarization rotation angle in radian as function of magnetic flux density for 532 nm laser wavelength for olive oil. Figure 5. polarization rotation angle in radian as function of magnetic flux density for 650 nm laser wavelength for olive oil. Figure 6. polarization rotation angle in radian as function of magnetic flux density for 804.3 nm laser wavelength for olive oil.
Verdet Constant Measurement of Olive Oil for Magnetic Field Sensor 367 By using equation 1 the verdet constant of olive oil can be obtained for each light wavelength as seen in Figure 7 and Table 2. Table -2 the verdet constant of virgin olive oil for different laser wavelength. Laser wavelength (nm) Verdet constant (rad/t.m) Verdet constant (deg/t.m) 405 15.3810 881.2664 532 0.1638 9.3850 632.8 33.3716 1912.0518 650 98.6808 5653.9934 804.3 1.0936 62.6587 Figure 7. verdet constant of virgin olive oil as function of light wavelength. IV.CONCLUSION From our result we can find that the verdet constant of olive oil is positive and the sign of rotation angle is positive also, i.e. the rotation is clockwise looking parallel to the vector of magnetic flux density for both direction of the propagation of the electromagnetic wave. It will be seen from Figure 7 the verdet constant of olive oil has its highest value at 650 nm laser wavelength while has small value at 532 nm and 804.3nm. when compared it with the verdet constant of terbium gallium garnet (TGG) crystal [6], we found that the olive oil`s verdet constant has close value with the TGG`s verdet constant at 650 nm as it is shown in Figure 8. And also we can find form Figure 8 that the verdet constant of olive oil is greater than the verdet constant of glass ( type : BK7 ) [5] the olive oil`s verdet constant is 22 greater than that for glass at 650nm laser wavelength. Therefore we can conclude that the olive oil has good verdet constant at 650nm wavelength and also it can be used as sensor for magnetic flux with good change in faraday rotation angle for each magnetic flux value above 12.55 mt as it is shown in Figure 5.
IJAEEE, Volume2, Number 3 Ali Adnan Shakir et al. Figure 8. Verdet constant as a function of the wavelength for virgin olive oil in comparison with TGG and BK7 glass. REFERENCE [1] R. K. Dani, Exploring Physical Properties of Nanoparticles for Biomedical Applications, Ph.D. thesis, Kansas State University, Manhattan, 2012. [2]A. Jain, J. Kumar, F. Zhou, and L. Li, A simple experiment for determining Verdet constants using alternating current magnetic fields, American Journal of Physics, vol. 67, no. 8, 1999, pp. 714-717. [3] K. Wick, Measurement of the Verdet Constant of Water, lab. manual for Methods of experimental Physics course, chapter 6, University of minisota, 2006. [4] F. A. Jenkins and H. E.White, Fundamentals of Optics, Fourth Edition, McGraw-Hill Science/Engineering/Math,2001. [5] H. Bach, N. Neuroth, The properties of Optical Glass, Second corrected printing, Springer, 1998. [6] A. B.Villaverde, D. A. Donatti, and D. G. Bozinis, Terbium gallium garnet Verdet constant measurements with pulsed magnetic field, J. Phys. C: Solid State Phys., vol. 11, 1978, pp. 495-498.