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Научни трудове на Съюза на учените в България-Пловдив. Серия В. Техника и технологии, естествен ии хуманитарни науки, том XVI., Съюз на учените сесия "Международна конференция на младите учени" 13-15 юни 2013. Scientific research of the Union of Scientists in Bulgaria-Plovdiv, series C. Natural Sciences and Humanities, Vol. XVI, ISSN 1311-9192, Union of Scientists, International Conference of Young Scientists, 13 - 15 June 2013, Plovdiv.
Student laboratory experiment on the Faraday effect
Tano Terziyski, Todorka L. Dimitrova, George Ivanov, George Vlahov University of Plovdiv "Paissi Hilendarski", Tzar Assen Str. 24, BG-4000
Plovdiv, Bulgaria e-mail: [email protected]
Abstract
Magneto-optics is a powerful tool in modem science allowing to penetrate in the matter at atomic scale. It is vastly used in high-tech applications such as memory devices, switches, modulators and waveguides. Magneto-optics started with Faraday's discovery of polarization rotation by a magnetic field. The simplicity of the Faraday effect makes it a suitable topic for introducing Bachelor students to the interaction of light, matter and magnetic fields. In this work we report on a student laboratory experiment for investigating the Faraday effect in water: the Verdet constant and its dispersion is inferred from measurements of the magnetic field dependence of the light polarization rotation at different wavelengths.
Introduction
The electromagnetic theory of light can explain most of its manifestations like propagation through space and matter. However, there are a group of specific optical phenomena related to the interaction between light and matter when the matter is subjected to a strong electric or magnetic field [1]. They are classed as magneto-optics experiments (when magnetic field is applied) and electro-optics experiments (when electric field is applied). The explanation of this class of phenomena is based on the Lorenz theory that takes in account the light emitted by an atom is due to energy level transition of electrons which itself are charged particles and, of course, their motion can be modified by an external magnetic or electric field.
Magneto-optics effects are widely used in the modern technologies such as: magneto-optical current transducers, magneto-optical transducers of information-measuring systems, magneto-optical disks, optical isolators, optical sensors, optical keys, observation technique, material science etc.
Usually some short introduction in the magneto-optics is given in the university bachelor course of optics and deeper knowledge is offered in the frame of specialized courses [2]. In this work is presented a simple laboratory exercise for Bachelors based on the linear Faraday effect.
2. Theory
The wide meaning of the magneto-optics effects includes any change of the optical response induced by magnetization. These phenomena are based on the Zeeman effect that is exhibiting in splitting a spectral line into several components in the presence of a static magnetic field. In general, this induces changes of intensity or polarization or double refraction as it is in the particular cases of the linear Faraday effect, the magneto-optics effect of Kerr, the Cotton-Mouton effect or the Voigt effect.
The Faraday effect is discovered in 1845 by Michael Faraday. It consists of rotation or circular dichroism of the plane of polarization of linear polarized light when propagating in a not optically
active medium (solid, liquid or gase) along the direction of the applied external magnetic field. According to the classical theory of the Zeeman effect, when entering in the medium, the linear polarized wave is separated in two - one left (LCP) and one right circular polarized (RCP) waves. If the medium has differential absorption of the LCP and RCP light, magnetic circular dichroism (Faraday Ellipticity) is observed.
The light electric field causes circle motion of the medium electrons, hence inducing their own magnetic field, which, however, will have opposite direction for LCP and for RCP light. In consecunce, the velocity of one of the beams will be slowed down more than the other, and this will result in a phase difference between the LCP and the RCP waves. The superposition of the two waves gives again linearly polarized light, but with a rotated plane of polarization. The rotation angle 6 is proportional to the magnetic field B , to the geometric length l which the light transmitted through the medium and the properties of the medium itself expressed by the Verdet constant V :
6 = VBl (1)
In comparison with the natural optical rotation the Faraday rotation is nonreciprocal what means that if the light is transmitted forth and back through the medium, the plane of polarization is rotating farther with each traversal. In this case the direction of the rotation is not connected with the anisotropy of the molecules at all, but it is related to the direction of the magnetic field. As the index of refraction n depends on the wavelength X, according to the microscopic theory of the electron [3], the Verdet constant will also undergo dispersion:
V (X) = -Vb
X dn c dX'
(2)
3. Student laboratory experiment on the Faraday effect a) Experimental setup
In Fig. 1 is shown sketch of the experimental setup. Photo of the setup is shown at Fig. 2a and 2b.
Fig. 1: Experimental setup
The magnetic field is created by a solenoid with total length of 80 cm and approximately 14'000 windings. The current is delivered by a DC power supply and can be varied from 0 to 4 A by step of 0,25 A. The examined liquid is filled in a stainless steel tube closed by optical windows and inserted coaxially inside of the solenoid. The optical system consists of: light source, linear polarizer, set of changeable colour filters with transmission band of AX «10nm, quarter wave plate, examined liquid, and analyzer, as well eyepiece for visible observation or, alternatively, photodiode and voltmeter for quantitative measurements. Different light sources are used according to the assignments - sodium lamp, green, red and blue lasers and a discharge lamp.
Fig. 2: Photo of the experimental setup: left — with calibration sodium lamp, right — with a laser.
q = V' B'l = V' l^-f = VM0INeff (3)
Neff.=—~ (4)
Calibration of the device
The winding of the solenoid are winded in multiple layers with the aim to increase the magnetic field and in the same time to avoid the use of very high electric current. To avoid the the calculation of the magnetic field the calibration of the device is made by measuring the rotation angle of water for sodium line (X = 589,2nm ) for which the Verdet constant is well know from
the literature (V' = 2,1.102 deg/ m.T ). For this measurement is followed the method of Loran,
where quarter wave plate is inserted after the polarizer. The rotating angle is equal to: N_f
l
Where Nef is the effective number of windings when considering the solenoid to be enough long (B = jU0INef ). This approximation can be useful to neglect the non homogeneity of the solenoid. From (2) one obtains: 1
V~Vo I
For example, for I = 1A the rotation angle is measured to be q' = 2,4 deg and, hence, the
effective number of the windings is calculated to be . Nef = 9'000 The average magnetic field in
this case is 0,14T. For any other wavelength the Verdet constant may be calculated by the formula:
V (X) = (5)
^0 INeff.
Experimental results
We are not going to present here full methodic description of the laboratory exercise. We will only show some experimental results to demonstrate that the device may be used as a student laboratory experiment.
There are two main assignments that the students should perform. First of them is to verify the Faraday law (eq. 1). Second is to study the Verdet constant dispersion.
The calibration of the device may be done either by using directly formula (4) when performing multiple measurements or from the clop the calibration curve 0' = f (I) for sodium line, shown in Fig. 1.
Fig. 1 Dependence of the rotation angle from the magnetic field (here the current of the solenoid).
From Fig. 1 can be obcerved also the linear dipendance of the rotation agle from the current (resp. form the magnetic field) for different wavelenghts. The calculation of the Verdet constant may be also done in two ways: by measuring the rotation angle at a fix magnetic field for different wavelents or, by calculating the relative slope from Fig. 1. In bouth cases the graphic V(A) must be plotted.
Fig. 2 Temperature dependence of the rotation angle at 1,5 A.
Despite of the encouraging results, at higher current the precision of the results is worsted due to heating of the water by the Joule heating. In Fig. 2 is shown an example of the temperature dependence of the rotation angle for the sodium line at 1,5A. On the other side, this fact may be
used for studying of the temperature dependence of the Verdet constant. The above results are obtained by keeping the price of the device low. However, the need of using more precise method is obvious.
4. Summary
In this work a student laboratory experiment on the Faraday effect is presented. The preliminary experimental results show she linear dependence of the rotation angle by the magnetic field and the dispersion of the Verdet constant. The relatively high electric current in the coil causes temperature drift and this influence the measurements. The experiment should be improved by using the more sensitive ±45° method which allows applying less small electric current.
Acknowledgements
The authors acknowledge financial support from the Scopes program (grant no. IZ73Z0-127942-1) of the Swiss National Science Foundation.
The authors kindly thank Prof. A. Weis from the University of Fribourg, Switzerland, for his competent advices.
References
Francis A. Jenkins, Harvey E. White, "Fundamentals of optics" McGRAW-HILL international Book Company, (1981).
T. Terziyski, T. Dimitrova, G. Ivanov - Multimedia demonstration of the effect of Faraday and the dispersion of the Verdet constant - Proc. Intern. Symposium "LTL'2005", (2005), 261-264. Andrey Apostolov, "Physics of the condense matter", University of Sofia "St. Kl. Ohrisdki", 2003.
