Enhancement of the Uniformity and Rotation of Large Aperture, Permanent Magnet, Tunable Faraday Rotators

We present new methods for increasing the magnitude and uniformity of rotation of a Faraday rotator with a large clear aperture . We show theoretically and experimentally that the amount of rotation and the uniformity of rotation across the aperture can be simultaneously increased by introducing a small separation between adjacent, oppositely oriented magnets . Furthermore we show that the uniformity can be increased by displacing the rod of rotator glass longitudinally from the centred position . We have constructed such a device and obtained an isolation ratio of 45 dB at 1 .06 gm . 1 . Introduction Faraday rotators are important in many applications [1, 2] . It is often desirable that the clear aperture of the rotator be quite large [3] . In designing Faraday rotators with large apertures it is difficult to maintain the uniformity of the rotation across the entire aperture . In this study we demonstrate two methods to optimize the uniformity for fixed as well as tunable wavelength Faraday rotators, while keeping the aperture and magnet radii fixed . Previous studies have shown that the rotation produced by a rod of rotator glass inside a magnet is increased by the addition of two flanking magnets, each oriented to repel the central magnet [4-6] . Additionally it has been shown that making the central magnet longer than the glass rotator rod increases the uniformity of rotation across the aperture of the rotator [7] . In this paper we present new theoretical predictions and experimental data on the optimum magnet spacing and rod position . We propose two methods for increasing the uniformity of rotation across the aperture of the Faraday rotator; one of these methods increases the angle of rotation of the plane of polarization as well . 2. Theory The rotation angle of the polarization can be found by adding the products of the Verdet constant and the difference in scalar potential across the length of the § Present address : Department of Physics, United States Military Academy, West Point, NY 10996, USA . 0950-0340/95 $10 . 00 © 1995 Taylor & Francis Ltd . D ow nl oa de d by [ U ni ve rs ity o f R oc he st er ] at 1 3: 34 2 8 M ay 2 01 5 1138 G. L . Fischer et al . given rotator rod for each rod in the Faraday rotator [7] . The on-axis magnetic potential b, due to each pole face, can be calculated as follows . Each on-axis point z is equidistant from rings of points on the pole face, the centre of which is taken to be at the origin. If we integrate over all concentric rings of width dp with radii ranging from p = 0 to p = R, where R is the radius of the magnet, we obtain R O=M f 2np d 27EM[(z2 +R2)112z], P+z (1) )12 where M is the magnetization of the magnet, which is assumed uniform . The term (z 2 + R2)'12 can be expanded using the binomial series ; for z < R one obtains 22 1 (z 2 l i(-1) (Z2 2 (z2 + R2 ) h / 2 = R \ 1 + 2 ) 1" = R [1 + 2 \R21 + 2! AR2 / i 3 (2,2 3 + 3! \R2/ (2) At all points in space away from the pole faces the potential 0 must satisfy Laplace's equation V 2 45 = 0 and thus can be expressed in the form I'(r, 6) _ [Air' + Bir(1 + t >]Pl(cos 0) . r=o Here P,(cos 0) is the lth-order Legendre polynomial . To find the coefficients AI and Bl, we set 0 = 0 (so that r = z), in equation (2) and match equal powers of z . The non-physical situation of an infinite potential is automatically avoided since B, = 0 for the case r < R, and A, = 0 for the case r > R . The final results for the two cases are : I(r,0)=2zcMLR-rcosO+Ri P2( 1+2zco 11!(j 0(+1)!(-1)1(8)2(1+1), r<R,