In this way, any back reflections that enter the second of the two linear polarizers (in the opposite direction) will be rotated "in the same angular direction" as it was during its initial traversing the of the rotator, because the magnetic field direction has reversed with respect to the beam. Therefore, it is common to place a Faraday isolator designed to rotate the beam 45 degrees, and have it surrounded by two linear polarizers whose polarization axis are 45 degrees apart. When traveling with the field, the polarization is rotated clockwise, and against the field, the polarization rotates counterclockwise. With this arrangement, it is easy to see that in one direction, the beam will traveling "with" the Magnetic field, and in the other direction, the beam will traveling "against" the field. These devices were not practical until advanced magnetic materials, such as Neodymium, were available in large sizes. The Faraday Rotator consists of establishing a large uniform magnetic field that surrounds the optical beam. In this notation, Lorentz reciprocity is equivalent to: A Faraday Rotation Isolator (FRI) is a device that utilizes the phenomenon of Faraday Rotation to ensure that optical signals are transmitted in one direction only. $$F(\theta) = \left(\begin,\,a_2,\perp$ are the two complex amplitudes of the two linear orthogonal polarisation states for ports 1 and 2, respectively, and the $b$ quantities are the analogous scattered complex amplitudes. A Faraday Rotator has the following one-pass $2\times2$ Jones matrix: FI-1060-3SC HP FARADAY ISOLATOR, Laser Optics - Faraday Isolator FI-1060-3 SC IL Fast and reliable. If, however, you seek the Faraday Rotator's rotation in one direction only, then you are in luck. Case 1: One-Directional Behaviour Only Important The unidirectional behaviour of a Faraday rotator is realisable with waveplates, the full bidirectional behaviour is not. So, depending on what exactly it is about the $45^o$ rotator you are trying to realise, your sought behaviour may or may not be realisable. So you positively cannot fully realise a Faraday rotator with waveplates. Then, the light passes through a transparent paramagnetic or ferrimagnetic material called a Faraday rotator, which rotates the polarization by 45 degrees. The vast majority of optical isolators are Faraday isolators, based on the Faraday effect, i.e., a rotation of the polarization direction caused by a magnetic field. One crucial difference between a waveplate and a Faraday rotator is that the former is reciprocal and the latter is not reciprocal. An isolator works by sending a light beam through a polarizer, which is angled to match polarization of the light.
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