![]() ![]() One can also use the movie monitor to observe the change in polarization as a function of time. As a result, the reflected fields will be completely polarized in the z direction (the figure below shows the Ex and Ez components of the reflected light): The reflected light will continue to change in the rotator, undergoing another angle of rotation of 45 degrees when it exits the rotator at the incident surface. In isolator.fsp,a mirror is placed at the point where the angle of rotation is 45 degrees. In the previous section, we used an incident plane wave polarized in the x direction, and found that a distance of ~11.94um will result in an angle of rotation of 45 degrees (see faraday.lsf). In this section, we will extend the Faraday effect described in the previous section to model the optical isolator. Note that the "Duplicate" function in the Visualizer makes it very easy to plot different field components in the same figure.įor an optical isolator (which is typically composed of a Faraday rotator and two polarizers as shown below), the polarizer in front of the Faraday rotator will not only polarize the incident light in the x direction, it will also function as a filter for the reflected light (with the opposite polarization as the incident light). ![]() We can also plot Ex and Ez as a function of y in the Visualizer to observe this change. The script faraday_plot.lsf plots the "TE fraction vs y" in the rotator: Here, we can define the polarization, at each point along y, by the TE fraction: In faraday.fsp, we start with a plane wave polarized in the x direction, and use a linear y DFT monitor to track the change in polarization of the light as it propagates through the Faraday rotator. The script faraday.lsf defines U and sets it as the transform matrix. $$U = \frac\right)$$Īnd use a Matrix Transform Grid Attribute to apply this rotation around the y axis. To do this, we define the following unitary matrix: Specifically, we have to rotate the reference frame such that it converts the field components from Cartesian coordinates into coordinates that represent circular polarization. To model this effect in FDTD, we will use an anisotropic material combined with a grid attribute object, which allows us to apply an arbitrary unitary matrix necessary for inducing the correct rotation. Where V is the Verdet constant, and B is the static magnetic flux density. is used in optical isolators that are integral part of any photonic circuit. The resulting angle of rotation β, is defined by Faraday Rotation (FR) is a classic experiment that brings together elements. The result of this is a rotation of the plane of polarization, which is linearly proportional to the component of the magnetic field in the direction of propagation. The Faraday effect is a magneto-optical effect where an external magnetic field leads to circular birefringence, and the left and right circularly polarized waves propagate at different velocities. We will also show how this effect can be utilized to create an optical isolator, allowing for transmission of light in only one direction (and preventing unwanted feedback). The proposed cryptographic system is faster than most of known public key cryptosystems, since it requires a small number of multiplications and additions, and does not require exponentiations for its implementation.In this example, we will model a Faraday rotator, a device which rotates the polarization of the incident light via the magneto-optical Faraday effect. Several numeric illustrations explain step-by-step how to precondition a plaintext, how to select secret control parameters, how to ensure feasibility of all private keys and how to avoid ambiguity in the process of information recovery. Also the proper selection of cryptographic system parameters is described. International Journal of Communications, Network and System Sciences,ĪBSTRACT: In this paper an encryption-decryption algorithm based on two moduli is described: one in the real field of integers and another in the field of complex integers. 714-716.ĭouble-Moduli Gaussian Encryption/Decryption with Primary Residues and Secret ControlsĪmbiguity-free information recovery, complex modulus, cryptosystem design, cycling identity, information hiding, plaintext preconditioning, primary residue, public-key cryptography, secret controls, threshold parameters Toom, “The Complexity of a Scheme of Functional Elements Realizing the Multiplication of Integers,” Soviet Mathematics Doklady, No. ![]()
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