The Faraday Effect and Inversion Symmetries

Abstract

Articles you may be interested inExperimental evidence of the inverse Faraday effect in laser-plasma interaction and a miniature magnetic bottle AIP Conf.

Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal

“…Contrary to the well-discussed PT symmetric models constructed by a periodic gain-loss medium, [12][13][14] this 2D MOPC separately breaks both P and T symmetries but obeys PT symmetry, which comes from the imaginary off-diagonal elements in its permeability matrix. We call this periodic microstructure a PT EM diode, which means that the transmission is unidirectional.…”

“…Analogous to the well-discussed PT symmetric systems, which require the real part of the potential to be an even function of position and the imaginary part to be odd, 12,13 in this case the real part of perturbation V with a pair of counterpropagating EM waves satisfies the even function, while the imaginary part with opposite magnetic fields or with a pair of mirror-symmetric (π x operation) incident EM waves is an odd function. [12][13][14] In other words, in this NRPC there are two cases for PT symmetry: (i) a pair of counterincident EM waves with opposite external magnetic fields; (ii) a pair of symmetric incident EM waves relative to the y axis (σ + π x = π y ) operation, which satisfies the even function real part of the potential and the odd imaginary part. Under this condition, the transmissions would not be one-way because the eigenvalues of Eq.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] For example, in optics, the one-way edge mode, as an optical counterpart to the quantum Hall effect, was reported in magneto-optical photonic crystals (MOPC's) with periodic and parity (P) symmetries 1-3 but broken time-reversal (T ) symmetry. [4][5][6][7][8][9] In condensed-matter physics, a single surface Dirac cone, due to spin-orbit coupling, results in a topological insulator with certain topological symmetry and unbroken T symmetry.…”

“…10,11 Recently, a new class of optical models constructed by gain and loss materials, which have non-Hermitian Hamiltonians with both broken P and T symmetries but which obey PT symmetry, was demonstrated with some intriguing light-propagation properties. [12][13][14] In all of these cases, the existence of off-diagonal components in the Hamiltonian matrix is an essential and common mathematic structure in determining the unpaired eigenvalues. In the context of the MOPC, it has imaginary off-diagonal elements in its permeability matrix, thus it could be considered to be an excellent candidate to explore the anomalous behaviors stemming from broken symmetries in optics.…”

On the origin independence of the Verdet tensor†

“…The rotation angle, φ, is proportional to the modulus of the magnetic flux density B, the length l of the material in the field and its Verdet constant, v, named after the French physicist Marcel Verdet (1824-66) [8][9][10][11], who used the name 'pouvoir rotatoire magnetique' for the first time in 1858 [10,12]. The sense of rotation with respect to the magnetic field's direction does not depend on the direction of light propagation, due to conservation of parity [13,14]. Time reversal, implying inversion of all the motions, leads exactly to the same phenomenology observed from the opposite direction, therefore the Faraday experiment is also characterised by reversality [13,14].…”