Canonical Quantization Of Electromagnetic Field Research Articles

Scattering of the quantized electromagnetic waves from a bi-anisotropic absorbing magneto-dielectric slab

A canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is provided. The quantized Maxwell’s equations in the presence of the slab are exactly solved and the time-space dependence of the quantized electric and magnetic fields are obtained. The Fock space of the total system is introduced. The scattering matrix of the bi-anisotropic magneto-dielectric slab is obtained in terms of the susceptibility tensors of the slab. The scattering matrix relates the annihilation operators of the outgoing quantized electromagnetic waves from the slab to the annihilation operators of the incoming quantized electromagnetic waves to the slab. The Fresnel’s coefficients of the bi-anisotropic magneto-dielectric slab are obtained in terms of the susceptibility tensors of the slab. The Fresnel’s coefficients relate the powers radiated by the outgoing quantized electromagnetic waves from the slab to the powers radiated by the incoming quantized electromagnetic waves to the slab. The radiated powers by the outgoing quantized electromagnetic waves are calculated in the special cases that the slab is in the thermal state and the incoming quantized electromagnetic waves to the slab are in the vacuum state and the coherent state.

Quantum vacuum torque on a bi-anisotropic absorbing magneto-dielectric cylindrical shell co-axis with a perfectly conductor cylindrical shell

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric cylindrical shell is provided. The mode expansions of the dynamical quantum fields, contained in the theory, is achieved and the ladder operators of the system are introduced. Using the Frobenius’s series technique, the Maxwell’s equations in the presence of the bi-anisotropic absorbing magneto-dielectric cylindrical shell are solved and the space–time dependence of the quantized electromagnetic field is obtained. Applying the conservation principle of the angular momentum, the net quantum vacuum torque exerted on the bi-anisotropic absorbing magneto-dielectric cylindrical shell is calculated. The net quantum vacuum torque exerted on the cylindrical shell is calculated in the vacuum state and the thermal state of the system. The quantum vacuum torque on the cylindrical shell identically vanishes when the bi-anisotropic absorbing magneto-dielectric cylindrical shell is converted to an isotropic one.

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers–Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Canonical Quantization of Electromagnetic Field in the Presence of Nonlinear Anisotropic Magnetodielectric Medium with Spatial-Temporal Dispersion

Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.

Canonical quantization of electromagnetic field in the presence of absorbing bi-anisotropic multilayer magnetodielectric media

A bi-anisotropic magnetodielectric medium is modeled by two independent set of three dimensional harmonic oscillators .A fully canonical quantization of electromagnetic field is demonstrated in the presence of a bi-anisotropic magnetodielectric medium. The electric and magnetic polarization fields of the medium are obtained in terms of the dynamical variable modeling the medium. The Heisenberg equations of the system are solved for a multilayer bi-anisotropic magnetodielectric medium.

Canonical quantization of electromagnetic field in an anisotropic polarizable and magnetizable medium

A fully canonical quantization of electromagnetic field is introduced in the presence of an anisotropic polarizable and magnetizable medium. Two tensor fields which couple the electromagnetic field with the medium and have an important role in this quantization method are introduced. The electric and magnetic polarization fields of the medium naturally are concluded in terms of the coupling tensors and the dynamical variables modeling the magnetodielectric medium. In Heisenberg picture, the constitutive equations of the medium together with the Maxwell laws are obtained as the equations of motion of the total system and the susceptibility tensors of the medium are calculated in terms of the coupling tensors. Following a perturbation method the Green function related to the total system is found and the time dependence of electromagnetic field operators is derived.