7.5 Interaction of Photons and Spins
169
7.5 Interaction of Photons and Spins
Polarization rotation of a linearly polarized light takes place when it travels through a
magnetized medium (Faraday effect). This effect shows that a magnetically ordered
medium affects photons by changing its state of polarization. Now the question arises
whether the inverse phenomenon is also feasible where polarized photons can indeed
affect the magnetization?
Let us discuss the possibility of photon–spin direct interaction using energy
considerations. It is known that for an isotropic, non-absorbing, magnetically ordered
medium having static magnetization M(0) in a monochromatic light field E(ω), the
thermo dynamical potential can be written as
= α i jk E i (ω)E j (ω)
∗ M k (0)
(7.1)
α ijk is the magneto-optical susceptibility (see Refs. Beaurepaire et al. (1996) and
Kirilyuk et al. (2010) and Ref. Wolf et al. (2001) for details.)
Optical polarization can be expressed as
P(ω) = ∂∂ /∂E(ω)
∗
(7.2)
Equation (7.1) shows that P(ω) should have a contribution P (m) proportional to
the magnetization M, and hence,
P
(m)
i
= α i jk E j (ω)M k (0).
(7.3)
Equation (7.3) can be used to determine the rotation of plane of polarization given
by
F = α i jk M k (0)ω L / cn
(7.4)
where, c is the speed of light in vacuum, n is the refraction coefficient of the medium,
ω is the light frequency and L is the propagation distance.
Now from Eq. (7.1), one can also find that an electric field of light at frequency ω
will act on the magnetization as an effective magnetic field directed along the wave
vector of the light k and can be written as
H k = − ∂∂/∂ M k = α i jk E i (ω)E j (ω)
∗
(7.5)
The magneto-optical susceptibility α ijk is a fully antisymmetric tensor having a
single independent element α in an isotropic media. Therefore, Eq. (7.5) can be
rewritten as
H k = α
E i (ω) × E j (ω)
∗
(7.6)
169
7.5 Interaction of Photons and Spins
Polarization rotation of a linearly polarized light takes place when it travels through a
magnetized medium (Faraday effect). This effect shows that a magnetically ordered
medium affects photons by changing its state of polarization. Now the question arises
whether the inverse phenomenon is also feasible where polarized photons can indeed
affect the magnetization?
Let us discuss the possibility of photon–spin direct interaction using energy
considerations. It is known that for an isotropic, non-absorbing, magnetically ordered
medium having static magnetization M(0) in a monochromatic light field E(ω), the
thermo dynamical potential can be written as
= α i jk E i (ω)E j (ω)
∗ M k (0)
(7.1)
α ijk is the magneto-optical susceptibility (see Refs. Beaurepaire et al. (1996) and
Kirilyuk et al. (2010) and Ref. Wolf et al. (2001) for details.)
Optical polarization can be expressed as
P(ω) = ∂∂ /∂E(ω)
∗
(7.2)
Equation (7.1) shows that P(ω) should have a contribution P (m) proportional to
the magnetization M, and hence,
P
(m)
i
= α i jk E j (ω)M k (0).
(7.3)
Equation (7.3) can be used to determine the rotation of plane of polarization given
by
F = α i jk M k (0)ω L / cn
(7.4)
where, c is the speed of light in vacuum, n is the refraction coefficient of the medium,
ω is the light frequency and L is the propagation distance.
Now from Eq. (7.1), one can also find that an electric field of light at frequency ω
will act on the magnetization as an effective magnetic field directed along the wave
vector of the light k and can be written as
H k = − ∂∂/∂ M k = α i jk E i (ω)E j (ω)
∗
(7.5)
The magneto-optical susceptibility α ijk is a fully antisymmetric tensor having a
single independent element α in an isotropic media. Therefore, Eq. (7.5) can be
rewritten as
H k = α
E i (ω) × E j (ω)
∗
(7.6)