The Optical Metric was defined by German theoretical physicist Walter Gordon in 1923 to study the geometrical optics in curved space-time filled with moving dielectric materials. Let ua be the normalized (covariant) 4-velocity of the arbitrarily-moving dielectric medium filling the space-time, and assume that the fluid’s electromagnetic properties are linear, isotropic, transparent, nondispersive, and can be summarized by two scalar functions: a dielectric permittivity ε and a magnetic permeability μ. Then optical metric tensor is defined as
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| - The Optical Metric was defined by German theoretical physicist Walter Gordon in 1923 to study the geometrical optics in curved space-time filled with moving dielectric materials. Let ua be the normalized (covariant) 4-velocity of the arbitrarily-moving dielectric medium filling the space-time, and assume that the fluid’s electromagnetic properties are linear, isotropic, transparent, nondispersive, and can be summarized by two scalar functions: a dielectric permittivity ε and a magnetic permeability μ. Then optical metric tensor is defined as (en)
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| - The Optical Metric was defined by German theoretical physicist Walter Gordon in 1923 to study the geometrical optics in curved space-time filled with moving dielectric materials. Let ua be the normalized (covariant) 4-velocity of the arbitrarily-moving dielectric medium filling the space-time, and assume that the fluid’s electromagnetic properties are linear, isotropic, transparent, nondispersive, and can be summarized by two scalar functions: a dielectric permittivity ε and a magnetic permeability μ. Then optical metric tensor is defined as where is the physical metric tensor. The sign of is determined by the metric signature convention used: is replaced with a plus sign (+) for a metric signature (-,+,+,+), while a minus sign (-) is chosen for (+,-,-,-). The inverse (contravariant) optical metric tensor is where ua is the contravariant 4-velocity of the moving fluid.Note that the traditional refractive index is defined as n(x) ≡ √εμ . (en)
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