Gravitational radiation admits polarization: general relativity has two transverse tensor modes, plus polarization and cross polarization, whose relative amplitudes and phase give linear, elliptical or circular gravitational-wave polarization. Their axes transform through twice a rotation of the transverse coordinate frame, unlike the vector polarization of electromagnetic radiation. Measuring these modes is physically plausible with several differently oriented detectors; a single detector generally measures only one projected combination.
Gravitational waves can exhibit interference. In linearized gravity, overlapping strains add, so coherent contributions can enhance or cancel the measured response. Independent astrophysical sources generally have unrelated phases and average to a stochastic background rather than stable fringes. More plausible coherent paths arise when gravitational lensing sends different parts of the same signal to the detector with different delays; fringes require sufficient overlap and coherence. The relevant quadratic radiative energy flux contains the cross terms even though the leading wave equation is linear.
In a local inertial frame in vacuum, gravitational waves travel at in general relativity; there is no ordinary material index of refraction analogous to a transparent dielectric. Ordinary matter couples so weakly that laboratory prisms for gravitational waves are implausible. Propagation through a varying background gravitational field nevertheless changes ray directions and travel times, giving gravitational lensing and Shapiro time delay. In weak static coordinates , the null condition gives an effective coordinate index of refraction . This useful description depends on coordinates and does not change the local propagation speed. Thus astronomical gravitational refraction is plausible, while a substantial everyday material effect is not.
Gravitational waves also exhibit diffraction: the geometrical optics ray description fails when a propagation structure or lens delay is not large compared with the wave's wavelength or period. For a compact lens of mass , a useful dimensionless parameter is ; of order one signals potentially appreciable wave effects, with cosmological lens redshift supplying an additional factor when needed. Astrophysical gravitational lensing can therefore produce diffraction and frequency-dependent amplification. Ordinary objects are poor opaque screens for gravitational waves, so everyday slit-and-screen demonstrations are implausible despite the large wavelengths, which are about km at Hz.
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