In nonlinear material light can be bent, what about the vacuum. Can it be bent by a strong Electric field or Magnetic Field in specific polarization (elliptical)?
If we derive a sinusoidal wave, what is the meaning of a third-order derivative? The first is velocity, second is acceleration.
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Light travel as electromagnetic (EM) waves and electromagnetic waves do not exert forces on each other, because there is no electric charge in an EM wave itself. Alternately, you can visualize light as photons when they interact with matter and a photon itself do not interact with another photon since photons are in the category of bosons, which have no net charge. Therefore, bending of light in vacuum due to an externally applied electric or magnetic field is highly unlikely to happen irrespective of the polarization and power. Also, note that, light in any other medium can bend depending on various properties of that medium.
As Kapila D. Dissanayaka said light consist of particles called as photon which have no charge on them, which mean you can't bend light via electromagnetic fields.
Although a magnetic field doesn't affect the photons of light directly, a magnet can distort the medium through which light passes and thereby “bend” the light rays. Light travels through space-time along a geodesic – the shortest possible path between two points on a curved surface.
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Light does bend in vacuum. This is the case when starlight travels in vacuum passing near the Sun where the geometry of space and time is curved due to the Sun's mass. The angle of deflection due to that light bending is calculated in Chapter 10 in the book "General Relativity:An Introduction for Physicists" by Hobson and Lasenby,where the Sun is assumed to be a spherically symmetric massive object surrounded by vacuum,resulting in a vacuum solution to Einstein's field equations.
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