3.6 Phase modulation through a moving mirror

Several optical components can modulate transmitted or reflected light fields. In this section we discuss in detail the example of phase modulation by a moving mirror. Mirror motion does not change the transmitted light; however, the phase of the reflected light will be changed as shown in Equation (11View Image).
View Image

Figure 19: A sinusoidal signal with amplitude as frequency ωs and phase offset φs is applied to a mirror position, or to be precise, to the mirror tuning. The equation given for the tuning ϕ assumes that ωs∕ω0 ≪ 1, see Section 2.5.

We assume sinusoidal change of the mirror’s tuning as shown in Figure 19View Image. The position modulation is given as xm = ascos(ωst + φs ), and thus the reflected field at the mirror becomes (assuming a4 = 0)

( ) a3 = ra1 exp(− i2ϕ0 )exp (i2kxm ) ≈ ra1exp (− i2ϕ0 )exp i2k0ascos(ωst + φs) , (62 )
setting m = 2k0as. This can be expressed as
( ( ) ( ) ) a3 = ra1 exp(− i2ϕ0 ) 1 + im-exp − i(ωst + φs) + im-exp i(ωst + φs) ( 2 ( 2) = ra1 exp(− i2ϕ0 ) 1 + m-exp − i(ωst + φs − π ∕2) (63 ) ( 2 )) + m2-exp i(ωst + φs + π ∕2) .

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