Reversed Doppler Effect in Photonic Crystals

Nonrelativistic reversed Doppler shifts have never been observed in nature and have only been speculated to occur in pathological systems with simultaneously negative effective permittivity and permeability. This Letter presents a different, new physical phenomenon that leads to a nonrelativistic reversed Doppler shift in light. It arises when light is reflected from a moving shock wave propagating through a photonic crystal. In addition to reflection of a single frequency, multiple discrete reflected frequencies or a 10 GHz periodic modulation can also be observed when a single carrier frequency of wavelength $1\mu \mathrm{m}$ is incident.

Figure 1

Dielectric as a function of position for three equally spaced instants in time, $t_1<t_2<t_3$. The shock front moves at a constant velocity, and the material behind the shock moves at a smaller constant velocity. For this model, the dielectric ranges from 2.1 to 11.0 before the shock front and 3.7 to 89.4 behind the shock front. These large values are for computational tractability only. All the results of this work can be observed with physically accessible values as discussed in the text.

Figure 2

Schematic of a shock wave moving to the right that compresses the lattice but lowers the band gap frequency due to a strain dependence of the dielectric. Light incident from the right reflects from the post-shock band gap with a reversed Doppler shift.

Figure 3

Reverse Doppler effect. Two moments in time during a computer simulation of a pulse of light reflecting from a time-dependent dielectric similar to Fig. 1. The shock front is moving to the right and its location is approximately indicated by the dotted green line. Light incident from the right receives a negative, i.e., reversed, Doppler shift upon reflection from the shock wave. Time is given in units of $a/c$.

Figure 4

Computer simulation of a pulse of light reflecting from a dielectric similar to Fig. 1, but with a sharper shock front than in Fig. 3 (by a factor of 20). The shock front is moving to the right and its location is approximately indicated by the dotted green line. Light incident from the right is reflected in multiple equally spaced frequencies due to the relatively sharp shock front.