# Dating pulse translate

From t = −1.66 ns to t = 0 ns, total force (red solid in Fig.3a) exerted on cloak is positive, so the cloak accelerates along positive direction.As and in media are not parallel to each other (also for and ), contributions of current terms (the last two terms in Eq. On the other hand, a Gaussian EM pulse is employed, where σ = 0.07, and ω = 5 GHz indicate width and central frequency respectively (shown in Fig. Before calculation of Lorentz force, we firstly decompose time-varying incident field into a series of time-harmonic components by Fourier transformation, where A(ω) denotes weight of each time-harmonic wave and .Firstly, the monochromatic field (r,ω) in real space is obtained from (r′, ω) in virtual space by coordinate transformation (r′ → r). When the center of pulse locates at the first boundary, we let it be the time moment t = 0 ns.It is well known that optical media create artificial geometry for light, and curved geometry acts as an effective optical medium.This correspondence originates from the form invariance of Maxwell’s equations, which recently has spawned a booming field called ‘transformation optics’.

The force distribution of stage four (when pulse reaches the right boundary) is opposite to that of stage two, and the total force is along . Stage five begins when the pulse completely leaves compressor (shown in Fig. Note that we here utilize quasi-static assumption in calculating Lorentz force, because velocity of macroscopic transformation media is negligible compared with light speed.

Here we investigate responses of three transformation media under electromagnetic pulses, and find that pulse radiation can induce unbalanced net force on transformation media, which will cause translation and rotation of transformation media although their final momentum can still be zero.

Therefore, the transformation media do not necessarily stay the same after an electromagnetic wave passes through., in which optical media with specified constitutive parameters are used to mimic prescribed distorted EM space.

Finally, the spatio-temporal Lorentz force distribution can be calculated with Eq. The interaction process between EM pulse and compressor can be separated into five stages as in Fig. The first stage show zero velocity and acceleration (v = 0) for the compressor, because pulse does not reach the compressor in stage one (shown in Fig. At stage two, pulse touches the left boundary but not completely enter, part of the pulse inside compressor starts to induce electric and magnetic current. Therefore compressor is moving and accelerating along direction with (v 0).

Total force applied on the compressor is along direction and reaches maximum (Fig. The oscillation of Lorentz force in stage two in Fig. That is because the velocity of pulse inside compressor is smaller than that in background.