Propagation in the time domain PHASE MODULATION n(t) or k(t) E(t) = (t) e i t-kz (t,0) e ik(t)d (t,0)
Chirped pulse LEADS TO : Propagation through a medium with time dependent index of refraction Pulse compression: propagation through wavelength dependent index
DISPERSION n( ) or k( ) ( ) ( ) e -ik z Propagation in the frequency domain Retarded frame and taking the inverse FT:
PHASE MODULATION DISPERSION
Application to a Gaussian pulse Inverse F.T.
Wigner function: What is the point? Uncertainty relation: Equality only holds for a Gaussian pulse (beam) shape free of any phase modulation, which implies that the Wigner distribution for a Gaussian shape occupies the smallest area in the time/frequency plane. Only holds for the pulse widths defined as the mean square deviation
APPLICATION OF SPACE-TIME ANALOGY TO TIME MULTIPLEXING
C H A F A X... X Y Z... C H A F A X... X Y Z... Electronics: 1ns, 12 bit Optical, 1 ps, 12 bit TIME MULTIPLEXING TIME DE-MULTIPLEXING PROPAGATION EMISSIONEMISSION RECEPTIONRECEPTION
C5FXC5FX C 5 F X PROPAGATIONPROPAGATION C 5 F X C5FXC5FX
White light interferometry
+ 500 m glass
ADDING FILTERS
Normalized Intensity (a.u.) Relative Delay ( m) Relative Delay (fs) 2 mm of glass
Fourier transform