1. Space-time analogy
True for all pulse/beam shapes
Paraxial approximation (use of Fourier transforms)
Gaussian beams (q parameters and matrices)
Geometric optics??
a dimensionless
a dimension of 1/v

2. SPACE
TIME
Fourier transform in time
Fourier transform in space

3. e(-r/M) e(r) Space-time analogy Geometric optics d1 d2 SPACE
DIFFRACTION
DIFFRACTION
By matrices:

4. e(--t/M) e(t) Space-time analogy Geometric optics d1 d2 TIME
DISPERSION
DISPERSION
By matrices:
y length in time T
= chirp imposed on the pulse

5. e(-r/M) e(r) Space-time analogy Gaussian optics d1 d2 SPACE
DIFFRACTION
DIFFRACTION
By matrices:

6. e(--t/M) e(t) Space-time analogy Gaussian optics d1 d2 TIME
DISPERSION
DISPERSION
By matrices:
= chirp imposed on the pulse
Find the image plane:

7. WHAT IS THE MEANING k”d? Lf
Fiber L
Prism Lg b
Gratings d
Fabry-Perot at resonance

8. e(-r/M) e(r) e(t) e1(t) TIME MICROSCOPE d1 d2 d2 d1 TIME LENS
DIFFRACTION
DIFFRACTION
e(t) d2 d1
DISPERSION
e1(t)
TIME
LENS
DISPERSION

9. e1(t) e1(t)eiat ep(t) = eeiat w1 w1 + wp wp TIME LENS DISPERSED INPUT
OUTPUT
w1 + wp
e1(t)eiat 2 wp
CHIRPED PUMP
ep(t) = eeiat 2

19. FEMTOSECOND COMMUNICATION:
Space-time analogy – application to fs communication
FEMTOSECOND COMMUNICATION:
Commercial fs lasers – a pulse duration of 50 fs.
(20 THz)
One can easily “squeeze” a 12 bit word in 1 ps

21. Propagation of time- multiplexed signals Time compressor Time
EMITTER
RECEIVER
1 ns
1 ns
1 ns
1 ns
Time
compressor
Time
stretcher
time
time, ps 4 3 2 1

24. Time “telescope” (reducing)
Time “microscope” (expanding)

28. e e e e e e e e e e e (a) (a) (b) (b) x x d d d d image image object1 1 2 2
image
image
object
object e ( r ) e e e ( -
r/M ) e e ( ( ) ) ( ( - -
r/M
r/M ) ) r r
(a)
(a)
diffraction
diffraction
diffraction
diffraction e ( t ) e e ( ( t t ) ) e ( -
t/M ) e ( -
t/M )
TIME
TIME
LENS
LENS
(b)
(b)
dispersion
dispersion
dispersion
dispersion