ch 7 superposition of quasi parallel PW

Question 1

Dispersion

Answer 1

diff freq components of a waveform exp diff phase velocities

this causes the wavefrom to undergo distortion as it propogates

Question 2

diff between narrowband and packets and broadband pulses wrt dispersion

Answer 2

Narrowband packets (narrow range of freq -> long duration):
- maintain their shape with some spreading while propagating at Vg

Broadband pulses (wide range of frequemcies and possibly of short duration) 
-distort secerely while propgating in materials

Question 3

what is superluminal Vg

Answer 3

Vgroup can become superluminal when significant absorption or ampligication of light pulse occurs
Causes the pulse to appear to move face through a reshaping effect
fix this with group delay theory
since E lost at the back of pulse and “added: to an already present forward portion st average “appears” to advance superliminallu
no info moves faster than c irl

Question 4

WHat assumptions to we make to simplyfy inital calc here

Answer 4

Km vectors are real - i.e. no absorption
PW components travel roughly // -> km are are // tp each of their E’s
time average Poynting vector computed

Question 5

Whats different here even though we get the same itnesnity expr as chapter 2 for the PW

Answer 5

In chp 2 we had only a single OW

Here we have many plane waves
we automatically time avergaed over rapid oscils and only retauned Vg slowly varying time dependent envelope

Question 6

=0 when

Answer 6

For standing waves no net flow of Energy
but still the usual intensity formula applies (here it already time avergaed)
Intensity only specifices whether atoms will exp an oscillating E filed, intensity does not specify the new flow of energycarried bya light field

Question 7

Vg is the

Answer 7

envelope velcoty - intensity detected is more associated with thsi VG, it describes the overall propagation fo the waveform
vp is the belocity of a SINGLE PW

Question 8

Spectrum

Answer 8

E(r,w)
units: field per freq
keeps track of the amplitude and phase of each PW that makes up the packet

E(r,t) is IFT of spectrum

Question 9

Which direction is t,w ft

Answer 9

f(t) —–>FT—–> f(w)

Question 10

What do we see from sepctrometer

Answer 10

Power spectrum I(r,w) not the FT of I(r,t) btw

Question 11

Purpose of IFT

Answer 11

f(W) -> f(t)
summming together many PW of diff freq to get a wave packet in time

obeys dw dt relation