Fourier Transforms Homework: Solving for Pulse Amplitude, Intensity & FWHM

[hasan_researc]

Homework Statement

A single optical pulse has an amplitude described by f(t) = Ae^-a*mod(t),

where A and a are constants.

NB: a*mod(t) means the modulus of t multiplied by a.

(a) Sketch the form of the pulse amplitude in time.

(b) Find an expression for the intensity of the pulse I(t).

(c) Find an expression for the FWHM width of the intensity of the pulse.

Homework Equations

The Attempt at a Solution

1) What is an optical pulse?

2) The amplitude is a function of time!?? As far as I am aware, the amplitude of any function/pulse is the maximum value the function can take over a period. Does this mean that the maximum value of the function over each period is falling? But then it should be a constant over each period, should it not?

Anyway, the first part is easy! (I hope) The function is an exponential on each side of the t-axis. The function falls off to 0 (from above) as t goes to positive or negative infinity. The maximum value A of the function is at t = 0. But should the graph not abruptly change its slope from positive to negative when passing through t = 0.

The intensity of the pulse is the square of the modulus of f(t). (Am I right?) So,
I(t) = A²e^-2a*mod(t). What do you think?

I have no idea how to go about the third one.

 

[Rajini]

Hi,
Optical pulse: it is just light pulse or it can also be some electromagnetic pulse.
Modulus of t means |t|, i.e. a positive value.
(a): I guess you need to draw the function.
(b): You need to find the expression I(t). So no need the calculate the maximum amplitude (or the value of amplitude).
Clue: you mentioned 'Fourier transforms' in subject. Got idea?
(c) FWHM (= full width at half maximum) what is it ? If you are able to solve (b) then (c) is easy.
cheers.