Fresnel and Fraunhofer diffraction

[Pages:36]Diffraction

? Interference with more than 2 beams

? 3, 4, 5 beams ? Large number of beams

? Diffraction gratings

? Equation ? Uses

? Diffraction by an aperture

? Huygen's principle again, Fresnel zones, Arago's spot ? Qualitative effects, changes with propagation distance ? Fresnel number again ? Imaging with an optical system, near and far field ? Fraunhofer diffraction of slits and circular apertures ? Resolution of optical systems

? Diffraction of a laser beam

LASERS 51

April 03

source

Interference from multiple apertures

L

Bright fringes when OPD=n

40

d OPD

two slits

Intensity

x

x

=

nL

d

position on screen

screen Complete destructive interference halfway between

OPD 1 OPD 2

OPD 1=n, OPD 2=2n all three wave4s0 interfere constructively

d

Intensity

source

LASERS 51

three

equally spaced

slits

screen

position on screen

OPD 2=n, n odd outer slits constructively interfere middle slit gives secondary maxima

April 03

Diffraction from multiple apertures

? Fringes not sinusoidal for more than two slits

2 slits

? Main peak gets narrower

? Center location obeys same equation

3 slits

? Secondary maxima appear between main peaks

4 slits

? The more slits, the more secondary maxima

5 slits

? The more slits, the weaker the secondary maxima become

? Diffraction grating ? many slits, very narrow spacing

? Main peaks become narrow and widely spaced

? Secondary peaks are too small to observe

LASERS 51

April 03

Reflection and transmission gratings

? Transmission grating ? many closely spaced slits ? Reflection grating ? many closely spaced reflecting regions

Input wave

opaque transmitting opening

Input Huygens wave

wavelets

screen

path length to observation point

wavelets

screen

path length to observation point

Transmission grating

absorbing reflecting

Reflection grating

LASERS 51

April 03

Grating equation ? transmission

grating with normal incidence

Diffracted

input

d light

sin d

=

p

l

?

d is angle of diffracted ray

Except for not making a small angle approximation,

? is wavelength

this is identical to formula

? l is spacing between slits

for location of maxima in multiple slit problem earlier

? p is order of diffraction

LASERS 51

April 03

Diffraction gratings ? general

incidence angle

? Grating equation

sin d

- sini

=

p

l

l=distance between grooves (grating spacing)

i

i=incidence angle (measured from normal) d

d=diffraction angle (measured from normal)

p=integer (order of diffraction)

? Same formula whether it's a transmission or reflection grating

? n=0 gives straight line propagation (for transmission grating) or

law of reflection (for reflection grating)

LASERS 51

April 03

Intensities of orders ? allowed orders

? Diffraction angle can be found only for

certain values of p

? If sin(d) is not between ?1 and 1, there is no allowed d

input beam

strong diffracted order

? Intensity of other orders

are different depending

on wavelength, incidence angle,

and construction of grating

weak diffracted order

? Grating may be blazed to make a particular order more intense than others

Blazed grating

? angles of orders unaffected by blazing

LASERS 51

April 03

Grating constant (groove density) vs. distance between grooves

? Usually the spacing between grooves for a grating is not given

? Density of grooves (lines/mm) is given instead

?

g

=

1 l

? Grating equation can be written in terms of grating

constant

sin(d ) - sin(i ) = pg

LASERS 51

April 03

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download