wave propagation

Question 1

(near field) propagation

Answer 1

fresnel

Question 2

(far field) propagation

Answer 2

fraunhofer

Question 3

First order approximation to propagation problem:

Answer 3

Geometric Optics

Question 4

the phase velocity changes in matter
compared to vacuum by a factor

Answer 4

n: refraction index

Question 5

for visible light: n1 ?? 1
for X-rays: n1 ?? 1

Answer 5

for visible light: n1 > 1
for X-rays: n1 < 1

Question 6

n is complex and for X-rays often written as

Answer 6

n = 1- delta + i*beta

delta: phase shift of wave in matter
beta: attenuation

Question 7

The direction of the waves is given
by the

Answer 7

wavevector: kn

kn = 2pi / (lambda n)

Question 8

snells law

Answer 8

n0 * sin(theta0) = n1 * sin(theta1)

Question 9

Huygens-Fresnel principle

Answer 9

Optical field in observation plane can be expressed as sum of spherical waves

exp(ikr)/abs(r)

Question 10

Corpuscular Theory

Answer 10

particle theory of light

Question 11

Interference of light
Double Slit Experiment done by

Answer 11

1804 Thomas Young

Question 12

1804 Intensity of interference
1815 Polarisation done by

Answer 12

Augustin Jean Fresnel

Question 13

Collimated work on electricity and magnetism
of Michael Faraday and André-Marie Ampère done by

Answer 13

1864 james clark maxwell

Question 14

For isotropic media the polarization does not ………and we restrict ourself to …….. waves

Answer 14

For isotropic media the polarization does not change and we restrict ourself to scalar waves

Question 15

à for electromagnetic waves of the velocity c

Answer 15

c = lambda * v
c = 1/sqrt(mu0*eps0)

Question 16

Gauss’ theorem

Answer 16

connects the flux of the vector field
through a closed surface surrounding a volume
with the diverence of this field in the volume

divergence of a vector field
within a volume is equal to flux of the vector field
through surface with
normal vector n

Question 17

the integral theorem of Helmholtz and Kirchhoff

Answer 17

it allows to calculate the field at point P0 by integrating over a closed surface around P0

Question 18

Geometric optics ………… to describe diffraction and interference

Answer 18

insufficient

Question 19

Scalar Theory:

Answer 19

only a single component of E or B
and no polarization

Question 20

What are the components of the Fresnel-Kirchhoff diffraction integral

Answer 20

Wave Source:

Integration Variables:
two integration variables: one representing the coordinates of the points on the diffracting aperture or obstacle, and the other representing the observation point in the far-field region where the diffracted wave is being analyzed.

Amplitude Factor:

Phase Factor:

Aperture Function:

Geometrical Factor:

Question 21

Paraxial ray is a ray that makes

Answer 21

small angle to optical axis

Question 22

With paraxial & Taylor assumptions
* Free space propagation impulse response becomes

Answer 22

parabolic shape

Question 23

When to use Fresnel propagation?
Fresnel propagation is valid if

Answer 23

Fresnel number F = a*a/(lambda * z) >= 1

Question 24

Fresnel propagation also known as

Answer 24

near field

Question 25

Huygens principle assumes

Answer 25

spherical wavefronts

Question 26

Propagated wavefront with Fresnel propagation is given by

Answer 26

by the iFT of the product of Fourier transform of wavefront multiplied by the Fresnel kernel

Question 27

Geometric Optics vs Diffraction

Answer 27

Geometric Optics: straight light rays refraction at surfaces snells law Diffraction: wave propagation diffraction at apertures fresnel-kirchoff integral

Question 28

How do we propagate a wave to the Fresnel regime?

Answer 28

By convolving with a Fresnel propagator (multiplying in Fourier space)

Question 29

Which wavefront shape is assumed by Fresnel diffraction?

Answer 29

parabolic

Question 30

If you propagate the TUM logo with a Fresnel propagator, what would you expect to see?

Answer 30

Slighly higher intensity at the edges of the TUM Logo.