1. A plane wave of intensity 10mW/cm2 and wavelength λ=600nm is incident onto a
rectangular slit of dimensions 10μm X 2μm.
a. At what distance away from the aperture is the Fraunhoffer approximation
valid?
b. A lens with a focal length of f=20mm is placed immediately after the
aperture. Plot the normalized diffraction pattern at the plane z=20mm.
2. A plane wave of intensity 10mW/cm2 and wavelength λ=600nm is incident onto a
lens with a focal length of f=10mm. The lens aperture has with a diameter of
D=10μm. What is the maximum irradiance of the pattern on a screen located at the
focus of the lens?
3. A plane wave is incident onto a lens with an aperture diameter of D=10mm, a
wavelength of 600nm, and a focal length of f=100mm. How close to the focal plane
of the lens must the analysis plane be in order to use a Fourier transform integral?
4. An aperture consists of a circular hole with a diameter of D=10mm with a circular
obscuration in the center. Immediately after the aperture is a lens with a focal length
of f=30mm.
a. Plot the width of the central beam (the distance between the first nulls in
the pattern) as a function of the diameter of the central obscuration.
b. Plot the relative amplitude of the first side lobe as a function of the
diameter of the central obscuration.
5. On the web site http://laser.physics.sunysb.edu/~thomas/report1/lens_report.html it
explains that a magnifying glass is used to start a fire. About half way down is a set
of numbers calculating the irradiance of magnifier 1 with specifications of f=15cm,
D=4.7cm, and incident irradiance of 1kW/m2. Calculate the maximum irradiance at
the focal plane of the lens.
6. The actual measured irradiance given on the web page was 551 kW/m2, which is a lot
less than the theoretical value measured. This difference is because of the aberrations
in the lens. Design a biconvex lens in OSLO with a diameter of D=4.7cm and focal
length of f=15cm. You will be using the Strehl Ratio to calculate the irradiance.
a. Look up Strehl Ratio in Wikipedia and explain what it is.
b. What is the Strehl Ratio of the lens that you designed. (Use OSLO to
calculate the Strehl Ratio. It is on the Spd menu.)
c. Calculate the irradiance of your lens. (The Strehl Ratio is defined in terms
of electric field rather than irradiance. Multiply your answer from the
previous problem by the Strehl Ratio squared. Your answer should be
close to the value given on the web site.)
Figure 1: Single period of the grating.
7. What is the transmission function, t(x), of the grating if Figure 1 shows a single
grating period? The material has an index of refraction of n. Your answer should be
in terms of , d, rect(x), (x), and n. Be sure to include the infinite periodicity of the
grating (There should be a convolution in your answer).
8. A binary surface relief phase grating is designed such that if the incident beam is
normally incident on the grating then the first diffraction order is transmitted through
the substrate at an angle of 45° with respect to the surface normal. Use a wavelength
of =500nm.
a. What is the grating period?
b. How many orders are there, which are transmitted through the grating into
air?
c. How many orders are confined to the substrate if the substrate has an
index of refraction of n=1.5?
9. A beam is normally incident onto a grating and the +/- 1 diffracted orders have a
propagation angle of 60° measured from the surface normal within the glass substrate
that has an index of refraction of n=1.5, =500nm.
a. What is the grating period?
b. At what incident angle will there be a diffracted order that is transmitted
through the substrate and into air?