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2012-11-03
Exercise Zemax 9: Physical optical modelling I
9Physical optical modelling I
9.1Gaussian Beams
9.2Physical Beam Propagation
9.3Polarization
9.4Polarization II
9Physical optical modelling I
9.1Gaussian Beams
Consider a simple model of a basic mode (TEMoo) laser resonator at a wavelength of = 632.8 nm. The retroreflecting mirror is plane and here the gaussian beam waist has a size of wo = 0.3 mm. After a distance of 50 mm, a thin ideal lens with focal length f = 150 mm is located inside the resonator. The outcoupling mirror has a radius of curvature of R2 = -100 mm (concave).
a) Determine the distance between the lens and the outcoupling mirror to get a stable gaussian fundamental mode. Prove the result with the gaussian beam transformation menue. What is the 2w-diameter of the beam at the outcoupling mirror ?
b) If the outcoupling component is a lens with 5 mm thickness and made of quarz, determine the outer radius to get a divergence of the outgoing laser beam of = 10 mrad.
c) What is the distance behind the resonator, where the beam diameter is 5 mm ?
9.2Physical Beam Propagation
Take the system of the previous exercise to evaluate the data by a more rigorous diffraction beam propagation.
a)First check the beam diameter at the outcoupling mirror.
b)Check the beam curvature and the final divergence of the outgoing beam.
c)If a plano convex lens is with focal length f = 30 mm, thickness 3 mm and of BK7 is used in a distance of 400 mm behind the resonator, calculate the obtained focus width. Compare the result with the ideal case of an unperturbed gaussian beam.
d)The last transition is a far field propagation. Try to improve the resolution be resampling the POP at the last surface or by using another operator.
9.3Polarization
Establish a system with only Hoya glasses. the incoming light is a collimated beam with 10 mm diameter at the wavelength 632.8 nm. There are 3 surfaces with the radii 30 / 5 / -30 mm. The first lens has the thickness 2 mm and is of BACL3, the second cemented lens with thickness 6 mm is of E-C3.
a)Show, that the refractive indices of the two glasses are very close together. Determine the incidence angle of the marginal ray at the cemented surface.
b)The refractive index of the glass is quite near to that of BK7. Therefore for all surfaces the coating ZEC-V633_BK7 is to be inserted in the corresponding surface property menue. Calculate the pupil map of the system, if the incoming collimated light is linear polarized in y-direction. What is the largest local transmission loss ? What is the mean transmission loss ?
c)Investigate the results, if a wrong coating is used at the surface No. 3. Try and compare the results for the wrong substrate (ZEC_V633_SF11) and the wrong wavelength (ZEC_V1550_BK7).
d)Analyse the properties especially of the cemented surface due to the large incidence angle by inspection of the coating here for the correct coating ZEC_V633_BK7.
9.4Polarization II
Establish an optical diode by ideal Jones matrix components and demonstrate their function by rotating the /4-plate.
a)First set up a system with polarisator in y-direction, rotatable /4-plate and crossed analysator plate in a collimated beam.
b)Find the rotation angle of the /4-plate, where the transmission is 10%.
c)Establish a universal plot for rotating the /4-plate and demonstrate the Malus-law. What is the largest transmission of the setup ? Now use as input a circular polarization. What is changed if the plate is rotated ?