OPTICAL MEASUREMENTS Wednesday July 22nd 2015
Prof. Cesare Svelto 4th Exam YR 2014/2015
Time available 1hr40min room T.2.2 at 9.15
SURNAME: ______Name: ______ (block capital)
MS Degree and year: ______
POLIMI-ID number and readable Signature ______
POINTS (per exercise) (7+6+8+6+6=33p)
YOU MUST cross all subpoints you gave, even partly, an answer [e.g. 1a), 1c), 1d) 2a), 2c), 3b) etc.].
YOU MUST be able solving all problems in order to conclude and deliver the test (no blank exercises).
SOLUTIONS
(25 min) Exercise 1
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1a) Provide a drawing of the 3level and 4level lasing schemes and explain in some detail how the LASER action can happen in these two different configurations.
Give specific numbers/information on the Nd:YAG levels and pump/lasing wavelengths and comment.
1b) List, also with brief numerical examples, the main properties of laser sources making them uncoparable to traditional light sources.
1c) Describe the causes of laser frequency instability in the case of a diodepumped solidstate laser.
How can we limit (passively) or reduce (actively) the laser frequency noise?
An Nd:YAG laser with linear cavity has an optical length variable between 20cm and 50cm, with a temperature coefficient a=(DL/L)/DT=4×106/°C. Calculate the laser frequency shift for a temperature variation of +5°C?
1d) Finesse(F) and Free Spectral Range(FSR) of a Fabry-Perot interferometer: provide definitions and formulas of these parameters in the case of an optical resonator made of two identical planeparallel mirrors.
Two mirrors, plane and parallel and each with a power reflectivity R=80%, are facing each other at the extreme points of the diameter of one circle having area 78.54m2. What is the Free Spectral Range of the interferometer? What is the Full Width at Half Maximum of this Fabry-Perot transmission peaks?
(15 min) Exercise 2
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2) An optical instrument for laser alignment uses a Nd:YLF laser source, frequency doubled in the green, with TEM00 output beam and beam waist w0L=100µm. The collimating optics is a telescope with lenses of focal lengths f=20mm and F=200mm. We ant to achieve an optical beam with maximum collimation over a range of ±500m.
2a) Evaluate the laser spot size in the center point and at the extreme limit of the measurement range.
2b) What is the plane divergence angle (qdiv) after the telescope? And the corresponding solid angle (Wdiv)?
2c) State the magnification M of the telescope. At which distance from the laser shall we place the telescope in order to obtain the requested collimation?
(25 min) Exercise 3
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3) We are working with the Michelson interferometer shown in the Figure, where M1 is the reference mirror and M2 the measurement mirror. The mirrors are ideal, with 100% reflectivity, and we have: L1=10cm, L2=2m. The interferometer is read using an HeNe laser (l=632.8nm) with single longitudinal and transverse mode, having an output power of 5mW and linewidth Dn=300kHz.
3a) Mirror M2 is moved by Ds=25mm, getting closer to the laser. How many interferometric fringes do we observe in the waveform at the photodiode (FD) output?
3b) Which is the frequency of the interferometric signal if the mirror M2 moves with constant velocity v=20cm/s?
3c) We want to measure small vibrations of the mirror M2 (with amplitude much small than the laser wavelength), operating the interferometer in quadrature. What is the minimum vibration amplitude correctly detectable?
3d) Evaluate the fringes visibility if the beamsplitter (BS) has a power transmission of 66% and no losses.
3e) What will happen if the mirrors are still and we change in a continuous way the laser wavelength for a global deviation dl=0.05nm? Can we measure the length L2? If yes, write the measurement equation.
(20 min) Exercise 4
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4) Using a Laser Doppler Velocimeter e want to measure the speed of a fluid, seeded with small scattering particles, while flowing within a transparent pipe. The fluid velocity range is between 1cm/s and 10m/s and we want to achieve a measurement resolution Dv=5mm/s.
4a) If the projecting lens has a focal length f=400mm, do evaluate the offaxis separation (2h) of the two incident beams in order to have a 10mm fringe spacing in the focusing/interference region?
4b) What photoreceiver bandwidth is required?
4c) What kind of spectrum analyzer, and why, shall we use to detect the velocity (and frequency) profile?
4d) In a specific experiment, the fluid average velocity is 2m/s, with a Gaussian profile (sv=0.1m/s).
Which is the corresponding average detected frequency?
What frequency resolution and span (fSTART and fSTOP) do we need for the spectral measurement?
(15 min) Exercise 5
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5) An ultracompact Optical Spectrum Analyzer(OSA) uses a diffraction grating to disperse different wavelengths of the incident spectrum toward a linear array CCD made of InGaAs (spectral sensitivity from 800nm to 1700nm). The CCD array, set at a distance L=30cm from the reticle, has 1024 pixel over a linear size DCCD=1cm. This OSA, for telecom applications, was designed to correctly measure optical signals spectra from 1200nm to 1610nm.
5a) Evaluate the dispersive power/coefficient (KDq®Dl=?mrad/nm) of the diffraction grating.
5b) Calculate the spectral resolutions, absolute and relative, at an operating wavelength l=1550nm.
How do these figures compare to the spectral resolution of a good laboratory OSA?
5c) If the ultracompact OSA needs to be placed inside a PC board (having maximum length slightly greater than 10cm), how can we obtain the distance L=30cm between the grating and the CCD? Strengthen your answer with a schematic drawing of the laser beam path inside this OSA.
Exercise ___ (continued)
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STATE A LINK TO THIS PAGE AT THE END OF THE CORRESPONDING EXERCISE
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