EOP4086 Optical Signal Processing - Lab 1 Coherence and Lasers

Lab 1: Coherence and Lasers

Precautions
All the equipments/components are extremely sensitive to their conditions as well as orientations. So, handle with great care. Keep the components away from dust as it would greatly affect the experiment, and the results may not be obtained that easily. Avoid fingerprints on mirrors and lenses.Never put your eyes directly in front of the laser beam. It is always advisable to put the rings and wrist watches off whenever one works with lasers.

1. Objective

To analyse the frequency separation of axial modes in the case ofHe-Ne laser

2. Apparatus

Part / Qty / Description
OB
LA
IC
BSA
LCA
CV
CX
BS
TA / 1
1
1
4
3
1
1
1
1 / Optical Breadboard
He-Ne Laser Assembly
Index Card with 2 mm Hole
Beam Steering Assembly with Plane Mirror
Lens Chuck Assembly
Concave lens (f = 25.4 mm)
Convex lens (f = +200 mm)
50/50 Beam Splitter
Target Assembly

3. Theory

The concept of coherence, when applied to light sources, determines the consistency of a light field from one point to another. How to make the comparison? The interference of light beam with itself does the comparison. If there is a constant relationof phase, amplitude and wavelength between one point on a laser beam and another point, then the interference of waves separated by that distance should produce a stable interference pattern. If, however, the amplitude, phase or wavelength changes between these two points, the interference, while it is still there at all times, will constantly vary with time. This unstable interference pattern may still exhibit fringes, but the fringes will be washed out. This loss of visibility of fringes as a function of the distance between the points of comparison is a measure of the coherence of light. This visibility can be measured by the contrast of the interference fringes. The contrast is defined by C = (Imax – Imin)/(Imax + Imin), where Imax is the irradiance of the bright interference fringes and Imin is that of the dark ones (Figure 1). This contrast is determined by passing the light from a source through a Michelson interferometer with unequal arms. By changing the opticalpath difference between the arms in the interferometer, the visibility of fringes as a function of this difference can be recorded. From these observations, the measurement of coherence of a source can be done using a Michelson interferometer.

If a source is absolutely monochromatic, there would be no frequency spread in its spectrum. That is, its frequency bandwidth would be zero. For this to be true, all parts of the wave exhibit the same sinusoidal dependence from one end of the wave to the other. Thus, a truly monochromatic wave would never show any lack of contrast in its fringes, no matter how large of a path length difference was made. But all sources, even laser sources contain a distribution of wavelengths. Therefore, as the path difference is increased, the wavefront at one point on the beam has different wavelengthswith another point on the beam. A measure of the distance at which this occurs is the coherence lengthlc of a laser. It is related to the frequency bandwidth of a laser by = c/lc, where c is the speed of light. Any measurement of the coherence length of a light source by observation of the visibility of fringes from a Michelson interferometer will yield information on the bandwidth of that source, and therefore, its coherence. For example, suppose the source is a laser with some broadening. As the length of one of the arms in a Michelson interferometer, as shown in Figure 2, becomes unequal (mirror moved from A to B), one part of a wave will interfere with another part that is delayed by a time equal to the difference in path length divided by the speed of light. Eventually, the waves begin to have different wavelengths and the fringe contrast begins to fall because the wavelengthrelation between the two waves is varying slightly due to the spread in frequencies in the light. The greater the broadening, the more rapidly the visibility of the fringes will go to minimum value.

The standard He-Ne laser used in the experiment produces three wavelengths separated in frequency by s =c/2L, where L is the distance between the ends of the laser mirrors.The experiment essentially employs the use of Michelson interferometer for determining the characteristics of lasers.

4. Experimental Setup

  1. Set up a Michelson interferometer on an optical breadboard as shown in Figure 3. (Hints: The index card with 2 mm hole is used to help to align an optical component which reflects laser beam back to the index card. The concave and convex lenses form a laser beam expander/collimator. All the optical components are located so that the laser beam intersects at the centers of the optical components.)
  2. Adjust the movable mirror position until the optical path difference between the two arms of the Michelson interferometer is zero. This will give the best fringe contrast.
  3. Align the movable mirror tiltsto get a series of dark and bright (circular) fringesappeared on the observation screen. Take note on the contrast of the fringes (if your handphone has camera, taking pictures will help for contrast comparison in the following steps).
  4. Translate the movable mirror away from the beam splitter by 0.5” increments. Each time the mirror is moved, align the mirror tilts until four to six fringes are observed. There will be a position in path difference where the fringes seem to fade in and out (or to reach minimum contrast). Carefully move the mirror about this position until the fringes cannot be made to appear. Record the position and calculate the optical path difference between the two arms of the interferometer.
  5. Continue to move the movable mirror away from the beam splitter by using the same technique as the previous step. Find the mirror position that gives the strongest possible contrast. Record the position and calculate the optical path difference between the two arms of the interferometer.

Note for calculation of frequency separation s:

The difference of the optical path differences forfringe contrast going from a maximum to a minimum, Lopis corresponding to half of the coherent length of a 3-wavelengthslaser. Therefore, s = c/4Lop.

5. Lab Report

The laboratory report should include the following

  1. Title and objective
  2. Experimental procedures
  3. Experimental observations and results
  4. Discussion on the questions in Section 7 (including the observations and results)
  5. Conclusion/Summary

The report must be submitted to the lab staff within 10 days from the date of experiment.

6. Assessment (follow Lab Rubrics Structure, to be mapped to)

  1. Preparation before coming for experiment – 2 marks
  2. Skills to set up and carry out experiment (including recording observations and results)– 2 marks
  3. Discussion (illustration/explanation/analysis) – 2 marks
  4. Conclusion/Summary – 2 marks
  5. Report writing ability (grammar, organization and tidiness) – 2 marks

7. Questionsfor Discussion

  1. Explain the physical significance of coherence. How is it important in the context of lasers?
  2. Identify your experimental setup if the He-Ne laser is replaced by a sodium lamp. What are expected observations and results?
  3. Illustrate the alignmentsof the concave lens, convex lens, fixed mirror and movable mirror with the help of the index card with 2 mm hole.
  4. Illustrate the alignment of the beam expander to collimate the laser beam.
  5. Determine the intensities of the two beams coming out from the beam splitter if the incoming laser intensity before entering the beam splitter is Io.
  6. Two laser beams which are emitted from two He-Ne laser assemblies are brought together to intersect. Justify whether interference fringes can be formed or not.
  7. Discuss on the experimental observations and results.

Updated May13, WO Siew

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