Laboratory 5

Optical detectors and Gaussian beams

Objective:

In this lab students will use a He-Ne laser (l = 633 nm) and a high-speed silicon detectors to measure the power of the laser light falling onto the detector, when the laser beam is not attenuated and when it is a attenuated by passing through different neutral density filters.

Students will then expand the laser beam and measure the beam profile to verify that it is a Gaussian profile. Students will sample the irradiance along a direction perpendicular to the beam direction using a detector with a small sensor area. This technique is adequate if the dimensions of the sensor area are much smaller than the beam radius in the plane of the measurement.

The output of a laser is different than that of most other light sources. The laser resonator determines the spatial characteristics of the laser beam. Most lasers have spherical-mirror Fabry-Perot resonators that have Hermite-Gaussian spatial modes. Usually only the lowest order transverse resonator (TEM₀₀) mode oscillates, resulting in a Gaussian output beam.

For a Gaussian beam the intensity profile of the beam is symmetric about the beam axis and varies with radial distance r from the axis as

I(r) = I₀exp(-2r²/r₁²)

Here r₁ is the radial extent of the beam where the irradiance has dropped to 1/e² of its value on the beam axis, I₀.

Equipment:

	Laser Assembly
	Beam Steering Assemblies
	Lens Chuck Assemblies
	Target Assembly
	Lens Kit
	Ruler
	Detectors
	Power Meter

Procedure:

Part 1:

	Mount the laser onto the breadboard. Turn it on and leave it on, so that it warms up and stays warm. Use a beam stop to block the beam from traveling across the room.
	Set up the Tektronix TDS 210 Digital Oscilloscope. Perform the functional check described on page 5 of the TDS-200 series user manual. If you are not familiar with this scope, read through “Operating Basics”, pages 23 – 36 in the user manual.
	Position the Thorlabs DET110 high-speed silicon detector so that the laser beam hits the photodiode. Place the filter wheel with the neutral density filters between the laser and the detector so that the laser beam passes through two empty holes.
	Connect the output of the DET110 to the input channel 1 of the scope, using a 50W cable and a tee with a 50W terminator. Press the Vertical Menu button for channel 1 and set the probe attenuation to 1X. (See page 8, user manual.)
	Turn the detector on and measure the output voltage with the oscilloscope. Use V = P K_PD(l) R_load to find the laser power P falling onto the detector. Determine K_PD at 633 nm from the graph below. R_load = 50 W.
	The neutral density filters provide uniform attenuation over a broad spectral range. The "optical density" is defined by ND=log₁₀(1/T), or T=10^-ND. Here T is the transmittance. Place filters with different optical densities between the laser and the detector and measure the power P falling onto the detector.
	Fill in the table below.

ND	Detector Voltage V	V/V_ND=0=P/P_ND=0 (measured)	P/P_ND=0 (expected)
0		1	1
0.2
0.3
0.4
0.5
0.6
1

	Plot P/P_ND=0 measured versus P/P_ND=0 (expected). Is the detector response linear?
	Replace the DET110 with the the Thorlab S110 power meter to measure the output power of your laser. Check the power meter manual, pages 6-9, for operating instructions. Compare the value for the output power measured with the power meter with the value you obtained when measuring the output power with the DET110.

Part 2:

Expand the laser beam with a Galilean telescope. Do not use the translation stage, but use base plates in the construction of your beam expander.

Use a f₀ = 200 - 300 mm and a f_e = -25 mm lens. Make sure that the resulting beam is well collimated by visually checking that the beam propagates virtually without divergence after the second lens.

Mount the Thorlabs Det210 high-speed silicon detector on a translation stage, so that it can be translated across the beam. The DET210 has an active area of 0.8 mm². Position the translation stage on the optical bench so that the active area is in the beam path and visually center the active area on the beam.

Measure the power at 0.5 mm intervals along the horizontal transverse direction. Make at least 20 measurements.

	A	B
1	position x	power P
2	X	X
3	X	X

Plot power versus position.

Try to fit a Gaussian curve to this plot to determine the beam radius r₁.
For example, using Excel's solver tool:

	A	B	C	D	E	F	G	H	I
1	position x	power P	Aexp(-2(x-x₀)²/r²)+B	difference²	A	x₀	r	B	monitor
2	X	X	=$E$2EXP(-2(A2-$F$2)^2/$G$2^2)+$H$2	=(B2-C2)^2	X	X	X	X	=SUM(D2:D22)
3	X	X	=$E$2EXP(-2(A3-$F$2)^2/$G$2^2)+$H$2	=(B3-C3)^2

Add another column (column C) to your spreadsheet, containing the formula Aexp(-2(x-x₀)²/r²)+B, where the values of A, x₀, r, and B are stored in cells E2-H2. Guess some reasonable values for those parameters.

In column D calculate the square of the differences between the entries in columns B and C.
IN cell I2 sum up those differences.

Click tools, solver. Choose as your target cell the cell I2. Choose to minimize the value in that cell by changing cells E2 through H2.
Keep the solver solutions. You now have the best Gaussian fit to your data. The value in cell G2 is the beam radius r₁.

Laboratory Report:

Open Microsoft Word and prepare a report using the template shown below.

Name:
E-mail address:

Laboratory 5 Report

	In a few words, describe the experiment. (What?)
	In a few words, state the objective of the experiment. (Why?)
	Comment on the procedure. Did you encounter difficulties or surprises? (How?)
	Present your results and comment on your results.

Print out your Word document, and hand it to your instructor, or save your Word document (your name_lab5.doc) and attach it to an e-mail message to your lab instructor.