Michelson wavemeter - Prelab questions

1. What conditions must exist for light waves to interfere? What properties must theyhave in common?

2. What is happening during destructive interference? Why dont we observe any light?

3. Find an expression for the wavelength of the unknown laser, U , in terms of the numberof fringes counted for each laser and the wavelength of the reference laser, R (seeEquation 1).

4. Using figure 1 or otherwise, show that NR = 2d/R. Diagrams may be useful.

5. Estimate how far the wavemeter cart (moving mirror, M1 in figure 1) must be movedin order to get a resolution of 1 part in 106. (Hint: you will probably need to count atleast as many fringes as the accuracy you want to get).

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Michelson wavemeter - Theory

The wavemeter in this lab is based on one designed and used by Michelson in the 19th

century. The Michelson interferometer splits a beam of light and sends it along two pathsto be recombined later (see figure 1). The difference in path lengths produces an interferencepattern when the beams recombine. Michelson used his interferometer to accurately measurethe wavelength of monochromatic sources of light and the refractive indices of various gases.His most famous use of the interferometer was in his experiment with Morley, where it wasconcluded that the speed of light was not affected by the movement of the Earth through theether. (The ether was assumed to be the medium through which light waves, and indeed allmatter, travelled.)

The accuracy achievable with this equipment is one part in a million (1106), high enoughto be used in research labs. (Indeed, we are borrowing part of the equipment from the opticsresearch group.)

We will be using both the wave and particle models of light in this experiment. Using waveinterference we can measure the wavelength of an unknown laser. Using a particle model wewill look at atomic transitions in rubidium.

Interference

The phenomenon utilised by a wavemeter is the interference of light waves. Under certainconditions, two light waves will interfere and produce an interference pattern. The principleof superposition explains that the amplitude of the resulting wave at any point will be thesum of the individual wave amplitudes at that point. Two waves in phase will interfereconstructively (producing a larger amplitude wave), while those out of phase by exactlyhalf a wavelength (/2) will interfere destructively (producing a zero amplitude wave). Thisholds true for sound waves, light waves, ocean waves...

The Michelson interferometer

The basic layout of a Michelson interferometer is shown schematically in figure 1. As mirrorM1 is moved, the path length difference between the two interferometer arms changes. Thisresults in changes in the phase difference between the two beams. As the phase differencechanges the amplitude at any point on the detector also changes, ranging from some maxi-mum to some minimum number. If the mirror is moved smoothly and continuously in onedirection, the amplitude at any point will oscillate from dark (zero amplitude) to light (maxi-mum amplitude) in a sinusoidal fashion. The number of oscillations or fringes, NR, countedas the mirror moves a distance d is given by:

NR = 2d/R (1)

where R is the wavelength of the reference laser. In our case, we use a Helium-Neon (HeNe)laser as our reference, with R = 632.823 nm. An unknown laser with a wavelength U , givesthe number of fringes as NU = 2d/U .

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If a reference laser and an unknown laser propagate through the interferometer simultane-ously, we have a wavemeter. The design of the wavemeter in this experiment is shown infigure 2. Following the arrows of the reference beam, you can see it is split by the beam-splitter (BS) and is reflected by the corner cubes (CC1 and CC2) in each arm. This causesa parallel shift in each arm on the return journey and results in two outputs on return to thebeamsplitter. The beams from each arm are recombined at BS and incident on a detectorwhich is connected to a counter. The other output, from the beamsplitter, can be used toalign the unknown laser easily, which travels in the opposite direction (counter propagating)to the reference laser. This output is incident on a second detector, spatially separated fromthe first.

M2

M1

d

LASER

Beamsplitter

Detector

Figure 1: The basic geometry of a Michelson interferometer. BS is a beamsplitter whichpartially transmits and partially reflects incident light.

HeNe laser

Unknown

M1BS

Detectors

M2

M3

M4

M5

CC1 CC2

NUNR

Collimator}

Figure 2: The geometry of the wavemeter. The arrows show the beam direction for thereference HeNe laser. (Note that the setup on the bench might be rotated some angle withrespect to this diagram.)

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Equipment

Safety

Lasers can be exceptionally damaging to the eyes. This particular unknown laser emits in theinfrared spectrum, so here your typically eye-saving blink reflex is non-existent! Stray re-flections should be eliminated (be careful when placing objects in the beam path and removeyour jewellery) and you should NEVER lower your head to the height of the laser beams.

NEVER EVER LOWER YOUR HEAD TO THE HEIGHT OF THE LASER BEAMS!

The wavemeter

The wavemeter is displayed schematically in figure 2. Do not open the perspex box, itcontains dangerous, delicate and expensive components. Realignment of the componentsinside takes several hours. The wavemeter cart (with corner cubes, CC1 and CC2) is on anair track to reduce friction. Dont touch the regulator on the wall as the air flow should below.

The black box in front of the wavemeter controls both the HeNe power, the counter and thephotodetectors. There is a switch at the back to turn it on. When this switch is turned on, theHeNe laser output will turn on. Unknown out is the output from the detector labelled NU infigure 2. HeNe out is the output from NR in the same figure.

To make a measurement, the cart travels the length of the track, from right to left. Springsare at each end of the track and only a slight push is needed for measurements. The standarddeviation in the measurement result is less than 0.001 nm, which is at the limit of the count-ing resolution of the device. The absolute accuracy, however, is limited by systematic errors.

The external cavity diode laser

This is the unknown laser. It is tunable, hence the big control box. Do not adjust any controlsuntil you are explicitly told to change something.

Rubidium cell and infrared camera

Rubidium gas ignites in the presence of oxygen. Do not touch, move or place any objectsnear the glass cell and do not pass anything over the cell.

The infrared (IR) camera is used to observe rubidium fluorescence. When the unknown laseris correctly tuned, the rubidium atoms will absorb the light and become excited. The atomswill then emit light of the same wavelength as they decay to the ground state. This emittedlight will be observed on the IR camera as fluorescence.

Both types of naturally occurring isotopes of rubidium are present in your vapour cell. Eachisotope has a ground state hyperfine splitting giving rise to four rubidium ground states.We distinguish each ground state for a particular isotope by its total angular momentum,F = I + J , with I the total nuclear spin of the atom, and J the total orbital angular mo-mentum of the electron. The excitation energy to the 5P3/2 excited state is different for eachground state. Recall the laser wavelength corresponds to the photon energy E = hc/.

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Michelson wavemeter - Procedure

First, make sure you understand how the beam paths of the two lasers compare to figure 2.Check that there are no objects in the beam paths that should not be there. Consult yourdemonstrator to ensure your understanding is correct.

Question 1 What is the purpose of including the collimator? What are they normally usedfor, and how would our experiment be affected if we removed it?

Question 2 Why do we include mirror M4? Why dont we just use mirrors M3 and M5 atright angles?

When ready, turn on both lasers as follows:

1. Turn on the switch at the back of the small black box attached to the wavemeter. Thered display should light up and bright red laser light should be visible on the mirrorswithin the perspex box.

2. Turn on the external cavity diode laser using the very large control box. Do not adjustany controls until you are explicitly told to change something.

3. To turn on the laser, first turn the key. Wait for a few seconds, then press the squarebutton above it. The green light should flash for five seconds before the beam starts.

The reference laser

The beams need to be precisely collinear and parallel to the track so that interference fringesare generated consistently as the cart moves. The reference laser is already aligned andis used as a guide for aligning the unknown laser. Do NOT open the perspex box: thisalignment is already complete. The bright red HeNe laser should be visible on NR. Checkthe output of the photodetector NR on an oscilloscope as follows:

1. Connect a BNC cable between the HeNe out connection on the wavemeter box andchannel 1 on the oscilloscope.

2. Try these settings: CH 1 - 1V/DIV, TIMEBASE - 5s, TRIG - CH 1.

3. Do you see a sinusoidal signal that varies with amplitude as the wavemeter cart moves?The alignment is sufficient if the amplitude remains roughly constant.

4. If the alignment is adequate coming from the HeNe out connection, you can com-mence the alignment process for the unknown laser.

Question 3 Why is the signal a varying sinusoidal? What causes this?

Question 4 Note both the maximum and minimum peak-to-peak amplitudes you observedfor the HeNe laser on the photodetector NR. Comment on exactly what the amplitudescorrespond to physically.

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Wavemeter PD

Rb cell

BS2

MX MY

Unknownlaser

PX

PYHeNe laser

Figure 3: Geometry of the unknown laser. Arrows show beam directions. Reference HeNelaser is small arrows, unknown laser is large arrows. NB: PD is not the photodiode mentionedin the following alignment section, it is a separate photodiode used to investigate rubidiumatoms in the final section.

Unknown laser alignment

1. Introduce the unknown laser into the system, collinear with the HeNe output tracerbeam as in figure 3 .

2. Use the infrared-sensitive laser alignment card to locate the unknown laser source. Youcan recharge the card by pointing it towards room lights for a few seconds.

3. Align the unknown laser using mirrors MX and MY . Each has a fine adjustment knobto control vertical and horizontal tilt. Do not adjust the unknown laser other thanthrough these knobs.

4. Perform the alignment so that the beam spots overlap on both mirrors, with the un-known and output beams fully counter-propagating. The following procedure is onemethod of aligning the unknown laser.

(a) Position the IR card at position PX in figure 3 with the active region facing awayfrom the perspex box. By chopping your hand between the perspex box and theIR card, you should notice there are two spots visible on the IR card. The oneyou are chopping is the HeNe.

(b) Position the IR card at position PY , with the active region facing the beamsplitter.By chopping your hand between the mirrorsMX andMY , you should notice thereare also two spots visible on the IR card. The one you are chopping is again theHeNe.

(c) When the card is in position PX , adjust the knobs on mirror MY to overlap thetwo spots. When the card is in position PY , use mirror MX to overlap the beams.

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It is helpful to align only one axis at at time. Alternate between axes. Repeat thisstepping alignment until the spots overlap at both PX and PY .

(d) This stepping process needs to be repeated, and can take up to 30 minutes. Oncecorrect you should see the bright HeNe laser incident on the output hole of theunknown laser.

5. To confirm alignment, check the Unknown out connection from the wavemeter box onchannel 1 on the oscilloscope. As with the known laser, do you see a sinusoidal signaland is it roughly constant?

6. If the oscilloscope does not trigger, first try adjusting the trigger level. If nothing,verify your alignment is incident as well as collinear on the photodetector NU .

Question 5 Note down in your logbook both the maximum and minimum peak-to-peak am-plitudes you observed for the unknown laser on the photo detector NU . Is the variation lessthan the photo detector NR ? Explain.

Measuring the wavelength of the unknown laser

1. Turn on the air supply to the wavemeter cart.

2. Give the cart a gentle push. If the wavemeter stops counting as it travels from right toleft and displays a number, your alignment is good.

3. Check several times to ensure that you can consistently measure the same number towithin the last digit. If you can do this, your alignment is finished.

4. If the wavemeter does not stop counting, or counts erratically, make sure there is noth-ing in the beam path. Also check that the function generator next to the unknown lasercontroller is OFF.

By now youre pretty familiar with how an interferometer works. Youve have some expe-rience with two counter-propagating lasers, alignment, and changes with path length differ-ence. Youll now focus on a particular application of an interferometer.

Adjusting the wavelength of the unknown laser

Were now interested in investigating the properties of rubidium. We first need to changethe unknown laser wavelength to match the wavelength at which rubidium absorbs light, = 780.033 nm in air. Most ways of changing the laser wavelength are NOT SUITABLE forour purposes:

Do not adjust the wavelength knob. This adjusts the angle of the diffraction gratingand hence the optical feedback to the laser cavity. This also adjusts the output angle ofthe laser and ruins your alignment.

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Do not adjust the temperature knob. This changes the cavity length inside the laser,but this is a very slow process.

DO adjust the CURRENT. This changes the current density of the laser gain medium, hencerefractive index, hence optical path length of the semiconductor diode cavity, and hence thewavelength.

Scanning the wavelength over a particular range

Now we know how to change the wavelength, we want to position the laser wavelength nearthe rubidium absorption dips, then sweep the wavelength more finely over that range.

1. Make sure the function generator is switched off and not connected to the laser.

2. Ensure the laser controller is not scanning the wavelength - ask your demonstrator.

3. Centre the piezo voltage at 50 V.

4. Change the current by a few mA and take 2-3 wavemeter measurements.

5. Note any real change in wavelength. Your target wavelength on the wavemeter shouldbe reasonably close to 780.033 nm.

6. Turn on the photodiode power supply and the LCD screen. You may notice on the LCDscreen that the laser beam becomes visible (flashes) within the vapour cell briefly asit passes through this range.

7. Connect the BNC cable from the small black photodiode (PD) next to the rubidiumcell to CHANNEL 1 on the oscilloscope.

8. Turn on the function generator. Make sure the BNC splitter is connected to the output.

9. Ensure one BNC cable is connected to the rear of the laser diode controller, and theother BNC cable is connected to EXT on the oscilloscope.

10. Set the function generator to a triangular waveform and frequency to 30 Hz.11. Set the oscilloscope to: timebase 25 ms/DIV; CH 1 about 2 V/DIV; trigger EXT, RIS-

ING and AUTO

12. You should see on oscilloscope something like the top trace in figure 4. The bottomtrace is what the function generator output should look like. Check this if you like.

13. Save a copy of your oscilloscope screen on to the USB by pushing the PRINT button.Print your traces and replace the USB key in the oscilloscope.

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Rb87 F=2

Rb87 F=1Rb85 F=2

Rb85 F=3

Figure 4: Rubidium absorption dips.

Measuring the wavelengths of rubidium ground state excitations

You will now measure the photon wavelength required for each of the four ground stateexcitations. Make sure the function generator is SWITCHED OFF.

1. Use either the fluroescence signal from the IR camera on the LCD screen, or the PDsignal on your oscilloscope, to locate one of the ground state excitations by slowlyturning the PIEZO VOLTAGE knob on the laser controller.

Question 6 What is the piezo voltage controlling? How exactly is the piezo voltage relatedto the appearance of the peaks?

2. Recall from figure 4 that each ground state transition has a different transition strengthand hence a different magnitude of fluorescence signal/absorption.

3. Record the wavelength of the weakest transition, taking three independent measure-ments and recording each.

4. Locate the next ground state transition 85Rb 5S1/2 (F = 2) 5P3/2 (F = 3) andmeasure the wavelength of this transition three times.

5. Do the same for the remaining two transitions. Make sure you have correctly labelledeach transition and that they are in the correct order.

Question 7 What are the two outer features in figure 4? Why do we see these?

Question 8 Why are the absorption dips all different depths?

Question 9 How accurately do you think you can measure a ground state excitation wave-length with this experimental setup? Explain your reasoning.

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F=1

F=2

3.036 GHz

F'=4

1.265 GHz

6.835 GHz80 MHz

2.483 GHz

F'=3

F=2

F=3

780.036 nm

5S1/2

5P3/2

5P3/2

5S1/2

85Rb, I=5/2, 72% 87Rb, I=3/2, 28%

Figure 5: Energy-level diagram for the ground and 5P3/2 states of both natural isotopes ofRb (Adapted from B. Sheehy et al. J. Opt. Soc. Am. B, 6:2165-2170, November 1989).

Question 10 The blackbody distribution of room temperature (T=298 K) rubidium atomshas a FWHM (full width at half maximum) of approximately vFWHM = 400m/s centred atv = 0. What is the resulting FWHM of the Doppler broadened 85Rb 5S1/2 (F = 3) 5P3/2 (F

= 4) transition?

Recall that the relativistic Doppler shift is given by

f = f

1 v/c1 + v/c

(2)

where f = c/ and c = 2.99792 108 m/s.

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