Module Labworks OpticsAbbe School of Photonics, Friedrich-Schiller-Universität,Physikalisch-Astronomische-Fakultät,Max-Wien-Platz 1, 07743 Jena, GermanyPhone: +49 3641 947 960 Fax: +49 3641 947 962E-mail: info-asp@uni-jena.de Web : www.asp.uni-jena.de

Contact person: Dr. Arkadi ChipoulinePhone : +49 3641 947 842 E-mail : arkadi.chipouline@uni-jena.de

Helium Neon Laser[ version of October 22, 2009]

Contents

1 Safety issues 31.1 Eye hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Chemical hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theoretical basics 32.1 Helium Neon Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Basics of resonator modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Transversal modes in a laser resonator . . . . . . . . . . . . . . . . . . . . . 72.4 Optical elements for the wavelength selection . . . . . . . . . . . . . . . . . 8

2.4.1 Brewster’s angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4.2 Fabry Perot Etalon . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4.3 Littrowprism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.4 Birefringent filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.5 Transmission grating . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Setup and equipment 123.1 Setup alignment procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.2 Further adjustment of the optical elemtents . . . . . . . . . . . . . . 13

4 Goals of the experimental work 15

5 Appendix 165.1 Preliminary questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.2 Final questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

He Ne Laser

1 Safety issues

1.1 Eye hazard

The delivered laser system is classified according to DIN IEC 60825-1 as a Class 2 Laserin the basic version without output coupler mirror. If additional optics like output mirrors,other mirrors, prisms or filters are used like in the full version of this system it is classifiedaccording to DIN IEC 60825-1 as a Class 3B Laser.This means the visible, continuous wave laser radiation that can be emitted during the laseroperation has an average power of less than 5 mW. Therefore the laser radiation itself andalso the stray light is potentially dangerous to the eye. It is recommended to use the appro-priate laser safety goggles in addition with protective sides against laser stray light causedby additional optics during the measurements. Because some measurements and the aign-ment procedure may require to remove temporary the protective goggles it’s very importen toremove all reflecting objects attached to your hands/wrist (e.g. rings, watches etc.).

1.2 Chemical hazard

Acetone and its vapours are toxic. Use the minimal required quantity of acetone while clean-ing the optical elements. Do not sniff the vapours of the acetone for prolonged periods. Avoidcontact with skin or eyes. If accidental contact happens, wash the interested area with abun-dant cold water. Do not hesitate to ask for assistance if pain persists.

2 Theoretical basics

2.1 Helium Neon Laser

A helium-neon laser is a gas laser, consisting of a mixture of helium and neon gas in a ratiobetween 5:1 and 20:1 bound in a glass tube. The pump energy of the laser is provided by anelectrical discharge of several hundred Volts between an anode and catode at each end of theglass tube. A current of 5 to 100 mA is typical for cw operation. The used HeNe tube hasBrewster’s angle windows at both ends. The HeNe Laser may work at different wavelengths.There are infrared transitions at 3,39 µm and 1,15 µm and different transitions in the visualspectrum. Normally a HeNe Laser is working on the red 632,816 nm wavelength with a verynarrow gain bandwidth of a few GHz, which is dominated by Doppler broadening. The laserprocess in a HeNe laser starts with collision of electrons from the electrical discharge withthe helium atoms in the gas, which excites helium from the ground state to the 23S1 and 21S0metastable excited states. Collision of the excited helium atoms with the ground-state neonatoms results in transfer of energy to the neon atoms, exciting neon electrons into the 3S2level. The difference between the energy states of the two atoms is in the order of 0,05 eV,which is supplied by a kinetic energy. The number of neon atoms in the excited states builds

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He Ne Laser

Figure 1: Energy level diagram of a He Ne system (origin: http://en.wikipedia.org/wiki/File:Hene-2.png)

up as further collisions between helium and neon atoms occur, causing a population inversion.Spontaneous and stimulated emission between the 3s2 and 2p4 states results in emission of632.82 nm wavelength light. After this, fast radiative decay occurs from the 2p to the 1sground state. For more details we recommend to read [6]. Also more basics about laserprinciples may be read in [7], specially about rate equations.

2.2 Basics of resonator modes

Laser light usually is assumed to have a Gaussian intensity distribution in the transverse plane.Details of the theory of Gaussian beams can be found in [2]. Here only final expressions aregiven.The intensity distribution of the laserspot in the beam waist plane for the fundamental modesTEM00 Mode is discribed by gaussian profile

I(r, z) = I0 exp−2r2

w(z)2 , (1)

with r as the distance from the beam center. Higher modes are characterised by the gaussiandistribution and the so called Hermit or Laguerre polynomials.The lasermode keeps the gaussian distribution along the resonator but the beam width (thedistance from the beam axis to the point where the intensity drops to 1/e2) increases withincreasing distance from the beam waist. In a certain distance z the beam width w(z) is givenby

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He Ne Laser

Figure 2: Gaussian beam width w(z) as a function of the axial distance z. w0: beamwaist; b: depth of focus; zR: Rayleigh range; θ: total angular spread (origin:http://en.wikipedia.org/wiki/Gaussian_beam)

w(z) = w0

√√1 +

λzπw2

0

2

. (2)

The radiation converge to the beam waist und diverge with increasing distance from thecenter of the resonator, having the wavefront plane in the waistplane. In distance z from thewaist the radius of the wavefront curvature R(z) is

R(z) = z

1 +πw2

0

λz

2 (3)

In a confocal resonator (the focal points of both mirrors are at the same point) the beamwaist is in the middle of the resonators with the distance d between the mirrors and the beamwaist is given by

w0 =

√λd2π

(4)

In a non confocal resoantor the stability parameters g1 and g2 have to be defined

g1 = 1 − (d/R1)

g2 = 1 − (d/R2), (5)

whereas d is the resonator length and R1 and R2 are the curvatures of the mirrors. To reacha stable resonator mode the wavefront curvature has to be equal to the curvature of the used

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He Ne Laser

Figure 3: Stability diagram for a two-mirror cavity. Blue-shaded areas correspond to stable configura-tions. (origin:http://en.wikipedia.org/wiki/Optical_cavity)

resonators. By this request it is possible to evaluate the position and size of the beam waist, andthe spot size on the the mirros may estimated. Hence we know the curvature of the beamfrontin two points, which we name z1 (distance of the beam waist to mirror 1) and z2 (distance ofthe beam waist to mirror 2). If one equalize R(z1) = R1 and R(z2) = R2 one may evaluate theposition of the beam waist

z1 =g2(1 − g1)

g1 + g2 − 2g1g2d, (6)

and the radius of the beamwaist

w0 =

(λdπ

)1/2 (g1g2(1 − g1g2)g1 + g2 − 2g1g2

)1/4

. (7)

The so called stability area is defined by

0 < g1 · g2 < 1. (8)

Whitin this region of resonator parameters stable mode structure is guaranteed. If g1 ·

g2 is >1 the spot size is imaginary or infinity. If g1 · g2 is nearly or equal to one the spot sizemay be greater than the resonators, resulting in significant losses, that means mode instability.

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He Ne Laser

2.3 Transversal modes in a laser resonator

In a laser with cylindrical symmetry, the transverse mode patterns are described by a com-bination of a Gaussian beam profile with a Laguerre polynomial. The modes are denotedTEMpl where p and l are integers labeling the radial and angular mode orders, respectively.The intensity at a point r,φ (in polar coordinates) from the centre of the mode is given by:

Ipl(ρϕ) = I0ρl[Ll

p(ρ)]2 cos2(lϕ)e−ρ (9)

where ρ = 2r2/w2, and Llp is the associate Laguerre polynomial of order p and index l, w is the

spot size of the mode corresponding to the Gaussian beam radius.With p=l=0, the TEM00 mode is the lowest order, or fundamental transverse mode of the laserresonator and has a form of a Gaussian beam. The pattern has a single lobe, and has a constantphase across the mode. Modes with increasing p show concentric rings of intensity, and modeswith increasing l show angularly distributed lobes. In general there are 2l(p+1) spots in themode pattern (except for l=0). The overall size of the mode is determined by the Gaussianbeam radius w, and this may increase or decrease with different distance form the beamwaist,however the modes preserve their general shape. Higher order modes are relatively largercompared to the TEM00 mode, and thus the fundamental Gaussian mode of a laser may beselected by placing an appropriately sized aperture in the laser cavity.

Figure 4: Rectangular transverse mode patterns TEM(mn) (origin:http://en.wikipedia.org/wiki/Transversemode)

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He Ne Laser

In many lasers, the symmetry of the optical resonator is restricted by polarizing elementssuch as Brewster’s angle windows. In these lasers, transverse modes with rectangular symme-try are formed. These modes are designated TEMmn with m and n being the horizontal andvertical orders of the pattern. The intensity at point x,y is given by:

Imn(x, y) = I0

Hm

√2xw

exp(−x2

w2

)2 Hn

√2yw

exp(−y2

w2

)2

(10)

where Hm(x) is the m-th order Hermite polynomial. The TEM00 mode corresponds to ex-actly the same fundamental mode as in the cylindrical geometry. Modes with increasing m andn show lobes appearing in the horizontal and vertical directions, with in general (m+1)(n+1)lobes present in the pattern. As before, higher-order modes have a larger spatial extent thanthe 00 mode. The overall intensity profile of a laser’s output may be a superposition of any ofthe allowed transverse modes of the laser’s cavity, though often it is desirable to operate onlyon the fundamental mode.

2.4 Optical elements for the wavelength selection

2.4.1 Brewster’s angle

Let us consider an electromagnetic wave having the polarisation parallel to the plane of inci-dence. There will be an incidence angle, called Brewster’s angle, for that no reflection occur,considering this particular polarisation state.

(a) (b)

Figure 5: (a)An illustration of the polarization of light which is incident on an interface at Brewster’sangle.(origin: http://en.wikipedia.org/wiki/Brewster_angle) (b) Reflection coefficient for differentangles of incidence (origin:http://en.wikipedia.org/wiki/Fresnel_equation)

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He Ne Laser

While the incident angle is equal to the Brewster’s angle the reflected and transmitted beamsare perpendicular to each other. Hence by using the law of refraction n1 · sin θB = n2 · sin θ onemay easily calculate the Brewster’s angle by

θB = arctann2

n1. (11)

2.4.2 Fabry Perot Etalon

A Fabry Perot Etalon consists of two exactly parallel high reflective mirrors. Transmission oflight by a given wavelength λ occurs only if

mλ = 2nd cos θ, (12)

with d is the distance between the two mirrors and θ is the angle between the optical axis andthe surfacenormal of the mirrors. Hence an Etalon is capable to seperate different wavelengthsby either tilting the etalon or increasing the distance of the mirrors.

Figure 6: Light enters the etalon and undergoes multiple internal reflections. (origin:http://en.wikipedia.org/wiki/Fabry_Perot)

The etalon used in this lab has a aperture of 12,7 mm and a thickness of 10 mm.

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He Ne Laser

2.4.3 Littrowprism

A littrow prism is built on a prism and a mirror fixed at one surface of the prism. Due tothe wavelength depending refraction of the prism each laser wavelength will propagate ata certain other direction trough the prism and hit the mirror with different angles. So onlyone wavelength will be back reflected in the incidence beam. Therefore one may separatewavelengths by turning the Littrowprism in the light pass.

Figure 7: If a shaft of light entering a prism is sufficiently narrow, a spectrum results. (origin:http://en.wikipedia.org/wiki/Prism_(optics))

2.4.4 Birefringent filter

Here another effect is used to select different wavelengths. In a birefrigent crystal the opticalproperties, as the index of refraction, vary with the direction of arrival. In the simplest case ananisotropic crystal has one axis of symmetry, called the optic axis. By propagation parallel tothe optic axis the index of refraction is independent on the oscillation direction of the E-fieldvector. If the propagation has another direction the incident ray is split into the ordinary andextraordinary ray. Each of them experiences another index of refraction (no and ne) dependingon the angle of incidence. Also the two beams propagate in different directions, according totheir index of refraction and the direction of the optic axis. In this lab the optic axis is parallelto the surface of the quartz crystal. Hence the ordinary and extraordinary ray have a differentindex of refraction but no walk off occur. Thus the quartz crystal may be used as phase plate.Here we may seperate the incident E field vector into one component parallel and one per-pendicular polarised to the optic axis. The component Ee, which is parallel to the optic axispolarised, will propagate as extraordinary wave with the index of refraction ne and the otherone as ordinary wave Eo with no. If no > ne the two beams will have after a certain propagationdistance d a phase difference of (no-ne)·d. If this phase difference is equal π/2 and the ampli-tude of the ordinary and extraordinary beam are equal the phase plate convert linear polarised

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He Ne Laser

light into circular polarised light. Such a phase plate is called λ/4 plate. After another transi-tion the light is again linear polarised. Hence each wavelength has another index of refractiononly a certain wavelength will be linear polarised after two transitions through a λ/4 plate.

2.4.5 Transmission grating

When a wave propagates, each point on the wavefront can be considered to act as a pointsource, and the wavefront at any subsequent point can be found by adding together the contri-butions from each of these individual point sources. An idealised grating is considered herewhich is made up of a set of long and infinitely narrow slits of spacing g. When a plane waveof wavelength λ is incident normally on the grating, each slit in the grating acts as a pointsource propagating in all directions. The light in a particular direction, θ, is made up of theinterfering components from each slit. Generally, the phases of the waves from different slitswill vary from one another, and will cancel one another out partially or wholly. However,when the path difference between the light from adjacent slits is equal to the wavelength, λ,the waves will all be in phase. Thus, the diffracted light will have maxima at angles θm givenby the grating equation

g sin θm = mλ, (13)

with m as an integer and d as the separation of the slits. The light that corresponds todirect transmission is called the zero order, and is denoted m = 0. The other maxima occur atangles which are represented by non-zero integers m. Note that m can be positive or negative,resulting in diffracted orders on both sides of the zero order beam.

Figure 8: Diffraction of light by a grating. (origin: http://de.wikipedia.org/wiki/Optisches_Gitter)

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He Ne Laser

3 Setup and equipment

The setup consists of the following components

• Profile Rail (1)

• HeNe Laser Tube with power supply (2)

• Laser mirror adjustment (3 + 4)

• Photo detector in holder (5)

• Alignment laser with power supply (6)

• Birefringent tuner (7)

• Littrow prism tuner (8)

• Single mode etalon (9)

• Set of laser mirros in holder (10)

– PLAN - plane mirror– FL1000 - mirror curvature 1000 mm– FL700 - mirror curvature 700 mm– OC24 - plane mirror output 2,4 %

• Grating (600 lines /mm)

• Translation stage with thin filament

3.1 Setup alignment procedure

3.1.1 Basics

For the whole setup it is very importent that all optic elements are well cleaned and that thereis no pollution on the optics.The first job is the definition of the optical axis of the laser system. For this purpose the align-ment laser may be used.The next step is to adjust the laser mirros perpendicular to the optical axis so that the backreflected beam hits itself exactly at its beam output aperture. The perfect alignment to thedefined optical axis can be recognized by observing a flickering laser beam caused by inter-ference effects with the plane mirror in the holder.Afterwards the main laser tube has to be centered in the adjustment beam. Be sure that theBrewster’s angle windows of the main laser (2) are well cleaned and its power supply is

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He Ne Laser

Figure 9: Setup of the used elements (origin: micos He-Ne Laser manual)

switched off. The goal is to adjust the main lasers capillary around the optical axis of the ad-justment laser. The actual position can be observed at a reflective screen like a piece of whitepaper.Finally to get the laser light arrange the pre-adjusted components 2,3 and 4 like in fig.9.Switch off the adjustment laser 6 and switch on the main laser tube 2. If no laser light can beobserved, a gentle twisting of max. +/- 45◦ of one of the adjustment screws shown in the draftabove cause the oscillation flicker up. If you get the laser oscillation the output power can beoptimized with the position of the laser mirrors and supplementary with the X/Y adjustmentsof the main tube. Afterwards the laser output power has to be optimized.Now you can start with the begin to measure teh laser output power depending of dif-ferent laser geometries (Task number 4) to 7)) For measuring of the wavelength the gratingand a screen should be used.

3.1.2 Further adjustment of the optical elemtents

Littrow prism The adjustment of the Littrow prism may be done with the same procedurelike the laser mirros were adjusted. Afterwards the parts 2 and 3 can be assembled again andthe main laser can be switched on. The cleaning of the optics is tremendously important. Ifthe laser starts oscillating, optimize it for very best intensity. The laser line tuning can be donewith the adjustment screws of the Littrow prism.Birefringent filter (BFP) Rotate the insert of the birefringent filer (8) to the brewster’s angle.Insert the birefringent filter (8) between the adjustment laser (6) and one plane mirror (4).

13

He Ne Laser

Repeat the alignment of the laser mirror to eliminate the beam displacement of the insertedoptic. If finished the set-up can be completed again. Anotehr way is to directly place the BFPin the adjusted laser. With a gentle twist of one of the adjustment screws, the laser may startagain. However this procedure is very fragile and only possible, when the laser runs at thehighest output power. If the BFP is rotated around it optical axis you can see the main lineseveral times. If the birefringent filter is rotated in small angles around one main line you canget additional wavelengths with different gains.Etalon The Etalon (9) will be placed on the rail instead of the BFP (8). If put into the resonatorthe laser normally keeps its oscillation more or less strong. If the back reflections at the mirrorsurface (3) are observed you can identify a non perpendicular adjustment with several spots.The zero order adjustment is achieved if all reflections fall into the beam of the main laser.Other orders can adjusted by tilting the etalon holder (9).The achievement of another laser wavelength then the main wavelength is very difficult andfragile. At first try to maximize the output power. By using the 700mm curvature mirrorand the 2,4% transmission mirror, an output of 3,5 mW is possible. Also by using the BFPa output power of 3 mW is possible. At such a high output power it’s very easy to get laseroscillation at different wavelengths. At a output power which is lower than 3 mW the gainof a wavelength different from the main wavelength may be to low to compensate the losseswithin the resoantor.The birefringent filter should be used at first. After the BFP is build into the resonator andthe laser is running, one may see the main line up to 4 times. The strongest one should bechoosen and the laser should optimized again. If the birefringent filter is rotated in smallangles around chosen main line one can gat additional wavelength with different gains. Onemay vary between different laser wavelengths by using the grating, as the position of thediffracted beam depends on the used wavelength.With the Littrow one may see the change of the wavelength easily because the colour changesfrom red to orange. Here the Littrow prism should be used instead of the outputcoupler,together with the 700 mm curvature mirror. Keep the distance between the prism and the lasertube as short as possible and minimize the resonator length. Afterwards you can place thegrating behind the curved mirror and use this faint laser output for the wavelengthselection.The Etalon will be places on the rail instead of the BFP. If put into the resonator the lasernormally keeps its oscillation more or less strong. By using the Etalon one may find anotherwavelength only if the Etalon is placed exactly perpendicular into the beam. That’s the case,if no backreflection occur. The zero order adjustment is achieved if all reflection fall into thebeam of the main laser. Afterwards one may achieve different wavelengths by a slight tilt ofthe etalon.

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He Ne Laser

4 Goals of the experimental work

In this lab different combinations of mirrors (M1 and M2) are used as resonator. These are:a) M1: plan, M2: R = 1000 mmb) M1: plan, M2: R = 700 mmc) M1: plan, M2: pland) M1: R = 700 mm, M2: R = 1000 mm

1. (at home, before the lab) Evaluate the beam width inside the resonator for a resonatorlength of d = 50 cm. Use all four mirror combinations.

2. (at home, before the lab) Evaluate the optical stability area for all given mirror combi-nations.

3. Build up and align a stable running He Ne Laser out of the given components.

4. Measure the dependence of the laser output power on the tube current for d = 50 cm forthe mirror combination a), b) and c).

5. Measure the dependence of the laser output power on the resonator length for I = 6,5 mAand mirror combination a) and b).

6. Measure the output power dependence on the laser tube position while using the mirrorcombination a) and c) and a tube length of 50 cm.

7. Measure the laser wavelength by using the grating.

8. Change the laser setup in order to achieve another laser wavelength by using differ-ent optic elements. Measure the wavelength and the gain in comparision to the mainwavelength.

9. Additional: Change the setup by using a thin filament in order to achieve higher TEMmodes.

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He Ne Laser

5 Appendix

5.1 Preliminary questions

What kind of Laser is used for this experiment? What are the main condition for a stablelaser generating? Is the used laser radiation polarized and when yes in which direction, why?Determine the Brewster’s angle for the air - quartz transition? What’s the meaning of thestabilty area of two mirrors? Which parameters are importent to achieve an high laser output?How can you achieve different output wavelengths of the laser? How can you measure this?Keywords: resonator, polarisation, wavelength, frequency, laser, gauss beam

5.2 Final questions

What’s the used setup? How does a He Ne works? How can you achieve a stable runningHe Ne Laser? What’s about the polarisation? Which parameters of the laser geometry canyou change? What consequences have these changes? What is about the laser wavelength?What’s the content of gaussian optics? Which optical elements have you used and how didthey work?

References

[1] Young, M.: Optics and lasers: including and optical waveguides. 4th edition. Springer,Berlin, 1993

[2] Saleh, B. E. A. ; Teich, M. C.: Fundamentals of Photonics (Wiley Series in Pure andApplied Optics). 2nd edition. JohnWiley & Sons, Hoboken, New Jersey, 2007

[3] Homepage of wikipediaURL=<http://www.wikipedia.org/>, 2007-10-06

[4] Träger, F.: Springer handbook of lasers and optics, (Springer). 1st Edition 2007.

[5] Homepage and encyclopedia of the RP Photonic Consulting GmbHURL=<http://www.rp-photonics.com/encyclopedia.html>

[6] Svelto, O.: Principles of Lasers

[7] Siegman, E.: Lasers, University Science Books (January 1986)

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