The helium-neon laserLuuk Vermunt

(Dated: 9 April 2015)

In this paper a detailed description of the physical properties of the helium-neon laser is presented. Aspectslike the energy level scheme, broadening mechanisms and gain coefficient will be discussed in detail and/orcalculated as example. In the end a short discussion of a recent experiment using a He-Ne laser and a back-of-the-envelop calculation of the output power of a typical He-Ne laser is given. This calculation leads to aoptimum output power of 28.3 mW/m2 for a typical 632.8 He-Ne laser.

I. INTRODUCTION

The helium-neon laser was one of the first lasers evermade. The physicist Ali Javan, William Bennett andDonald Herriott developed it in the same year as thefirst functioning laser ever was made (which was in 1960).However, the He-Ne laser differed from its predecessorsbecause it was the first gas and truly continuous-wavelaser. Javan et al.1 used the 1.152 μm transition of Neonin their demonstration, but nowadays almost all possibletransitions have been explored. The most famous He-Nelaser is the typical 632.8 nm red-light laser, discoveredby White and Ridged2. The highest gain in the visiblespectrum can be achieved with this transition and it istherefore the most used He-Ne laser.

Helium-neon lasers have been used a lot in scientific re-search, but because of the relative low output power andadvances in semiconductor diode laser technology mostof them are replaced nowadays. They were even pre-dicted to become obsolete twenty years ago, but luckilythis prediction turned out to be wrong. He-Ne lasers arestill manufactured a lot and are sold more than all otherlasers together3.

In this paper physical properties of the He-Ne laser willbe discussed in detail. First of all a short introductioninto gas lasers will be given after which we delve intoJavan’s discovery. In the end a small calculation of theoutput power of the 632.8 nm transition and a discussionof a recent experiment on wheat seedlings which used aHe-Ne laser will be given.

A. Lasers

A laser is a light source based on the optical ampli-fication of stimulated emission (hence the acronym forlaser: Light Amplification by Stimulated Emission ofRadiation). Stimulated emission, which is the processwhere a photon induces an excited atom to emit a newphoton identical to the incident one, was proposed byAlbert Einstein in 1917 and is one of the three ways inwhich light can interact with atoms. Absorption andspontaneous emission, respectively the process where anatom in the ground state absorbs a photon and moves tothe excited state and the process where an excited atomemits a photon and decays to the ground state, are the

two other possibilities.

To obtain optical amplification, there have to be suf-ficient stimulated emission to overcome the absorptionprocess. This is a rare property of a system, called popu-lation inversion, which can not be achieved in a thermalequilibrium. It is also impossible to obtain a populationinversion with just two energy levels because the lifetimeof a typical excited atom is too short (about 10-8 sec-onds). This means that the electron will drop back asfast as they can be pumped up. More energy level sys-tems are needed as requirement for a laser. A typicalhelium-neon laser uses two helium and four neon energylevels and is therefore called a four-level laser. The energylevel scheme will be discussed in more detail in sectionII.

B. Gas lasers

Most of the gas lasers use electrical discharge as excit-ing mechanism, but there are also experiments performedwhere the laser was driven by optical pumping mecha-nisms or excitation by chemical reaction4. However, He-Ne lasers are no exception and the exciting mechanismis just an electrical discharge. The simplest form of sucha laser is illustrated in Figure 1. A gas is placed in along cylindrical tube connected to a voltage source forthe discharge process and a pair of mirrors at the end ofthe tube to amplify the radiation.

An electrical discharge in a gas will lead to a lot ofdifferent interactions but not all of them ensure a popu-lation inversion. Which specific process is responsible de-pends on variables like the total pressure, the nature and

FIG. 1. A schematic illustration of a gas laser driven byelectrical discharge. The voltage source is used to excite theatoms in the gas discharge tube which will lead to a popula-tion inversion. On both ends of the tube a mirror is placedto amplify the radiation.

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lifetime of the atomic/molecular energy levels, the elec-tron energy, electron density and the dimensions of thetube. A list of all mechanisms goes far beyond the scopeof this paper, but a small enumeration can be given. Themajor part of the gas lasers, including the He-Ne laser,use one of these five basic mechanisms5:

• Collisions of the first kind.• Collisions of the second kind.• Line absorption.• Molecular dissociation via repulsive states.• Photo-dissociation.

II. THE HELIUM-NEON LASER

In a helium-neon laser the He atom is excited by anelectrical discharge. Collisions of the second kind be-tween helium and neon atoms ensure the required popu-lation inversion between the neon energy states. A sec-ond kind collision is a process where the energy of ametastable state of one gas lies very close to the energyof an excited state of an other gas. An inelastic colli-sion between the two different atoms will then providea transfer of excitation energy. For the He-Ne laser thiscollision will look like this (where subscript ’ex’ meansthe exited state and ’gr’ the ground state):

Heex + Negr → Hegr + Neex + ∆E.

The transfer cross-section of the collision, which tells youhow likely it is for this event to happen, will depend onthe energy difference (∆E) and the velocity of the atoms(so the temperature of the gas mixture). For low pressuredischarges used in most gas lasers, cross-sections of theorder 10-16 cm2 can be obtained for energy differences of0.025 to 0.050 eV (or ∆E = 200 to 400 cm-1)6. For higherenergy differences the cross-section of the collision maybe considered negligible and collisions of the second kindare no longer sufficient to obtain a population inversion.

Transitions between one quantum state to another, likecollisions of the second kind, are constrained by selectionrules. An example is the Wigner Spin Rule7. This is a se-lection rule that applies to the collisions between heliumand neon. Such a collision is only likely (note that it isnot impossible) when the total spin of the system is con-served. So the two series |SHe+SNe| to |SHe−SNe| beforeand after the collision need a common term. Surprisingly,the transition between the helium and neon atom is oneof the relatively rare collisions where this rule is violated.The spin of the excited helium atom is 1, where the spinsof the three other states are 0, so spin is not conserved.

A selection rule which is not violated and needed forthe He-Ne laser to work is the parity selection rule. Thisrule ensures that the excited helium atoms do not decayby electric dipole transitions to their ground state. Aelectric dipole transition requires a change in parity, butboth He states have even parity, and a transition between

these states is therefore highly forbidden. Because of thisthe excited energy levels are metastable and can be usedto excite neon atoms.

There are also selection rules for the transitions in theneon atom itself, which have been calculated for l = 1,2 and 3 using the j-l coupling scheme of Racah8. Therules for allowed transitions are ∆jc = 0, ∆le = ±1,∆k = ∆(jc + le) = 0 and ∆J = ∆(jc + je) = 0 or ± 1(where subscript ’c’ means core and subscript ’e’ excitedelectron).

A. Energy level scheme

Two of the energy levels of the excited helium atomlie very close to those of the neon atom and can there-fore be used as driving mechanism to obtain a popula-tion inversion. These two combinations are the 21S0 Helevel with the 2p55s Ne level (3s2 in the more standardPaschen notation) and the 23S1 He level with the 2p54sNe level (2s2). The energy difference between these twolevels is respectively 386 cm-1 and 313 cm-1, which issmall enough for the cross-section to not be negligible9.Collisions of the second kind lead to a population inver-sion between the just enumerated neon states with thelower 2p54p and 2p53p energy levels (respectively 3p4

and 2p4). Between these levels slow decays in the visibleand infra-red will happen (lifetimes of the order τ2 ≈ 110ns). The two lower states decay by relative fast UV tran-sitions to the 2p53s configuration (τ1 ≈ 20 ns). The ratioof the two lifetimes (τ2/τ1) is therefore very favourablewhich ensures that the population inversion between the3s2/2s2 and 3p4/2p4 states is maintained and lasing ispossible.

For the 2p55s and 2p54s state relative fast decays viaelectric dipole transitions in the vacuum violet towardsthe ground state of neon (τ2 ≈ 10−20 ns) are also possi-ble. These transitions can destroy the population inver-sion which is needed for lasing, so a way to block themis needed. Fortunately a solution have been found by in-creasing the neon pressure. At pressures above 0.05 Torrthe probability to reabsorb the emitted resonance radia-tion by neon atoms in their ground state is so high thatthese electric dipole transitions can be considered as fullyblocked.

There exists also a possibility that the 2p53p configu-ration gets populated by electron impact with the 2p53sconfiguration. This is another problem which breaksdown the population inversion, so a fast way is neededto destroy these metastable 2p53s states. This can beachieved by making at least one dimension of the cavitysufficiently small. In this case, the atoms in the 2p53sstate will diffuse to the walls and return to the groundstate of the Neon atom before they can interact withelectrons.

So the He-Ne laser is based on a four level pumpingscheme where the helium, which is the one who gets

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FIG. 2. The energy level scheme of the He-Ne laser in thePaschen notation10. The helium atom is excited by electricaldischarge and interact with the neon atom using a inelasticcollision. The Ne atom gets excited by this collision towardsthe 3s2 or 2s2 state from which the laser transition can hap-pen.

pumped by electrical discharge, is only used to excite theneon atoms to the energy level where the laser transitionoccurs. This pumping scheme, in the Paschen notation,is illustrated in Figure 2. To obtain a high output powerwith these transitions, the He:Ne ratio has to be approx-imate 6:1 and a pressure-tube diameter of 3.6 Torr mmis needed9.

When the electron density of the discharge is increased,the number of excited He atoms tend towards an satu-rated value. This is because the ionization of excitedatoms by electron collisions will increase, which is a ma-jor destruction process for the excited atoms. A satura-tion value for the excited helium states has of course alsoconsequences on the excitation rate of the Ne 3s2 and 2s2energy levels. Unfortunately, little can be done to solvethis problem.

B. Broadening mechanisms

A transition which is used in a laser is never perfectly’sharp’, the outgoing spectrum will always be broadenedbecause the transition has a finite lifetime. However, thisnatural line width is mostly not the real limit. A broad-ening caused by the random movements of molecules ina gas, called the Doppler shift, has more impact. Alsothe pressure, which indicates the number of collisions,can broaden the spectrum. Each broadening process canbe classified in two types. If the broadening mechanismis the same for each quantum emitter the broadening

is called homogeneous, while the broadening is inhomo-geneous when every emitter has a different broadeningfluctuation.

The broadening of the He-Ne laser is depicted as acombination of a homogeneous curve from the naturalline width of neon and a inhomogeneous part from theDoppler shifts. However, the increase in neon bandwidthdue to the homogeneous part is quite small, so the tran-sition spectrum of a He-Ne laser will be mainly inhomo-geneously broadened. The FWHM value for this broad-ening is 1.5 GHz for the 632.8 nm transition (but only315 MHz for the 3.391 μm transition)6.

C. Amplification

For a He-Ne laser to work amplification (also calledgain), which is provided by stimulated emission in thegaseous helium-neon medium, is needed. The strength ofthis interaction is parametrized by the stimulated emis-sion cross-section. The gain has to overcome the lossesin the cavity (for example through diffraction at the mir-rors, scattering in the medium or absorption of the pho-tons by neon atoms) to reach a steady-state with a non-zero intensity. If this threshold is overcome, the inten-sity will grow with each passage through the cavity (for a632.8 nm He-Ne laser this is about 2-4 percent per round-trip)9. However, this can not go on forever. The gaincoefficient, which describes the growth of the spectral in-tensity of the beam, is a function of the intensity itself.At high intensities the increased rate of stimulated emis-sion will reduce the population inversion. This is calledgain saturation which leads to a saturation intensity.

I will now give three small calculations for the stim-ulated emission cross-section, gain coefficient and thesaturation intensity. A He-Ne laser operating at 632.8nm with a 60 mA discharge current, tube diameter of6 mm, He-Ne mixture ratio of 7:1 and a pd of 3.6 Torrmm is used. The emission for this laser is dominatedby Doppler broadening with a line width of ∆νD = 1.5GHz (∆νH = 14 MHz11) and a transition probability ofA21 = 3.4 · 106 s-1. The gain cross-section and the stim-ulated emission cross-section (also called homogeneouscross-section) can be calculated with respectively equa-tion 1 and 2:

σD21 =

√ln 2

16π3

λ221A21

∆νD= 3.4 · 10−13 cm2, (1)

σ21 =λ221A21

4π2∆νH= 2.5 · 10−11 cm2. (2)

To calculate the gain coefficient the population inver-sion density N∗ is needed. Data8 can be found fromwhich follows that N∗ ≈ 109 cm-3 is a good approx-imation for a 632.8 He-Ne laser. The gain coefficient,α = N∗σ21, is therefore 2.5 m-1.

To calculate the saturation intensity the recovery timeτR = τ2 + g2/g1τ1(1 − A21τ2) = 117 ns is needed. This

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FIG. 3. Cross-sectional view of a Melles Griot He-Ne laserhead. The discharge runs from the anode along the lengthof the tube to the cathode. A getter is used to clean up anresidual traces of molecular gases. The entire tube is sealedwith a shutter which prevents the laser against inadvertentexposure.12

leads to an saturated intensity of:

Isat =hc

λ21τRσ21= 1.0 · 103 W/m2. (3)

III. LASER CONSTRUCTION

The construction of a modern He-Ne laser operatingat the 632.8 nm transition is indicated in Figure 3. Adetailed description of all parts goes outside the scope ofthis paper, but a few things are still worth to mention.

Nowadays, the cavity mirrors are sealed directly on theends of the discharge tube but this was not the case in thefirst He-Ne lasers. These were constructed with the mir-rors external to the gas envelope which resulted, logically,in more losses per round-trip. To reach the gain thresh-old of the laser, the gas envelope needed to be closed withwindows tilted at Brewster’s angle. This led to a trans-mission of 100% for a certain polarization of the incidentlight. Using this mechanism the threshold was exceeded,however the output of the laser was completely plane po-larized. With the cavity mirrors sealed on the ends ofthe gas tube, as in present-day He-Ne lasers, Brewster’swindows are not necessary any more and the laser out-put is unpolarized. It is still possible though to achievelinear polarized light by fitting in a Brewster window inthe indicated box in Figure 3.

The mirrors of He-Ne lasers are curved in a stable,near-confocal arrangement. The right mirror is a highreflector with a coated mirror surface to obtain maxi-mum reflectivity at the lasers wavelength. The radiationfrom other transitions is deflected by small angles at thismirror and can be absorbed afterwards. So only radia-tion with the right wavelength will oscillate and profitfrom the population inversion in the cavity. The typicallengths of the cavities of modern He-Ne lasers are 15 to

50 cm. Such a length allows two to eight longitudinalmodes to oscillate in the cavity. The left mirror trans-mits 0.5 to 1% of the radiation, which means that theintensity in the cavity is up to 200 times more intensethan the output of the laser.

For the laser to operate sufficiently, a pure mixture ofhelium and neon is needed in the gas tube. Because thelaser is filled with only a small amount of gas (1 Torr =1/760 atmosphere), this mixture can be easily ruined byleakage from outside the laser. To prevent this a getteris placed inside the laser. The material of the getter isavailable to chemically combine with unwanted moleculesinside the cavity. Because helium and neon are noblegasses they do not interact with the getter and so thepure mixture is maintained.

A. Calculation of the output power

In this section a back-of-the-envelope calculation of theoutput power of a typical He-Ne laser is given. I will usethe same laser as in subsection II C for which σD

21, σ21,α0 and Isat have already been calculated. The propertiesof the laser are summarized in Table I.

With the exception of the 3.39 μm, all helium-neonlasers are low-gain lasers. This makes the calculationof the output power considerably easier because we canassume that the right- and left-going beams (respectivelyI+ and I− in the cavity have a near-constant intensity.In equation form this assumption means I(z) = I+(z) +I−(z) ≈ 2I+(z) ≈ 2I+. Because the increase in intensityis small per round-trip, we can also assume that the gaincoefficient does not change appreciably with position inthe gain medium. The saturated gain coefficient αI istherefore not dependent on z.

The total intensity of the right-going beam will growaccording to,

dI+dz≈ I+(ltube)− I+(0)

ltube= αII+. (4)

The round-trip gain is twice this value, so the fractionalincrease in intensity δgain = 2αI lg with αI = α0/(1 +2I+/Isat).

Variable Symbol Value [Dimension]

Wavelength λ21 632.8 [nm]Discharge current Idischarge 60 [mA]Diameter tube dtube 6 [mm]Length tube ltube 30 [cm]Mixture He:Ne 7:1Pressure x diameter pd 3.6 [Torr mm]Gain cross-section σD

21 3.4 · 10−13 [cm2]Stim. emis. cross-section σ21 2.5 · 10−11 [cm2]Gain coefficient α0 2.5 [m-1]Saturated intensity Isat 1.0 · 103 [W/m2]

TABLE I. Properties of the used He-Ne laser.

5

0.0 0.5 1.0 1.50

5

10

15

20

25

30

35

T2 @DimensionlessD

P@m

W�m

2D

Output Power 632.8 nm He-Ne laser versus transmission coefficient T2

PHT2LTopt = 0.224

Popt = 28.3 mW�m2

FIG. 4. The output power of a 632.8 nm He-Ne laser versusthe transmission coefficient T2 using the values from Table I.

We can characterize the losses in the cavity after oneround trip in a similar way:

δtotal loss = 1−R1R2exp(−2κILc) (5)

≈ (A1 +A2 + T1 + 2κILc) + T2

= δloss + T2

with A the absorption and T the transmission coefficientsand κILc representing the attenuation of the beams byscattering or other losses inside the cavity. UnfortunatelyI could not find these values for this kind of laser, so Iwill assume δloss ≈ 0.5.

Under steady-state conditions the round-trip gainmust be the same as the round-trip losses: δgain =δloss + T2. From this equation we can find the intensityof the right-going beam,

I+ =1

2Is(

2α0ltubeT2 + δloss

− 1), (6)

where the output power is simply P = T2I+Amode withAmode the cross-sectional area of the beam. We nowcan calculate the output power for different T2 using thevalues given in Table I. This output power versus thetransmission coefficient is plotted in Figure 4. At val-ues of T2 > Tth ≈ 1.5 the losses in the cavity are toolarge and no laser oscillation can occur anymore. Asthis plots shows there is an optimum output coupling atT2,opt = 0.224 which yields an optimum output power ofPopt = 28.3 mW/m2. This is approximate the same as isstated in the literature9.

IV. EXPERIMENT USING A HE-NE LASER

I will now shortly discuss an experiment from 2014which used a He-Ne laser. As I already said in the in-troduction, most He-Ne lasers are replaced by semicon-ductor diode lasers and unfortunately I could not finda physics related paper using this laser. However, in

FIG. 5. Comparison of the effects of He-Ne laser treatmenton wheat seedlings exposed to enhanced UV-B radiation. CK:control group; B: enhanced UV-B treatment group; L: He-Nelaser treatment group; B+L: combined enhanced UVB andHe-Ne laser radiation.13

other areas like for example plant biology the advancesof He-Ne lasers are just being discovered. The paperI will discuss was published in Laser Physics and writ-ten by H. Chen and R. Han13. They explored the ef-fect of continuous wave He-Ne laser radiation (632.8 nmand 5 mW/mm2) on the physiological indexes of wheatseedlings at their early growth stages which are exposedto enhanced UV-B radiation (10 KJ m-2 d-1). Because ofthe depletion of the ozone layer the level of UV-B radi-ation have increased in the last decades. This radiationhas deleterious effects on the photosynthesis parametersin wheat (for example the chlorophyll content and elec-tron transport rate). Chemical methods are used nowa-days to protect the plants, but physical methods like He-Ne radiation can be more effective and beneficial.

The use of low power continuous wave He-Ne radia-tion have only been explored recently, but the resultsare already impressive. He-Ne radiation treatment hasconsiderable biological effects on seed metabolism, en-hances the drought stress resistance and helps accelerateseedling growth and development13. Furthermore it canhelp repair UV-B-induced damage and shorten the recov-ery time. It is therefore a very interesting and promisingsubject to study.

The authors of this paper examined the effects of theHe-Ne laser treatment on the photosynthesis of wheatseedlings. After selecting representative seedlings, fourdifferent treatments were performed. The control group(group CK) with no radiation, the single enhanced UV-Btreatment (B), He-Ne laser treatment (L) and finally thecombined UV-B and He-Ne radiation treatment (BL).Some of the results are shown in Figure 5 and 6. Af-ter treatment of only the enhanced UV-B radiation,the chloroplast membrane was damaged, the contest ofchloroplast proteins were reduced and the activities inthe CF1 ATPase and the Hill reaction were significantlyreduced compared to the control group. For the com-bined UV-B and He-Ne laser group, these values werenear the ones of the control group, and for the L groupall parameters were improved.

So for all investigated parameters the trend was as fol-lows: L > CK > BL > B. The authors therefore con-

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FIG. 6. Influence of different treatments on wheat chloro-plasts. CK : control group; B: 10 KJ/m2 UV-B radiation; L:1 min, 5 mW He-Ne laser radiation; BL: combined UV-B andHe-Ne radiation treatment.13

cluded that He-Ne laser irradiation stimulated the ac-tivities of key enzymes and altered various parametersinvolved in wheat seedling photosynthesis. Single He-Nelaser radiation improved the parameters, while the com-bined He-Ne with UV-B radiation exhibited rehabilita-tion effects. When He-Ne laser radiation keeps showingpositive effects in further research, it could be an inter-

esting replacement for the chemical methods.

V. BIBLIOGRAPHY

1A. Javan et al. Population Inversion and Continuous OpticalMaser Oscillation in a Gas Discharge Containing a He-Ne Mix-ture. Phys. Rev. Lett., 6(3):106–110, 1961.

2A. White and J. Ridgen. Continuous Gas Maser Operation inthe Visible. Proc. Inst. Radio Engrs., 50:1697, 1962.

3L. Tsufura and A. White. Handbook of Laser Technology andApplications. Institute of Physics Publishing, 2004.

4W. Bennett. Gaseous Optical Masers. Appl. Opt., 1(S1):24–61,1962.

5L. Allen and D. Jones. Principles of Gas Lasers. London But-terworths, 1967.

6Berkeley. Gas Lasers. http://socrates.berkeley.edu/

~phylabs/adv/ReprintsPDF/CO2%20Reprints/02%20-%20Gas%

20Lasers.pdf. April 5, 2015.7H. Massey. Electronic and Ionic Impact Phenomena. Oxford,Clarendon Press, 1952.

8C Willet. An Introduction to Gas Lasers: Population InversionMechanisms. Pergamon Press, 1974.

9S. Hooker and C. Webb. Laser Physics. Oxford University Press,2010.

10DrBob. Energy level diagram of a helium-neon laser. http://

commons.wikimedia.org/wiki/File:Hene-2.png. April 4, 2015.11S. Goldwasser. Chapter 7. Conditions for Producing a

Laser. http://legacy.wlu.ca/documents/51776/HandoutsCh7.

pdf. April 9, 2015.12S. Goldwasser. Helium-Neon Lasers. http://www.repairfaq.

org/sam/laserhen.htm#henhlt1a. April 7, 2015.13H. Chen and R. Han. He-ne laser treatment improves the pho-

tosynthetic efficiency of wheat exposed to enhanced UV-B radi-ation. Laser Phys., 24(10), 2014.