A gas laser is a device related to optical quantum generators.
The main element of a continuous helium-neon laser is a gas discharge tube T(Figure 1), having a heated cathode K and anode A. The tube is filled with a helium mixture ( Not) (partial pressure Not 1 mmHg st) and neon ( Ne) (partial pressure Ne 0.1 mmHg st). The inner diameter of the tube is 1...10 mm, length from several tens of centimeters to 1.5...3 m. The ends of the tube are closed with plane-parallel glass or quartz windows P 1 and P 2, installed at a Brewster angle to its axis. For linearly polarized radiation with an electric vector in the plane of incidence, the reflection coefficient from them is zero. Therefore, Brewster windows provide linear polarization of laser radiation and eliminate energy losses when light propagates from the active zone to the mirrors and back. The tube is placed in a resonator formed by mirrors B 1 and B 2 with a multilayer dielectric coating. Such mirrors have a very high reflectance in the operating spectral range and practically do not absorb light. The throughput of the mirror through which the laser radiation predominantly exits is usually 1...2%, the other - less than 1%.
A voltage of 1...2 kV is applied to the tube electrodes. With a heated cathode and a specified voltage, a glowing electric discharge can be maintained in the gases filling the tube. The glow discharge creates conditions for the occurrence of level population inversion in neon. The typical current strength in a gas discharge is tens of milliamps.
The visible radiation of the discharge is produced by neon, but the excitation of atoms necessary for this is carried out with the help of helium atoms. Simplified schematic picture of atomic energy levels Not And Ne shown in Figure 2.
Due to collisions with electrons, atoms Not go into an excited state (2 3 S and 2 1 S). These levels are metastable with energies of 19.82 and 20.61 eV, respectively. Spontaneous radiative transition from these levels to the main level is prohibited according to the selection rules, i.e. happens with very low probability.
 Figure 2 |
Lifetime of an atom at levels 2 1 S and 2 3 S is large compared to the lifetime at ordinary excited levels, so many atoms accumulate at these metastable levels Not. But neon levels 3 S and 2 S practically coincide with metastable levels 2 1 S and 2 3 S helium Due to this, when excited atoms collide Not with atoms Ne atomic transitions occur Ne into an excited state with resonant transfer of energy from helium atoms to neon atoms.
Process of excitation of atoms Ne depicted by horizontal dotted arrows (Figure 2). As a result of the concentration of neon atoms at levels 3 S and 2 S increase strongly, and an inverse population of energy levels appears with respect to level 2 R. An active medium consisting of atoms is created in the tube Ne, which have an inverse population of electron energy levels.
Spontaneous emission of individual excited atoms leads to the propagation in the active medium of photons corresponding to electronic transitions in neon atoms from levels 3 S to levels 2 P.
Under the influence of the electromagnetic field of photons propagating in the discharge (first spontaneously emitted by excited neon atoms), induced coherent emission of other excited neon atoms occurs, i.e. active medium filling the laser tube. The massive increase in this process is ensured by the repeated passage of radiation between the mirrors IN 1 and IN 2 resonators, which leads to the formation of a powerful induced flow of directed coherent laser radiation. The minimum angular width of a laser light beam is determined by diffraction associated with the limitation of the cross section of the beam, i.e. only with the wave properties of light. This most important circumstance distinguishes a laser source from any other light source.
4 DEVICES AND ACCESSORIES
1 Gas laser LG78.
2 Optical bench.
3 Power supply.
4 Diffraction grating.
5 Glass plates with microparticles sprayed between them.
6 Screen with millimeter scale.
5 Working with a gas laser
Turn on the "Network" toggle switch. The "Current Adjustment" switch is set in the working position by the teacher or laboratory assistant. It is strictly forbidden to transfer it to another position.
When working with a laser, remember that exposure to direct laser radiation in the eyes is dangerous for vision .
Therefore, when working with a laser, its light is observed after reflection on a screen with a scattering surface.
6 ORDER OF PERFORMANCE
Exercise 1
Measuring the wavelength of laser radiation using
diffraction grating
The directionality and spatial coherence of laser radiation allows it to be used in a number of measurements without preliminary collimation.
The setup for this exercise includes a laser, a rater with a diffraction grating, and a screen with a millimeter scale for observing the diffraction pattern (Figure 3).
 Figure 3 |
The diffraction grating is installed perpendicular to the axis of the light beam emerging from the laser. To do this, the light flare reflected from the grating plane must be directed exactly to the middle of the laser output window, i.e. achieve coincidence of the light beam emerging from the laser and its reflection from the grating plane.
Due to the monochromatic nature of the laser radiation, many non-overlapping diffraction spectra of various positive and negative orders are observed on the screen. These spectra form a series of red stripes on the screen, repeating the cross section of the primary light beam incident on the grating.
The screen is installed perpendicular to the light beam, and the orders of the spectra are arranged symmetrically relative to the zero of the screen scale.
The distance between the diffraction spectra and the zero-order spectrum must be understood as the distance between the centers of the observed spectra (strips).
The wavelength is calculated using the formula
Where d- lattice constant (in our case d= 0.01 mm);
- diffraction angle;
k- spectrum order;
l is the wavelength of laser radiation.
 Figure 4 |
The diffraction angle is determined from the relation
(2)
where is the distance between the left and right maxima of the order k;
L- distance from the plane of the diffraction grating to the plane of the screen (Figure 4).
Substituting (2) into (1), we get
Procedure for performing exercise 1
1 Measure the distance in the spectrum of the first ( k= 1), second ( k= 2) and third ( k= 3) orders of magnitude at different distances of the screen from the diffraction grating.
2 Enter the measurement results in table 1.
3 Calculate the wavelength corresponding to the laser radiation.
Table 1
| Spectrum order k | L, m | X k, m | l i, m | | Dl i, m | , m | Dl, m | e, % | |
Processing of experimental data
1 Calculate the wavelength for each measurement using formula (3).
2. Calculate the average where n- number of measurements.
3 Calculate the absolute errors of individual measurements
5 Set the reliability value a (as directed by the teacher).
6 Determine using the Student’s table and calculate the boundaries of the confidence interval
7 Calculate the relative error Use the value of the found value l in the calculations required in the next exercise.
Exercise 2
Fraunhofer diffraction of laser radiation
on small round particles
The monochromatic, well collimated and spatially coherent laser beam makes it possible to directly observe the diffraction of light by round particles.
In order for the diffraction angles on particles to be significant, the particle size must be small. However, if one small particle is placed in a light beam, then the diffraction pattern given to it on a remote screen will be difficult to observe, because the picture will be projected onto a light background created by the part of the light beam that has not experienced diffraction.
To obtain a clearly visible diffraction pattern, you need to place a lot of randomly located identical particles in the path of the light beam. Indeed, since Fraunhofer diffraction is studied, any individual particle, regardless of its position in the cross-sectional plane of the light beam, produces the same distribution of diffracted light.
In the simultaneous presence of many particles in the beam cross-section, the angular distribution of diffracted light created by each particle separately is not disrupted if there is no systematic interference effect between light beams diffracted by different particles.
If the particles are randomly located in the cross-sectional plane of the light beam, then, due to the equal probability of all values of the phases of waves diffracted in different directions, only the intensities of light beams diffracted by different particles will add up. Diffraction pattern from N particles will increase in intensity in N times compared to the diffraction pattern of an individual particle, without changing its structure. This circumstance is used in the present experiment.
The installation remains the same as in Exercise 1, but instead of a diffraction grating, a mandrel with glass plates is installed on the rater, between which particles of lycopodium (moss moss plant spores), which are balls of approximately the same small size, are sprayed.
On the screen, after turning on the laser, you can observe a system of concentric light and dark diffraction rings surrounding the light circle.
Corner radii a i dark rings obey the following relations:
Corner radii a i light rings
(5)
Where r- radius of the particle that caused the diffraction of light.
Values sina i are calculated from the condition
(6)
Where D i- linear diameter of the corresponding diffraction ring on the screen;
L- distance from the glass plate to the screen.
Procedure for performing exercise 2
and processing of experimental data
1 Measure the diameters of the first ( D 1) and second ( D 3) dark rings at different distances L. Enter the results in the table. 2.
2 Build a dependence graph D=f(L) for each of the diffraction minima, i.e. D 1 = f(L)And D 3 = f(L).
3 Determine the tangents of the diffraction angles corresponding to the first and second dark rings using formula (6), and the average value of the particle radius using relations (4).
4 Determine the measurement error. Write the final result in the form r = <r> ±
5 Draw conclusions from the work.
The helium-neon laser, along with diode or semiconductor lasers, is one of the most commonly used and most affordable lasers for the visible region of the spectrum. The power of laser systems of this kind, intended mainly for commercial purposes, ranges from 1 mW to several tens of mW. Especially popular are not so powerful He-Ne lasers of the order of 1 mW, which are used mainly as quoting devices, as well as for solving other problems in the field of measurement technology. In the infrared and red ranges, the helium-neon laser is increasingly being replaced by the diode laser. He-Ne lasers are capable of emitting orange, yellow and green lines in addition to red lines, which is achieved thanks to appropriate selective mirrors.
Energy Level Diagram
The energy levels of helium and neon that are most important for the function of He-Ne lasers are shown in Fig. 1. Laser transitions occur in the neon atom, with the most intense lines resulting from transitions with wavelengths 633, 1153 and 3391 (see Table 1).
The electronic configuration of neon in its ground state looks like this: 1 s 2 2s 2 2p 6 and the first shell ( n= 1) and the second shell ( n= 2) are filled with two and eight electrons, respectively. Higher states in Fig. 1 arise as a result of the fact that there is 1 s 2 2s 2 2p 5-shell, and the luminous (optical) electron is excited according to the scheme: 3 s, 4s, 5s,..., Z R, 4R,... etc. We are therefore talking about a one-electron state that communicates with the shell. In the LS (Russell - Saunders) scheme, a single-electron state is indicated for the energy levels of neon (for example, 5 s), as well as the resulting total orbital momentum L (= S, P, D...). In the notation S, P, D,..., the lower index shows the total orbital momentum J, and the upper index indicates the multiplicity 2S + 1, for example, 5 s 1 P 1 . Often, a purely phenomenological designation according to Paschen is used (Fig. 1). In this case, the sublevels of excited electronic states are counted from 2 to 5 (for s-states) and from 1 to 10 (for p-states).
Excitation
The active medium of a helium-neon laser is a gas mixture to which the necessary energy is supplied in an electric discharge. The upper laser levels (2s and 2p according to Paschen) are selectively populated based on collisions with metastable helium atoms (2 3 S 1, 2 1 S 0). During these collisions, not only kinetic energy is exchanged, but also the energy of excited helium atoms is transferred to neon atoms. This process is called a collision of the second kind:
He* + Ne -> He + Ne* + ΔE, (1)
where the asterisk (*) symbolizes the excited state. The energy difference in the case of excitation of the 2s level is: &DeltaE=0.05 eV. During a collision, the existing difference is converted into kinetic energy, which is then distributed as heat. For the 3s level, identical relationships hold. This resonant energy transfer from helium to neon is the main pumping process when creating a population inversion. In this case, the long lifetime of the metastable state does not have a favorable effect on the selectivity of population of the upper laser level.
The excitation of He atoms occurs based on the collision of electrons - either directly or through additional cascade transitions from higher levels. Due to long-lived metastable states, the density of helium atoms in these states is very high. The upper laser levels 2s and 3s can - taking into account the selection rules for electrical Doppler transitions - go only to the underlying p-levels. For successful generation of laser radiation, it is extremely important that the lifetime of s-states (upper laser level) = approximately 100 ns exceeds the lifetime of p-states (lower laser level) = 10 ns.
Wavelengths
Next, we will consider the most important laser transitions in more detail using Fig. 1 and data from table 1. The most famous line in the red region of the spectrum (0.63 μm) arises due to the transition 3s 2 → 2p 4. The lower level is split as a result of spontaneous emission within 10 ns into the 1s level (Fig. 1). The latter is resistant to splitting due to electric dipole radiation, so it is characterized by a long natural life. Therefore, atoms are concentrated in a given state, which turns out to be highly populated. In a gas discharge, atoms in this state collide with electrons, and then the 2p and 3s levels are excited again. At the same time, population inversion decreases, which limits the laser power. The depletion of the ls state occurs in helium-neon lasers mainly due to collisions with the wall of the gas-discharge tube, and therefore, as the diameter of the tube increases, a decrease in gain and a decrease in efficiency are observed. Therefore, in practice, the diameter is limited to approximately 1 mm, which, in turn, limits the output power of He-Ne lasers to several tens of mW.
The electronic configurations 2s, 3s, 2p and 3p participating in the laser transition are split into numerous sublevels. This leads, for example, to further transitions in the visible region of the spectrum, as can be seen from Table 2. For all visible lines of a He-Ne laser, the quantum efficiency is about 10%, which is not so much. The level diagram (Fig. 1) shows that the upper laser levels are located approximately 20 eV above the ground state. The energy of red laser radiation is only 2 eV.
Table 2. Wavelengths λ, output powers and linewidths Δ ƒ He-Ne laser (Paschen transition designations)
| Color | λ nm |
Transition (according to Paschen) |
Power mW |
Δ ƒ MHz |
Gain %/m |
| Infrared | 3 391 | 3s 2 → 3p 4 | > 10 | 280 | 10 000 |
| Infrared | 1 523 | 2s 2 → 2p 1 | 1 | 625 | |
| Infrared | 1 153 | 2s 2 → 2p 4 | 1 | 825 | |
| Red | 640 | 3s 2 → 2p 2 | |||
| Red | 635 | 3s 2 → 2p 3 | |||
| Red | 633 | 3s 2 → 2p 4 | > 10 | 1500 | 10 |
| Red | 629 | 3s 2 → 2p 5 | |||
| Orange | 612 | 3s 2 → 2p 6 | 1 | 1 550 | 1.7 |
| Orange | 604 | 3s 2 → 2p 7 | |||
| Yellow | 594 | 3s 2 → 2p 8 | 1 | 1 600 | 0.5 |
| Yellow | 543 | 3s 2 → 2p 10 | 1 | 1 750 | 0.5 |
Emission in the infrared range around 1.157 μm occurs through 2s → 2p transitions. The same applies to the slightly weaker line at approximately 1.512 µm. Both of these infrared lines are used in commercial lasers.
A characteristic feature of the line in the IR range at 3.391 μm is its high gain. In the area of weak signals, that is, with a single passage of weak light signals, it is about 20 dB/m. This corresponds to a factor of 100 for a laser 1 meter long. The upper laser level is the same as for the known red transition (0.63 μm). The high gain, on the one hand, is caused by the extremely short lifetime at the lower 3p level. On the other hand, this is explained by the relatively long wavelength and, accordingly, low frequency of radiation. Typically, the ratio of stimulated to spontaneous emissions increases for low frequencies ƒ. The amplification of weak signals g is generally proportional to g ~ƒ 2 .
Without selective elements, the helium-neon laser would emit at the 3.39 µm line rather than in the red region at 0.63 µm. The excitation of the infrared line is prevented either by the selective mirror of the resonator or by absorption in the Brewster windows of the gas-discharge tube. Thanks to this, the lasing threshold of the laser can be raised to a level sufficient to emit 3.39 µm, so that only a weaker red line appears here.
Design
The electrons necessary for excitation are generated in a gas discharge (Fig. 2), which can be used with a voltage of about 12 kV at currents from 5 to 10 mA. The typical discharge length is 10 cm or more, the diameter of the discharge capillaries is about 1 mm and corresponds to the diameter of the emitted laser beam. As the diameter of the gas-discharge tube increases, the efficiency decreases, since collisions with the tube wall are required to empty the ls-level. For optimal power output, the total filling pressure (p) is used: p·D = 500 Pa·mm, where D is the tube diameter. The He/Ne mixture ratio depends on the desired laser line. For the known red line we have He: Ne = 5:l, and for the infrared line about 1.15 μm - He:Ne = 10:l. Optimization of current density also seems to be an important aspect. The efficiency for the 633 nm line is about 0.1%, since the excitation process in this case is not very efficient. The service life of a helium-neon laser is about 20,000 operating hours.
|
Rice. 2. Design of a He-Ne laser for polarized radiation in the mW range
The gain under such conditions is at the level of g=0.1 m -1 , so it is necessary to use mirrors with high reflectivity. To exit the laser beam only on one side, a partially transmitting (translucent) mirror is installed there (for example, with R = 98%), and on the other side - a mirror with the highest reflectivity (~ 100%). The gain for other visible transitions is much smaller (see Table 2). For commercial purposes, these lines have only been achieved in recent years using mirrors characterized by extremely low losses.
Previously, with a helium-neon laser, the output windows of the gas-discharge tube were fixed with epoxy resin, and the mirrors were mounted externally. This caused helium to diffuse through the glue and water vapor to enter the laser. Today, these windows are fixed by direct welding of metal to glass, which reduces helium leakage to approximately 1 Pa per year. In the case of small mass-produced lasers, the mirror coating is applied directly to the output windows, which greatly simplifies the entire design.
Beam properties
To select the direction of polarization, the gas-discharge lamp is equipped with two inclined windows or, as shown in Fig. 2, a Brewster plate is inserted into the resonator. The reflectivity on an optical surface becomes zero if the light is incident at the so-called Brewster angle and is polarized parallel to the plane of incidence. Thus, radiation with this direction of polarization passes through the Brewster window without loss. At the same time, the reflectivity of the component polarized perpendicular to the plane of incidence is quite high and is suppressed in the laser.
The polarization ratio (the ratio of power in the direction of polarization to the power perpendicular to this direction) is 1000:1 for conventional commercial systems. When a laser operates without Brewster plates with internal mirrors, unpolarized radiation is generated.
The laser usually generates in the transverse TEM 00 mode (lowest order mode), and several longitudinal (axial) modes are formed at once. When the distance between the mirrors (laser cavity length) is L = 30 cm, the intermode frequency interval is Δ ƒ` = c/2L = 500 MHz. The central frequency is at the level of 4.7·10 14 Hz. Since light amplification can occur within the range Δƒ = 1500 MHz (Doppler width), at L = 30CM three different frequencies are emitted: Δƒ/Δƒ`= 3. When using a smaller mirror spacing (<= 10см) может быть получена одночастотная генерация. При короткой длине мощность будет весьма незначительной. Если требуется одночастотная генерация и более высокая мощность, можно использовать лазер большей длины и с оснащением частотно-селективными элементами.
Helium-neon lasers around 10 mW are often used in interferometry or holography. The coherence length of such mass-produced lasers ranges from 20 to 30 cm, which is quite sufficient for holography of small objects. Longer coherence lengths are obtained by using serial frequency-selective elements.
When the optical distance between the mirrors changes as a result of thermal or other effects, the axial natural frequencies of the laser cavity shift. With single-frequency generation, a stable radiation frequency is not obtained here - it moves uncontrollably in the line width range of 1500 MHz. By means of additional electronic regulation, frequency stabilization can be achieved precisely in the center of the line (for commercial systems, frequency stability of several MHz is possible). In research laboratories it is sometimes possible to stabilize a helium-neon laser to a range of less than 1 Hz.
By using suitable mirrors, different lines from Table 4.2 can be excited to generate laser radiation. The most commonly used visible line is around 633 nm with typical powers of several milliwatts. After suppression of an intense laser line around 633 nm, other lines in the visible range may appear in the cavity through the use of selective mirrors or prisms (see Table 2). However, the output power of these lines is only 10% of the output power of an intensive line or even less.
Commercial helium-neon lasers are available in a variety of wavelengths. In addition to them, there are also lasers that generate on many lines and are capable of emitting waves of many lengths in a variety of combinations. In the case of tunable He-Ne lasers, it is proposed to select the required wavelength by rotating the prism.
WORK 17. STUDYING THE CHARACTERISTICS OF LASER RADIATION
GOAL OF THE WORK:
1. Familiarize yourself with the operating principle and design of a helium-neon laser.
2. Familiarize yourself with interference, diffraction and polarization of laser radiation.
3. Determine the periods of the two-dimensional structure.
4. Determine the divergence angle of the laser beam.
BRIEF THEORY
Laser is a fundamentally new light source. Laser radiation differs from the radiation of conventional sources (incandescent lamps, fluorescent lamps, etc.) in that it is close to monochromatic, has exceptionally high temporal and spatial coherence, and very low divergence , and, therefore, an exceptionally high density of electromagnetic energy. In addition, the laser beam is polarized.
The operating principle of the laser is based on three physical phenomena: stimulated emission, population inversion and positive feedback.
The behavior of atoms (molecules) obeys the laws of quantum mechanics, according to which the values of physical quantities (for example, energy E) can take only certain (discrete) values. For energy, these values are usually depicted graphically in the form of so-called energy levels (Fig. 1).
The lowest energy level is called the ground level, since it corresponds to the most stable state of the particle. The remaining levels with higher energy values are called excited.
A process accompanied by an increase in atomic energy is depicted as a transition to a higher energy level, a process with a decrease in energy is depicted as a transition to a lower level.
Let's consider the interaction of electromagnetic radiation (light) with atoms.
First type of interaction: an atom, being in the ground state, absorbs a photon, the energy of which is sufficient for the transition to one of the excited states (Fig. 1a).
And second: an atom in an excited state,
spontaneously (spontaneously) transitions to a lower energy state: this transition is accompanied by the emission of a photon (Fig. 1c).
During spontaneous transitions, different atoms emit non-simultaneously and independently, therefore, the phases of the emitted photons are not related to each other, the direction of the radiation, its polarization are random, and the frequency of the radiation fluctuates within certain limits, determined by the width of the energy levels E 1 and E 2.
Spontaneous emission is non-directional, non-polarized, non-monochromatic.
There is, however, third type of interaction, which is called stimulated emission. If an atom in an excited state (Fig. 2) is incident on radiation with a frequency ν corresponding to the transition of the atom to a lower state (1), then the atom passes into it forcibly under the influence of this photon, emitting its own photon, which is called stimulated emission.
It is extremely important to note the characteristic property of stimulated emission: the emitted wave (photon) has exactly the same direction and phase, which is also compelling. In addition, these two waves have the same frequencies and polarization states.
During transitions 1→2 (Fig. 1a), external radiation is absorbed, and during forced transitions 2→1 (Fig. 2), on the contrary, it is amplified, because the photon emitted by the atom is added to the external photon. The probabilities of transitions 1→2 and 2→1 are the same. If the majority of atoms are in an excited state, then 2→1 transitions will occur more often . In other words, to enhance external radiation it is necessary that population level 2 was higher than the population of level 1 or it is necessary to create inversion population levels.
At temperature T, the number of atoms N in a state with energy E is determined by the Boltzmann formula
N ~ exp(-E/kT)
where k is Boltzmann’s constant.
From this it can be seen that the higher the energy of the state E, the smaller the number N of atoms in this state. This means that in the equilibrium state, the lower levels are more populated, and the absorption of light prevails over the amplification.
The inversion of the population of levels corresponds to the nonequilibrium state of the atoms of the medium.
Such a state can be created artificially by summing up
energy to the working substance, due to which atoms are transferred to the upper energy level. This process is called pumped up. In different types of lasers, pumping is carried out in different ways: in solid-state lasers it is carried out by absorbing light from additional lamps, in gas lasers - by transferring the energy of electrons accelerated by an electric field to gas atoms during their collisions.
The medium in which the population inversion is carried out is called the active medium.
The word "laser" is made up of the initial letters of the English phrase: "Light Amplification by Stimulated Emission of Radiation", which means: "amplification of light using stimulated radiation." Lasers are also called optical quantum oscillators (OQOs).
Gas lasers. Helium-neon laser.
The main element of a helium-neon continuous-wave laser
action is tube 2 (Fig. 3), filled with a mixture of helium and neon with partial pressures of the order of 1 and 0.1 mmHg, respectively. The ends of the tube are closed with plane-parallel glass plates 3, installed at a Brewster angle to its axis.
Pumping in a gas laser is carried out using the energy of a power source that maintains a glow discharge between cathode 4 and anode 5. The discharge in the tube occurs at 1.5-2.0 kV. The discharge current of the tube is tens of milliamps.
The working atoms of a helium-neon laser are the atoms
neon, emitting red photons (λ =632.8 nm), In Fig. Figure 4 shows a simplified diagram of the levels of neon and helium atoms.
In pure neon, the population of 3S states during pumping is ineffective, since this level has a short lifetime, and the neon atom spontaneously transitions to the 2P state.
The situation changes when helium is added to neon. The energy of the 2S level of helium is equal to the energy of the 3S level of neon. The 2S energy level of helium is long-lived and is effectively populated during pumping. When excited helium atoms collide with neon atoms, energy is transferred to the neon atoms. As a result, an inverse population of the working level of 3S neon is created.
 |
After this, numerous events occur in the active medium.
acts of spontaneous transitions 3S→2P, appearing photons (λ =632.8 nm) lead to forced transitions. Those photons that move at a certain angle to the tube axis do not participate in producing the laser beam. The laser beam is formed only by photons emitted along the axis of the tube.
The beam is amplified much faster if the light is returned back to the active medium, where it will again be amplified due to forced transitions. This situation is referred to as feedback. To create positive feedback in lasers, an optical cavity is used, which consists of two mirrors 1 (Fig. 3).
The intensity of stimulated emission increases like an avalanche, and it becomes significantly greater than the intensity of spontaneous emission, which can be ignored in the future.
Generation of a laser beam begins at the moment when the increase in radiation energy due to forced transitions exceeds the energy loss for each pass of the resonator. To extract the beam from the resonator, one of the mirrors 1 is made translucent. The surfaces of both mirrors are covered with films, the thickness of which is selected in such a way that waves of the desired wavelength are reflected, and all others are extinguished.
The transparency of the resonator mirrors is usually less than 1%.
Characteristics of laser radiation.
Related information.
As an example, consider the design and operating principle of the helium-neon laser used in our laboratory. The working substance is neon atoms ( Ne). Electric pumping is used: a flow of electrons flows through a gas-discharge tube; When fast electrons collide with neon atoms, the latter are excited and their electrons move to higher energy levels. However, for neon atoms, direct pumping by electron impact turned out to be insufficiently effective. To speed up the transfer of energy, helium is added to neon ( He).
The pumping circuit is shown in Fig. 4.2. As a result of collisions with electrons, helium atoms move from the ground level to the level 2
S. These excited helium atoms collide with neon atoms and release their stored energy to them. As a result, neon atoms move from the ground level to a level that is close to the level 2
S helium As a result, on 
neon level is created by 
significant population. At the same time, the level 
is sparsely populated, since it is quickly cleared due to spontaneous transitions to lower levels. At the crossing 
an inverse population arises. Transition of the neon atom from the top 
level to lower level 
results in laser radiation with a wavelength 
µm, which corresponds to red light.
P 
Let there be an environment in which an inverse population is created, i.e. condition (4.7) holds. In such an environment, stimulated emission is stronger than absorption. Therefore, the medium will amplify transmitted light with a frequency ν
(wavelength λ)
, corresponding to the transition between levels with inverted population (see formula (4.2)). However, this gain is small: in a helium-neon laser, light, having passed through the active medium in 1
m, amplified by only 2
%. Therefore, to obtain bright radiation, it is necessary that the light path in the active medium be very long. This is achieved using optical resonator. An active medium with population inversion and an optical cavity are the two main parts of any laser.
In Fig. 4.3 schematically shows the device of a helium-neon laser. In the middle there is a gas discharge tube (GDT) with an active medium - a helium-neon mixture. Partial pressure of helium – 1 mmHg. ( 133 Pa), and neon - 0,1 mmHg. ( 13,3 Pa). The tube has a cathode TO and anode A. When the cathode is heated and a high voltage is applied between the cathode and the anode, a luminous electric discharge can be maintained in the gases filling the tube. During the discharge, the anode voltage drop in the tube reaches 1,5 kV, the current through the tube reaches 30 mA. When a current passes through a mixture, a population inversion occurs in it.
The optical resonator consists of two high-quality mirrors Z1 And Z2(flat or spherical), one of which ( Z2) translucent. The mirrors are installed at the ends of the gas-discharge tube parallel to each other. Light, reflected from the resonator mirrors, passes repeatedly through the gas-discharge tube. As a result, the path of light in the active medium is extended so much that the light amplification reaches a large value. Before laser generation begins, there is a certain amount of spontaneous emission in the medium. This radiation, reflected from the mirrors, passes through the active medium many times. At each pass it is amplified due to stimulated radiation of the medium. The result is a bright laser beam emerging from a translucent mirror.
However, only a small part of the spontaneous emission will excite lasing. An optical resonator has great selectivity: among spontaneous radiation, it selects waves with a certain direction of propagation. Indeed, only waves propagating along the optical axis of the resonator will experience multiple reflections. Spontaneous emission, coming at an angle to the axis, leaves the resonator and does not participate in laser generation. For this reason, the laser generates a narrow, low-diverging beam of light.
The radiation of a helium-neon laser is elliptically polarized. This is caused by the fact that the windows of the gas discharge tube are installed at the Brewster angle 
. Reflection of transmitted light from the windows of the gas-discharge tube suppresses laser generation. By installing windows at the Brewster angle, we ensure that the light in which the vector E oscillates in the plane of incidence, passes through the window with virtually no reflection. As a result, only such polarized light is generated by the laser.
Thus, a narrow beam of red, elliptically polarized light emerges from a helium-neon laser. This light is the result of stimulated emission. Along with stimulated emission, there is spontaneous emission, which is not polarized and exits the laser in all directions. This radiation does not participate in laser generation. Spontaneous laser radiation is much weaker than stimulated radiation, its brightness is approximately the same as that of a conventional gas-discharge tube.
The purpose of the work is to study the main characteristics and parameters of a gas laser, in which a mixture of helium and neon gases is used as an active substance.
3.1. Operating principle of helium-neon laser
The He-Ne laser is the typical and most common gas laser. It belongs to atomic gas lasers and its active medium is a mixture of neutral (non-ionized) atoms of inert gases - helium and neon. Neon is a working gas, and transitions occur between its energy levels with the emission of coherent electromagnetic radiation. Helium plays the role of an auxiliary gas and contributes to the excitation of neon and the creation of a population inversion in it.
To start lasing in any laser, two most important conditions must be met:
1. There must be a population inversion between the working laser levels.
2. The gain in the active medium must exceed all losses in the laser, including “useful” losses for radiation output.
If there are two levels in the system E 1 And E 2 with the number of particles on each of them respectively N 1 And N 2 and degree of degeneracy g 1 And g 2, then population inversion will occur when the population N 2 /g 2 upper levels E 2 there will be more population N 1 /g 1 lower level E 1, that is, the degree of inversion Δ N will be positive:
If the levels E 1 And E 2 are non-degenerate, then for inversion to occur it is necessary that the number of particles N 2 on the top level E 2 was more than the number of particles N 1 at the lower level E 1 . Levels between which the formation of population inversion and the occurrence of forced transitions with the emission of coherent electromagnetic radiation are called working laser levels.
The population inversion state is created using pumping– excitation of gas atoms by various methods. Due to the energy of an external source called pump source, Ne atom from the ground energy level E 0, corresponding to the state of thermodynamic equilibrium, goes into the excited state Ne*. Transitions can occur to different energy levels depending on the pumping intensity. Next, spontaneous or forced transitions to lower energy levels occur.
In most cases there is no need to consider all possible transitions between all states in the system. This makes it possible to talk about two-, three- and four-level laser operating schemes. The type of laser operating circuit is determined by the properties of the active medium, as well as the pumping method used.
The helium-neon laser operates according to a three-level scheme, as shown in Fig. 3.1. In this case, the pumping and radiation generation channels are partially separated. Pumping of the active substance causes transitions from the ground level E 0 to excited level E 2, which leads to the occurrence of population inversion between the operating levels E 2 and E 1 . An active medium in a state with population inversion of operating levels is capable of amplifying electromagnetic radiation with a frequency 
due to stimulated emission processes.
Rice. 3.1. Diagram of energy levels of the working and auxiliary gas, explaining the operation of a helium-neon laser
Since the broadening of energy levels in gases is small and there are no broad absorption bands, obtaining population inversion using optical radiation is difficult. However, other pumping methods are possible in gases: direct electronic excitation and resonant energy transfer during collisions of atoms. The excitation of atoms in collisions with electrons can be most easily accomplished in an electric discharge, where electrons accelerated by an electric field 
can acquire significant kinetic energy. During inelastic collisions of electrons with atoms, the latter go into an excited state E 2:
It is important that process (3.4) is resonant in nature: the probability of energy transfer will be maximum if the excited energy states of different atoms coincide, that is, they are in resonance.
The energy levels of He and Ne and the main operational transitions are shown in detail in Fig. 3.2. Transitions corresponding to inelastic interactions of gas atoms with fast electrons (3.2) and (3.3) are shown with dotted upward arrows. As a result of electron impact, helium atoms are excited to the 2 1 S 0 and 2 3 S 1 levels, which are metastable. Radiative transitions in helium to the ground state 1 S 0 are prohibited by selection rules. When excited He atoms collide with Ne atoms located in the ground state 1 S 0, excitation transfer (3.4) is possible, and neon goes to one of the 2S or 3S levels. In this case, the resonance condition is satisfied, since the energy gaps between the ground and excited states in the auxiliary and working gas are close to each other.
Radiative transitions can occur from the 2S and 3S levels of neon to the 2P and 3P levels. The P levels are less populated than the upper S levels, since there is no direct transfer of energy from He atoms to these levels. In addition, the P levels have a short lifetime, and the nonradiative transition P → 1S devastates the P levels. Thus, a situation arises (3.1), when the population of the upper S levels is higher than the population of the underlying P levels, i.e., between the S and P levels a population inversion, which means transitions between them can be used for laser generation.
Since the number of S and P levels is large, a large set of different quantum transitions between them is possible. In particular, from four 2S levels to ten 2P levels, the selection rules allow 30 different transitions, most of which generate lasing. The strongest emission line during 2S→2P transitions is the line at 1.1523 μm (infrared region of the spectrum). For the 3S→2P transitions, the most significant line is 0.6328 μm (red region), and for 3S→3P – 3.3913 μm (IR region). Spontaneous emission occurs at all listed wavelengths.
Rice. 3.2. Energy levels of helium and neon atoms and operating diagram of a He-Ne laser
As stated earlier, after radiative transitions to P levels, nonradiative radiative decay occurs during transitions P→1S. Unfortunately, the 1S levels of neon are metastable, and if the gas mixture does not contain other impurities, then the only way for neon atoms to transition to the ground state from the 1S level is through collision with the walls of the vessel. For this reason, the system gain increases as the diameter of the discharge tube decreases. Since the states of 1S neon are emptied slowly, the Ne atoms are retained in these states, which is very undesirable and determines a number of features of this laser. In particular, when the pump current increases above the threshold value j pores there is a rapid increase, and then saturation and even a decrease in the laser radiation power, which is precisely explained by the accumulation of working particles at the 1S levels and then their transfer to the 2P or 3P states when colliding with electrons. This does not make it possible to obtain high output radiation powers.
The occurrence of population inversion depends on the pressure of He and Ne in the mixture and the temperature of the electrons. The optimal gas pressure values are 133 Pa for He and 13 Pa for Ne. The electron temperature is set by the voltage applied to the gas mixture. Typically this voltage is maintained at a level of 2...3 kV.
To obtain laser lasing, it is necessary that positive feedback exist in the laser, otherwise the device will only work as an amplifier. To do this, the active gas medium is placed in an optical resonator. In addition to creating feedback, the resonator is used to select types of oscillations and select the lasing wavelength, for which special selective mirrors are used.
At pump levels close to the threshold, lasing using one type of oscillation is relatively easy. As the excitation level increases, unless special measures are taken, a number of other modes arise. In this case, generation occurs at frequencies close to the resonant frequencies of the resonator, which are contained within the width of the atomic line. In the case of axial types of oscillations (TEM 00 mode), the frequency distance between adjacent maxima 
, Where L– length of the resonator. As a result of the simultaneous presence of several modes in the radiation spectrum, beats and inhomogeneities arise. If only axial modes existed, then the spectrum would consist of separate lines, the distance between which would be equal to c
/
2L. But in the resonator it is also possible to excite non-axial types of oscillations, for example TEM 10 modes, the presence of which strongly depends on the configuration of the mirrors. Therefore, additional satellite lines appear in the radiation spectrum, located symmetrically in frequency on both sides of the axial types of oscillations. The emergence of new types of oscillations with increasing pump level is easily determined by visual observation of the structure of the radiation field. You can also visually observe the effect of cavity adjustment on the structure of coherent radiation modes.
Gases are more homogeneous than condensed media. Therefore, the light beam in the gas is less distorted and scattered, and the radiation of a helium-neon laser is characterized by good frequency stability and high directivity, which reaches its limit due to diffraction phenomena. Diffraction limit of divergence for a confocal cavity
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,where λ – wavelength; d 0 is the diameter of the light beam in its narrowest part.
The radiation of a helium-neon laser is characterized by a high degree of monochromaticity and coherence. The emission line width of such a laser is much narrower than the “natural” spectral line width and is many orders of magnitude less than the maximum resolution of modern spectrometers. Therefore, to determine it, the beat spectrum of various modes in the radiation is measured. In addition, the radiation of this laser is plane-polarized due to the use of windows located at the Brewster angle to the optical axis of the resonator.
Evidence of the coherence of radiation can be observed by observing the diffraction pattern when radiation received from different points of the source is superimposed. For example, coherence can be assessed by observing the interference from a system of multiple slits. From Young's experience it is known that to observe the interference of light from an ordinary “classical” source, the radiation is first passed through one slit, and then through two slits, and then interference fringes are formed on the screen. In the case of using laser radiation, the first slit is unnecessary. This circumstance is fundamental. In addition, the distance between two slits and their width can be disproportionately greater than in classical experiments. At the exit window of the gas laser there are two slits, the distance between which is 2 a. In the case when the incident radiation is coherent, on a screen located at a distance d from the slits, an interference pattern will be observed. In this case, the distance between the maxima (minimum) of the bands
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