Creation of an inverse population. The nature of light
At first glance, a population inversion can be created in a medium with two energy levels Е 1 and Е 2 >Е 1. For example, one can try to do this by irradiating the medium with photons with a frequency . Because under normal conditions N 2
However, when the populations are equal to N 2 =N 1, the processes of stimulated emission and absorption will compensate each other and it will be impossible to create an inversion.
Therefore, for lasers, media are used in which particles can occupy not two, but three or four levels.
In the case of a three-level system (Fig.), the E2 level must be metastable; the lifetime of a particle at this level is much longer than the lifetime at other levels of the excited state. This means W 21<
In the case of a four-level system, the level E 2 is metastable, while W 21<
The principle of minimum potential energy:
Any closed system tends to move to a state in which its potential energy is minimal. This state is energetically favorable and the most stable.
In accordance with this principle, the number of atoms of the active substance of the laser, which are at the lower energy level, is always greater than the number of excited atoms. When the pumping system is turned off, the population of the lower energy level is maximum, and at the top, at the excited level, there are no atoms at all or there are very few of them.
When pumping is turned on, the position begins to change: some of the atoms pass into the “excited” category. The higher the pump power, the larger the population of the upper level and the smaller the population of the lower level.
The more excited atoms become, the greater the probability of transitions in the opposite direction, due to spontaneous and induced emission. But photon avalanches cannot yet arise.
We are discussing a two-level pumping system: the system pumps the atoms with energy, transferring them to an excited state, and they, spontaneously or through induced radiation, jump back down.
Theory and practice have shown that the maximum achievable in the operation of a two-level pumping system is dynamic equilibrium when the populations of the upper and lower energy levels are numerically equal.
But this is not enough for the laser to work! There should be more atoms "above" than "below".
Inverse population - the state of the active substance, in which atoms that are on an excited energy level, more than at the lower, main level .
It was possible to overcome the limited capabilities of the two-level pumping system with the help of a three-level system. There were also systems with a greater number of levels.
Natural for atoms is the duration of their stay in an excited state of the order of τ 1 = 10 -8 s. It was possible to overcome such a rapid return of excited atoms to a stable ground state due to the fact that quantum systems can have metastable states with a lifetime τ much longer than τ 1 = 10 -8 s. Metastable state (from Greek μετα "through" and Latin stabilis "stable") - a state of quasi-stable equilibrium in which the system can be for a long time.
The duration of the metastable state of excited atoms can reach 2 = 10 -3 s. Please note: τ 2 > τ 1 by 100,000 times; and for such a time it is quite possible to create an inverse population, "outwitting" the principle of minimum potential energy. On fig. Figure 3 shows the energy level diagram of a three-level pumping system.
Rice. 3 Diagram of a three-level pumping system.
A three-level pumping system transfers the atoms of the active substance to the levels E 2 and E 3 . In this case, the active substance has in the vicinity of the E 3 level many closely spaced energy levels with a short lifetime of the excited state τ 3 . They are not shown in the diagram; E 3 is the average value of their energy.
Quanta close to E 3 have an increased probability of being absorbed: any energy quantum of the pumping system at one of these many levels will be useful, will be absorbed. Overall effect: the pumping system works effectively to increase the population of the E 3 energy level due to the fact that it is “wide vertically” due to a family of close levels.
On the diagram of Fig. 3, the inclined arrow shows the transition from the E 3 level to the E 2 level, which symbolizes the nonradiative transition of excited atoms to the E 2 level, since the situation allows: instead of a large difference in E 3 - E 2, there is something like a ladder of close levels.
There is a contribution of the "narrow" E 2 level to the creation of its own inverse population, but it is much more modest.
To create an active medium, selective excitation of atoms is necessary, which ensures the preferential population of one or several energy levels. One of the simplest and most effective methods is the method of optical pumping, which was used in the first L. on a ruby. Ruby is a crystal of aluminum oxide Al2O3 with an admixture (~ 0.05%) of Cr3+ ions replacing Al atoms. Energy levels of the Cr3+ ion in ruby. The absorption of light corresponding to the blue and green regions of the spectrum transfers Cr3+ ions from the ground level E1 to excited levels that form two broad bands 1 and 2. Then, in a relatively short time (~ 10 . The excess energy is then transferred to vibrations of the crystal lattice. The lifetime of Cr3+ ions at levels E 2 and is 10-3 sec. Only after this time has elapsed do the ions return to the ground level E1 again. The E2® E1 and ® E1 transitions correspond to radiation in the red region of the spectrum. If a ruby crystal is illuminated with light from a source with a sufficiently high intensity in the blue and green regions of the spectrum (pump bands), then Cr3+ ions accumulate at the E2 levels and an inversion of the populations of these levels with respect to the ground level E1 occurs. This made it possible to create a laser operating on the E2® E1 and ® E1 transitions, generating light with a wavelength l "0.7 μm.
To create an inversion of the populations of the E2 levels relative to E1, it is necessary to transfer more than half of the Cr3+ ions to the E2 levels, in a time not exceeding 10-3 sec. This places great demands on the power of the pump source. Impulse xenon lamps are used as such sources. The duration of the pump pulse is usually ~ 10-3 sec. During this time, several J of energy are absorbed in each cm3 of the crystal.
The method of creating an active medium directly in an electric discharge in various gases has become widespread. The possibilities of obtaining high-energy generation pulses using this method are limited mainly by the low density of the working medium; population inversion is easier to obtain in comparatively rarefied gases. However, this method makes it possible to use a wide variety of atomic and molecular gases and their mixtures, as well as various types of electrical discharges in gases, as an active medium for lasers. As a result, it was possible to create lasers operating in the infrared, visible, and ultraviolet regions of the spectrum. In addition, excitation in an electric discharge makes it possible to realize a continuous mode of operation of lasers with a high efficiency of converting electrical energy into radiation energy of lasers (see Gas laser).
In the most powerful gas-discharge L. of continuous action on a mixture of molecular gases CO2 and N2 (with the addition of a number of other components), the mechanism for the formation of population inversion is as follows: the electrons of a gas-discharge plasma, accelerated by an electric field, excite vibrations of N2 molecules during collisions. Then, as a result of collisions of excited N2 molecules with CO2 molecules, one of the vibrational levels of CO2 is populated, which ensures the occurrence of a population inversion. All stages of this process are very efficient, and the efficiency reaches 20-30%.
Subsequently, it turned out to be possible to create a gas-dynamic laser based on a mixture of CO2 and N2, in which the gas mixture is heated to a temperature of T ~ 2000 K, a supersonic flow is formed, which, leaving the nozzle, expands and thereby rapidly cools. As a result of rapid cooling, an inversion of the populations of the working levels of CO2 occurs (see Gas-dynamic laser). The efficiency of converting thermal energy into gas-dynamic laser radiation is low (~ 1%). Nevertheless, gas-dynamic lasers are very promising, because, firstly, in this case the task of creating large-sized lasers of high power is facilitated and, secondly, when using thermal energy sources, the question of the efficiency of lasers is less acute than in the case of electric discharge lamps. When burning 1 g of fuel (for example, kerosene), energy of the order of tens of thousands of J is released, while the electrical energy stored in the capacitors that feed the flash lamps is of the order of 0.1 J per 1 cm 3 of the volume of the capacitor .
Since the chemical bonds of molecules are an exclusively energy-intensive energy storage device, it is promising to directly use the energy of chemical bonds to excite particles, i.e. creation of an active environment L. as a result of chemical reactions. An example of chemical pumping is the reaction of hydrogen or deuterium with fluorine. If in a mixture of H2 and F2 k.-l. dissociate a small number of F2 molecules, then a chain reaction occurs F + H2 ® HF + H, H + F2 ® HF + F, etc. The HF molecules formed as a result of this reaction are in an excited state, and the population inversion conditions are satisfied for a number of quantum transitions. If CO2 is added to the initial mixture, then, in addition to L. on HF transitions (l ~ 3 μm), it is also possible to create L. on CO2 transitions (l = 10.6 μm). Here, vibrationally excited HF molecules play the same role as N2 molecules in gas-discharge CO2 lasers. In this case, a mixture of D2, F2 and CO2 is more effective. In this mixture, the coefficient of conversion of chemical energy into the energy of coherent radiation can reach 15%. Chemical lasers can operate both in pulsed and continuous modes; Various variants of chemical L. have been developed, including those similar to gas-dynamic L.
It turned out to be possible to create an active medium in semiconductors in various ways: 1) by injection of current carriers through an electron-hole junction; 2) excitation by electron impact; 3) optical excitation.
Lecture 1 2 .
The nature of the world. Spontaneous and forced emission. Energy level population inversion. The principle of operation of the laser.
1. Atoms can be in stationary states with discrete energy values for an arbitrarily long time without radiating energy.
1.1. The transition from one stationary state to another stationary state is accompanied by the absorption or emission of a quantum of electromagnetic radiation.
1.2. When absorbing a quantum of electromagnetic radiation, the electron passes to a level with a higher energy value, and the atom itself passes into a higher-energy excited state, in which it can only stay for 10-8 s.
1.2.1. Since a strictly defined energy value is necessary for the transition to a higher energy level, when atoms are excited by electromagnetic radiation quanta, only those quanta are absorbed whose energy is equal to the difference between the energies of the initial and final states.
1.2.2. If a substance is excited by radiation with a continuous spectrum, then only those quanta will be absorbed, the energies of which correspond to the energies of the electron's transition to higher energy levels. As a result of the passage of such radiation through a substance, dark lines appear in the spectrum of this radiation, which are called absorption spectrum .
1.3. The transition of an atom to the ground state can occur either directly or by sequentially moving an electron to lower energy levels.
1.4. The transition of an electron to a level with a lower energy is accompanied by the emission of a quantum of electromagnetic radiation, the energy of which is equal to the difference between the energies of the levels of the initial and final states.
1.5. Since there can be quite a lot of excited states, the emitted quanta have different energies, and, consequently, different wavelengths.
1.6. Since the excited states have discrete energy values, the set of emitted quanta forms a line spectrum.
1.6.1. Transitions of electrons from high energy levels to one level form series of lines in the spectrum, the parameters of which are characteristic of a given element and differ from the parameters of a similar series of another element.
1.6.2. The set of series forms a spectrum characteristic radiation substance, which is an unambiguous characteristic of this substance.
1.6.3. On the basis of measurements of the parameters of the characteristic spectrum, methods of spectral analysis have been developed.
2. The emission of quanta by an excited atom in the absence of external action usually occurs spontaneously, and the resulting radiation is called spontaneous emission .
2.1. In spontaneous emission, each quantum occurs randomly and has its own phase of oscillations, and therefore spontaneous emission does not have temporal coherence .
2.2. According to quantum theory, the probability pν finding an atom in a state with energy εν obeys the Boltzmann distribution
which allows, for a given value of the energy supplied to the atom, to determine the ability of an electron to occupy one or another energy level.
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2.3. The number of electrons that are simultaneously in the energy level is called level population .
2.4. In the absence of external influences, the equilibrium population of levels at a given temperature is maintained by spontaneous emission of quanta.
3. The form of the spontaneous emission spectrum depends on the state of the atom emitting this spectrum.
3.1. Isolated atoms emit radiation with atomic spectrum .
3.1.1. The composition of the atomic spectrum for the hydrogen atom and hydrogen-like ions can be easily calculated using the Balmer-Rydberg formula.
3.1.2. For other atoms and ions, the calculation of atomic spectra is a more difficult problem.
3.2. If atoms form a molecule, then there is molecular spectrum (striped spectrum ). Each band in this spectrum is a collection of closely spaced spectral lines.
3.2.1. As in atomic spectra, each line in the molecular spectrum results from a change in the energy of the molecule.
3.2.2. The energy of a molecule can be represented as
where is the energy of the translational motion of the molecule; is the energy of the rotational motion of the molecule; is the energy of vibrational motion of the atoms of the molecule relative to each other; is the energy of the electron shell of the molecule; is the intranuclear energy of the molecule.
3.2.3. The energy of the translational motion of a molecule is not quantized and its changes cannot lead to the appearance of a molecular spectrum, and the effect on the molecular spectrum can be ignored in the first approximation.
3.2.4. According to Bohr's frequency rule
where , , are the changes in the corresponding parts of the energy of the molecule.
3.2.5. The formation of bands is due to the fact that
3.2.6. Molecular spectra have a rather complex form.
3.2.6.1. The spectrum due only to the transition from one rotational level to another rotational level ( rotational spectrum ), located in the far infrared region (wavelength 0.1 ¸ 1 mm).
3.2.6.2. The spectrum due only to the transition from one vibrational level to another vibrational level ( vibrational spectrum ), located in the infrared region (wavelength 1 ¸ 10 microns).
3.2.6.3. The spectrum due only to the transition from one electronic level to another electronic level ( atomic spectrum ), located in the visible, ultraviolet and X-ray regions of the spectrum (wavelength 0.8 microns ¸ 10-10 m).
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3.2.6.4. When the energy of vibrational motion of a molecule changes, the energy of rotational motion can also change. This gives rise to vibrational-rotational spectrum , which is a vibrational spectrum, each line of which is accompanied by closely spaced lines of rotational transitions.
3.2.6.5. Transitions between the electronic levels of a molecule are often accompanied by transitions between vibrational levels. The result is a spectrum called electronic-oscillatory , and, since vibrational transitions are accompanied by rotational transitions, the vibrational levels in the electronic-vibrational spectrum appear as smeared bands.
3.3. Raman scattering ( independent study).
4. The transition of atoms from a more excited state to a less excited state under the influence of an external quantum of electromagnetic radiation is called stimulated emission .
4.1. The probability of stimulated emission depends on the energy of the quantum acting on the excited atoms. The maximum probability of the occurrence of stimulated emission will be when the energy of the exciting quantum of the transition energy is equal.
4.2. When a quantum passes through a system of excited atoms, a flow of quanta arises, the energy of which is equal to the energy of the exciting quantum ( optical amplification effect ).
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4.3. The absorption of light in matter occurs in accordance with the Bouguer-Lambert law
where is the natural absorption rate, and X is the thickness of the absorbing layer.
The amplification of the flux of quanta when passing through matter is similar to negative absorption coefficient (negative adsorption of light ).
4.4. For a medium with a negative absorption coefficient, the Bouguer-Lambert-Fabrikant law is valid
The light intensity sharply increases with increasing layer thickness.
4.5. A medium with a negative absorption coefficient is called active medium .
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5. Three types of transitions are possible between two energy levels
- the transition of an electron to a higher energy state upon absorption of a quantum (1); spontaneous transition of an electron to a less high-energy state (2); forced transition of an electron to a less high-energy state (3).
5.1. The number of electrons at excited levels obeys the Boltzmann distribution and is called level population .
5.2. In the usual scheme of radiation, the population N the higher energy level is less than the population of the lower energy level.
5.3. The number of quantum absorption events is proportional to the population N 1 less high-energy level, and the number of emission events is proportional to the population N 2 higher energy levels.
5.4. The natural absorption index in the Bouguer-Lambert law is proportional to the difference between the number of absorption and emission events
where k- coefficient of proportionality.
5.5. With the usual radiation scheme, the Boltzmann distribution of electrons due to spontaneous transitions ().
5.6. Due to the intense excitation of the system of atoms ( pumping ) it is possible to achieve such a violation of the Boltzmann distribution that N 2 will get bigger N 1 (population inversion ). Then the natural absorption index becomes less than zero and we get the Bouguer-Lambert-Fabrikant law.
6. The appearance of stimulated emission is implemented in lasers .
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6.1. Initially, to obtain stimulated emission, a three-level scheme was used in ruby, the crystal lattice of which contains an impurity of Cr, which creates a narrow double additional level AT in the zone of excited states.
6.1.1. When an atomic system is excited by the light of a xenon lamp ( optical pumping ) a large number of electrons during the absorption of quanta (1) is transferred from the ground level BUT to excited levels C and D .
6.1.2. Electrons from these levels, through spontaneous transitions (2) without radiation, populate a lower energy level AT , creating an inverse population on it. In this case, the transition energy is transferred to the crystal lattice and increases the temperature of the substance.
6.1.3. Transitions from the inverse level B to the main level A are carried out under the action of quanta with an energy corresponding to the energy difference between the inverse level and the main level.
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6.2. The hardware circuit of the laser is a rod BUT from the active substance, limited at the ends by two mirrors - opaque AT and translucent FROM.
6.2.1. After pumping the active substance, the very first transition from the inverse level to the ground level leads to the formation of a quantum that triggers the process of laser radiation.
6.2.2. The propagation of a quantum in an active medium leads to the initiation of forced transitions. According to the Bouguer-Lambert-Fabrikant law, quanta propagating along the rod have the highest efficiency.
6.2.3. When reflected from a semi-transparent mirror, a part of the quantum flux goes out of the active medium, which is laser radiation. The rest of the quantum flux returns to the active medium to initiate forced transitions.
6.2.4. A slight deviation of the direction of propagation of quanta from the axis of the crystal is eliminated using the curved surface of the reflecting mirrors AT and FROM.
6.2.5. The effect of quantum amplification increases significantly with multiple passage of initiating quanta through the active medium.
6.2.6. The inverted chromium level consists of two sublevels, and therefore the radiation of a ruby laser consists of quanta with two wavelengths (0.6927 nm and 0.6943 nm).
7. Currently, the following are used as an active medium in lasers:
- solids (ruby; neodymium-activated yttrium-aluminum garnet; neodymium-activated glass); gases and gas mixtures (N2; CO; CO2; metal vapours); liquids (solutions of organic dyes); semiconductors.
7.1. Laser radiation in solids arises during transitions between the energy levels of impurity atoms. Wavelength within 0.35¸1.06 µm at power up to 1 kW.
7.2. Laser radiation in gases most often arises during electronic-vibrational transitions between different electronic states (N2-laser, excimer lasers) or vibration-rotational transitions within the same electronic state (CO2-, CO-lasers). Wavelength within 5¸11 microns at power up to 15 kW.
7.3. Laser radiation in liquids during electronic transitions between the energy levels of dyes. Wavelength within 0.2¸5 µm at power up to 1.5 W. A smooth tuning of the wavelength is possible.
7.4. The population inversion in semiconductor lasers is created on transitions between states in the valence bands of a semiconductor crystal, and not between discrete levels. Wavelength within 0.75¸30 µm at power up to 0.5 W.
8. The main characteristics of laser radiation are:
- Spatial and temporal coherence of radiation
. The coherence time reaches 10-3 s. This corresponds to a coherence length of approximately 105 m. Good monochromaticity of radiation
. The impurity levels are much narrower than the levels of the main substance, and therefore the spectral width of the radiation may not exceed 10-11 ± 10-10 m. Small beam divergence
:
0.5¸10 mrad for gas lasers;
0.2¸5 mrad for solid state lasers.
- High power density
in a focused beam (up to 1010 W/m2).
Passage of radiation through matter. Inverse population of levels. Consider again a two-level medium with energy levels and . If monochromatic radiation is incident on this medium with a frequency
then when it propagates over a distance dx the change in the spectral energy density will be associated with both resonant absorption and induced (forced) emission of atoms in the system. Due to stimulated emission, the spectral energy density in the beam increases, and this increase in energy should be proportional to:
.
Here is the dimensional proportionality factor.
Similarly, due to the processes of absorption of photons, the spectral energy density in the beam decreases:
.
folding and , find the total change energy density:
Given the equality of the Einstein coefficients and introducing the absorption coefficient a, we write this equation in the form
The solution to this differential equation has the form
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.This formula gives the spectral energy density u in a beam of photons when they pass through a layer of matter with a thickness x, where corresponds to the point x = 0 .
Under conditions of thermodynamic equilibrium, in accordance with the Boltzmann distribution, , therefore, the absorption coefficient a is positive () :
Thus, the radiation energy density, as can be seen from (6.18), decreases as it passes through the substance, that is, the light is absorbed. However, if we create a system in which , then the absorption coefficient will become negative and there will be no weakening, but intensity enhancement Sveta. The state of the environment in which it is called state with inverse level population, and the environment itself is then called active medium. The inverse population of levels contradicts the equilibrium Boltzmann distribution and can be created artificially if the system is taken out of thermodynamic equilibrium.
This creates the fundamental possibility of amplifying and generating coherent optical radiation and is used in practice in the development of sources of such radiation - lasers.
The principle of operation of the laser. The creation of a laser became possible after the methods of implementing the inverse population of levels in certain substances (active media) were found. The first practical generator in the visible region of the spectrum was created in (USA by Maiman (1960)) based on ruby. Ruby is a crystal lattice containing a small ( 0,03 % – 0,05 % ) admixture of chromium ions (). On fig. 6.1 shows a diagram of the energy levels of chromium ( three-tier environment). Wide level used to excite chromium ions with the light of a powerful gas discharge lamp with a wide frequency band in the green-blue region of visible light - pump lamps. The excitation of chromium ions due to the pump energy from an external source is shown by an arrow .
Rice. 6.1. Scheme of an active three-level medium (ruby)
Electrons from the short-lived level make a fast ( c) nonradiative transition to the level (depicted by the blue arrow) . The energy released in this case is not emitted in the form of photons, but is transferred to the ruby crystal. In this case, the ruby is heated, so the design of the laser provides for its cooling.
Lifetime of a long-lived narrow level is c, that is, 5 orders of magnitude greater than that of the broadband level . With sufficient pump power, the number of electrons in a level (it is called metastable) becomes more than level , that is, an inverse population is created between the "working" levels and .
A photon emitted during a spontaneous transition between these levels (depicted by a dashed arrow) induces the emission of additional (forced) photons - (the transition is shown by an arrow), which in turn cause induced radiation of a whole cascade of photons with a wavelength .
Example 1 Let us determine the relative population of working levels in a ruby crystal at room temperature under conditions of thermodynamic equilibrium.
Based on the wavelength emitted by the ruby laser, we find the energy difference:
.
At room temperature T = 300 K we have:
From the Boltzmann distribution it now follows
.
Realization of an active medium with an inverse level population is only half the battle. For the laser to work, it is also necessary to create conditions for generating light, that is, to use positive feedback. The active medium itself can only amplify the transmitted radiation. To implement the generation regime, it is necessary to amplify the stimulated emission, which would compensate for all losses in the system. For this, the active substance is placed in optical resonator, formed, as a rule, by two parallel mirrors, one of which is semitransparent and serves to output radiation from the resonator. Structurally, the first ruby lasers used cylindrical crystals with a length 40 mm and diameter 5 mm. The ends were polished parallel to each other and served as resonator mirrors. One of the ends was silver-plated so that the reflection coefficient was close to unity, and the other end was translucent, that is, it had a reflection coefficient less than unity, and was used to output radiation from the resonator. The source of excitation was a powerful pulsed xenon lamp coiled around the ruby. The ruby laser device is schematically shown in fig. 6.2.
Rice. 6.2. Ruby laser device: 1- ruby rod; 2- impulse discharge lamp; 3- translucent mirror; four- mirror; 5- stimulated emission
With sufficient pump lamp power, most (about half) of the chromium ions are transferred to an excited state. After the population inversion is reached for the working levels with the energy and , the first spontaneously emitted photons corresponding to the transition between these levels do not have a preferred direction of propagation and cause stimulated emission, which also propagates in all directions in a ruby crystal. Recall that the photons generated by stimulated emission fly in the same direction as the incident photons. Photons whose directions of motion form small angles with the axis of the crystalline rod experience multiple reflections from its ends. Photons propagating in other directions exit the ruby crystal through its lateral surface and do not participate in the formation of the outgoing radiation. So in the resonator is generated narrow beam light, and the multiple passage of photons through the active medium induces the emission of more and more photons, increasing the intensity of the output beam.
The generation of light radiation by a ruby laser is shown in fig. 6.3.
Rice. 6.3. Ruby laser generation
Thus, the optical resonator performs two functions: firstly, it creates a positive feedback and, secondly, it forms a narrow directed radiation beam with a certain spatial structure.
In the considered three-level scheme, in order to create an inverse population between the working levels, it is necessary to excite a sufficiently large fraction of atoms, which requires a significant expenditure of energy. More efficient is four-level scheme, which is applied in solid-state lasers, for example, using neodymium ions. In the most common gas laser on neutral atoms - helium- neon laser - the conditions for generation according to the four-level scheme are also satisfied. The active medium in such a laser is a mixture of inert gases - helium and neon with ground state energy (which we take as the zero level). Pumping is carried out in the process of an electric gas discharge, due to which atoms pass into an excited state with energy . Level in neon atoms (Fig. 6.4) is close to the level in helium, and in the collision of helium atoms with neon atoms, the excitation energy can be effectively transferred to the latter without radiation.
Rice. 6.4. He level scheme- Ne-laser
Thus, the level neon turns out to be more populated than the lower level . The transition between these working levels is accompanied by radiation with a wavelength 632.8 nm, which is the main in industrial Not-Ne-lasers. At the level neon atoms do not linger for a long time, quickly returning to the ground state. Note that the level in neon is extremely slightly populated, and therefore, to create an inverse population between and it is necessary to excite a small number of helium atoms. This requires much less energy for both pumping and cooling the setup, which is typical for a four-level generation scheme. Other levels of neon (not shown in Fig. 6.4) can also be used for laser generation, giving radiation both in the visible and in the IR range, and helium is used only for the pumping process.
Example 2 Let us find the relative equilibrium population of the level in neon at room temperature.
This problem differs from the previous one only in numerical values. For a change, we will carry out calculations in electron volts. Let us first express the Boltzmann constant in these units:
so at room temperature
.
Now we can easily find
From a practical point of view, such a small number does not differ from zero; therefore, even with weak pumping, an inverse population is created between the levels and .
The radiation of lasers is characterized by characteristic features:
high temporal and spatial coherence (radiation monochromaticity and low beam divergence);
high spectral intensity.
The characteristics of the radiation depend on the type of laser and the mode of operation, however, some parameters close to the limit values can be noted:
Short (picosecond) laser pulses are indispensable for studying fast processes. An extremely high peak power (up to several GW) can develop in the pulse, which is equal to the power of several NPP units of a million kW each. In this case, the radiation can be concentrated in a narrow cone. Such beams allow, for example, "welding" the retina to the fundus.
Types of lasers. Within the framework of the general physics course, we cannot dwell in detail on the specific features and technical applications of various types of lasers due to their extreme diversity. We restrict ourselves to a fairly brief review of the types of lasers that differ in the characteristics of the active medium and in the methods of pumping.
solid state lasers. Usually they are pulsed, the first such laser was the ruby laser described above. Popular lasers on glass with neodymium as a working substance. They generate light with a wavelength of about 1.06 µm, have large dimensions and peak power up to TW. Can be used for controlled thermonuclear fusion experiments. An example is the huge Shiva laser at the Livermore Laboratory in the USA.
Neodymium yttrium aluminum garnet (Nd:YAG) lasers are very common, emitting in the IR range at a wavelength micron. They can operate both in continuous generation mode and in pulsed, with a pulse repetition rate of up to several kHz (for comparison: a ruby laser has 1 pulse every few minutes). They have a wide range of applications in electronic technology (laser technology), optical location, medicine, etc.
gas lasers. Usually these are continuous lasers. They differ in the correct spatial structure of the beam. Example: HeNe laser generating light at wavelengths 0,63 , 1,15 and 3.39 µm and having a power of the order of mW. Widely used in engineering - laser with a power of the order of kW and wavelengths 9,6 and 10.6 µm. One of the methods for pumping gas lasers is an electric discharge. A variety of lasers with an active gaseous medium are chemical and excimer lasers.
chemical lasers. Population inversion is created during a chemical reaction between two gases, such as hydrogen (deuterium) and fluorine. Based on exothermic reactions
.
molecules HF are already born with excitation of oscillations, which immediately creates an inverse population. The resulting working mixture is passed at supersonic speed through an optical resonator, in which part of the accumulated energy is released in the form of electromagnetic radiation. Using a system of resonator mirrors, this radiation is focused into a narrow beam. Such lasers emit high energy (more than 2 kJ), the pulse duration is about 30 ns, power up to Tue. Efficiency (chemical) reaches 10 % , while it is usually fractions of a percent for other types of lasers. Wavelength generated - 2.8 µm(3.8 µm for lasers on D.F.).
Of the numerous types of chemical lasers, hydrogen fluoride (deuterium) lasers have been recognized as the most promising. Problems: The radiation of hydrogen fluoride lasers with the specified wavelength is actively scattered by water molecules, which are always present in the atmosphere. This greatly reduces the brightness of the radiation. The deuterium fluoride laser operates at a wavelength for which the atmosphere is practically transparent. However, the specific energy release of such lasers is one and a half times less than that of lasers based on HF. This means that when using them in space, much more chemical fuel will have to be removed.
excimer lasers. Excimer molecules are diatomic molecules (for example,), which can only be in an excited state - their unexcited state turns out to be unstable. This is the main feature of excimer lasers: the ground state of excimer molecules is unfilled, that is, the lower working laser level is always empty. Pumping is carried out by a pulsed electron beam, which transfers a significant part of the atoms to an excited state, in which they are combined into excimer molecules.
Since the transition between operating levels is broadband, it is possible to tune the generation frequency. The laser does not produce tunable radiation in the UV region ( nm) and has high efficiency ( 20 % ) energy conversion. At present, excimer lasers with a wavelength 193 nm used in ophthalmic surgery for superficial evaporation (ablation) of the cornea.
liquid lasers. The active substance in the liquid state is uniform and can be circulated for cooling, which is an advantage over solid-state lasers. This makes it possible to obtain high energies and powers in pulsed and continuous modes. The first liquid lasers (1964–1965) used rare earth compounds. They were replaced by lasers based on organic dye solutions.
Such lasers usually use optical pumping of radiation from other lasers in the visible or UV range. An interesting property of dye lasers is the possibility of tuning the generation frequency. By selecting a dye, it is possible to obtain generation at any wavelength from the near IR to the near UV range. This is due to the wide continuous vibrational-rotational spectra of liquid molecules.
semiconductor lasers. Solid-state lasers based on semiconductor materials stand out in a separate class. Pumping is carried out by electron beam bombardment, powerful laser irradiation, but more often by electronic methods. Semiconductor lasers use transitions not between discrete energy levels of individual atoms or molecules, but between allowed energy bands, that is, sets of closely spaced levels (energy bands in crystals are discussed in more detail in subsequent sections). The use of various semiconductor materials makes it possible to obtain radiation at wavelengths from 0,7 before 1.6 µm. The dimensions of the active element are extremely small: the length of the resonator can be less than 1 mm.
Typical power on the order of several kW, pulse duration approx. 3 ns, the efficiency reaches 50 % , are widely used (fiber optics, communications). Can be used to project a TV image onto a large screen.
Free electron lasers. A beam of high-energy electrons is passed through a "magnetic comb" - a spatially periodic magnetic field that forces the electrons to oscillate at a given frequency. The corresponding device - an undulator - is a series of magnets that are located between the sections of the accelerator, so that relativistic electrons move along the axis of the undulator and oscillate transversely to it, emitting a primary ("spontaneous") electromagnetic wave. In an open resonator, where the electrons then enter, the spontaneous electromagnetic wave is amplified, creating a coherent directional laser radiation. The main feature of free electron lasers is the ability to smoothly tune the generation frequency (from the visible to the IR range) by changing the kinetic energy of the electrons. The efficiency of such lasers is 1 % at medium power up to 4 W. With the use of devices for returning electrons to the resonator, the efficiency can be increased to 20–40 % .
X-ray laser With nuclear pumping. This is the most exotic laser. Schematically, it is a nuclear warhead, on the surface of which up to 50 metal rods are fixed, oriented in different directions. The rods have two degrees of freedom and, like gun barrels, can be directed to any point in space. Along the axis of each rod is a thin wire made of a high-density material (of the order of the density of gold) - the active medium. The source of laser pumping energy is a nuclear explosion. During the explosion, the active substance passes into the plasma state. Cooling instantly, the plasma emits coherent radiation in the soft X-ray range. Due to the high concentration of energy, radiation, hitting the target, leads to explosive evaporation of the substance, the formation of a shock wave and the destruction of the target.
Thus, the principle of operation and the device of the X-ray laser make it obvious and the scope of its application. The described laser does not include resonator mirrors, which cannot be used in the X-ray range.
Some types of lasers are shown in the figure below.
Some types of lasers: 1-
laboratory laser; 2-
continuous laser on ;
3
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technological laser for punching holes; four-
powerful technological laser
