Which state is called population inversion. Population inversion. Excitons in solids

Passage of radiation through matter. Inverse population of levels. Consider again a two-level medium with energy levels And . If monochromatic radiation with a frequency falls on this medium

then when it spreads over a distance dx the change in the spectral energy density will be associated with both resonant absorption and induced (stimulated) emission of the atoms of the system. Due to stimulated emission, the spectral energy density increases in the beam, and this increase in energy must be proportional to:

Here is the dimensional proportionality coefficient.

Similarly, due to photon absorption processes, the spectral energy density in the beam decreases:

folding And , we find the complete change energy density:

Considering the equality of the Einstein coefficients and entering the absorption coefficient a, we write this equation in the form

The solution to this differential equation has the form

This formula gives the spectral energy density u in a beam of photons as they pass through a layer of matter thick x, where corresponds to the point x = 0 .

Under thermodynamic equilibrium conditions, 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 matter, that is, light is absorbed. However, if you create a system in which , then the absorption coefficient will become negative and there will be not attenuation, but increasing intensity Sveta. The state of the environment in which it is called state with inverse population of levels, and the environment itself is then called active medium. The inverse population of levels contradicts the Boltzmann equilibrium distribution and can be created artificially if the system is taken out of the state 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 laser operation. The creation of a laser became possible after methods were found to invert the population of levels in some substances (active media). The first practical generator in the visible region of the spectrum was created in (USA by Mayman (1960)) based on ruby. Ruby is a crystal lattice containing a small ( 0,03 % – 0,05 % ) admixture of chromium ions (). In Fig. 6.1 shows the diagram energy levels chromium ( three-tier environment). Wide level used to excite chromium ions with light from a powerful gas-discharge lamp with a wide frequency band in the green-blue region visible light - pump lamps. Excitation of chromium ions due to pump energy from an external source is depicted by an arrow .

Rice. 6.1. Diagram of an active three-level environment (ruby)

Electrons from a short-lived level make a fast ( c) non-radiative transition to a level (depicted by a 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 heats up, so the laser design provides for its cooling.

Lifetime of a long-lived bottleneck amounts to c, that is, 5 orders of magnitude more than the broadband level . With sufficient pump power, the number of electrons at the level (called metastable) becomes more than level , that is, an inverse population is created between the “working” levels and .

The photon emitted during a spontaneous transition between these levels (depicted by a dashed arrow) induces the emission of additional (stimulated) photons - (the transition is shown by an arrow), which in turn cause induced emission of a whole cascade of photons with wavelength .

Example 1. Let us determine the relative population of working levels in a ruby crystal at room temperature under thermodynamic equilibrium conditions.

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

Implementation of an active medium with inverted population of levels is only half the battle. For the laser to operate, it is also necessary to create conditions for generating light, that is, use positive feedback. The active medium itself can only amplify the transmitted radiation. To implement the lasing mode, it is necessary to amplify the stimulated radiation in such a way that would compensate for all losses in the system. To do this, the active substance is placed in optical resonator, formed, as a rule, by two parallel mirrors, one of which is translucent 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 silvered 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 wrapping a spiral around the ruby. The device of a ruby laser is shown schematically in Fig. 6.2.

Rice. 6.2. Ruby laser device: 1- ruby rod; 2- pulsed gas discharge lamp; 3- translucent mirror; 4- mirror; 5- stimulated emission

With sufficient pump lamp power, the majority (about half) of chromium ions are transferred to an excited state. After population inversion is achieved for operating levels with 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 the ruby crystal. Recall that photons produced by stimulated emission fly in the same direction as the incident photons. Photons, the directions of motion of which form small angles with the axis of the crystal rod, experience multiple reflections from its ends. Photons propagating in other directions exit the ruby crystal through its side surface and do not participate in the formation of the outgoing radiation. This is how it is generated in the resonator narrow bun light, and repeated 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. Generation of radiation from a ruby laser

Thus, the optical resonator performs two functions: firstly, it creates positive feedback and, secondly, it forms a narrow directed beam of radiation with a certain spatial structure.

In the considered three-level scheme, to create a population inversion between the working levels, it is necessary to excite a sufficiently large fraction of atoms, which requires significant energy expenditure. More effective is four-level scheme, which is used 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 a four-level scheme are also met. The active medium in such a laser is a mixture of inert gases - helium and neon with ground state energy (which we take to be the zero level). Pumping is carried out in the process of an electric gas discharge, due to which the atoms go into an excited state with energy . Level in neon atoms (Fig. 6.4) is close to the level in helium, and when helium atoms collide with neon atoms, the excitation energy can be effectively transferred to the latter without radiation.

Rice. 6.4. Level diagram Not- Ne-laser

Thus the level neon turns out to be more populated than more low level . The transition between these operating levels is accompanied by radiation with a wavelength 632.8 nm, which is basic in industrial Ne-Ne-lasers. At the level neon atoms do not stay long, quickly returning to the ground state. Note that the level neon is populated extremely insignificantly, 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 installation, which is typical for a four-level generation scheme. For laser lasing, other levels of neon can be used (not shown in Fig. 6.4), producing radiation in both the visible and IR ranges, with helium 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 variety, let's do the 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 .

Laser radiation is different characteristic features:

high temporal and spatial coherence (monochromatic radiation and low beam divergence);

high spectral intensity.

The radiation characteristics depend on the type of laser and operating mode, however, some parameters close to the limiting values can be noted:

Short (picosecond) laser pulses are indispensable when studying fast processes. An extremely high peak power (up to several GW) can be developed in a pulse, which is equal to the power of several nuclear power plant units of a million kW each. In this case, the radiation can be concentrated in a narrow cone. Such beams make it possible, for example, to “weld” the retina to the fundus of the eye.

Types of lasers. As part of a general physics course, we cannot dwell in detail on specific features and technical applications of lasers of various types due to their extreme diversity. Let's limit ourselves to just enough a brief overview types of lasers differing in the characteristics of the active medium and pumping methods.

Solid state lasers. They are usually pulsed; the first such laser was the ruby laser described above. Glass lasers with neodymium as a working substance are popular. They generate light with a wavelength of the order of 1.06 µm, are large in size and have a peak power of up to TW. Can be used for experiments on controlled thermonuclear fusion. An example is the huge Shiva laser at the Livermore Laboratory in the USA.

Very common lasers are yttrium aluminum garnet with neodymium (Nd:YAG), emitting in the infrared range at the wavelength µm. They can operate both in continuous generation mode and in pulsed mode, with a pulse repetition rate of up to several kHz (for comparison: a ruby laser has 1 pulse every few minutes). Have wide range applications in electronic technology (laser technology), optical location, medicine, etc.

Gas lasers. These are usually continuous lasers. They are distinguished by the correct spatial structure of the beam. Example: Helium-neon 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 technology - laser with power on the order of kW and wavelengths 9,6 And 10.6 µm. One way to pump gas lasers is through an electric discharge. A variety of lasers with an active gaseous medium are chemical and excimer lasers.

Chemical lasers. Population inversion is created in the process chemical reaction between two gases, such as hydrogen (deuterium) and fluorine. Based on exothermic reactions

Molecules HF are already born with the 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 2 kJ), pulse duration approx. 30 ns, power up to W. Efficiency (chemical) reaches 10 % , while usually for other types of lasers - fractions of a percent. Generated wavelength - 2.8 µm(3.8 µm for lasers on DF).

Of the numerous types of chemical lasers, hydrogen fluoride (deuterium) lasers are 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 almost 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 larger amounts of chemical fuel will have to be removed.

Excimer lasers. Excimer molecules are diatomic molecules (for example, ) that can only be in an excited state - their unexcited state turns out to be unstable. The main feature of excimer lasers is connected with this: 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 combine into excimer molecules.

Since the transition between operating levels is broadband, tuning the generation frequency is possible. The laser does not produce tunable radiation in the UV region ( nm) and has high efficiency ( 20 % ) energy conversion. Currently, 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 homogeneous and allows circulation for cooling, which creates advantages over solid-state lasers. This allows you 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 using solutions of organic dyes.

Such lasers usually use optical pumping of radiation from other lasers in the visible or UV range. Interesting property Dye lasers have the ability to tun the generation frequency. By selecting a dye, lasing can be obtained 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 are classified into a separate class. Pumping is carried out by bombardment with an electron beam, 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 is on the order of several kW, pulse duration is about 3 ns, efficiency reaches 50 % , have wide application(fiber optics, communications). Can be used to project television images 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 undulator axis and oscillate transversely to it, emitting a primary (“spontaneous”) electromagnetic wave. In an open resonator, where electrons then enter, the spontaneous electromagnetic wave is amplified, creating coherent directed laser radiation. main feature The advantage of free electron lasers is the ability to smoothly adjust 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 average power up to 4 W. Using 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 represents a nuclear warhead, on the surface of which up to 50 metal rods are mounted, 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 there is a thin wire made of a high-density material (on the order of the density of gold) - the active medium. The source of laser pumping energy is a nuclear explosion. During an explosion, the active substance goes into a plasma state. Instantly cooling, the plasma emits coherent radiation in the soft X-ray range. Due to the high energy concentration, the radiation hitting the target leads to explosive evaporation of the substance, the formation of a shock wave and destruction of the target.

Thus, the operating principle and design of the X-ray laser make the scope of its application obvious. The described laser does not have cavity mirrors, the use of which in the X-ray range is not possible.

Some types of lasers are shown in the figure below.

Some types of lasers: 1- laboratory laser; 2- continuous laser on;
3 - technological laser for punching holes; 4- powerful technological laser

If the system is in a state of thermodynamic equilibrium with the external environment, then the probability that any atom is at the energy level is characterized by the factors or If total number atoms making up the system, then the number of atoms inhabiting the energy levels, i.e., the population of these levels, is equal

Here are the statistical weights of these levels (degrees of degeneracy), i.e., the number of different states or sets of quantum numbers for a given energy level.

Consequently, the ratio of the populations of these energy levels is determined by the expression

In the case of non-degenerate states, i.e. when we have

If then, at thermodynamic equilibrium, the population and temperature, expressed through the ratio of the level populations, will be equal to

According to the second law of thermodynamics, the system always tends to equilibrium, and if any external influence leads to

it from a state of thermodynamic equilibrium (for example, the state of activator atoms in ruby after optical pumping), then the system, by redistributing energy, will itself move into a new thermodynamic equilibrium. Typically, such processes that return the system to a state of equilibrium are called relaxation processes. Let us analyze the expression of the temperature of the system through the populations of energy levels.

1. if, i.e., all atoms are essentially in a stable state.

2. if the population i.e. low energy levels have a higher population than high ones. These states of the system approach an equilibrium state.

3. If, as a result of an external influence, we managed to redistribute particles in the system so that the population of high energy levels became greater than that of low ones, i.e., then it is easy to verify that this state corresponds to a negative temperature value. This state of the system is called a state with inverted population. However, it should be taken into account that with an inverted population the Boltzmann distribution does not apply, therefore the determination of negative temperature can only be considered as a determination of a nonequilibrium state.

Lecture 1 2 .

The nature of light. Spontaneous and stimulated emission. Inversion of the population of energy levels. The principle of laser operation.

1. Atoms can be in stationary states with discrete energy values arbitrarily for a long time without emitting 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 a quantum of electromagnetic radiation is absorbed, the electron moves to a level with a higher energy value, and the atom itself goes into a higher-energy excited state, in which it can only remain for 10-8 s.

1.2.1. Since a strictly defined energy value is required for a transition to a higher energy level, when atoms are excited by quanta of electromagnetic radiation, 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 whose energies correspond to the energies of the electron’s transition to higher energy levels. As a result of the passage of such radiation through matter, 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 through the successive movement of an electron to levels with lower energy.

1.4. The transition of an electron to a level with 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 excited states have discrete energy values, the collection of emitted quanta forms a line spectrum.

1.6.1. Transitions of electrons from high-energy levels to one particular 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 totality of series forms a spectrum characteristic radiation substance, which is an unambiguous characteristic of this substance.

1.6.3. Methods for spectral analysis have been created based on measurements of the parameters of the characteristic spectrum.

2. The emission of quanta by an excited atom in the absence of external influence usually occurs spontaneously, and the resulting radiation is called spontaneous emission .

2.1. With spontaneous emission, each quantum appears randomly and has its own oscillation phase 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.

2.3. The number of electrons simultaneously present in an 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 the spontaneous emission of quanta.

3. The type of 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, calculating atomic spectra is a more complex task.

3.2. If atoms form a molecule, then molecular spectrum (striped range ). 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 translational motion of the molecule; – energy of rotational motion of the molecule; – energy of vibrational motion of atoms of a molecule relative to each other; – energy electron shell molecules; – intranuclear energy of the molecule.

3.2.3. The energy of 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 as a first approximation.

3.2.4. According to Bohr's frequency rule

where , , are changes in the corresponding parts of the energy of the molecule.

3.2.5. The formation of stripes occurs due to the fact that

3.2.6. Molecular spectra have a rather complex appearance.

3.2.6.1. The spectrum caused only by 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. A spectrum caused only by a transition from one vibrational level to another vibrational level ( vibrational spectrum ), located in the infrared region (wavelength 1 ¸ 10 µm).

3.2.6.3. The spectrum caused only by 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 µm ¸ 10-10 m).

3.2.6.4. When the energy of vibrational motion of a molecule changes, the energy of rotational motion can also change. In this case, there arises 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 electronic levels molecules are often accompanied by transitions between vibrational levels. The result is a spectrum called electronically vibrational , and since vibrational transitions are accompanied by rotational transitions, vibrational levels in the electronic-vibrational spectrum are represented as blurred bands.

3.3. Raman scattering ( self-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 is equal to the transition energy.

4.2. When a quantum passes through a system of excited atoms, a stream of quanta appears, the energy of which is equal to the energy of the exciting quantum ( optical gain effect ).

4.3. The absorption of light in a substance occurs in accordance with the Bouguer-Lambert law

Where - natural indicator absorption, and X– thickness of the absorbing layer.

The increase in the flux of quanta when passing through matter is similar negative absorption coefficient (negative light adsorption ).

4.4. For a medium with a negative absorption coefficient, the Bouguer-Lambert-Fabricant law is valid

The light intensity increases sharply with increasing layer thickness.

4.5. A medium with a negative absorption coefficient is called active medium .

5. Three types of transitions are possible between two energy levels

transition of an electron to a higher energy state upon absorption of a quantum (1); spontaneous transition of an electron to a lower energy state (2); forced transition of an electron to a lower-energy state (3).

5.1. The number of electrons in excited levels obeys the Boltzmann distribution and is called level population .

5.2. With the usual radiation scheme, 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 rate in the Bouguer-Lambert law is proportional to the difference between the number of absorption and emission events

Where k– proportionality coefficient.

5.5. In a conventional radiation scheme, the Boltzmann distribution of electrons is 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 be more N 1 (inverse population ). Then the natural absorption rate becomes less than zero and we get the Bouguer-Lambert-Fabricant law.

6. The occurrence of stimulated emission is realized in lasers .

6.1. Initially, to obtain stimulated emission, a three-level scheme was used in ruby, the crystal lattice of which contains an admixture of Cr, creating a narrow double additional level IN 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 upon absorption of quanta (1) are transferred from the ground level A to excited levels C And D .

6.1.2. Electrons from these levels, through spontaneous transitions (2) without radiation, populate a lower energy level IN , creating an inverse population on it. 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 influence of quanta with an energy corresponding to the energy difference between the inverse level and the main level.

6.2. The laser hardware circuit is a rod A from active substance, limited at the ends by two mirrors - opaque IN and translucent WITH.

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, which triggers the process of laser radiation.

6.2.2. The propagation of a quantum in the active medium leads to the initiation of forced transitions. In accordance with the Bouguer-Lambert-Fabricant law, quanta propagating along the rod have the greatest efficiency.

6.2.3. When reflected from a translucent mirror, part of the flux of quanta, which is laser radiation, leaves the active medium. The rest of the flow of quanta returns to the active medium to initiate forced transitions.

6.2.4. A slight deviation of the direction of propagation of quanta from the crystal axis is eliminated using the curved surface of reflecting mirrors IN And WITH.

6.2.5. The effect of quantum amplification increases significantly when initiating quanta pass repeatedly through the active medium.

6.2.6. The inverse level of chromium 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 active media in lasers:

solids (ruby; neodymium activated yttrium aluminum garnet; neodymium activated glass); gases and gas mixtures (N2; CO; CO2; metal vapors); liquids (solutions of organic dyes); semiconductors.

7.1. Laser radiation in solids occurs during transitions between energy levels of impurity atoms. Wavelength within 0.35¸1.06 microns at power up to 1 kW.

7.2. Laser radiation in gases most often occurs during electronic-vibrational transitions between different electronic states (N2 laser, excimer lasers) or during vibrational-rotational transitions within one electronic state (CO2-, CO-lasers). Wavelength within 5¸11 microns with power up to 15 kW.

7.3. Laser radiation in liquids during electronic transitions between energy levels of dyes. Wavelength within 0.2¸5 microns at power up to 1.5 W. Smooth adjustment of the wavelength is possible.

7.4. Population inversion in semiconductor lasers is created by transitions between states in the valence bands of a semiconductor crystal, and not between discrete levels. Wavelength within 0.75¸30 microns at power up to 0.5 W.

8. The main characteristics of laser radiation are:

Spatial and temporal coherence of radiation

Good monochromatic radiation

Low beam divergence

0.5¸10 mrad for gas lasers;

0.2¸5 mrad for solid-state lasers.

High power density

Pumping is carried out, as a rule, in one of two ways: optical or electrical. During optical pumping, the radiation of a powerful light source is absorbed by the active medium and thus transfers the atoms of the active medium to the upper level. This method is particularly suitable for solid-state or liquid-state lasers. The mechanisms of line broadening in solids and liquids lead to a very significant broadening of spectral lines, so that we usually deal not with pumping levels, but with pumping absorption bands. These stripes absorb a significant portion of the light emitted by the pump lamp. Electrical pumping is carried out through a fairly intense electrical discharge, and is especially suitable for gas and semiconductor lasers. In particular, in gas lasers, due to the fact that their spectral width of absorption lines is small and the pump lamps produce broadband radiation, it is quite difficult to carry out optical pumping. Optical pumping could be used very effectively for semiconductor lasers. The fact is that semiconductors have a strong absorption band. However, the use of electric pumping in this case turns out to be more convenient, since electric current passes through the semiconductor very easily.

Another pumping method is chemical. There are two noteworthy types of chemical pumping: 1) an associative reaction, leading to the formation of an AB molecule in an excited vibrational state, and 2) a dissociative reaction, leading to the formation of a B particle (atom or molecule) in an excited state.

Another way to pump a gas molecule is the supersonic expansion of a gas mixture containing a given molecule (gadodynamic pumping). Mention should also be made of a special type of optical pumping, when a laser beam is used to pump another laser (laser pumping). The properties of a directional laser beam make it very convenient for pumping another laser, without the need for special brighteners, as in the case of (incoherent) optical pumping. Due to the monochromatic nature of the pump laser, its application is not limited to solid-state and liquid lasers, but it can also be used to pump gas lasers. In this case, the line emitted by the pump laser must coincide with the absorption line of the pumped laser. This is used, for example, to pump most far-IR lasers.

In the case of optical pumping, light from a powerful incoherent lamp is transmitted to the active medium using an appropriate optical system. In Fig. Figure 1 shows the three most commonly used pumping schemes. In all three cases, the medium has the shape of a cylindrical rod. Shown in Fig. 1a the lamp has the shape of a spiral; in this case, light enters the active medium either directly or after reflection from a mirror cylindrical surface (Figure 1 in Fig.). This configuration was used to create the first ruby laser and is still sometimes used for pulsed lasers. in Fig. 1b the lamp has the shape of a cylinder (linear lamp), the radius and length of which are approximately the same as those of the active rod. The lamp is placed along one of the focal axes F1 of the specularly reflecting elliptical cylinder (1), and the laser rod is located along the other focal axis F2. Most of the light emitted by the lamp is reflected from the elliptical cylinder into the laser rod. In Fig. Figure 1c shows an example of the so-called close-packed configuration. The laser rod and the linear lamp are positioned as close to each other as possible and are tightly surrounded by a cylindrical reflector (1). The efficiency of a close-packed configuration is usually not much lower than that of an elliptical cylinder. Often, instead of specular reflectors, the circuits in Fig. 1a and c use cylinders made of diffusely reflective materials. Complex types of illuminators are also used, the design of which uses more than one elliptical cylinder or several lamps in a densely packed configuration.

Let us define the pumping efficiency of a continuous-wave laser as the ratio of the minimum pump power Pm required to create a certain pump speed to the electrical pump power P actually supplied to the lamp. The minimum pump power can be written as: , where V is the volume of the active medium, vp is the frequency difference between the main and upper laser levels. The propagation of the pumping speed along the active rod is in many cases non-uniform. Therefore, it is more correct to determine the average minimum pump power, where averaging is performed over the volume of the active medium. Thus

For a pulsed laser, by analogy, the average pump efficiency is

where the time integral is taken from the beginning to the end of the pump pulse, and E is the electrical energy supplied to the lamp.

The pumping process can be considered to consist of 4 different stages: 1) emission of radiation from the lamp, 2) transfer of this radiation to the active rod, 3) absorption of it in the rod and 4) transfer of the absorbed energy to the upper laser level.

From expression (1) or (!a) you can find the pumping speed Wp:

Electric pumping is used in gas and semiconductor lasers. Electrical pumping of a gas laser is carried out by passing a direct, high-frequency (RF) or pulsed current through the gas mixture. Generally speaking, current through a gas can flow either along the laser axis (longitudinal discharge, Fig. 2a) or across it (transverse discharge, Fig. 2b). In longitudinal discharge lasers, the electrodes often have a ring shape, and in order to reduce the degradation of the cathode material due to collisions with ions, the surface area of the cathode is made much larger than that of the anode. In lasers with a transverse discharge, the electrodes are extended over the entire length of the laser medium. Depending on the type of laser, the most various designs electrodes. Longitudinal discharge circuits are usually used for continuous wave lasers, while transverse discharge is used for pumping with constant, pulsed and RF current. Since the transverse dimensions of a laser are usually significantly smaller than the longitudinal dimensions, in the same gas mixture the voltage that must be applied in the case of a transverse configuration is significantly lower than the voltage for a longitudinal configuration. However, a longitudinal discharge, when it occurs in a dielectric (eg glass) tube (Fig. 2a), makes it possible to obtain a more uniform and stable pump distribution.

An electrical discharge produces ions and free electrons, and since they acquire additional energy from the applied electric field, they can excite neutral atoms upon collision. Due to their large mass, positive ions are accelerated much worse than electrons and therefore do not play a significant role in the excitation process.

5.20. Optical resonators. Gaussian light beams.

In open structures such as a Fabry-Perot interferometer, there are characteristic vibrational modes. To date, a large number of modifications of open resonators are known, differing from each other in configuration and mutual arrangement of mirrors. The resonator formed by two spherical reflectors with equal curvature, their concave surfaces facing towards each other and located at a distance of a radius of curvature equal to the radius of the spheres from each other, is distinguished by the greatest simplicity and convenience. The focal length of a spherical mirror is equal to half the radius of curvature. Therefore, the foci of the reflectors coincide, as a result of which the resonator is called confocal (Fig. 1). The interest in the confocal resonator is due to the convenience of its adjustment, which does not require the reflectors to be parallel to each other. It is only necessary that the axis of the confocal resonator intersect each reflector far enough from its edge. Otherwise, the diffraction losses may be too large.

Let's look at the confocal resonator in more detail.

Let all dimensions of the resonator be large compared to the wavelength. Then the resonator modes, field distribution in it and diffraction losses can be obtained based on the Huygens-Fresnel principle by solving the corresponding integral equation. If the reflectors of the confocal resonator have a square cross-section with side 2a, which is small compared to the distance between the mirrors l, equal to their radius of curvature R, and the Fresnel numbers are large, then the eigenfunctions of the integral equation of the Fox and Lee type are approximated by the products of Hermite polynomials Hn(x) by Gaussian function.

In the Cartesian coordinate system, the origin of which is placed at the center of the resonator, and the z axis coincides with the axis of the resonator (Fig. 1), the transverse field distribution is given by the expression

where defines the size of that area cross section, at the exit at which the field intensity in the resonator, proportional to S2, drops by a factor of e. In other words, this is the width of the intensity distribution.

Hermite polynomials of the first few degrees have the form:

The eigenfunctions of the equation, which give the transverse distribution (1), correspond to the eigenfrequencies determined by the condition

In Fig. Figure 2 graphically presents the first three Hermite-Gaussian functions for one of the transverse coordinates, constructed according to formula (1) taking into account (2). These graphs clearly show the nature of the change in the transverse field distribution with increasing transverse index n.

Resonances in a confocal cavity occur only for integer values. Spectrum of mods is degenerate, increasing m+n by two units and decreasing q by one gives the same frequency value. The main mode is TEM00q, the transverse field distribution is determined by a simple Gaussian function. The width of the intensity distribution varies along the z axis according to the law

where , and has the meaning of the beam radius in the focal plane of the resonator. The value is determined by the length of the resonator and is

On the surface of the mirror, the area of the fundamental mode spot, as can be seen from (4) and (5), is twice as large as the cross-sectional area of the caustic neck.

Solution (1) was obtained for the field inside the resonator. But when one of the mirrors is partially transparent, as is the case with active laser cavities, the outgoing wave is a traveling wave with a transverse distribution (1).

Essentially, separating the fundamental mode of an active confocal cavity is a way to produce a Gaussian beam of monochromatic light. Let us consider them in more detail.) width, which corresponds to the angular divergence

As a result, the main part of the Gaussian launch energy is concentrated in the solid angle

Thus, the divergence of laser radiation in the fundamental mode is determined not by the transverse, but by the longitudinal size of the laser cavity.

Essentially, formula (8) describes the diffracted wave resulting from the self-diffraction of a Gaussian trigger. The diffraction pattern described by (8) is characterized by a monotonic decrease in intensity when moving away from the axial direction, i.e. complete absence any oscillations in the brightness of the diffraction pattern, as well as a rapid decrease in wave intensity on the wings of the distribution. Diffraction of a Gaussian beam at any aperture has this character, as long as its size sufficiently exceeds the width of the beam intensity distribution.

Population inversion is the concentration of atoms with the same energy state; in thermodynamic equilibrium obeys Boltzmann statistics:

Where is the concentration of atoms, the state of electrons in which corresponds to energy levels with energy and .

When the concentration of unexcited atoms is greater than that of excited atoms, the value Δn = negative, therefore, the population is normal. When the concentration of excited atoms is greater than that of unexcited atoms (which is ensured by the pump energy), the value of Δn becomes positive, that is, population inversion occurs and transmitted radiation can be amplified due to excited atoms.

Formally, the condition Δn > 0 is satisfied at absolute negative temperature T< 0, поэтому состояние с инверсной населенностью иногда называют состоянием с отрицательной температурой, а среду, в которой осуществлено состояние с инверсной населенностью – активной средой.

In semiconductor lasers, inversion between the populations of the energy levels of the conduction band and valence band is achieved by injection of carriers at a positive bias of the pn junction.

Laser amplification

Laser amplification is the amplification of optical radiation based on the use of inducing radiation - when a radiation quantum acts on an atom in an excited state, an electron transitions from a state with energy to a state with energy, accompanied by the emission of a radiation quantum with an energy equal to the energy of the exciting quantum hν = – .

In a medium with a sufficient concentration of excited atoms when radiation is passed through it, it is possible to obtain an amplification mode if the number of photons produced is significantly greater than the losses due to absorption and scattering.

The injection laser is shown in Figure 1.3

Rice. 1.3. Scheme of the device of a semiconductor injection laser (laser diode)

In Fig. 1. Figure 4 shows the position of the Fermi level in intrinsic and impurity semiconductors. One of the important properties of the Fermi level is that in a system consisting of n- and p-type semiconductors and if no voltage is applied to them, their Fermi levels are leveled off (Fig. 1. 4 a). And if they are under different potentials, then the Fermi levels in them shift by the amount of the potential difference (Fig. 1. 4. b).

Fig.1. 4. Energy diagram of an injection semiconductor laser: p-n junction without applied external voltage (a); p-n junction when applying external voltage in the forward direction (b). d - width p-n junction, l is the actual width of the area that ensures laser operation.

In this case, in p-n zone transition, an inverted population is created and electrons make a transition from the conduction band to the valence band (recombine with holes). In this case, photons are emitted. An LED works on this principle. If a positive feedback is created for these photons in the form of an optical resonator, then p-n areas transition at large values of the external applied voltage, laser lasing can be obtained. In this case, the process of formation and recombination of nonequilibrium carriers occurs chaotically and the radiation has low power and is incoherent and non-monochromatic. This corresponds to the LED mode of operation of the semiconductor emitter. When the current increases above the threshold value, the radiation becomes coherent, its spectral width narrows greatly, and the intensity increases sharply - the laser mode of operation of the semiconductor emitter begins. At the same time, the degree of linear polarization of the generated radiation also increases.

In Fig. 1. Figure 5 schematically shows the design of a semiconductor laser and the intensity distribution of the output radiation. As a rule, in such a laser a resonator is created by polishing two diametrically opposite sides crystal, perpendicular to the plane of the p-n junction. These planes are made parallel and polished with high degree accuracy. The exit surface can be considered as a slit through which radiation passes. The angular divergence of laser radiation is determined by the diffraction of radiation at this slit. At thickness p-n transition is 20 µm and width is 120 µm, the angular divergence corresponds to approximately 60 in the XZ plane and 10 in the YZ plane.

Fig.1. 5. Schematic diagram of a pn junction laser. 1-region of p-n junction (active layer); 2-section of the laser beam in the XY plane.

Modern semiconductor lasers widely use so-called semiconductor heterostructures, to the development of which Academician of the Russian Academy of Sciences Zh. I. Alferov made a significant contribution ( Nobel Prize 2000). Lasers based on heterostructures have better characteristics, for example, higher output power and lower divergence. An example of a double heterostructure is shown in Fig. 1. 6, and its energy diagram is in Fig. 1. 7.

Rice. 1.6. Semiconductor double heterostructure. 1-conductive metallized layer to create electrical contact; 2-layer GaAs (n); 3-layer Al0.3Ga0.7As (n); 4-layer corresponding to the charge carrier injection zone (p-n junction); 5-layer Al0.3Ga0.7As (p); 6-layer GaAs (p); 7-non-conducting metal oxide layer to limit the current through the p-n junction, forming the radiation generation zone; 8,9-adjacent layers to create electrical contact; 10-substrate with heat sink.

Rice. 1.7. Energy diagram of a double heterostructure, the Y axis and layer numbers correspond to Fig. 1. 6. ΔEgc-bandgap width; ΔEgv is the band gap of the p-n junction.

Rice. 1. 8. Semiconductor laser with a heterostructure: l - cavity length

Active environment

An active medium is a substance in which an inverse population is created. IN different types In lasers, it can be solid (crystals of ruby or yttrium aluminum garnet, glass with an admixture of neodymium in the form of rods of various sizes and shapes), liquid (solutions of aniline dyes or solutions of neodymium salts in cuvettes) and gaseous (a mixture of helium with neon, argon, carbon dioxide, water vapor low pressure in glass tubes). Semiconductor materials and cold plasma, chemical reaction products also produce laser radiation. Lasers are named depending on the active medium used.

Although semiconductor lasers are solid-state, they are usually classified into a special group. In these lasers, coherent radiation is produced due to the transition of electrons from the lower edge of the conduction band to the upper edge of the valence band.

There are two types of semiconductor lasers.

The first has a pure semiconductor wafer, where gallium arsenide GaAs, cadmium sulfide CdS or cadmium selenide CdSe are used as semiconductors

The second type of semiconductor laser - the so-called injection laser - consists of impurity semiconductors in which the concentration of donor and acceptor impurities is 1018-1019. Gallium arsenide GaAs is mainly used for injection lasers.

The condition for creating population inversion for semiconductors at frequency v has the form:

∆F= - >hv

That is, in order for radiation in a semiconductor single crystal to be amplified, the distance between the Fermi levels for electrons and holes must be greater than the energy of the light quantum hv. The lower the frequency, the lower the excitation level, the inverse population is achieved.

Pumping system

Pumping creates an inverse population in active media, and for each medium the most convenient and effective method pumping. In solid-state and liquid lasers, pulsed lamps or lasers are used, gaseous media are excited by an electric discharge, and semiconductors are excited by an electric current.

Semiconductor lasers use pumping with an electron beam (for semiconductor lasers from a pure semiconductor) and a direct voltage (for injection semiconductor lasers).

Pumping by an electron beam can be transverse (Fig. 3.1) or longitudinal (Fig. 3.2). During transverse pumping, two opposite faces of the semiconductor crystal are polished and play the role of mirrors of an optical resonator. In the case of longitudinal pumping, external mirrors are used. With longitudinal pumping, the cooling of the semiconductor is significantly improved. An example of such a laser is a cadmium sulfide laser, generating radiation with a wavelength of 0.49 μm and having an efficiency of about 25%.

Rice. 3.1 - Transverse pumping by an electron beam

Rice. 3.2 - Longitudinal pumping with an electron beam

An injection laser has a pn junction formed by two degenerate impurity semiconductors. When a forward voltage is applied, the potential barrier in the pn junction is lowered and electrons and holes are injected. In the transition region, intense recombination of charge carriers begins, during which electrons move from the conduction band to the valence band and laser radiation occurs (Fig. 3.3).

Rice. 3.3 - Principle of injection laser design

Pumping provides pulsed or continuous laser operation.

Resonator

The resonator is a pair of mirrors parallel to each other, between which the active medium is placed. One mirror (“deaf”) reflects all the light falling on it; the second, translucent, returns part of the radiation to the environment for stimulated emission, and part is output outside in the form of a laser beam. A full internal prism is often used as a “deaf” mirror, and a stack of glass plates is used as a translucent mirror. In addition, by selecting the distance between the mirrors, the resonator can be configured so that the laser generates radiation of only one, strictly defined type (the so-called mode).

The simplest optical resonator, widely used in all types of lasers, is a flat resonator (Faby-Perot interferometer), consisting of two plane-parallel plates located at a distance from each other.

As one plate, you can use a reflective mirror, the reflection coefficient of which is close to unity. The second plate must be translucent so that the generated radiation can exit the resonator. To increase the reflectivity of the surfaces of the plates, multilayer dielectric reflective coatings are usually applied to them. There is virtually no light absorption in such coatings. Sometimes reflective coatings are applied directly to the plane-parallel ends of the active medium rods. Then there is no need for remote mirrors.

Rice. 4.1. Types of optical resonators: a - flat, b - prism, c - confocal, d - semi-concentric, e - composite, f - ring, g, h - crossed, i - with Bragg mirrors. Active elements are shaded.

A rectangular prism can be used as a reflective mirror in an optical cavity (Fig. 4.1, b). Light rays incident perpendicular to the inner plane of the prism, as a result of double total reflection, emerge from it in a direction parallel to the axis of the resonator.

Instead of flat plates, concave translucent mirrors can be used in optical resonators. Two mirrors with identical radii of curvature, located so that their foci are at the same point Ф (Fig. 4.1, c), form a confocal resonator. The distance between the mirrors is l=R. If this distance is halved so that the focus of one mirror is on the surface of the other, then a confocal resonator will be obtained.

For scientific research and various practical purposes, more complex resonators are used, consisting not only of mirrors, but also of other optical elements that make it possible to control and change the characteristics of laser radiation. For example, fig. 4. 1, d. – a composite resonator in which the generated radiation from four active elements is summed up. Laser gyroscopes use a ring resonator in which two beams propagate in opposite directions along a closed broken line (Fig. 4. 1, e).

To create logical elements of computers and integrated modules, multicomponent crossed resonators are used (Fig. 4. 1. g, h). It is essentially a collection of lasers that can be selectively excited and linked together by strong optical coupling.

A special class of lasers are lasers with distributed feedback. In conventional optical resonators, feedback is established due to the reflection of the generated radiation from the resonator mirrors. When distributing feedback reflection occurs from an optically inhomogeneous periodic structure. An example of such a structure is a diffraction grating. It can be created mechanically (Fig. 4. 1, i) or by selective action on a homogeneous medium.

Other resonator designs are also used.

By definition, resonator elements must also include passive and active shutters, radiation modulators, polarizers and other optical elements used to obtain lasing.

Cavity losses

The generation of radiation can be simplified as follows: the working substance of the laser is placed in a resonator and the pumping system is turned on. Under the influence of external excitation, an inverse population of levels is created, and the absorption coefficient in a certain spectral range becomes less than zero. During the excitation process, even before the creation of population inversion, the working substance begins to luminesce. Passing through the active medium, spontaneous emission is enhanced. The magnitude of the gain is determined by the product of the gain and the length of the light path in the active medium. In each type of resonator there are such selected directions that light rays, due to reflection from mirrors, pass through the active medium an in principle infinite number of times. For example, in a flat resonator, only rays propagating parallel to the axis of the resonator can pass through the active medium. All other rays incident on the mirrors at an angle to the axis of the resonator emerge from it after one or more reflections. This is how losses appear.

There are several types of losses on the resonator:

1.Losses on mirrors.

Since part of the radiation generated in the medium must be removed from the resonator, the mirrors used (at least one of them) are made translucent. If the intensity reflection coefficients of the mirrors are equal to R1 and R2, then the useful loss coefficient for the radiation output from the resonator per unit length will be given by the formula:

2.Geometric losses

If the beam propagates inside the resonator not strictly normal to the surfaces of the mirrors, then after a certain number of reflections it will reach the edges of the mirrors and leave the resonator.

3. Diffraction losses.

Let us consider a resonator formed by two plane-parallel circular mirrors of radius a. Let a parallel beam of radiation with wavelength λ be incident on mirror 2. The beam is reflected from the mirror and simultaneously diffracts into an angle of order d ϕ ≈ λ a. The Fresnel number for a given resonator is the number of passes between the mirrors when the final beam divergence reaches the angle of radiation exit beyond the edges of the mirrors ϕ=a/L

4. Scattering by inhomogeneities of the active medium.

If the resonator is filled with an active medium, then additional sources of losses arise. When radiation passes through the active medium, part of the radiation is scattered by inhomogeneities and foreign inclusions, and is also attenuated as a result of non-resonant absorption. Non-resonant absorption is understood as absorption associated with optical transitions between levels that are not operational for a given medium. This may also include losses associated with partial scattering and absorption of energy in mirrors.