The laser necessarily consists of three main components:

1) active environment, in which states with population inversion are created;

2) systemspumping− devices for creating inversion in the active medium;

3) opticalabout resonator− a device that forms the direction of the photon beam.

In addition, the optical resonator is designed for multiple amplification of laser radiation.

Currently as active (working) environments laser uses various aggregate states of matter: solid, liquid, gaseous, plasma.

To create an inverse population of the laser medium, various pumping methods . The laser can be pumped both continuously and pulsed. In a long-term (continuous) mode, the pump power introduced into the active medium is limited by the overheating of the active medium and related phenomena. In the mode of single pulses, it is possible to introduce much more energy into the active medium than during the same time in the continuous mode. This causes a large power of a single pulse.

Without exaggeration, the laser can be called one of the most important discoveries of the 20th century.

What is a laser

In simple words, laser - This is a device that creates a powerful narrow beam of light. The name "laser" ( laser) is formed by adding the first letters of the words that make up English expression l night a mplification by s simulated e mission of r radiation, which means "amplification of light by stimulated emission". The laser creates light beams of such strength that they are able to burn holes even in very durable materials, spending only a fraction of a second on it.

Ordinary light scatters from a source in different directions. To assemble it into a beam, various optical lenses or concave mirrors are used. And although such a light beam can even kindle a fire, it energy cannot be compared with the energy of a laser beam.

The principle of operation of the laser

The physical basis of laser operation is the phenomenon forced, or induced, radiation . What is its essence? What kind of radiation is called stimulated?

In a stable state, an atom of a substance has the lowest energy. Such a state is considered main , and all other states excited . If we compare the energy of these states, then in the excited state it is excessive in comparison with the ground state. When an atom passes from an excited state to a stable state, the atom spontaneously emits a photon. This electromagnetic radiation is called spontaneous emission.

If the transition from an excited state to a stable state occurs forcibly under the influence of an external (inducing) photon, then a new photon is formed, the energy of which is equal to the difference in the energies of the transition levels. Such radiation is called forced .

The new photon is an "exact copy" of the photon that caused the emission. It has the same energy, frequency and phase. However, it is not absorbed by the atom. As a result, there are already two photons. Influencing other atoms, they cause the further appearance of new photons.

A new photon is emitted by an atom under the influence of an inducing photon when the atom is in an excited state. An atom in an unexcited state will simply absorb the inducing photon. Therefore, in order for the light to be amplified, it is necessary that there be more excited atoms than unexcited ones. Such a state is called population inversion.

How the laser works

The design of the laser includes 3 elements:

1. The source of energy, which is called the "pumping" mechanism of the laser.

2. The working body of the laser.

3. System of mirrors, or optical resonator.

Energy sources can be different: electrical, thermal, chemical, light, etc. Their task is to “pump” the working body of the laser with energy in order to cause the generation of a laser light flux in it. The source of energy is called mechanism"pumping" the laser . They may be chemical reaction, other laser, flash lamp, electric spark gap, etc.

working body , or laser materials , name the substances that perform the functions active environment. It is in the working body that the laser beam originates. How does it happen?

At the very beginning of the process, the working fluid is in a state of thermodynamic equilibrium, and most of the atoms are in a normal state. In order to cause radiation, it is necessary to act on the atoms so that the system goes into a state population inversions. This task is performed by the laser pumping mechanism. As soon as a new photon appears in one atom, it will start the process of producing photons in other atoms. This process will soon become an avalanche. All the photons produced will have the same frequency, and the light waves will form a light beam of enormous power.

Solid, liquid, gaseous and plasma substances are used as active media in lasers. For example, in the first laser, created in 1960, the active medium was ruby.

The working fluid is placed in optical resonator . The simplest of them consists of two parallel mirrors, one of which is translucent. It reflects some of the light and transmits some. Reflecting from the mirrors, the beam of light comes back and intensifies. This process is repeated many times. A very powerful light wave is produced at the output of the laser. There may be more mirrors in the resonator.

In addition, other devices are used in lasers - mirrors that can change the angle of rotation, filters, modulators, etc. With their help, you can change the wavelength, pulse duration, and other parameters.

When was the laser invented?

In 1964, the Russian physicists Alexander Mikhailovich Prokhorov and Nikolai Gennadievich Basov, as well as the American physicist Charles Hard Towns, became laureates Nobel Prize in physics, which was awarded to them for the discovery of the principle of operation of a quantum generator on ammonia (maser), which they made independently of each other.

Alexander Mikhailovich Prokhorov

Nikolai Gennadievich Basov

It must be said that the maser was created 10 years before this event, in 1954. It emitted coherent electromagnetic waves centimeter range and became the prototype of the laser.

The author of the first working optical laser is the American physicist Theodore Maiman. On May 16, 1960, he first received a red laser beam from a red ruby ​​rod. The wavelength of this radiation was 694 nanometers.

Theodor Maiman

Modern lasers come in a variety of sizes, from microscopic semiconductor lasers to huge football field-sized neodymium lasers.

Application of lasers

It is impossible to imagine modern life without lasers. Laser technologies are used in various industries: science, technology, medicine.

In everyday life we ​​use laser printers. Stores use laser barcode readers.

With the help of laser beams in industry it is possible to carry out surface treatment with the highest precision (cutting, spraying, alloying, etc.).

The laser made it possible to measure the distance to space objects with an accuracy of centimeters.

The advent of lasers in medicine has changed a lot.

It is hard to imagine modern surgery without laser scalpels, which provide the highest sterility and cut tissue accurately. With their help, almost bloodless operations are carried out. With the help of a laser beam, the vessels of the body are cleansed of cholesterol plaques. The laser is widely used in ophthalmology, where it is used to correct vision, treat retinal detachments, cataracts, etc. With its help, kidney stones are crushed. It is indispensable in neurosurgery, orthopedics, dentistry, cosmetology, etc.

In military affairs, laser location and navigation systems are used.

Test

LASERS BASED ON CONDENSED MATTER

Introduction

2.2. ruby laser

3.2. neodymium laser

3.7. Fiber lasers

5. Semiconductor lasers

5.1. Operating principle

5.2. DHS lasers

5.3. DFB and VRPI lasers

BIBLIOGRAPHY

Introduction

Lasers based on substances in a condensed state include lasers whose active medium is created:

1) in solids - mainly in dielectric crystals and glasses, where the active particles are ionized atoms of actinides, rare earth and other transition elements alloying the crystal, as well as in crystals with semiconductor properties,

2) in liquids, into which active particles are introduced - molecules of organic dyes.

In these media, stimulated laser radiation arises due toinduced radiativetransitions (see Section 1) between the energy levels of activator ions or terms of molecules. In semiconductor structures, stimulated emission occurs as a result of the recombination of free electrons and holes. In contrast to gas lasers (see Section 4), population inversion in solid-state and liquid lasers is always created at transitions that are close to the ground energy state of the active particle.

Since dielectric crystals do not conduct electric current, for them, as well as for liquid media, the so-called.optical pumping– pumping of the laser transition by optical radiation (light) from an auxiliary source.

In semiconductor lasers, electric current pumping is more often used ( injection current) flowing through the semiconductor in the forward direction, less often - other types of pumping: optical pumping, or pumping by electron bombardment.

1. Specific features of optical pumping of the laser active medium

An important feature of OH is its selectivity , namely: by selecting the wavelength of OH radiation, it is possible to selectively excite the desired quantum state of active particles. Let us find the conditions that ensure the maximum efficiency of the process of excitation of active particles due to optical pumping (OH), as a result of which the active particle experiences a quantum transition from the energy state ‘ i ’ into an excited state higher on the energy scale ‘ k '. To do this, we use the expression for the radiation power of the OH source absorbed by the active particles of the irradiated medium (see Section 1.9)

. (1)

Eq. (1) includes the frequency dependence of the spectral energy density of the radiation of the OH source and the function of the shape of the absorption line of the medium, i.e. its frequency dependence (form factor).

Obviously, the absorption rate and the amount of absorbed power will be maximum when:

1) the concentration of particles in the state ‘ i ’ will be the largest, i.e. OH is effective at a high density of active particles, namely, from the whole variety of media - for media that are in a condensed state (solids and liquids);

2) In the TDS state, the distribution of particles over states with different values ​​of internal (potential) energy is described by the Boltzmann formula, namely: the ground (lowest) energy state of the particle and the ensemble as a whole has the maximum population. It follows that the state i ’ must be the ground energy state of the particle;

3) for the most complete absorption of the energy of the OH source (the largest Δ Pik ) it is desirable to have an environment with highest value absorption coefficient at the quantum transition: (see f-lu (1.35)), and since it is proportional to the Einstein coefficient B k i , a B ki A ki (see f-lu (1.11, b)), it is desirable that the absorbing transition be “allowed” and “resonant”;

4) It is desirable that the width of the radiation spectrum of the pump source would not be greater than the width of the absorption contour of active particles. When pumped by spontaneous emission of lamps, this, as a rule, cannot be achieved. Ideal from this point of view is “ coherent ” pumping – pumping by monochromatic laser radiation, in which the entire line (entire spectrum) of OH radiation “falls” into the absorption contour. Such an absorption regime was considered by us in Section 1.9;

5) it is obvious that the OH efficiency will be the higher, the greater the fraction of radiation will be absorbed by active particles through a quantum transition with pumping of the desired level. So, if the active medium is a crystal (matrix) doped with active particles, then the matrix should be chosen such that it does not absorb OH radiation, i.e. so that the matrix would be “transparent” for the pump radiation, which excludes, among other things, the heating of the medium. At the same time, the overall efficiency of the “OH source–laser active medium” system is usually determined to a large extent by the efficiency of converting the electrical energy deposited in the pump source into its radiation;

6) In Section 1.9, it was shown that in a quantum system with two energy levels, it is fundamentally impossible to obtain a population inversion for any values ​​of the intensity of external radiation (i.e., optical pumping): at →∞, it is only possible to equalize the populations of the levels.

Therefore, to pump a quantum laser transition with optical radiation and create a population inversion on it, active media with one or two auxiliary energy levels are used, which, together with two levels of the laser transition, forms a three- or four-level scheme (structure) of the energy levels of the active medium.

2. Quantum devices with optical pumping, operating according to the “three-level scheme”

2.1. Theoretical analysis three-level scheme. In such a scheme (Fig. 1), the lower laser level "1" is the ground energy state of the ensemble of particles, the upper laser level "2" is a relatively long-lived level, and the level "3", associated with level "2" by a fast nonradiative transition, isauxiliary. Optical pumping operates on channel "1" → "3".

Let us find the condition for the existence of inversion between levels "2" and "1". Assuming the statistical weights of the levels are the same g 1 = g 2 = g 3 , we write the system of kinetic (balance) equations for levels "3" and "2" in the stationary approximation, as well as the relation for the number of particles at the levels:

(2)

where n 1 , n 2 , n 3 are particle concentrations at levels 1,2 and 3, Wn 1 and Wn 3 are the rates of absorption and induced emission at transitions between levels "1" and "3" under the action of pump radiation, the probability of which is W; wik are the probabilities of transitions between levels, N

From (2) we can find the level populations n 2 and n 1 as a function of W , and their difference Δ n in the form

, (3)

which defines the unsaturated gainα 0 of the ensemble of particles at the transition "2"→"1". In order toα 0 >0, it is necessary that, i.e. the numerator in (3) must be positive:

, (4)

where W then is the threshold level of pumping. Since always W then >0, then it follows that w 32 > w 21 , i.e. the probability of pumping level "2" by relaxation transitions from level "3" should be greater than the probability of its relaxation to state "1".

If

w 32 >> w 21 and w 32 >> w 31 , (5)

then from (3) we get: . And finally, if W >> w 21 , then the inversion Δ n will be: Δ n ≈ n 2 ≈ N , i.e. at level "2" you can "collect" all the particles of the environment. Note that relations (5) for the relaxation rates of the levels correspond to the conditions for the generation of peaks (see Section 3.1).

Thus, in a three-level system with optical pumping:

1) inversion is possible if w 32 >> w 21 and maximum when w 32 >> w 31 ;

2) inversion occurs when W > W then , i.e. creation wears threshold character;

3) for low w 21 conditions are created for the “spike” regime of free generation of the laser.

2.2. ruby laser. This solid-state laser is the first laser to operate in the visible wavelength range (T. Meiman, 1960). Ruby is a synthetic crystal A l 2 O 3 in the modification of corundum (matrix) with an admixture of 0.05% activator ions Cr3+ (ion concentration ~1.6∙10 19 cm 3 ), and is denoted as A l 2 O 3 : Cr 3+ . The ruby ​​laser operates according to a three-level scheme with OH (Fig. 2a). Laser levels are electronic levels Cr3+ : lower laser level "1" is the ground energy state Cr 3+ in A l 2 O 3 , the upper laser level "2" is a long-lived metastable level withτ 2 ~10 3 with. Levels "3a" and "3b" areauxiliary. Transitions "1" → "3a" and "1" → "3b" belong to the blue (λ0.41 μm) and "green" (λ0.56 μm) parts of the spectrum, and are wide (with Δλ ~50nm) absorption contour (stripes).

Rice. 2. Ruby laser. (a) Energy level diagram Cr 3+ in Al 2 O 3 (corundum); (b ) is a structural diagram of a laser operating in a pulsed regime with Q-switching. 1 - ruby ​​rod, 2 - pump lamp, 3 - elliptical reflector, 4a - fixed resonator mirror, 4b - rotating resonator mirror that modulates the Q factor of the resonator, C n - storage capacitor R - charging resistor, " Kn » - button to start the current pulse through the lamp; shows the inlet and outlet of the cooling water.

Optical pumping method provides selective population of auxiliary levels "3a" and "3b" Cr3+ through channel "1"→"3" by ions Cr3+ when absorbed by ions Cr3+ radiation from a pulsed xenon lamp. Then, in a relatively short time (~10 8 c) there is a nonradiative transition of these ions from "3a" and "3b" to levels "2". The energy released in this case is converted into vibrations of the crystal lattice. With a sufficient density ρ of the radiation energy of the pump source: when, and at the transition "2" → "1" there is a population inversion and generation of radiation in the red region of the spectrum at λ694.3 nm and λ692.9 nm. The threshold value of pumping, taking into account the statistical weights of the levels, corresponds to the transfer to level "2" of about ⅓ of all active particles, which, when pumped from λ0.56 μm, requires specific radiation energy E pore > 2J / cm 3 (and power P pore > 2 kW / cm 3 at pump pulse durationτ ≈10 3 s ). Such a high power input into the lamp and the ruby ​​rod at stationary OH can lead to its destruction; therefore, the laser operates in a pulsed mode and requires intensive water cooling.

The laser scheme is shown in fig. 2b. A pump lamp (flash lamp) and a ruby ​​rod to increase the pumping efficiency are located inside a reflector with a cylindrical inner surface and a cross section in the form of an ellipse, and the lamp and rod are located at the focal points of the ellipse. As a result, all the radiation coming out of the lamp is focused in the rod. A lamp light pulse occurs when a current pulse is passed through it by discharging a storage capacitor at the moment the contacts are closed with the button " Kn ". Cooling water is pumped inside the reflector. The laser radiation energy per pulse reaches several joules.

The pulse mode of operation of this laser can be one of the following (see Section 3):

1) “free generation” mode at a low pulse repetition rate (usually 0.1 ... 10 Hz);

2) “Q-switched” mode, usually optical-mechanical. On fig. 2b, Q-switching of the OOP is carried out by rotating the mirror;

3) “mode-locking” mode: with the width of the emission line Δν not one ~10 11 Hz,

number of longitudinal modes M~10 2 , pulse duration ~10 ps.

Ruby laser applications include holographic image recording systems, material processing, optical rangefinders, etc.

Widely used in medicine and laser on BeAl 2 O 4 : Cr 3+ (chrysoberyl doped with chromium, or alexandrite), emitting in the range of 0.7 ... 0.82 microns.

2.3. Erbium Fiber Optic Quantum Amplifier. Such an amplifier, often referred to as “ EDFA ” (abbreviation for “ Erbium Dopped Fiber Amplifier ”), works according to a three-level scheme on quantum transitions between electronic states Er 3+ in erbium-doped silica fiber: SiO2 : Er3+ (Fig. 3a). The lower quantum state "1" is the ground electronic state Er 3+ - 4 I 15/2 . The upper quantum states "2" are the group of lower sublevels of the split electronic state 4 I 13/2 . Splitting into a number of closely spaced sublevels occurs due to the interaction of ions Er 3+ with intracrystalline field SiO2 (Stark effect). Upper sublevels of the electronic state 4 I 13/2 and separate level 4 I 11/2 are auxiliary levels "3a" and "3b".

Under the action of pump radiation at wavelengths of 980 nm (or 1480 nm), ions Er 3+ go from state "1" to short-lived states "3a" or "3b", and then fast nonradiative transitions ( w 32 ~10 6 s –1 ) to state “2”, which is quasi-metastable ( w 21 ~10 2 s –1 , and τ 2 ~10ms). Thus the requirement w 32 >> w 21 is carried out, and at level "2" there is an accumulation of particles, the number of which, when the pump level exceeds its threshold value, W > W then , exceeds the population of level "1", i.e. there will be a population inversion and amplification at wavelengths in the range of 1.52…1.57 μm (Fig. 3b). It turns out that the inversion threshold is reached when one third of the particles are transferred to level "2". Threshold level OH– W then and the frequency dependence of the gain are determined by the structure of the fiber (Fig. 3b), concentration Er 3+ and wavelength of OH radiation. The pump efficiency, namely the ratio of the unsaturated gain to unit power of the OH source, is for pumping from λ980nm to 11dB m–1 ∙mW –1 , and for λ1480nm - about 6dB m–1 ∙mW –1 .

Gain Frequency Compliance EDFA the third “transparency window” of quartz fiber causes the use of such amplifiers as linear loss compensators of modern fiber-optic communication lines (FOCL) with frequency multiplexing of channels (systems WDM : Wavelength Division Multiplexing , and DWDM : Dense Wavelength Division Multiplexing ). A section of the cable-amplifier, pumped by the radiation of a semiconductor laser, is quite simply included in the FOCL (Fig. 3c). The use of erbium fiber amplifiers in FOCL replaces the technically much more complex method of signal “regeneration” - the extraction of a weak signal and its restoration.

Rice. 3. Erbium fiber optic quantum amplifier ( EDFA ). (a) energy level diagram Er 3+ in SiO 2 (quartz), (b) signal amplification in quartz with various additives, ( in ) - a simplified scheme for switching on an amplifier in an FOCL: 1 - input radiation (from the transmission path), 2 - a semiconductor pump laser, 3 - a multiplexer ( coupler ), 4– EDFA (SiO 2 : Er 3+ ), 5—optical isolator, 6—output radiation (into the transmission path).

3. Optically pumped lasers operating according to the “four-level scheme”.

3.1. Theoretical analysis of the four-level scheme. In such a scheme of levels (Fig. 4), level “0” is the ground energy state of an ensemble of particles, level “1”, associated with a quantum transition with level “0”, is the lower laser level, long-lived level “2” is the upper laser level, and level "3" is auxiliary. Pumping operates on channel "0" → "3".

Let us find the condition for the existence of inversion between levels "2" and "1". Assuming the statistical weights of the levels to be the same, and also assuming that

and, (6)

Let's write a simplified system of kinetic equations for levels "3", "2" and "1" in the stationary approximation, as well as the relation for the number of particles at all levels:

(7)

where n 0 , n 1 , n 2 , n 3 , – particle concentrations at levels 0,1,2,3; Wn 0 and Wn 3 are the rates of absorption and induced emission at transitions between levels "0" and "3" under the action of pump radiation, the probability of which is W; wik are the probabilities of transitions between levels, N is the total number of active particles per unit volume.

From (6 and 7) we can find the level populations n 1 and n 2 as a function of W , and their difference Δ n in the form

, (8)

which determines the unsaturated gain α 0 at the transition "2"→"1".

Obviously, the gain will be positive and maximum when:

. (9)

From this we can conclude that in the case of a four-level scheme with OH, when conditions (6) and (9) are satisfied:

1) inversion is not of a threshold nature and exists for any W;

2) the laser output power, determined by expression (2.14), depends on the optical pumping rate Wn 0 .

3) compared to the three-level, the four-level scheme is more versatile and allows you to create a population inversion, as well as to carry out both pulsed and continuous and generation at any pump levels (when the gain exceeds the losses in the OER).

3.2. neodymium laser. The laser uses a quantum transition between electronic energy levels Nd 3+ , laser generation is carried out according to a four-level scheme with OH (Fig. 5). The most widely used crystal matrix for ions Nd 3+ is yttrium aluminum garnet: Y 3 Al 5 O 12 , and the doped crystal is denoted as Y 3 Al 5 O 12 : Nd 3+ or YAG: Nd 3+ . Nd3+ concentration , which does not deform the YAG crystal - up to 1.5%. Other matrices for Nd 3+ are phosphate and silicate glasses (denoted as glass : Nd 3+ ), crystals of gadolinium-scandium-gallium garnet (GSHG: Nd 3+ ), yttrium-lithium fluoride– YLiF 4 : Nd 3+ , yttrium orthovanadate, organometallic liquids. Due to the cubic structure of the matrix, the YAG luminescence spectrum has narrow lines, which determines the high gain of neodymium solid-state lasers, which can operate in both pulsed and cw generation modes.

Simplified electronic energy level diagram Nd 3+ in YAG is shown in Fig. 5 Lower laser level "1" 4 I 11/2 the most intense quantum transition Nd 3+ with a wavelength of λ1.06 μm is located approximately 0.25 eV above the ground energy state "0" - 4 I 9/2 , and under normal conditions is practically unpopulated (0.01% of the population of the ground state), which determines the low generation threshold of this laser. Level 4 F 3/2 , whose lifetime is 0.2ms, is the upper laser level "2". Groups of levels (energy “zones”) "3a" ... "3 d ” play the role of an auxiliary electronic level “3”. Optical pumping is carried out through the channel "0" → "3", the absorption bands have wavelengths near 0.52; 0.58; 0.75; 0.81 and 0.89 µm. From the states "3a" ... "3 d » there is a fast relaxation by nonradiative transitions to the upper laser state «2».

For pumping, krypton and xenon discharge lamps, halogen lamps with alkali metal additives in the filling gas, as well as semiconductor lamps are used. GaAs lasers (λ0.88 µm) and LEDs based on Ga 1 x Al x As (λ0.81 µm) (Fig. 6).

YAG laser radiation power: Nd 3+ with a wavelength of λ1.06 μm in the continuous mode reaches 1 kW, the record values ​​achieved in the pulsed mode: the pulse energy is about 200 kJ, and the power is 200 TW at a pulse duration of ~1 ns (a laser designed for experiments on controlled laser thermonuclear fusion - LTS).

In a YAG crystal, a laser line Nd 3+ with λ1.06 μm is uniformly broadened (up to 0.7 nm), while in glasses there is a significant inhomogeneous broadening due to the Stark effect (Δν not one ≈3∙10 12 Hz,), which makes it possible to successfully apply the longitudinal mode locking mode (see Section 3.3) with M ~10 4 and receive ultrashort pulses with a duration of the order of 1 ps.

An increased concentration of activator ions in media such as neodymium pentaphosphate ( NdP 5 O 14 ), lithium neodymium tetraphosphate ( LiNdP 4 O 12 ) and others, provides efficient absorption of semiconductor laser radiation at distances of the order of fractions of a millimeter, which allows you to create miniature modules called minilasers : semiconductor laser - neodymium laser.

The high radiation power of a neodymium laser with λ1.06 μm makes it possible to convert the frequency of its radiation using nonlinear crystals. To generate the second and higher optical harmonics, crystals with quadratic and cubic nonlinear susceptibility are used (potassium dihydrogen phosphate - KDP , potassium titanyl phosphate - KTP ), with direct and (or) sequential (cascade) conversion. So, if a chain of crystals is used for radiation of a neodymium laser, then in addition to IR radiation at the fundamental frequency with λ1.06 μm, it is possible to obtain generation of the 2nd, 4th and 5th harmonics with wavelengths of λ0.53 μm (green radiation); λ0.35 μm, λ0.26 μm and λ0.21 μm (UV radiation) - (Fig. 7).

The main areas of application of neodymium lasers: technological and medical installations, experiments on controlled laser thermonuclear fusion, studies of the resonant interaction of radiation with matter, in underwater vision and communication systems (λ0.53 µm), optical information processing; spectroscopy, remote diagnostics of impurities in the atmosphere (UV radiation), etc.

In lasers using glasses as a matrix (silicate, borate, etc.), other activator ions can also be successfully used: Yb 3+ , Er 3+ , Tm 3+ , Ho 3+ with radiation in the range of 0.9 ... 1.54 μm.

3.3. Frequency conversion of radiation in a nonlinear medium. The phenomenon of doubling and adding the frequencies of light waves is as follows. When light propagates in a medium under the action of an electric field of an electromagnetic wave E , there is a corresponding displacement of atomic electrons relative to the nuclei, i.e. the medium is polarized. The polarizability of the medium is characterized by the magnitude of the electric dipole moment per unit volume - R associated with the magnitude of the field E through the dielectric susceptibility of the mediumχ : . If this field is small, then the dielectric susceptibilityχ \u003d χ 0 \u003d Const, p is a linear function of E : , and the displacement of charges causes radiation with the same frequency as the initial radiation (“ linear” optics).

At high power, when the electric field of the radiation begins to exceed the value of the intraatomic field, the polarizability becomes a nonlinear function E : That is, apart from linearly dependent on E term at small E , when we are dealing with linear optics, in the expression for R appears nonlinear with respect to E term (“nonlinear ” optics). As a result, when a “pump” wave propagating in a medium with a frequency ν 0 and wave vector (where is the refractive index of the medium), a new wave appears - the second optical harmonic with a frequency and a wave vector, as well as a number of higher-order harmonics. Obviously, the energy of a pump wave with a frequency will be most efficiently transferred to a new wave with a frequency if the propagation velocities of these two waves are the same, i.e. if there is a so-called.: . This condition can be met using a crystal with birefringence, when two waves propagate at a certain angle to its main optical axis.

When two waves propagate in the crystal with frequencies and and wave vectors and, in addition to the harmonics of each of the waves, a wave with a total frequency is generated in the crystal: , and a wave with a difference frequency. The condition of wave synchronism in this case has the form: .

In a certain sense, the described phenomena can be considered as the generation of harmonics during coherent optical pumping of a nonlinear crystal.

3.4. Tunable dye lasers. Lasers based on solutions of complex organic compounds (including dyes: rhodamines, coumarins, oxazoles, etc.) in alcohols, acetone and other solvents belong to the group liquid lasers. Such solutions have intense absorption bands at OH and emission bands in the near UV, visible, or near IR spectral regions. Their main advantage is a wide luminescence line (up to 50...100 nm), which makes it possible to smoothly tune the operating frequency of the laser within this line.

The electronic states of most dyes used in such lasers are wide, up to 0.1 eV, continuous energy bands resulting from the addition of hundreds of “overlapping” vibrational and rotational sublevels, which also leads to broad, as a rule, structureless absorption and luminescence bands. , as a result of the addition of "overlapping" transitions between such sublevels (Fig. 8a). Between sublevels “inside” these bands, there are fast nonradiative transitions with probabilities w ~10 10 …10 12 s –1 , and the probabilities of relaxation transitions between electronic states are two to four orders of magnitude lower (~10 8 s–1).

Generation occurs according to a “four-level” scheme on transitions of the dye molecule from the lower vibrational sublevels of the first excited singlet electronic state S1 (Fig. 8, a), analogues of level "2" in the diagram in Fig. 4 - to the upper sublevels of the ground electronic state S0 , analogues of level "1". The analogue of level "0" is the lower sublevels of the main electronic term, and the analogue of the auxiliary level "3" is the upper vibrational sublevels of the excited electronic term S1.

Since fast transitions take place inside the electronic terms, the distribution of the population of states corresponds to Boltzmann's law: the upper sub-levels "3" and "1" are weakly populated, and the lower "0" and "2" are strongly populated. Such a ratio for levels "0" and "3" determines for them a high efficiency of the RS along the channel "0" → "3", and the ratio for levels "2" and "1" determines the population inversion, amplification and generation at this transition.

To obtain a narrow generation line, as well as to be able to tune it in frequency within a wide luminescence band of dye molecules, a dispersive resonator with spectral selective elements (prisms, diffraction gratings, interferometers, etc.) is used (Fig. 8b).

The possibility of tuning in wavelength within the luminescence line (Fig. 8, in ) without power loss is determined by fast nonradiative transitions within the electronic terms "2" and "1", the probability of which exceeds the probability of induced transitions. So, when tuning the resonator to any wavelength within the luminescence line of the "2" → "1" transition, laser radiation occurs at the transition between the corresponding sublevels "2ʹ" and "1ʹ ”, resulting in sublevel “2ʹ » by induced transitions is “cleared”, and «1ʹ » - is additionally populated. However, due to OH and fast transitions from neighboring sublevels within the term, the population of the “generating” sublevel “2ʹ » is continuously restored. At the same time, sublevel "1ʹ ” is continuously cleared by fast transitions, eventually relaxing to the “0” state. Thus, the entire pumping of the upper electron term "2" becomes the pumping of the transition "2ʹ»→«1ʹ » and turns into narrow-band monochromatic laser radiation at the tuning frequency of the dispersive resonator, and this frequency can be varied.

In addition to radiative transitions S 1 → S 0 ("2" → "1") There are also a number of transitions that reduce the generation efficiency. These are the transitions: S 1 → T 1 , which reduce the population of levels “2ʹ ”, transitions T 1 →"1", increasing the population of levels "1ʹ", and transitions T 1 → T 2 absorbing laser radiation.

There are two types of dye lasers: incoherent (lamp) optical pumping by radiation of pulsed lamps and pulsed operation; and also with coherent pumping by laser radiation of other types (gas or solid-state) in continuous, quasi-continuous or pulsed operation. If a change of dyes is used in the laser, and there are more than a thousand of them, then in this way it is possible to “cover” the entire visible and part of the IR region of the spectrum (0.33 ... 1.8 μm) with radiation. In lasers with coherent pumping, ion pumps are used as pump sources to obtain a continuous regime. Ar - or Kr -gas lasers. To pump dyes in a pulsed mode, gas lasers are used on N 2 , copper vapor, excimers, as well as ruby ​​and neodymium lasers with frequency multiplication. It is often necessary to use pumping of the dye solution, as a result of which molecules that have undergone dissociation under the action of pump radiation are removed from the active zone and fresh ones are introduced.

Dye lasers, having Δν not one ~10 13 Hz and M>10 4 , make it possible to generate ultrashort radiation pulses (τ~10 14 …10 13 s).

Dye lasers with distributed feedback (DFB) form a special group. In DFB lasers, the role of a resonator is played by a structure with a periodically changing refractive index and (or) gain. It is usually created in an active medium under the action of two interfering pump beams. A DFB laser is characterized by a narrow generation line (~10 2 cm 1 ), which can be tuned within the gain band by changing the angle between the pump beams.

Dye laser applications include: photochemistry, selective pumping quantum states in spectroscopy, in the separation of isotopes, etc.

3.5 Tunable titanium-doped sapphire laser. A smooth tuning of the generation wavelength is also ensured by a solid-state laser based on a titanium-activated corundum crystal ( Al 2 O 3 : Ti 3+ ), called sapphire.

Every electronic state Ti 3+ , consists of a large number of "overlapping" vibrational sublevels, which leads to structureless absorption and luminescence bands even wider than those of a dye as a result of the addition of "overlapping" transitions between such sublevels. Inside these states, there are fast nonradiative transitions with probabilities w ~10 9 s 1 , while the relaxation probabilities between electronic states are of the order of 10 5 …10 6 s 1 .

The sapphire laser belongs to the group of so-called. vibronic lasers, which differ in that their main electronic term is a band of vibrational sublevels (crystal lattice), due to which the laser operates according to a four-level scheme, and, like a dye laser, creates the possibility of smoothly tuning the generation in the range of λ660 ... 1180 nm. The absorption band extends from λ0.49 µm to λ0.54 µm. Short lifetime of the excited state "2" Ti 3+ makes the lamp pumping of this laser ineffective, which, as a rule, is carried out by a cw argon laser (λ488 nm and λ514.5 nm), the second harmonic of a neodymium laser (λ530 nm) or copper vapor laser radiation pulses (λ510 nm).

The undoubted advantages of a sapphire laser with titanium are a much higher permissible pump power without degradation of the working substance and a wider inhomogeneously broadened luminescence line. As a result, a sequence of pulses with a duration of about tens of femtoseconds (1fs=10 15 c), and with subsequent compression (squeezing) of pulses in nonlinear optical fibers - up to 0.6 fs.

3.6. Tunable color center lasers. Such lasers, like the solid-state lasers discussed above, use ionic crystals as an active substance, but with color centers called F - centers , which allows the tuning of their radiation. Laser materials for such lasers: crystals of fluorides and chlorides of alkali metals ( Li, Na, K, Rb ), as well as fluorides Ca and Sr . The impact on them of ionizing radiation: gamma quanta, high-energy electrons, X-ray and hard UV radiation, as well as the calcination of crystals in alkali metal vapors, leads to the appearance of point defects in the crystal lattice, which localize electrons or holes on themselves. A vacancy that captures an electron forms a defect whose electronic structure is similar to that of a hydrogen atom. Such a color center has absorption bands in the visible and UV regions of the spectrum.

The scheme of laser generation on color centers is similar to schemes of liquid lasers on organic dyes. For the first time, generation of stimulated emission at color centers was obtained in crystals of K Cl - Li under pulsed optical pumping. On the this moment generation was observed at a large number of different color centers with IR radiation in pulsed and continuous modes with coherent RS. The radiation frequency is tuned using dispersive elements (prisms, diffraction gratings, etc.) placed in the resonator. However, poor thermal and photostability hinder the widespread use of such lasers.

3.7. Fiber lasers. fiber called lasers, the resonator of which is built on the basis of an optical fiber-waveguide, which is also the active medium of the laser in which radiation is generated (Fig. 9). Doped quartz fiber is used rare earth elements ( Nd, Ho, Er, Tm, Yb etc.), or passive fiber using the effect of stimulated Raman scattering. In the latter case, the optical resonator forms a light guide in combination with “Bragg” refractive index gratings “embedded” in the fiber. Such lasers are called fiber Raman ” lasers. The laser radiation propagates inside the optical fiber, and therefore the fiber laser cavity is simple and does not require alignment. In a fiber laser, it is possible to obtain both single-frequency generation and generation of ultrashort (femtosecond, picosecond) light pulses.

4. Parametric light generation

Parametric light generation(POS) is carried out under the action of laser optical pumping radiation in solid-crystals with nonlinear properties, and is characterized by a fairly high conversion coefficient (tens of percent). In this case, it is possible to smoothly tune the frequency of the output radiation. In a certain sense, the OPO, as well as the phenomenon of frequency multiplication and addition considered above, can be considered as the generation of tunable radiation during coherent optical pumping of a nonlinear crystal.

At the heart of the OPO phenomenon, as in the case of multiplication and addition of frequencies, are non-linear optical phenomena in media. Let us consider the case when a medium with nonlinear properties and located in an open optical cavity (OOR) interacts with laser radiation of a sufficiently high intensity, having a frequency ν 0 (pumping). Due to pumping the energy of this wave, two new light waves can appear in the medium:

1) a wave of “noise” nature with a certain frequency ν 1 ;

2) a wave with a difference frequency (ν 0 – v 1 ), which is the result of the nonlinear interaction of pump radiation and a random (noise) wave with frequency ν 1 .

Moreover, the frequencies ν 1 and (ν 0 – ν 1 ) must be natural frequencies of the OOP and for all three waves,wave synchronism condition: . In other words, the pump light wave with frequency ν 0 using an auxiliary noise wave with frequency ν 1 , transforms into a wave with a frequency (ν 0 – v 1 ).

Frequency tuning of the OPO radiation is carried out by selecting the orientation of a birefringent nonlinear crystal by rotating it, i.e. changing the angle between its optical axis and the axis of the resonator in order to performwave synchronism condition. Each value of the angle corresponds to a strictly defined combination of frequencies ν 1 and (ν 0 – ν 1 ), for which the condition of wave synchronism is currently satisfied.

Two schemes can be used to implement PGS:

1) “two-resonator” scheme, when the generated waves with frequencies ν 1 and (ν 0 – ν 1 ) occur in one OER, while the loss of OER for them should be small;

2) “single resonator” scheme, when only one wave with frequency (ν 0 – v 1 ).

A crystal can be used as an active medium LiNbO 3 (lithium niobate), pumped by the radiation of the second harmonic of the YAG: Nd 3+ (λ0.53 μm) and smooth tuning can be carried out in the range up to λ3.5 μm within 10%. A set of optical crystals with different areas of nonlinearity and transparency allows tuning in the IR region up to 16 µm.

5. Semiconductor lasers

semiconductorcalled such solid-state lasers in which semiconductor crystals of various compositions with population inversion at a quantum transition are used as an active medium (working substance). A decisive contribution to the creation and improvement of such lasers was made by our compatriots N.G. Basov, Zh.I. Alferov and their collaborators.

5.1. Operating principle. In semiconductor lasers, unlike lasers of other types (including other solid-state ones), radiative transitions are used not between isolated energy levels of atoms, molecules and ions that do not interact or weakly interact with each other, but between allowedenergy zonescrystal. Radiation (luminescence) and generation of stimulated emission in semiconductors is due to quantum transitions of electrons both between the energy levels of the conduction band and the valence band, and between the levels of these bands and impurity levels: transitions donor level–acceptor level, conduction band–acceptor level, donor level– valence band, including through exciton states. Each energy zone corresponds to a very large (~10 23 …10 24 ) the number of allowed states. Since electrons are fermions; then, for example, valence the zone can be completely or partially filled with electrons: with a density decreasing from bottom to top along the energy scale - similar to the Boltzmann distribution in atoms.

The radiation of semiconductors is based on the phenomenonelectroluminescence. A photon is emitted as a result of an act recombination charge carriers – an electron and a “hole” (an electron from the conduction band occupies a vacancy in the valence band), while the radiation wavelength is determined byband gap. If we create such conditions that the electron and hole before recombination will be in the same region of space, it is enough long time, and at this moment a photon with a frequency that is in resonance with the frequency of the quantum transition passes through this region of space, then it can induce the recombination process with the emission of a second photon, and its direction, the vector polarization and phase will exactly match the same characteristics as the first photon. For example, in own (“pure”, “impurity-free”) semiconductors, there is a filled valence band and an almost free conduction band. During interband transitions, in order to cause inversion and obtain generation, it is necessary to create excess nonequilibrium concentrations of charge carriers: in the conduction band - electrons, and in the valence band - holes. In this case, the interval between the quasi-Fermi levels must exceed the band gap, i.e., one or both quasi-Fermi levels will be inside the allowed bands at distances of no more than kT from their borders. And this presupposes an excitation of such intensity that degeneration in the conduction band and in the valence band.

The first semiconductor lasers used gallium arsenide (GaAs), operated in a pulsed mode, emitted in the IR range and required intense cooling. Further research has made it possible to make many significant improvements in the physics and technology of lasers of this type, and at present they emit in both the visible and UV ranges.

The degeneracy of a semiconductor is achieved by heavily doping it at a high dopant concentration, such that the properties of the dopant, rather than those of the intrinsic semiconductor, are exhibited. Every atom donor impurity gives one of its electrons to the conduction band of the crystal. On the contrary, the atomacceptorimpurity captures one electron, which was shared by the crystal and was in the valence band. degeneratena semiconductor is obtained, for example, by introducing intoGaAstellurium impurities (concentration 3...5 1018 cm3 ), and the degeneratepsemiconductor - zinc impurities (concentration 1019 cm3 ). Generation is carried out at IR wavelengths from 0.82 µm to 0.9 µm. Structures grown on substrates are also widespread.InP(IR region λ1…3 µm).

The semiconductor crystal of the simplest laser diode operating on a “homojunction” (Fig. 10) has the form of a very thin rectangular plate. Such a plate is essentially an opticalwaveguidewhere the radiation propagates. The top layer of the crystaldopedfor creatingparea, and in the bottom layer is creatednregion. The result is a flatpnlarge area crossing. The two sides (ends) of the crystal are cleaved and polished to form smooth parallel reflective planes that form an open optical cavity.- Fabry-Perot interferometer. Random photon of spontaneous emission emitted in a planepntransition perpendicular to the reflectors, passing along the resonator, will cause stimulated recombination transitions, creating new and new photons with the same parameters, i.e. the radiation will be amplified, generation will begin. In this case, the laser beam will be formed due to repeated passage through the optical waveguide and reflection from the ends.

The most important type of pumping in semiconductor lasers isinjectionpumping. In this case, free charge carriers serve as active particles - excess nonequilibrium conduction electrons and holes, whichinjectedinpn-transition (active medium), when passing through it electric current in the “direct” direction with a “direct” displacement, which reduces the height of the potential barrier. This allows direct conversion of electrical energy (current) into coherent radiation.

Other methods of pumping are electrical breakdown (in the so-called.streamerlasers), electron beam pumping, and optical pumping.

5.2. DHS lasers. If you arrange a layer with a narrowerforbidden zone(active region) between two layers with a wider bandgap, a so-called.heterostructure. The laser that uses it is called a double laser.heterostructure(DHS laser, or “double heterostructure”, DHS- laser). This structure is formed by joininggallium arsenide(GaAs) andaluminum gallium arsenide(AlGaAs). The advantage of such lasers is the small thickness of the middle layer - the active region where electrons and holes are localized: light is additionally reflected from heterojunctions, and the radiation will be contained in the region of maximum amplification.

If two more layers with a lower refractive index compared to the central ones are added on both sides of the DHS laser crystal, then a resemblinglight guidestructure that more effectively traps radiation (DHS laserwith separate hold, or "separate confinement heterostructure”, SCHS- laser). Most of the lasers produced in recent decades are made using this technology. The development of modern optoelectronics, solar energy is based on quantum heterostructures: incl. with quantum "wells", quantum "dots".

5.3. DFB and VRPI lasers. In lasers withdistributed feedback(ROS or “distributedfeedback”– DFBlaser) nearp- ntransition, a system of transverse relief “strokes” is applied, forminggrating. Thanks to this grating, radiation with only one wavelength returns back to the resonator, and generation occurs on it, i.e. stabilization of the radiation wavelength is carried out (lasers for multi-frequency fiber-optic communication).

A semiconductor “edge” laser that emits light in a direction perpendicular to the crystal surface and is called a “vertical resonator surface-emitting” laser (VRTS laser, or “verticalcavitysurface- emitting”: VCSElaser), has a symmetrical radiation pattern with a small divergence angle.

In the active medium of a semiconductor laser, a very high gain (up to 104 cm-1 ), due to which the dimensions of the active element P. l. lasers are extremely small (resonator length - 50 μm ... 1 mm). In addition to compactness, features semiconductor lasers are: ease of intensity control by changing the current value, low inertia (~109 c), high efficiency (up to 50%), the possibility of spectral tuning and a large choice of substances for generation in a wide spectral range from UV, visible to mid-IR. At the same time, compared with gas lasers, semiconductor lasers are characterized by a relatively low degree of monochromaticity and coherence of radiation and cannot emit at different wavelengths simultaneously. Semiconductor lasers can be either single-mode or multi-mode (with a large active zone width). Multimode lasers are used in cases where the device requires a high output power, and the condition of low beam divergence is not set. The areas of application of semiconductor lasers are: information processing devices - scanners, printers, optical storage devices, etc., measuring devices, pumping of other lasers, laser designators, fiber optics and technology.

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Laser (from the English "light amplification by stimulated emission of radiation "- "amplification of light by stimulating radiation") or an optical quantum generator is a special type of radiation source with feedback, the radiating body in which is an inversely populated medium. The principles of laser operation are based on the propertieslaser radiation: monochromaticity and high coherence (spatial and temporal). TAlso, a small angular divergence is often attributed to the number of radiation features (sometimes one can come across the term “high radiation directivity”), which, in turn, allows us to speak of a high intensity of laser radiation. Thus, in order to understand the principles of laser operation, it is necessary to talk about the characteristic properties of laser radiation and an inversely populated medium, one of the three main components of a laser.

Spectrum of laser radiation. Monochromatic.

One of the characteristics of the radiation of any source is its spectrum. The sun, household lighting devices have a wide spectrum of radiation, in which there are components with different wavelengths. Our eye perceives such radiation as white light, if the intensity of the different components is approximately the same in it, or as light with some shade (for example, green and yellow components dominate in the light of our Sun).

Laser radiation sources, on the other hand, have a very narrow spectrum. In some approximation, we can say that all photons of laser radiation have the same (or close) wavelengths. So, the radiation of a ruby ​​laser, for example, has a wavelength of 694.3 nm, which corresponds to red light. The first gas laser, helium-neon, also has a relatively close wavelength (632.8 nm). In contrast, an argon-ion gas laser has a wavelength of 488.0 nm, which is perceived by our eyes as a turquoise color (between green and blue). Lasers based on sapphire doped with titanium ions have a wavelength in the infrared region (usually near the wavelength of 800 nm), so its radiation is invisible to humans. Some lasers (for example, semiconductor lasers with a rotating diffraction grating as an output mirror) can tune the wavelength of their radiation. Common to all lasers, however, is that the bulk of their radiation energy is concentrated in a narrow spectral region. This property of laser radiation is called monochromaticity (from the Greek "one color"). On fig. To illustrate this property, Figure 1 shows the radiation spectra of the Sun (at the level of the outer layers of the atmosphere and at sea level) and a semiconductor laser manufactured by the company Thorlabs.

Rice. 1. Radiation spectra of the Sun and a semiconductor laser.

The degree of monochromaticity of laser radiation can be characterized by the spectral width of the laser line (the width can be specified as a detuning in wavelength or frequency from the intensity maximum). Usually the spectral width is given by the level 1/2 ( FWHM ), 1/ e or 1/10 of the maximum intensity. Some modern laser systems have achieved a peak width of several kHz, which corresponds to a laser linewidth of less than one billionth of a nanometer. For specialists, we note that the width of the laser line can be orders of magnitude narrower than the width of the spontaneous emission line, which is also one of the distinguishing characteristics of the laser (compared, for example, with luminescent and superluminescent sources).

Coherence of laser radiation

Monochromaticity is an important but not the only property of laser radiation. Another defining property of laser radiation is its coherence. Usually one speaks of spatial and temporal coherence.

Let us imagine that the laser beam is divided in half by a semitransparent mirror: half of the beam energy passed through the mirror, the other half was reflected and went into the system of guiding mirrors (Fig. 2). After that, the second beam converges with the first one again, but with some time delay. The maximum delay time at which the beams can interfere (i.e., interact taking into account the phase of the radiation, and not just its intensity) is called the coherence time of the laser radiation, and the length of the additional path that the second beam traveled due to its deflection is called the length of the longitudinal coherence. The longitudinal coherence length of modern lasers can exceed a kilometer, although for most applications (for example, for industrial material processing lasers) such a high spatial coherence of the laser beam is not required.

It is possible to divide the laser beam in another way: instead of a translucent mirror, put a completely reflective surface, but block it not the entire beam, but only part of it (Fig. 2). Then the interaction of radiation will be observed, which propagated in different parts beam. The maximum distance between the points of the beam, the radiation in which will interfere, is called the length of the transverse coherence of the laser beam. Of course, for many lasers, the transverse coherence length is simply equal to the diameter of the laser beam.

Rice. 2. Toward an explanation of the concepts of temporal and spatial coherence

Angular divergence of laser radiation. Parameter M 2 .

No matter how we strive to make the laser beam parallel, it will always have a non-zero angular divergence. The minimum possible angle of divergence of laser radiationα d (“diffraction limit”), in order of magnitude, is given by:

α d~ λ /D, (1)

where λ is the wavelength of laser radiation, and D is the width of the beam emerging from the laser. It is easy to calculate that at a wavelength of 0.5 μm (green radiation) and a laser beam width of 5 mm, the divergence angle will be ~10 -4 rad, or 1/200 of a degree. Despite being so small, the angular divergence can be critical for some applications (for example, for the use of lasers in satellite combat systems), since it sets an upper limit on the achievable laser power density.

In general, the quality of the laser beam can be set by the parameter M2 . Let the minimum achievable spot area created by an ideal lens when focusing a Gaussian beam be S . Then if the same lens focuses the beam from the given laser into the area spot S 1 > S , parameter M 2 laser radiation is equal to:

M 2 = S 1 / S (2)

For the highest quality laser systems, the parameter M2 is close to unity (in particular, lasers with the parameter M2 equal to 1.05). However, it should be borne in mind that a low value of this parameter is currently achievable for far from all classes of lasers, which must be taken into account when choosing a laser class for a specific task.

We have briefly summarized the main properties of laser radiation. Let us now describe the main components of a laser: a medium with an inverted population, a laser resonator, laser pumping, and a scheme of laser levels.

Medium with population inversion. Scheme of laser levels. quantum output.

The main element that converts the energy of an external source (electrical, non-laser radiation energy, energy of an additional pump laser) into light energy is a medium in which an inverted population of a pair of levels is created. The term "population inversion" means that a certain fraction of the structural particles of the medium (molecules, atoms or ions) is transferred to an excited state, and for a certain pair of energy levels of these particles (upper and lower laser levels) there are more particles at the upper energy level than on the bottom.

When passing through a medium with an inverted population, radiation whose quanta have an energy equal to the difference between the energies of two laser levels can be amplified, while removing the excitation of some of the active centers (atoms/molecules/ions). Amplification occurs due to the formation of new quanta of electromagnetic radiation, having the same wavelength, propagation direction, phase and polarization state as the original quantum. Thus, packets of identical (equal in energy, coherent and moving in the same direction) photons are generated in the laser (Fig. 3), which determines the main properties of laser radiation.

Rice. 3. Generation of coherent photons under stimulated emission.

It is impossible, however, in the classical approximation to create an inversely populated environment in a system consisting of only two levels. Modern lasers usually have a three-level or four-level system of levels involved in laser generation. In this case, the excitation transfers the structural unit of the medium to the highest level, from which the particles relax in a short time to a lower energy value - the upper laser level. One of the lower levels is also involved in laser generation - the ground state of the atom in a three-level scheme or an intermediate state in a four-level one (Fig. 4). The four-level scheme turns out to be more preferable due to the fact that the intermediate level is usually populated by a much smaller number of particles than the ground state; accordingly, it turns out to be much easier to create an inverse population (an excess of the number of excited particles over the number of atoms at the lower laser level) (to start lasing, you need to inform environment with less energy).

Rice. 4. Three-level and four-level systems of levels.

Thus, during laser generation, the minimum value of the energy imparted to the working medium is equal to the excitation energy of the highest level of the system, and generation occurs between two lower levels. This causes the fact that the laser efficiency is initially limited by the ratio of the excitation energy to the energy of the laser transition. This ratio is called the quantum yield of the laser. It should be noted that usually the efficiency of a laser from the mains is several times (and in some cases even several tens of times) lower than its quantum yield.

Semiconductor lasers have a special structure of energy levels. The process of radiation generation in semiconductor lasers involves the electrons of two bands of the semiconductor, however, due to the impurities that form the light-emitting p - n transition, the boundaries of these zones in different parts of the diode are shifted relative to each other. Population inversion in an area p - n transition in such lasers is created due to the flow of electrons into the transition region from the conduction band n -site and holes from the valence band p -plot. More information about semiconductor lasers can be found in the specialized literature.

Modern lasers use various methods to create population inversion, or laser pumping.

Laser pumping. Pumping methods.

In order for a laser to start generating radiation, it is necessary to supply energy to its active medium in order to create an inverted population in it. This process is called laser pumping. There are several basic pumping methods, the applicability of which in a particular laser depends on the type of active medium. So, for excimer and some gas lasers operating in a pulsed mode (for example, CO2 - laser) it is possible to excite the molecules of the laser medium by an electric discharge. In cw gas lasers, a glow discharge can be used for pumping. Semiconductor lasers are pumped by applying a voltage to p‑n laser transition. For solid-state lasers, you can use an incoherent radiation source (a flash lamp, a ruler, or an array of light-emitting diodes) or another laser whose wavelength corresponds to the energy difference between the ground and excited states of an impurity atom (in solid-state lasers, as a rule, laser generation occurs on atoms or ions impurities dissolved in the matrix grid - for example, for a ruby ​​laser, chromium ions are an active impurity).

Summarizing, we can say that the laser pumping method is determined by its type and features of the active center of the generating medium. As a rule, for each specific type of lasers, there is the most effective method pumping, which determines the type and design of the system for supplying energy to the active medium.

laser resonator. Condition of laser generation. Stable and unstable resonators.

The active medium and the energy delivery system to it are still not enough for the emergence of laser generation, although some devices can already be built on their basis (for example, an amplifier or a superluminescent radiation source). Laser generation, i.e. the emission of monochromatic coherent light occurs only in the presence of feedback, or a laser resonator.

In the simplest case, the resonator is a pair of mirrors, one of which (the laser output mirror) is semitransparent. As another mirror, as a rule, a reflector with a reflection coefficient at the generation wavelength close to 100% (“deaf mirror”) is used to avoid “two-way” laser generation and unnecessary energy loss.

The laser resonator ensures the return of part of the radiation back to the active medium. This condition is important for the occurrence of coherent and monochromatic radiation, since the photons returned to the medium will cause the emission of photons of the same frequency and phase. Accordingly, the radiation quanta newly emerging in the active medium will be coherent with those that have already gone beyond the resonator. Thus, the characteristic properties of laser radiation are ensured to a large extent by the design and quality of the laser resonator.

The reflection coefficient of the output semitransparent mirror of the laser resonator is selected in such a way as to ensure the maximum output power of the laser, or based on the technological simplicity of manufacturing. For example, in some fiber lasers, an evenly cleaved end of a fiber light guide can be used as an output mirror.

An obvious condition for stable laser generation is the condition that the optical losses in the laser cavity (including the losses due to the output of radiation through the cavity mirrors) and the radiation gain in the active medium are equal:

exp( a× 2L) = R1 × R2 × exp( g× 2L) × X,(3)

where L = active medium length,ais the gain in the active medium, R1 and R2 are the reflection coefficients of the resonator mirrors andg- “gray” losses in the active medium (i.e., radiation losses associated with density fluctuations, defects in the laser medium, radiation scattering and other types of optical losses that cause the attenuation of radiation when passing through the medium, except for the direct absorption of radiation quanta by the atoms of the medium). The last multiplier X » denotes all other losses present in the laser (for example, a special absorbing element can be introduced into the laser so that the laser generates pulses of short duration), in their absence it is equal to 1. To obtain the condition for the development of laser generation from spontaneously emitted photons, it is obvious that the equality should be replaced with ">".

Equation (3) implies the following rule for choosing the output laser mirror: if the radiation amplification factor of the active medium, taking into account gray losses (a- g) × L small, the reflection coefficient of the output mirror R1 must be chosen large so that the lasing is not damped due to the emission of radiation from the resonator. If the gain is large enough, it usually makes sense to choose a smaller value. R1 , since a high reflection coefficient will lead to an increase in the radiation intensity inside the resonator, which can affect the lifetime of the laser.

However, the laser cavity needs to be aligned. Let us assume that the resonator is composed of two parallel but not aligned mirrors (for example, located at an angle to each other). In such a resonator, the radiation, having passed through the active medium several times, leaves the laser (Fig. 5). Resonators in which the radiation goes beyond its limits in a finite time are called unstable. Such resonators are used in some systems (for example, in high-power pulsed lasers of a special design), however, as a rule, attempts are made to avoid resonator instability in practical applications.

Rice. 5. Unstable resonator with misaligned mirrors; stable resonator and

stationary beam of radiation in it.

To increase the stability of the resonator, curved reflective surfaces are used as mirrors. At certain values ​​of the radii of the reflecting surfaces, this resonator is insensitive to small misalignments, which makes it possible to significantly simplify the work with the laser.

We briefly described the minimum required set of elements for creating a laser and the main features of laser radiation.

In such a scheme (Fig. 1), the lower laser level "1" is the ground energy state of the ensemble of particles, the upper laser level "2" is a relatively long-lived level, and the level "3", associated with level "2" by a fast nonradiative transition, is an auxiliary . Optical pumping operates on channel "1">"3".

Rice. one. "Three-level" scheme with optical pumping

Let us find the condition for the existence of an inversion between levels "2" and "1". Assuming the statistical weights of the levels to be the same g1=g2=g3, we write down the system of kinetic (balance) equations for levels "3" and "2" in the stationary approximation, as well as the relation for the number of particles at the levels:

where n1, n2, n3 are the concentrations of particles at levels 1, 2 and 3, Wn1 and Wn3 are the rates of absorption and induced emission at transitions between levels "1" and "3" under the action of pump radiation, the probability of which is W; wik are the probabilities of transitions between levels, N is the total number of active particles per unit volume.

From (2) one can find the populations of levels n2 and n1 as a function of W, and their difference Дn in the form

which determines the unsaturated gain 60 of the ensemble of particles at the "2">"1" transition. In order for 60>0, it is necessary that, i.e. the numerator in (3) must be positive:

where Wthr is the threshold level of pumping. Since Wport is always >0, it follows from here that w32>w21, i.e. the probability of level 2 being pumped by relaxation transitions from level 3 must be greater than the probability of its relaxation to state 1.

If

w32 >>w21 and w32 >>w31, (5)

then from (3) we get: . And, finally, if W>>w21, then the inversion of Дn will be: Дn?n2?N, i.e. at level "2" you can "collect" all the particles of the environment. Note that relations (5) for the relaxation rates of the levels correspond to the conditions for the generation of spikes (see Section 3.1).

Thus, in a three-level system with optical pumping:

1) inversion is possible if w32>>w21 and is maximum when w32>>w31;

2) inversion occurs when W>Wthr, i.e. creation is threshold;

3) at low w21, conditions are created for the "spike" mode of free generation of the laser.

This solid-state laser is the first laser to operate in the visible wavelength range (T. Meiman, 1960). Ruby is a synthetic Al2O3 crystal in the modification of corundum (matrix) with an admixture of 0.05% Cr3+ activator ions (ion concentration ~1.6 1019 cm_3), and is designated as Al2O3:Cr3+. The ruby ​​laser operates according to a three-level scheme with OH (Fig. 2a). The laser levels are the electronic levels of Cr3+: the lower laser level "1" is the ground energy state of Cr3+ in Al2O3, the upper laser level "2" is a long-lived metastable level with f2~10_3s. Levels "3a" and "3b" are auxiliary. Transitions "1" > "3a" and "1" > "3b" belong to the blue (λ0.41 μm) and "green" (λ0.56 μm) parts of the spectrum, and represent wide (with Dl ~ 50 nm) absorption contours (bands ).

Rice. 2. ruby laser. (a) Energy level diagram of Cr3+ in Al2O3 (corundum); (b) - constructive diagram of a laser operating in a pulsed regime with Q-switching. 1 - ruby ​​rod, 2 - pumping lamp, 3 - elliptical reflector, 4a - fixed resonator mirror, 4b - rotating resonator mirror modulating the quality factor of the resonator, Cn - storage capacitor, R - charging resistor, "Kn" - button to start the current pulse through lamp; shows the inlet and outlet of the cooling water.

The optical pumping method provides selective population of auxiliary levels "3a" and "3b" of Cr3+ via channel "1">"3" with Cr3+ ions when Cr3+ ions absorb radiation from a pulsed xenon lamp. Then, in a relatively short time (~10 – 8 s), these ions undergo a nonradiative transition from "3a" and "3b" to levels "2". The energy released in this case is converted into vibrations of the crystal lattice. With sufficient density c of the radiation energy of the pump source: when, and at the "2"> "1" transition, population inversion occurs and radiation is generated in the red region of the spectrum at λ694.3 nm and λ692.9 nm. The threshold value of pumping, taking into account the stat weights of the levels, corresponds to the transfer to level "2" about? of all active particles, which, when pumped from l0.56 μm, requires specific radiation energy Еpor>2J/cm3 (and power Рpor>2kW/cm3 at pump pulse duration f?10_3s). Such a high power input into the lamp and the ruby ​​rod at stationary OH can lead to its destruction; therefore, the laser operates in a pulsed mode and requires intensive water cooling.

The laser scheme is shown in fig. 2b. A pump lamp (flash lamp) and a ruby ​​rod to increase the pumping efficiency are located inside a reflector with a cylindrical inner surface and a cross section in the form of an ellipse, and the lamp and rod are located at the focal points of the ellipse. As a result, all the radiation coming out of the lamp is focused in the rod. A lamp light pulse occurs when a current pulse is passed through it by discharging a storage capacitor at the moment the contacts are closed with the "Kn" button. Cooling water is pumped inside the reflector. The laser radiation energy per pulse reaches several joules.

The pulse mode of operation of this laser can be one of the following (see Section 3):

1) "free generation" mode at a low pulse repetition rate (usually 0.1-10 Hz);

2) "Q-switched" mode, usually optical-mechanical. On fig. 2b, Q-switching of the OOP is carried out by rotating the mirror;

3) "mode-locking" mode: with a width of the emission line Dnneodn ~ 1011Hz,

number of longitudinal modes M~102, pulse duration ~10 ps.

Ruby laser applications include holographic image recording systems, material processing, optical rangefinders, etc.

The BeAl2O4:Cr3+ laser (chromium-doped chrysoberyl or alexandrite) emitting in the range of 0.7-0.82 µm is also widely used in medicine.