The oscillatory system of a laser contains an active medium, so the spectrum of laser radiation must be determined by both the spectral properties of the medium and the frequency properties of the resonator. Let us consider the formation of the emission spectrum in cases of inhomogeneous and uniform broadening of the spectral line of the medium.

Emission spectrum with non-uniform spectral broadening; lines. Let us consider the case when the shape of the spectral line of the medium is mainly determined by the Doppler effect, and the interaction of particles of the medium can be neglected. The Doppler broadening of the spectral line is inhomogeneous (see.§ 12.2).

In Fig. 15.10, a shows the frequency response of the resonator, and in Fig. Figure 15.10b shows the contour of the spectral line of the medium. Typically, the width of the spectral line with Doppler broadening ∆ ν = ∆ νD is much larger than the interval ∆ νq between the frequencies of neighboring resonator modes. The value ∆ νq, determined by formula (15.2), for example, with a resonator length L = 0.5 m will be 300 MHz, while the spectral line width due to the Doppler effect ∆ νD in accordance with formula (12.31) can be about 1 GHz. In this example, within the spectral linewidth of the medium∆ ν≈∆ νД; three longitudinal modes are placed. With a larger resonator length, the number of modes within the line width increases, since the frequency interval ∆ νq of neighboring modes decreases.

Doppler broadening is inhomogeneous, i.e. spontaneous emission in a selected frequency range less than ∆ νD is created by a certain group of particles, and not by all

particles of the environment. Let us assume that the natural spectral linewidth of a particle is significantly less than the difference in frequencies of neighboring modes (for example, the natural linewidth

neon is close to 16 MHz). Then particles that excite a certain mode with their spontaneous emission will not cause excitation of other modes.

To determine the laser radiation spectrum, we will use the frequency dependence of the absorption coefficient æ in Bouguer’s law (12.50). This indicator is proportional to the difference in populations of the upper and lower transition levels. In a medium without population inversion, æ >0 and characterizes the absorption of electromagnetic field energy. In the presence of inversionæ<0 и определяет усиление поля. В этом случае модуль показателя называют показателем усиления активной средыæ а (æ а =|æ |).

The frequency dependence of the gain æ a (ν) in accordance with formula (12.44) coincides with the shape of the spectral line of the medium when the level populations are constant or change slightly as a result of forced transitions. Such a coincidence will be observed if a population inversion is created, and the conditions for self-excitation of the laser have not yet been met (for example, there are no cavity mirrors). In Fig. 15.10, the dotted line shows such an initial frequency dependence. With Doppler broadening of the spectral line, the dependence is expressed by a Gaussian function and has a width ∆ νD as shown in Fig. 15.10, b.

Let us assume that the self-excitation conditions are met. Then the spontaneous emission of one particle will cause forced transitions of other particles if the frequency of the spontaneous emission of the latter lies approximately within the natural width of the spectral line of the exciting particle. As a result of population inversion, forced transitions from top to bottom will prevail, i.e., the population of the upper level should decrease, the population of the lower level should increase, and the gain index æ a should decrease.

The field in the resonator is maximum at the resonant frequencies of the modes. At these frequencies the greatest change in the populations of the transition levels will be observed. Therefore, dips will appear on the æ a (ν) curve in the vicinity of the resonant frequencies (see Fig. 15.10, c).

After the self-excitation condition is met, the depth of the dip at resonant frequencies increases until the regime occurs; stationary oscillations, at which the gain index will become equal to the loss index α in accordance with condition (15.13). The width of each dip is approximately equal to the natural width of the particle line if the power generated at the frequency in question is small. The greater the power, and therefore the volumetric energy density of the field, which affects the number of forced transitions, the wider the gap. At low power, the gain within one notch is independent of the gain within another notch, since the notches do not overlap due to the initial assumption that the natural linewidth is less than the distance between the resonant frequencies. Oscillations at these frequencies can be considered independent. In Fig. Figure 15.10d shows that the laser emission spectrum contains three emission lines corresponding to three longitudinal modes of the resonator. The radiation power of each mode depends on the difference between the initial and stationary values ​​of the gain index,

as in formula (15.21), i.e., it is determined by the depth of the corresponding dips in Fig. 15.10, at. We will determine the width of each emission line δν at the end of the section, and now we will discuss the effect of pump power on the number of generated modes for given losses.

If the pump power is so low that the maximum value of the medium gain (curve 1 in Fig. 15.11, b) does not reach the threshold value equal to α, then none of the modes determined by the frequency response of the resonator is excited (Fig. 15.11, a). Curve 2 corresponds to a higher pump power, which ensures that the central frequency of the spectral line of the medium ν0 exceeds the threshold value. This case corresponds to one dip in Fig. 15.11,c and generation of one longitudinal mode (Fig. 15.11,d). A further increase in the pump power will ensure that the self-excitation conditions are met for other modes (curve 3). Accordingly, dips in the indicator curve and the emission spectrum will be depicted as in Fig. 15.10, in Ig.

Emission spectrum with uniform broadening of the spectral line. A uniform broadening of the spectral line is observed in the case when the main cause of broadening is the collision | (or interaction) of particles of the medium(§ 12.2) .

Let us assume, as in the case of inhomogeneous broadening, that several natural frequencies of the resonator fall within the spectral line of the medium. In Fig. 15.12a shows the frequency response of the resonator, indicating the frequency and width of the resonance curves of each mode ∆ νp. Curve 1 in Fig. 15.12b depicts the frequency dependence of the gain index of a medium with population inversion before self-excitation of the laser.

The spectral line of each particle and the entire medium coincide with uniform broadening, therefore spontaneous emission of any particle can cause stimulated

transitions of other particles. Consequently, during forced transitions in the specified environment with population inversion, the frequency dependence of æ a during generation (curve 2) will remain the same in shape as before generation (curve 1), but will be located below it. The dips observed with inhomogeneous line broadening (see Fig. 15.11c) are absent here, since now all particles of the medium participate in creating the laser radiation power.

In Fig. 15.12, b, the self-excitation conditions æ a > α are satisfied for three modes with frequencies νq-1, νq = ν0 and νq+1. However, at the central frequency of the spectral line ν0, the gain per single passage of radiation through the active medium is maximum. As a result of a larger number of passages, the main contribution to the radiation power will come from the mode with the central frequency.

Thus, in lasers with uniform broadening of the spectral line of the medium, it is possible to obtain a single-frequency mode with high power (Fig. 15.12c), since, unlike the case of inhomogeneous broadening, a reduction in the pump power is not required to obtain this mode.

Monochromaticity of laser radiation. The generation of oscillations in any quantum devices begins with spontaneous emission, the frequency dependence of the intensity of which is characterized by the spectral line of the medium. However, in the optical range, the width of the spectral line of the medium is significantly greater than the width of the resonance curves ∆ νp of a passive (without active medium) resonator due to the high quality factor Q of the latter. Value ∆ νP =ν0 /Q, where ν0 is the resonant frequency. If there is an active medium in the resonator, losses are compensated (regenerative effect), which is equivalent to an increase in the quality factor and a decrease in the width of the resonance curve ∆ νp to the value δ ν.

In the case of generation of one mode with frequency ν0, the laser radiation linewidth can be estimated using the formula

where P is the radiation power. An increase in radiation power corresponds to greater

compensation of losses, increasing the quality factor and reducing the emission linewidth. If ∆ νp =l MHz, ν0 =5·1014 Hz, Р =1 mW, then δ νtheor ≈ 10-2 Hz, and the ratio δ νtheor /ν 0 ≈2·10-17. Thus, the theoretical value of the emission linewidth turns out to be extremely

small, many orders of magnitude smaller than the width of the resonance curves ∆ νp. However, in real conditions Due to acoustic influences and temperature fluctuations, instability of the resonator dimensions is observed, leading to instability of the natural frequencies of the resonator and, consequently, the frequencies of the laser radiation lines. Therefore, the real (technical) radiation linewidth, taking into account this instability, can reach δ ν = 104 –105 Hz.

The degree of monochromaticity of laser radiation can be assessed by the width of the laser radiation line and the width of the envelope of the laser radiation spectrum containing several emission lines (see Fig. 15.10, d). Let ∆ ν=104 Hz, ν0 =5·1014 Hz, and the width of the spectrum envelope δ o.c .=300 MHz. Then the degree of monochromaticity along one line will be δ ν/ν0 ≈ 2·10-11, and along the envelope δ ν/ν0 ≈ 6·10-7. The advantage of lasers is the high monochromaticity of the radiation, especially along one radiation line, or in a single-frequency operating mode

§ 15.4. Coherence, monochromaticity and directionality of laser radiation

IN When applied to optical vibrations, coherence characterizes the connection (correlation) between the phases of light vibrations. There are temporal and spatial coherence, which in lasers are associated with monochromaticity and directionality of radiation.

IN In the general case, when the correlation of radiation fields is studied at two points in space, respectively, at times shifted by a certain value τ, the concept of mutual coherence function is used

where r 1 and r 2 are the radius vector of the first and second points; E 1 (r 1,t+ τ) and E* 2 (r 2, t) are the complex and complex conjugate values ​​of the field strength at these points. The normalized mutual coherence function characterizes the degree of coherence:

where I (r 1) and I (r 2) are the radiation intensity at selected points. Module γ 12 (τ) varies from zero to one. When γ 12 τ =0 there is no coherence, in the case of |γ 12 (τ )|=l there is complete coherence

Temporal coherence and monochromaticity of radiation. Temporal coherence is the correlation between field values ​​at one point in space at moments of time that differ by a certain amountτ. In this case, the radius vectors r 1 and r 2 in determining the mutual coherence function Г 12 (r 1, r 2, τ) and functions γ 12 (τ ) turn out to be equal, the mutual coherence function turns into an autocorrelation function, and the normalized function turns into a functionγ 11 (τ ), characterizing the degree of temporal coherence.

It was previously noted that during spontaneous transitions, the atom emits trains of vibrations that are not related to each other (Fig. 15.13). The correlation of oscillations at one point in space will be observed only in a time interval shorter than the duration of the train. This interval is called coherence time, and it is taken equal to the lifetime of spontaneous transitions m. The distance traveled by light during coherence time is called coherence length£. At τ ≈ 10-8 с £ =c τ =300 cm. The coherence length can also be expressed through the width of the spectral line ∆ ν. Since ∆ ν≈ 1/τ, then £ ≈ c /∆ ν.

Temporal coherence and monochromaticity are related. Monochromaticity is quantitatively determined by the degree of monochromaticity ∆ ν/ ν0 (see § 15.3). The higher the degree of temporal coherence, i.e., the longer the coherence time, the smaller the frequency spectrum ∆ ν occupied by the radiation, and the better the monochromaticity. In the limit, with complete time coherence (τ →∞), the radiation became completely monochromatic (∆ ν→0).

Let us consider the temporal coherence of laser radiation. Let us assume that a certain particle of the active medium has emitted a quantum, which we will represent in the form of a train of oscillations (see Fig. 15.13). When a train interacts with another particle, a new train will appear, the phase of oscillations of which, due to the nature of forced transitions, coincides with the phase of oscillations of the original train. This process is repeated many times, while the phase correlation is maintained. The resulting oscillation can be considered as a train with a duration significantly greater than the duration of the initial train. Thus, the coherence time increases, i.e., the temporal coherence and monochromaticity of the radiation improves.

In connection with this consideration, it becomes obvious that an optical resonator increases the temporal coherence of laser radiation, since it ensures repeated passage of trains through the active medium. The latter is equivalent to an increase in the lifetime of the emitters, an increase in temporal coherence and a decrease in the linewidth

	laser radiation discussed in § 15.3.
	The coherence time of laser radiation can be determined
	through the technical width of the laser radiation line δ ν. By
	formula τ =1/2πδ ν.. At δ ν=103 Hz coherence time
	is τ =1.5·10-4 s. The coherence length in this case
	L =cτ =45 km. Thus, the coherence time and length
	coherence in lasers is many orders of magnitude greater than in
	conventional light sources.

Spatial coherence and directionality of radiation, Spatial coherence is the correlation between field values ​​at two points in space at the same point in time. In this case, the formulas for the mutual coherence function Г 12 (r 1 ,r 2 , τ ) and normalized coherence functionγ 12 (τ ) should be substitutedτ =0. Function γ 12 (0) characterizes the degree of spatial coherence.

Radiation from a point source is always spatially coherent. The degree of spatial coherence of an extended source depends on its size and the distance between it and the observation points. It is known from optics that the larger the source size, the smaller the angle within which the radiation can be considered spatially coherent. A light wave with the best spatial coherence should have a flat front.

In lasers, the radiation has a high directivity (flat front), determined by the properties of the optical cavity. The self-excitation condition is satisfied only for a certain direction in the resonator for the optical axis or directions close to it. As a result, very large number reflections from mirrors, the radiation travels a long way, which is equivalent to an increase in the distance between the source and the observation point. This path corresponds to the coherence length and can be tens of kilometers for gas lasers. The high directivity of laser radiation also determines high spatial coherence. It is significant that the effect of increasing distance in a laser is accompanied by an increase in radiation power due to its amplification in the active medium, whereas in conventional sources an improvement in spatial coherence is associated with a loss of light intensity.

The high degree of temporal coherence of radiation determines the use of lasers in information transmission systems, measuring distances and angular velocities, and in quantum frequency standards. A high degree of spatial coherence (directivity) makes it possible to efficiently transmit light energy and focus the light flux into a spot of a very small size, comparable to the wavelength. This makes it possible to obtain enormous values ​​of energy density, field strength and light pressure necessary for scientific research and various technical applications.

November 4, 2013 at 9:33 pm

Ghetto-style spectroscopy: Exploring the spectrum and (safe) dangers of lasers

• DIY or Do It Yourself

I think everyone who reads this article has played with laser pointers. IN Lately The Chinese are raising the radiation power higher and higher - and we will have to take care of safety ourselves.

In addition to this, I also managed to look at the spectrum of the laser radiation on my knee - whether it generates at one frequency, or at several at once. This may be necessary if you want to try recording a hologram at home.

Let's remember the design of green DPSS lasers

An 808nm infrared laser diode shines onto a Nd:YVO4 or Nd:YAG neodymium laser crystal, which emits light at a wavelength of 1064nm. Then frequency doubling occurs in the nonlinear KTP crystal - and we get 532nm green light.

The obvious problem here is that 808nm and 1064nm radiation can exit the laser (if there is no output filter, or it is of poor quality) at an unknown angle, and unbeknownst to us, artistic cutting on the retina can occur. The human eye does not see 1064 nm at all, and 808 nm radiation is very weak, but can be seen in the dark (this is not too dangerous only with scattered radiation at low power!).

However, what is the radiation in the focused part of the laser radiation? Let's try to find out.

First approach: a sheet of paper and a CD

The idea is simple - we shine a laser through a hole in a sheet of A4 paper onto the surface of a stamped CD. The grooves on the surface of the disk - to a first approximation - work like a diffraction grating, and sort the light into a spectrum.

Each wavelength forms several images at once - several positive and several negative orders.

As a result, with the eye and a regular camera we will see the following:

However, if we look at a sheet of paper with a camera without an IR filter, we notice a strange purple dot between the first and second dots from the center:

Second approach: dispersion prisms

The prism also splits light into a spectrum, but the difference in refraction angles for different lengths waves - much less. That is why it was not immediately possible for me to implement this option - I continued to see one point. The situation was aggravated by the fact that my prisms were made of ordinary glass, which decompose light into a spectrum twice as poorly as specialized ones.

The result is achieved: the 808nm, 1064nm and green 532nm points are clearly visible. The human eye, in place of the IR dots, sees nothing at all.

Using a 1W green laser, using a “finger high-precision power meter” (abbreviated as PVIM), it was possible to find out that in my case the overwhelming majority of the radiation is 532 nm, and 808 nm and 1064 nm, although detectable by the camera, their power is 20 or more times less, below the limit detection of PVIM.

It's time to check the glasses

The Chinese promise that the attenuation is 10 thousand times (OD4) for the ranges of 190-540 nm and 800-2000 nm. Well, let's check that the eyes aren't official.

We put the glasses on the camera (if you put them on the laser, the hole will melt, they are plastic), and we get: 532nm and 808nm are weakened very much, a little remains from 1064nm, but I think it’s not critical:

Out of curiosity, I decided to test colored anaglyph glasses (with red and blue glass). The red half retains green well, but for infrared light they are transparent:

The blue half has virtually no effect at all:

Does the laser generate at one frequency or several?

As we remember, the main design element of a DPSS laser is a Fabry-Perot resonator, which consists of 2 mirrors, one translucent, the other regular. If the wavelength of the generated radiation does not fit into the length of the resonator an integer number of times, due to interference the waves will cancel themselves. No application special means the laser will simultaneously generate light at all permissible frequencies at once.

The larger the resonator, the greater the number of possible wavelengths at which the laser can generate. In the lowest-power green lasers, the neodymium laser crystal is a thin plate, and often only 1 or 2 wavelengths are possible for lasing.

When the temperature (=resonator size) or power changes, the generation frequency can change smoothly or abruptly.

Why is it important? Lasers that generate light at a single wavelength can be used for holography at home, interferometry (ultra-precise distance measurements) and other fun things.

Well, let's check it out. We take the same CD, but this time we will observe the spot not from 10 cm, but from 5 meters (since we need to see a difference in wavelengths of the order of 0.1 nm, and not 300 nm).

1W green laser: Due large sizes resonator - frequencies occur at small intervals:

10mW green laser: The resonator dimensions are small - only 2 frequencies fit in the same spectral range:

When the power is reduced, only one frequency remains. You can write a hologram!

Let's look at other lasers. Red 650nm 0.2W:

Ultraviolet 405nm 0.2W:

Expanding the spectral range of the laser. One of the main tasks of specialists developing laser devices is to create sources of coherent radiation, the wavelength of which can be tuned over the entire spectral range from the far infrared region to ultraviolet and even shorter wavelength radiation.

The creation of a dye laser turned out to be extremely important event from this point of view, since their radiation can be tuned in the wavelength range beyond the visible region of the spectrum. However, there are significant gaps in the spectrum of laser radiation, i.e., regions in which known laser transitions are rare, and tuning their frequency is possible only in narrow spectral ranges.

The broad fluorescence bands on which the operation of a tunable dye laser is based are not detected in the far infrared region of the spectrum, and the dyes used in lasers are quickly destroyed by intense pump radiation when the dye is excited, when it is necessary to generate lasing in the ultraviolet region of the spectrum.

Nonlinear optics.

In search of ways to fill these gaps, many laser scientists have exploited nonlinear effects in some optical materials. In 1961, researchers from the University of Michigan focused the light of a ruby ​​laser with a wavelength of 694.3 nm into a quartz crystal and detected in the radiation passed through the crystal not only the ruby ​​laser light itself, but also radiation with a double frequency, i.e., at a wavelength of 347. 2 nm. Although this radiation was much weaker than at a wavelength of 694.3 nm, nevertheless, this short-wave radiation had the monochromaticity and spatial coherence characteristic of laser light.

The process of generating such short-wave radiation is known as frequency doubling, or second harmonic generation. SHG is one example of many nonlinear optical effects that have been used to expand the tunable spectral range of laser radiation. SHG is often used to convert infrared radiation 1.06 µm and other lines of a neodymium laser into radiation falling in the yellow-green region of the spectrum, for example, 530 nm, in which only a small number of intense laser lines can be obtained.

Harmonic generation can also be used to produce radiation with a frequency three times higher than that of the original laser radiation. The nonlinear characteristics of rubidium and other alkali metals are used, for example, to triple the frequency of a neodymium laser to a value corresponding to a wavelength of 353 nm, i.e., falling in the ultraviolet region of the spectrum.

Theoretically, processes of generating harmonics higher than the third are possible, but the efficiency of such conversion is extremely low, so from a practical point of view they are of no interest. The possibility of generating coherent radiation at new frequencies is not limited to the process of harmonic generation. One such process is the process of parametric amplification, which is as follows.

Let a nonlinear medium be affected by three waves: a powerful light wave with frequency 1, a pump wave, and two weak light waves with lower frequencies 2 and 3. When condition 1 23 and the wave synchronism condition are met, the energy of a powerful wave with frequency 1 is pumped into the energy of waves with frequencies 2 and 3. If a nonlinear crystal is placed in an optical cavity, we get a device that is very reminiscent of a laser and is called a parametric oscillator.

Such a process would be useful even if its use were limited to obtaining the differences between the frequencies of two existing ones. laser sources. In fact, a parametric oscillator is a device capable of generating coherent optical radiation, the frequency of which can be tuned in almost the entire visible range. The reason for this is that there is no need to use additional sources of coherent radiation at frequencies 2 and 3. These oscillations can themselves arise in the crystal from noise photons of thermal noise, which are always present in it.

These noise photons have a wide range of frequencies, located predominantly in the infrared region of the spectrum. At a certain temperature of the crystal and its orientation relative to the direction of the pump wave and to the axis of the resonator, the above-mentioned condition of wave matching is satisfied for a certain pair of frequencies 2 and 3. To adjust the radiation frequency, it is necessary to change the temperature of the crystal or its orientation.

The operating frequency can be any of the two frequencies 2 and 3, depending on what frequency range of the device’s radiation is needed. Rapid frequency tuning in a limited spectral range can be obtained using electro-optical changes in the refractive indices of the crystal. As with a laser, there is a threshold pump power level that must be exceeded to obtain steady-state oscillations. Most parametric oscillators use visible lasers, such as an argon laser or the second harmonic of a neodymium laser, as a pump source.

The output of the device produces tunable infrared radiation. 2.

End of work -

This topic belongs to the section:

Dye laser

The emission parameters of a solid-state laser largely depend on the optical qualities of the crystal used. Inhomogeneities in the crystal structure can seriously limit.. At the same time, liquid lasers are not as bulky as gas systems and are easier to operate. Of the calculated types..

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OPTICAL FREQUENCY STANDARDS - lasers with a frequency stable over time (10 -14 - 10 -15), its reproducibility (10 -13 - 10 -14). O. s. hours are used in physical sciences. research and find practical application in metrology, location, geophysics, communications, navigation and mechanical engineering. Frequency division O.s. hours before the radio range made it possible to create a time scale based on the use of the optical period. .
O. s. h. have advantages compared to quantum frequency standards Microwave range: experiments related to measuring frequency when using lasers require less time, because abs. the frequency is 10 4 - 10 5 times higher than non-laser frequency standards. Abs. intensity and width, which are frequency references, in optical. range 10 5 - 10 6 times more than in the microwave range, at the same relative. width. This allows you to create O. s. hours with a higher short-term duration. frequency stability. When dividing the frequency of O. s. h. refers to the radio range. the width of the emission line practically does not change (if a microwave standard is used, the fluctuation spectrum of its signal expands significantly when the frequency is multiplied by 10 5 - 10 6 times). The role of quadratic Doppler effect, limiting longevity. frequency stability and reproducibility are the same.

The principle of stabilization. Stabilization of the laser frequency, as well as radio standards, is based on the use of spectral lines of atomic or molecular gas (optical reference points), to the center of which the frequency is “linked” v using an electronic automatic system. frequency adjustments. Because laser gain lines usually significantly exceed the bandwidth optical resonator, then instability ( v) frequencies v Generation in most cases is determined by a change in optical. resonator length Main. sources of instability l are thermal drift, mechanical. and acoustic disturbances of structural elements, fluctuations of the refractive index of gas-discharge plasma. Using optical reference point, the auto-tuning system produces a signal proportional. the magnitude and sign of the detuning between the frequency v and frequency v 0 center of the spectral line, with the help of which the laser frequency is tuned to the center of the line ( = v - v 0= 0). Relates. setting accuracy inversely proportional the product of the spectral line ( - line width) and the signal-to-noise ratio during its display.
To obtain a narrow emission line and high short duration. frequency stability (stability over time s), it is necessary to use benchmarks of sufficiently high intensity with a width significantly exceeding the characteristic range of frequency disturbances. gas lasers characteristic width of the acoustic spectrum. disturbances ~ 10 3 - 10 4 Hz, therefore the required resonance width is Hz (relative width 10 -9 - 10 -10). This allows the use of automatic systems. frequency adjustments with a wide band (10 4 Hz) for eff. suppression of fast fluctuations in the resonator length.
To achieve high durability. stability and frequency reproducibility are required optical. lines of high quality factor, since this reduces the influence of decomposition. factors on frequency shifts of the line center.

Optical benchmarks. The methods used in the microwave range for obtaining narrow spectral lines turned out to be inapplicable in optical applications. spectral region (Doppler broadening is small in the microwave range). For O. s. Particularly important are the methods that make it possible to obtain resonances in the center of the spectral line. This makes it possible to directly relate the radiation frequency to the frequency of the quantum transition. Three methods are promising: the method of saturated absorption, two-photon resonance and the method of spaced optical beams. fields. Basic Results on laser frequency stabilization were obtained using the saturated absorption method, which is based on the nonlinear interaction of counterpropagating light waves with a gas. A nonlinear absorbing cell with low-pressure gas can be located inside the laser cavity (active reference) and outside it (passive reference). Due to the saturation effect (equalization of the population levels of gas particles in a strong field), a dip with a uniform width appears in the center of the Doppler-broadened absorption line, the edges can be 10 5 - 10 6 times less than the Doppler width. In the case of an internal absorbing cell, a decrease in absorption in the center of the line leads to the appearance of a narrow peak in the contour of the dependence of power on generation frequency. Width of nonlinear resonance in molecular gas low pressure is determined primarily by collisions and effects caused by the finite time of flight of a particle through a light beam. A decrease in the resonance width is accompanied by a sharp drop in its intensity (proportional to the cube of pressure).
Naib. narrow saturated absorption resonances with a width of 10 -11 were obtained in CH 4 on components E oscillatory-rotate. lines R(7) stripes v 3 (see Molecular spectra), which are close to the center of the gain line of the helium-neon laser at = 3.39 microns. To accurately align the amplification and absorption lines, use 22 Ne and increase the He pressure in the active medium of the laser or place the active medium in a magnetic field. field (for E-Components).
Scheme O. s. h., using ultra-narrow resonance (with a relative width of 10 -11 - 10 - 12 ) as a reference, consists of an auxiliary frequency-stable laser 2 with a narrow radiation line, a tunable laser 2 and a system for obtaining a narrow resonance (Fig. 1). The narrow emission line of a tunable laser, which is used to obtain an ultra-narrow resonance, is ensured by phase synchronization of this laser with a stable one.

Rice. 1. Scheme of the optical frequency standard: FFA - frequency-phase auto-tuning; SUR - system for obtaining ultra-narrow resonance; AFC - automatic frequency control system; ZG - sound generator; RG - radio generator; D - photo detector.

We'll have a long time. stability of the tunable laser is achieved smooth tuning its frequencies to the maximum ultra-narrow resonance using an extreme auto-tuning system. In this case, it is possible to simultaneously receive high values short term and long lasting. stability and frequency reproducibility.
Frequency stability. Naib. high frequency stability was obtained in the IR range with a He - Ne laser ( = 3.39 μm) with internal. absorption cell. Because abs. its frequency is known with high accuracy (10 -11), then this laser can be used independently. secondary frequency standard for measuring abs. frequencies in optical and IR ranges. The emission linewidth of such a laser is 0.07 Hz (Fig. 2). Frequency stability for averaging times = 1 - 100 s is equal to 4 x 10 -15 (Fig. 3).
We'll have a long time. stability and frequency reproducibility of He - Ne lasers with telescopic. beam expansion, stabilized by resonances in CH 4 on absorption lines F 2 2 and E(see above) with a quality factor of ~10 11, reach ~10 -14. The principal factor limiting frequency reproducibility and accuracy is quadratic.

Lit.: Basov N. G., Letokhov V. S., Optical frequency standards, "UFN", 1968, v. 96, p. 585; Jennings D. A., Petersen F. R., Evenson K. M., Direct frequency measurement of the 260 THz (1.15mm) 20 Ne Laser and beyond, in: Laser spectroscopy. IV. Proc. 4th-Intern. Conf., Rottach-Egern, Fed. Rep. of Germany, June 11 - 15 1979, ed. by H. Walther, K. W. Kothe, V. -, 1979, p. 39; Proceedings of Third Symposium on Freq. Standards and Metrology, Aussois, France, 12 - 15 Oct. 1981, "J. Phys.", 1981, v. 42, Colloq. S 8, No. 12; Bagaev S.N., Chebotaev V.P., Laser frequency standards, "UFN", 1986, v. 148, p. 143; Knight D. J. E., A tabulation of absolute laser - frequency measurements, "Metrologia", 1986, v 22, p. 251.

V. P. Chebotaev.

1.1. Types of spectra.

At first glance, the laser beam seems very simple in structure. This is practically single-frequency radiation that has a spectrally pure color: the He-Ne laser has red radiation (633 nm), the cadmium laser emits Blue colour(440 nm, an argon laser emits several lines in the blue-green region of the spectrum (488 nm, 514 nm, etc.), a semiconductor laser emits red radiation (650 nm), etc. In fact, the laser emission spectrum has a rather complex structure and is determined by two parameters - the emission spectrum of the working substance (for a He-Ne laser, for example, this is the red spectral line of neon emission excited by an electric discharge) and resonance phenomena in the optical resonator of the laser.

For comparison, the figures on the right show the emission spectra of the sun (A) and a conventional incandescent light bulb (B) (top picture), the spectrum of a mercury lamp (picture right) and a greatly enlarged emission spectrum of a He-Ne laser (bottom picture).

The spectrum of an incandescent lamp, like the solar spectrum, belongs to continuous spectra that completely fills the visible spectral range electromagnetic radiation(400-700 nm). The spectrum of a mercury lamp belongs to the line spectra, which also fills the entire visible range, but consists of individual spectral components of varying intensities. By the way, before the advent of lasers, monochromatic radiation was obtained by isolating individual spectral components of the radiation from a mercury lamp.

1.2. Emission spectrum in a He-Ne laser.

The laser radiation spectrum is monochromatic, that is, it has a very narrow spectral width, but, as can be seen from the figure, it also has a complex structure.

We will consider the process of forming a laser spectrum on the basis of a well-studied He-Ne laser. Historically, it was the first laser continuous action, operating in the visible range of the spectrum. It was created by A. Javan in 1960.

In Fig. on the right are the energy levels of an excited mixture of helium and neon. An excited helium or neon atom is an atom in which one or more electrons of the outer shell, in collisions with electrons and ions of a gas discharge, move to higher energy levels and can subsequently move to a lower energy level or return back to a neutral level, with emission of a light quantum - a photon.

Atoms are excited electric shock passing through the gas mixture. For a He-Ne laser, this is a low-current, glow discharge (typical discharge currents are 20-50 mA). The picture of energy levels and the radiation mechanism are quite complex even for such a “classical” laser, which is the He-Ne laser, so we will limit ourselves to considering only the main details of this process. Helium atoms excited to the 2S level in collisions with neon atoms transfer accumulated energy to them, exciting them to the 5S level (therefore, there is more helium in the gas mixture than neon). From the 5S level, electrons can move to a number of lower energy levels. We are only interested in the 5S - 3P transition (both levels are actually split into a number of sublevels due to the quantum nature of the excitation and emission mechanisms). The wavelength of photon emission during this transition is 633 nm.

Let's note one more important fact, fundamentally important for obtaining coherent radiation. With the correct proportions of helium and neon, the pressure of the gas mixture in the tube and the value of the discharge current, electrons accumulate at the 5S level and their number exceeds the number of electrons located at the lower 3P level. This phenomenon is called level population inversion. However, this is not laser radiation yet. This is one of the spectral lines in the neon emission spectrum. The width of the spectral line depends on several reasons, the main of which are: - the finite width of the energy levels (5S and 3P) involved in the radiation and determined by the quantum uncertainty principle associated with the residence time of neon atoms in the excited state, - line broadening associated with constant movement excited particles in a discharge under the influence electric field(the so-called Doppler effect). Taking these factors into account, the width of the line (experts call it the contour of the working transition) is approximately two ten thousandths of an angstrom. For such narrow lines, it is more convenient to use its width in the frequency domain in calculations. Let's use the transition formula:

dn 1 =dl c/l 2 (1)

where dn 1 is the width of the spectral line in the frequency domain, Hz, dl is the width of the spectral line (0.000002 nm), l is the wavelength of the spectral line (633 nm), c is the speed of light. Substituting all values ​​(in one measurement system), we obtain a line width of 1.5 GHz. Of course, such a narrow line can be considered completely monochromatic in comparison with the entire spectrum of neon radiation, but this cannot yet be called coherent radiation. To obtain coherent radiation, the laser uses an optical cavity (interferometer).

1.3. Laser optical cavity.

An optical resonator consists of two mirrors located on the optical axis and facing each other with reflective surfaces, Fig. on right. Mirrors can be flat or spherical. Flat mirrors are very difficult to align and laser output can be unstable. A resonator with spherical mirrors (confocal resonator) is much more stable, but the laser beam may be inhomogeneous across the cross-section due to the complex, multimode composition of the radiation. In practice, a semi-confocal resonator with a rear spherical and front flat mirror is most often used. Such a resonator is relatively stable and produces a homogeneous (single-mode) beam.

The main property of any resonator is the formation of standing electromagnetic waves. In the case of a He-Ne laser, standing waves are generated to emit a neon spectral line with a wavelength of 633 nm. This is facilitated by the maximum reflection coefficient of the mirrors, selected just for this wavelength. Laser cavities use dielectric mirrors with multilayer coating, allowing a reflection coefficient of 99% or higher. As is known, the condition for the formation of standing waves is that the distance between the mirrors must be equal to an integer number of half-waves:

nl =2L (2)

where n is an integer or order of interference, l is the wavelength of radiation inside the interferometer, L is the distance between the mirrors.

From the resonance condition (2) we can obtain the distance between the resonant frequencies dn 2:

dn 2 =c/2L (3)

For a one and a half meter gas laser cavity (He-Ne laser LGN-220) this value is approximately 100 MHz. Only radiation with such a frequency period can be repeatedly reflected from the resonator mirrors and amplified as it passes through an inverse medium - a mixture of helium and neon excited by an electric discharge. Moreover, what is extremely important, when this radiation passes along the resonator, its phase structure does not change, which leads to coherent properties of the amplified radiation. This is facilitated by the inverse population of the 5S level, which was mentioned above. An electron moves from the upper level to the lower level synchronously with the photon initiating this transition, therefore the phase parameters of the waves corresponding to both photons are the same. This generation of coherent radiation occurs along the entire radiation path inside the resonator. In addition, resonant phenomena lead to a much greater narrowing of the emission line, resulting in the greatest gain being obtained at the center of the resonant peak.
After a certain number of passes, the intensity of coherent radiation becomes so high that it exceeds the natural losses in the resonator (scattering in the active medium, losses on mirrors, diffraction losses, etc.) and part of it goes beyond the resonator. For this purpose, the output, flat mirror is made with a slightly lower reflection coefficient (99.6-99.7%). As a result, the laser emission spectrum has the form shown in the third Fig. above. The number of spectral components usually does not exceed ten.

Let us summarize once again all the factors that determine the frequency characteristics of laser radiation. First of all, the working transition is characterized by the natural width of the contour. In real conditions due to various factors the outline widens. Within the broadened line, the resonant lines of the interferometer are located, the number of which is determined by the width of the transition contour and the distance between adjacent peaks. Finally, at the center of the peaks are extremely narrow spectral lines of laser emission, which determine the spectrum of the laser output.

1.4. Coherence of laser radiation.

Let us clarify what coherence length is provided by the He-Ne laser radiation. Let's use the formula proposed in the work:

as it passes through an inverse medium - a mixture of helium and neon excited by an electric discharge. Moreover, what is extremely important, when this radiation passes along the resonator, its phase structure does not change, which leads to coherent properties of the amplified radiation. This is facilitated by the inverse population of the 5S level, which was mentioned above. An electron moves from the upper level to the lower level synchronously with the photon initiating this transition, therefore the phase parameters of the waves corresponding to both photons are the same. This generation of coherent radiation occurs along the entire radiation path inside the resonator. In addition, resonant phenomena lead to a much greater narrowing of the emission line, resulting in the greatest gain being obtained at the center of the resonant peak.

dt =dn -1 (4)

where dt is the coherence time, which represents the upper limit of the time interval over which the amplitude and phase of the monochromatic wave are constant. Let's move on to the coherence length l that is familiar to us, with the help of which it is easy to estimate the depth of the scene recorded on the hologram:

l=c/dn (5)

Substituting the data into formula (5), including the full spectrum width dn 1 = 1.5 GHz, we obtain a coherence length of 20 cm. This is quite close to the real coherence length of a He-Ne laser, which has inevitable radiation losses in the cavity. Measurements of the coherence length using a Michelson interferometer give a value of 15-17 cm (at the level of a 50% decrease in the amplitude of the interference pattern). It is interesting to estimate the coherence length of an individual spectral component isolated by the laser cavity. The width of the resonant peak of the interferometer dn 3 (see the third figure from the top) is determined by its quality factor and is approximately 0.5 MHz. But, as mentioned above, resonance phenomena lead to an even greater narrowing of the laser spectral line dn 4, which is formed near the center of the resonant peak of the interferometer (third from the top in the figure). Theoretical calculation gives a line width of eight thousandths of a hertz! However, this value does not have much practical meaning, since the long-term existence of such a narrow spectral component requires values ​​of the mechanical stability of the resonator, thermal drift and other parameters that are absolutely impossible under real operating conditions of the laser. Therefore, we will limit ourselves to the width of the resonant peak of the interferometer. For a spectrum width of 0.5 MHz, the coherence length calculated using formula (5) is 600 m. This is also very good. All that remains is to isolate one spectral component, estimate its power and keep it in one place. If, during the exposure of the hologram, it “passes” along the entire working circuit (due, for example, to the temperature instability of the resonator), we will again obtain the same 20 cm of coherence.

1.5. Spectrum of ion laser generation.

Let's talk briefly about the generation spectrum of another gas laser - argon. This laser, like the krypton laser, belongs to ion lasers, i.e. in the process of generating coherent radiation, it is no longer argon atoms that participate, but their ions, i.e. atoms, one or more electrons of the outer shell of which are torn off under the influence of a powerful arc discharge that passes through the active substance. The discharge current reaches several tens of amperes, electric power power supply - several tens of kilowatts. Mandatory intensive water cooling active element, otherwise its thermal destruction will occur. Naturally, under such harsh conditions, the picture of excitation of argon atoms is even more complex. Generation of several laser spectral lines occurs at once; the width of the working contour of each of them is significantly larger than the width of the He-Ne laser line contour and amounts to several gigahertz. Accordingly, the laser coherence length is reduced to several centimeters. To record large format holograms, frequency selection of the generation spectrum is required, which will be discussed in the second part of this article.

1.6. Generation spectrum of a semiconductor laser.

Let us move on to consider the emission spectrum of a semiconductor laser, which is of great interest for the process of teaching holography and for beginning holographers. Historically, injection semiconductor lasers based on gallium arsenide were the first to be developed, Fig. on right.

Since its design is quite simple, let us consider the principle of operation of a semiconductor laser using its example. The active substance in which radiation is generated is a single crystal of gallium arsenide, which has the shape of a parallelepiped with sides several hundred microns long. The two side faces are made parallel and polished with a high degree of precision. Due to the large refractive index (n = 3.6), a sufficiently large reflection coefficient (about 35%) is obtained at the crystal-air interface, which is sufficient to generate coherent radiation without additional deposition of reflecting mirrors. The other two faces of the crystal are beveled at a certain angle; induced radiation does not escape through them. The generation of coherent radiation occurs in the p-n junction, which is created by the diffusion of acceptor impurities (Zn, Cd, etc.) into the region of the crystal doped with donor impurities (Te, Se, etc.). Thickness of the active region perpendicular to p-n junction direction is about 1 µm. Unfortunately, in this design of a semiconductor laser, the threshold pump current density turns out to be quite high (about 100 thousand amperes per 1 sq. cm.). Therefore, this laser is instantly destroyed when operating in continuous mode at room temperature and requires strong cooling. The laser operates stably at liquid nitrogen (77 K) or helium (4.2 K) temperatures.

Modern semiconductor lasers are made on the basis of double heterojunctions, Fig. on right. In such a structure, the threshold current density was reduced by two orders of magnitude, to 1000 A/cm. sq. At this current density, stable operation of a semiconductor laser is possible even at room temperature. The first laser samples operated in the infrared range (850 nm). With further improvement of the technology for forming semiconductor layers, lasers appeared with both an increased wavelength (1.3 - 1.6 μm) for fiber-optic communication lines, and with generation of radiation in the visible region (650 nm). There are already lasers that emit in the blue region of the spectrum. The big advantage of semiconductor lasers is their high efficiency (ratio of radiation energy to electrical energy pumping), which reaches 70%. For gas lasers, both atomic and ion, the efficiency does not exceed 0.1%.

Due to the specific nature of the radiation generation process in a semiconductor laser, the width of the radiation spectrum is much greater than the width of the He-Ne laser spectrum, Fig. on right.

The width of the working contour is about 4 nm. The number of spectral harmonics can reach several tens. This imposes a serious limitation on the laser coherence length. If we use formulas (1), (5), the theoretical coherence length will be only 0.1 mm. However, as shown by direct measurements of the coherence length on a Michelson interferometer and recording of reflective holograms, the real coherence length of semiconductor lasers reaches 4-5 cm. This suggests that the real emission spectrum of a semiconductor laser is not so rich in harmonics and does not have such a large contour width worker transition, as theory predicts. However, in fairness, it is worth noting that the degree of coherence of semiconductor laser radiation varies greatly both from sample to sample and from its operating mode (pump current value, cooling conditions, etc.