Coherent wave. Coherent waves of matter

Engineering systems 20.09.2019

Engineering systems

To form a stable interference pattern, it is necessary that the sources of the waves have the same frequency and the difference in the phases of their oscillations was constant. Sources satisfying this condition are called coherent *.

From the Latin word Cohaereus - interrelated.

Waves such sources are also called coherent.

Coherence of waves It happens temporary and spatial. Sources in which the phase difference remains constant, is called coherent. The easiest way to create coherent sources is to use the real source and its image. Exist various methods Creating coherent sources. The main monitoring schemes of interference in the non-chromatic light use the division of the wave front (usually from a point source) or dividing the amplitude of the wave. In this case, two coherent waves are created, which are interferred with a small movement difference.

The consistency of the waves, which lies in the fact that the phase difference remains unchanged over time for any point of space is called temporary coherence.

The consistency of the waves, which lies in the fact that the phase difference remains constant at different points of the wave surface, is called spatial coherence.

Real sources can practically be coherent.

What is temporary coherence

This type of coherence is characterized by a length and duration. It occurs when we are dealing with a non-shoe point source. An example is the bands observed in the interference in a special device - Michelson interferometer: the higher the optical difference, the less clear the strips are becoming (up to a complete disappearance). The main reason for the temporal coherence of light lies in the length of the source and the finite luminescence time.

Consider coherence in terms of two approaches. The first is made to call the phase, and the second frequency. The phase approach is that the frequencies of formulas describing the oscillatory processes at a certain point of space, excited by two superimposed waves, will be permanent and equal to each other ω 1 \u003d ω 2.

It is important that δ (t) \u003d α 2 (t) is α 1 (t). Here, the expression 2 I 1 I 2 COS Δ (T) is the so-called interference member.

If we measure the interference process by any device, it is necessary to take into account that in any case will have time inertia. The response time of the device can be designated as t i. Then, if, in order equal to T i, Cos δ (T), it will take values \u200b\u200bin the interval of minus one to plus units, then 2 i 1 i 2 cos δ t \u003d 0.

In this case, the studied waves are not coherent. If during the specified time the value of COS δ (T) is preserved almost unchanged, then the interference becomes obvious, and we obtain coherent waves.

Of all this we can conclude about the relativity of the concept of coherence. With a small inertia of the device, the interference is usually detected, and if the device has a lot of inertia, then we can simply not see the desired picture.

Definition 2.

Coherence timeMade as T k O G is a time for which a random change in the wave phase A (T) occurs, approximately equal to π.

If t i "t k o g, then an even interference picture becomes visible in the instrument.

Definition 3.

Cherecy length - This is a certain distance, when moving along which the phase undergoes a random change, approximately equal to π.

If we divide the natural light wave into two parts, then in order to see the interference, you need to maintain the optical difference of the course less than L k o g.

The coherence time has a dependence on the frequency interval, as well as on the wavelengths presented in the overall light wave.

Temporary coherence is associated with the scatter of the magnitudes of the module of the wave number K →.

What is spatial coherence

If we are dealing with a monochromatic extended, and not a point source of light, then the concept of spatial coherence is introduced here. It has characteristics such as width, radius and angle.

Spatial coherence depends on the variability of the directions of the vector K →. The directions of this vector can be characterized using a single vector E K →.

The length of spatial coherence, or the coherence radius, is the distance ρ k o g.

The letter φ is indicated by the corner size of the light wave source.

Note 1.

If the wave of light is located near the heated body, its spatial coherence is only a few wavelengths. The larger the distance from the light source, the higher the degree of spatial coherence.

Example 1.

Condition: Suppose that the angular size of the sun is equal to 0, 01 p a d. It emits the waves of light, equal to 500 N m. Calculate the radius of the coherence of the data of the waves.

Decision

To estimate the coherence radius, we use the formula ρ k o g ~ λ φ. Calculate:

ρ k o g ~ 500 · 10 - 9 0, 01 \u003d 5 · 10 - 5 (m).

Interference sun ray It can not be visible to the naked eye, since the radius of its coherence is very small and is outside the resolution of the human eye.

Answer: ρ k o g ~ 50 m to m.

Example 2.

Condition: If two units of light source emit waves, why will these waves be coherent?

Decision

To give an explanation for this phenomenon, we turn to the mechanism for the emergence of radiation at the atomic level. If light sources are independent, then the atoms in them emit light waves also independently. The duration of the radiation of each atom is approximately 10 to 8 C E K, after which the atom returns to the usual state, and the radiation of the wave stops. An excited atom will be emitted light with an original phase, it means that the difference in the radiation phases of two similar atoms will be variable. Consequently, waves spontaneously emitting light are not coherent. This model will be fair for any light sources with finite sizes.

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We are surrounded by objects of certain sizes; We know exactly where our body ends, and we are confident that on one chair comfortably sit only one. However, in the world of very small things, or in the microcant world, everything is not as pronounced: the chair and the table, reduced about ten billion times, to the size of atoms, will lose their clear boundaries and can even take one place in space, without interfering with each other. . The reason is that the objects of the quantum world are more like waves penetrating into each other than the objects limited in space. Therefore, in the microcant world you can sit on one chair and threesome, and in theater.

Things like waves

So that the wave properties can be experienced experimentally, objects need to be made not only small, but also very cold, that is, with a strongly reduced rate of chaotic atoms. Thus, atoms need to be cooled to a billion dollars of the degree of Kelvin, and the wave properties of the table and the chair from the macromir should be noticeable at unthinkable small temperatures - colder than 10 -40 K.

Remarkable properties of waves - their ability to coherently fold. Coherently - it means consistently, ordered in time or in space. Sample coherent in time sound waves - Music. Each sound of the melody, its height, duration and power are in strictly defined in accordance with each other.

The conductor of the symphony orchestra closely monitors the coherence of the sound flow from hundreds, and even thousands of sounds. We will perceive coherence as a fake sound, and its complete loss is like noise. Actually, coherence and distinguishes the melody from the incoherent set of sounds. Similarly, in the quantum world, the coherence of the wave properties of objects can give them completely new qualities that are not only very unusual, but also important to create new materials that can radically change the existing technologies. Almost half of the Nobel Prizes in Physics, awarded over the past ten years, is associated with coherent phenomena: in laser radiation (2005), in cold atoms (1997, 2001), in liquid helium (1996) and in superconductors (2003).

Most domestic nobel Laureaatov Physics received its awards for coherent phenomena: Peter Kapitsa (1978), Landau Landau (1962), Nikolay Basov and Alexander Prokhorov (1964), Alexey Apricos and Vitaly Ginzburg (2003).

Coherence of light

The concept of coherence was formed in early XIX. century after the experiments of the English scientist Thomas Jung. In them, two light waves from different sources fell on the screen and folded. Light from two ordinary light bulbs that give incoherent radiation, it is simple: the screen illumination is equal to the sum of the illumination from each lamp. The mechanism here is so. In light waves from the lights, the phase difference is chaotically change over time. If one maximum of the wave came in one point of the screen, then the next moment from one lamp can come at least, and from another - maximum. The result of the addition of waves will give "ripples on water" - an unstable interference picture. Ripple light waves so fast that eyes do not have time for her and see a uniformly lit screen. By analogy of the world of sounds - this is noise.

The result will be completely different if two coherent waves are folded on the screen (Fig. 1). Such waves are the easiest way to get from one laser beam, breaking it into two parts, and then folded them. Then the lanes will occur on the screen. Bright - these are the areas of the screen, where the maxima of light waves always come simultaneously (in phase). The wonderful optical effect is that the illumination will increase not twice, as in the case of incoherent waves, and four. This is because in the bright strip all the time there are maxima waves, that is, their amplitudes, and the illumination is proportional to the square of the amount of wave amplitudes. In dull stripes, coherent waves from different sources are quenched by each other.

Now imagine many coherent waves coming into some point in the phase. For example, a thousand waves. Then the illumination of the bright area will grow a million times! Coherent radiation of a huge, about 10 22, the number of atoms gives a laser beam. The invention of the principles of his work brought in 1964 the Nobel Prize in Physics to American Charles Towns and two Soviet physicists Nikolai Basva and Alexander Prokhorov. For 40 years, the laser penetrates our everyday life, with it, for example, we save information on compact disks and convey it on optical fiber for huge distances.

Coherent waves of matter

Our world is designed in such a way that each particle of the substance can show the properties of the wave. Such waves refer to the waves of matter, or de Broglyl waves. The wonderful French physicist Louis de Broglil in 1923 proposed a very simple formula that binds the wavelength λ (distance between the maxima) with a mass of the particle M and its velocity V: λ \u003d H / MV, where H is a constant plank.

The fundamental property of waves of any nature is the ability to interfer. However, in order to obtain not uniform noise, but, as in the case of light, the bright strip, it is necessary to ensure the coherence of the de Broglie waves. This prevents the thermal movement - atoms with different speeds differ in their wavelengths. When cooled atoms, according to the de Broglie formula, the wavelength λ increases (Fig. 2). And as soon as its value exceeds the distance between the particles, the de Broglie waves different particles They will give a stable interference pattern, since the maxima waves corresponding to the position of the particles will be overlapped.

In an optical microscope, the interference picture of the de Brogly waves can be seen if their lengths are about 1 μm. For this, as follows from the de Broglie formula, the atom speed should be approximately 1 cm / s, which corresponds to extremely low temperatures - less than one microelvin. Such chilled gas from alkali metal atoms managed to prepare, and today it is an interesting object of research. (How to cool the atoms to low temperatures and make the ultralone clock on the basis of them, it was told in "Chemistry and Life", 2001, No. 10. - Note. ed.) We note that Soviet physics from the Institute of Spectroscopy of the USSR Academy of Sciences, led by Vladilen Lethaokov in 1979, put forward and implemented key ideas on the basis of which atoms are now cooled to ultra-low temperatures.

What are interfering particles of matter? We are accustomed that the substance can be represented in the form of solid small balls that do not penetrate each other. And the waves, on the contrary, can fold and penetrate each other. By analogy with the interference of the world, we must get a "bright point on the screen" - a small area in space, where the maxima of the waves of matter is in phase. It is unexpected that the coherent waves of many and many atoms can take one area in space, forming as it were, a set of a huge number of de Broglie waves. In language quantum mechanics This means that the probability of detecting coherent atoms in the "bright point" is maximum. This amazing state of the substance is called the condensate Bose Einstein. Albert Einstein predicted him in 1925 on the basis of the works of Indian Physics Schtenendranata Bose. In condensate, all atoms are in one quantum state and behave like one big wave.

Experimentally observe Bose-Einstein condensate (BEK) succeeded only 70 years later: a report on this in 1995 published two groups of American scientists. In their experiments, atoms from the cloud of sodium or rubidium vapors or a magnetic trap fell into condensate. These pioneering works were awarded the Nobel Prize in Physics 2001, awarded by Eric Cornell, Wolfgangu Ketterle and Karl Vierhan. A bright imaging representation of the behavior of ultra-powder atoms falling into the back was shown on the cover of the December magazine Science. For 1995: In the center marches the group of identical blue cyborgs - these are backing atoms with zero temperatures, and cyborgs are chaotic around them - the cyborgs of warmer colors are moved - the above-minded slightly preheated atoms. The coherence of atoms falling into the BAC was demonstrated in a brilliant experiment in 1997 by V. otterle with colleagues from the Massachusetts Institute of Technology. For this, the magnetic trap was divided into two parts by a partition from light (Fig. 3a). Two condensate prepared from the clouds of sodium atoms, and then the trap and the partition turned off: the clouds began to expand and overlap. At the place of their overlap, a clear interference pattern arose (Fig. 3b), similar to the interference of coherent laser beams (see Fig. 1). It was observed by the shadow dropped by the cloud of atoms on the screen, "Zebra" in Fig. 3B and there is a shadow of interfering waves of matter; Dark areas correspond to maxima waves of atoms. It's surprising that when we fold atoms from different condensates, then their amount can give zero - the "substance disappears" in the region corresponding to the light zebra strip. Of course, at the very atoms do not disappear - they are simply concentrated in areas throwing the shadow.

Is it possible to observe the manifestation of wave properties for more massive objects than atoms? It turns out, it is possible. The group of Anton Tsaylinger from Vienna in 2003 it was possible to observe the interference of fullerenes and biomolecules containing about a hundred atoms. For how large particles of the substance will be able to observe the wave properties - the question is open today.

Atomic laser

From the point of view of quantum physics, atoms and photons are similar to the fact that a large number of these particles can be simultaneously in one quantum state, that is, be coherent. For example, in laser radiation, all photons are coherent: they have the same color, the direction of distribution and polarization. Therefore, it is possible to obtain powerful coherent laser beams consisting of a huge number of photons in one state.

And how to get coherent atomic bundles? The idea is simple: it is necessary to carefully remove the coherent coherent atoms from the back, just as the radiation of the laser is output from its resonator using a translucent mirror. Such a device was called an atomic laser. The first atomic laser in 1997 created all the same V. ketterle. In such a laser, the magnetic trap of two coils holds sodium atoms that form backs. Radiopol pulses applied with a period of 5 milliseconds unfold the backs of atoms, and they can no longer be held in a trap. A clutch of the freedomed atoms is the radiation of an atomic laser - freely falls under the action of gravity, which is visualized by the methods of the theater of the shadows described above. Today, the power of atomic lasers is small: they emit 10 6 atoms per second, which is incomparably less than the power of optical lasers. For example, an ordinary laser-pointer radiates for about 10 9 times more photons.

Unlike weightless photons, atoms have a weighing of peace. So, the grave is much stronger on them - the interference of coherent waves of matter will be strongly dependent on the gravitational field deflecting the beams of atoms. Let two coherent atomic beams interfer in the area of \u200b\u200btheir intersection similarly to laser beams (see Fig. 1). Suppose that the gravitational field on the way of one of the atomic bundles has changed. Then the length of the path of this beam to a meeting with another beam will also change. As a result, the maxima waves of the mother of two atomic bundles will meet elsewhere, which will lead to displacement of the interference pattern. Measuring such a displacement, you can determine the change in the gravitational field. Based on this idea, the gravitational field sensors were already created, capable of detecting the difference in the amount of acceleration of free fall less than 10 -6%. They can come in handy as for fundamental studies (Verification of physical theories, measurement of constants), and for important applied developments in navigation (the creation of precision gyroscopes), geology (useful mineral testing) and other sciences. Fistist writers, for example, you can find the plot when, using the device for measuring the slightest changes, the severity archaeologists read the inscriptions, knocked on the buried in the thicker of the Earth.

Coherent substance

Especially interesting effects occur when the properties of coherent waves of matter can be observed as the macroscopic properties of the condensed substance, that is, a solid or liquid. One of the bright examples of such properties - superfluidity in liquid helium during cooling below 2.2 K. Soviet physics performed pioneer studies of superfluidity: this phenomenon opened Peter Kapitsa in 1938, and explained Landau Landau. Superfluid helium can flow through small holes at a huge speed: at least 108 times faster than water. If we were able to fill conventional bath Superfluch helium, then it is a bit from it in less than one second through a hole size with a tiny needle ear. In 2004, the Americans Yun Song Kim and Moses Chan reported the discovery of superfluidity in solid helium. Their thin experiment consisted in the following: solid chilled helium, under pressure at a temperature of about 0.2 K, was placed on a twisted pendulum. If part of the helium passes into the superficial state, the frequency of the steep oscillations should grow, since the superfluid component remains fixed, facilitating the oscillations of the pendulum. According to Kim and Chan, about 1% of solid helium passed into the superfluid state. These experiments demonstrate that atoms can move freely over the superfluid solid bodyTherefore, it is capable of passing a lot of substances through itself unhindered: the prospect of passing through the walls in such a world seems quite real!

This amazing phenomenon can explain the wave properties of atoms. Waves, in contrast to particles, bypass obstacles in their path. Let us explain this on the example of the interference of two light beams on the screen. Cut out in the opening screen in the area light bands Zebra (interference painting). Such an obstacle Cherent light will not feel: the screen is preserved only in the unlit parts of Zebra. If the bundles are not coherent, then a uniformly illuminated screen with holes will inevitably detain a part of the world. From here you can understand how coherent waves of matter overcome obstacles without loss.

Another unusual macroscopic quantum phenomenon, similar to superfluidity, is superconductivity, open Dutchman Heik Challing-Oness in 1911 in mercury during its cooling to the temperature of liquid helium (Nobel Prize 1913). Superconducting electrons move without resistance, bypassing the obstacle, in the role of which the thermal motion of atoms. For example, the current in the ring from the superconductor can flow indefinitely for a long time, since nothing prevents him. It can be said that superconductivity is superfluidity electronic liquid. For such a superfluidity, it is necessary for a large number of charges in one quantum state, such as photons in a laser beam. This requirement is based on a restriction established by the outstanding Swiss physicist Wolfgang Pauli in 1924: If the spin number of the particle is 1/2, as in an electron, then only one particle may be in one quantum state. Such particles are called fermions. As a whole, the spin value in one quantum state can be condensed how many particles can be condensed. Such particles are called bosons. Therefore, for superconducting current, particles need electric charge with whole spin. If the pair of electrons (fermions) was able to form an integral part, then the spin of the pair would be an integer. And then the composite particles will become bosons capable of forming the back and give a superconducting current.

However, the associated pairs of electrons can really occur in the conductors, despite the fact that the Coulomb forces repel the electrons from each other - this idea was based on the theory explaining superconductivity in simple metals (John Bardine, Leon Cooper, John Sriffer, Nobel Prize in Physics for 1972).

Superfluidity Beck

So, in the second half of the 20th century, physicists came to understand that the backing can possess the properties of superfluidity. Naturally, after receiving gas backs of scientists, the idea of \u200b\u200bexperiments demonstrating superfluidity in it seized. In 2005, Group V. Ketterle presented the final proof of the gas backup superfluidity. The idea of \u200b\u200bthe experiment is based on the fact that the superfluid fluid behaves during rotation unusual. If we managed to stir the superfluid liquid with a spoon, as if coffee in a cup, it would be not entirely rotating, but would have broken into a lot of small vortices. Moreover, they would be in a strict order, forming the so-called lattice of Abrikosov vortices. The diagram of this filigree experiment is as follows (Fig. 4). Gas condensate captured by a laser beam and magnetic field, started to rotate additional laser beams; They spun condensate as a spoon - coffee. Then the trap, that is, the bundles and the coil, turned off, and the condensate was granted himself. He expanded and gave a shadow that resembled Swiss cheese (Fig. 4b). "Drops in the cheese" meet superfluid vortices. The most important feature of these experiments is that they are done not only in bosons (sodium atoms), but also in fermion gas (lithium atoms). Superfluidity in lithium gas was observed only when lithium atoms formed molecules or weak pairs. This was the first observation of fermion gas superfluidity. It failed a durable experimental foundation under the theory of superconductivity based on the idea of \u200b\u200bcondensation Bose Einstein.

Spearing lithium atoms physicists can be used using the so-called Feshbach resonance, which occurs in a trap while simultaneously acting fields of magnetic coils and laser beams. The magnetic field is adjusted in the area of \u200b\u200bFeshbach resonance so that it strongly changes the interaction forces between the gas atoms. You can make atoms attract each other or - repel. Physics came up with other ways to control the properties of ultra-oxide atomic gas. One of the most elegant is to place atoms into the interfering field of laser beams - a kind of optical lattice. In it, each atom will be in the center of one of the bands of the interference pattern (see Fig. 1), so that the waves of light will hold the waves of the substance, like a form for storing eggs. Atoms in the optical lattice are an excellent model of the crystal, where, using the parameters of laser beams, the distance between atoms is changed, and with the help of Feshbach resonance - regulate the interaction between them. As a result of physics, a long-standing dream was realized - to obtain a sample of a substance with controlled parameters. Scientists believe that super-grain gas - a model not only crystal, but also more exotic forms Matters, such as neutron stars and a quark-gluon plasma of the early universe. Therefore, some researchers do not believe without reason that the overall gas will help to understand the early stages of the evolution of the universe.

Coherent future

The phenomena of superfluidity and superconductivity show that the coherence of the de Broglie waves big number particles gives unexpected and important properties. These phenomena were not predicted, moreover, the explanation of superconductivity in simple metals was required for almost 50 years. A phenomenon of high-temperature superconductivity, discovered in 1986 in metal-oxide ceramics at 35 degrees Kelvin by German Johanes Balnoz and Swiss Karl Muller (the Nobel Prize 1987), has not yet received a generally accepted explanation, despite the enormous efforts of physicists around the world.

Another area of \u200b\u200bresearch in which without coherent quantum states Do not do, - quantum computers: only in such a state it is possible to carry out high-performance quantum calculations, inaccessible to the most modern supercomputers.

So coherence means preserving the phase difference between the folding waves. Waves themselves can be various nature: and light, and de Broglie waves. On the example of gas back, we see that the coherent substance actually represents new form Matters previously inaccessible to man. The question arises: is it always the observation of coherent quantum processes in the substance requires very low temperatures? Not always. At least there is one very successful example - laser. The ambient temperature for the laser operation is usually not significant, since the laser works under conditions that are far from thermal equilibrium. The laser is a strongly non-equilibrium system, since the energy flow is supplied to it.

Apparently, we are still at the very beginning of studies of coherent quantum processes with the participation of a huge number of particles. One of the exciting questions, on which there is no certain answer is not yet, - are macroscopic coherent quantum processes in wildlife? Maybe the life itself can be characterized as a special state of a substance with increased coherence.

Definition 1.

Coherence of waves is an prerequisite Wave interference observations. Coherence is defined as coherence in time and space of several oscillations or wave processes. Sometimes the concept of the degree of coherence of waves (degree of consistency) is used. Coherence are divided by temporary and spatial.

Temporary coherence

This type of coherence is characterized by time and long coherence. Temporary coherence is considered when the point, but non-monochromic. For example, the interference bands in the Michelson interferometer are blurred with an increase in the optical difference in the movement of the waves up to the disappearance. The reason for this is associated with the final time and the coherence length of the light source.

When considering the issue of coherence, two approaches are possible: "Phase" and "frequency". Let the frequency in formulas that describe oscillations at one point of space excited by two overlapping waves:

equal to each other ($ (\\ omega) _1 \u003d (\\ omega) _2 $) and constant. This is a phase approach. The intensity of light in the studied point of the space at the same time will determine the expression:

where $ \\ delta \\ left (t \\ right) \u003d \\ alpha_2 \\ left (t \\ right) - \\ alpha_1 \\ left (t \\ right). \\ $ Expression $ 2 \\ SQRT (I_1I_2) COS \\ Delta \\ Left (T \\ Right ) $ called interference member. Any device that registers the interference pattern has inertia time. Denote this time of the device's response through $ T_I $. If, in the time $ T_i $ $ COS \\ Delta \\ left (T \\ Right) $ takes equal values \u200b\u200bfrom $ -1 $ to $ + $ 1, then $ \\ left \\ Langle 2 \\ SQRT (I_1I_2) COS \\ Delta \\ Left ( T \\ RIGHT) \\ Right \\ Rangle \u003d 0 $. At the same time, the total intensity in the expiratory test will be equal to:

at the same time, the waves should be considered non-coherent. In the event that, during the $ T_i $ $ COS \\ Delta \\ Left (T \\ Right) $ is almost unchanged, the interference can also be detected and the waves should be considered coherent. This means that the concept of coherence is relative. If the inertia of the device is small, then it can detect interference, while the device with a long time inertia under the same conditions the interference picture "will not see".

Coherence time ($ T (KOG) $) is defined as the time during which a random change in the wave phase ($ \\ alpha (t) $) is about equal to $ \\ pi. $ During this time ($ T (KOG) $), the oscillation becomes incoherent. If condition is satisfied:

that interference device does not record. With $ T_I \\ LL T_ (KOG) $ interference picture is a clear.

The distance defined as:

call coherence length (tsuga long). The coherence length is called such a distance when moving on which a random phase change is about equal to $ \\ pi. $ In the division of a natural light wave into two parts, in order to obtain an interference pattern, the optical difference ($ \\ triangle $) is less than $ L_ (KOG). $

The coherence time is associated with the frequency interval ($ \\ triangle \\ nu $) or wavelengths, which are presented in the wave of light:

Respectively:

In the event that the difference in the optical movement of the waves reached the values \u200b\u200bof about $ (\\ l) _ (KOG), the $ interference bands do not differ. The limit order of interference ($ M_ (PRED) $) We define as:

Temporary coherence is associated with the scatter of the magnitudes of the wave number module ($ \\ overrightarrow (k) $).

Spatial coherence

In the event that the light source is characterized as monochromatic, but extended, then they speak of spatial coherence. Spatial coherence is characterized by a width, radius and angle of coherence.

This type of coherence is associated with the variability of the directions of $ \\ overrightarrow (k) $. The directions of the vector $ \\ overrightarrow (k) $ are characterized by the unit vector $ \\ overrightarrow (E_K) $.

The distance $ (\\ rho) _ (KOG) $ is called long spatial coherence (coherence radius), it can be defined as:

where $ \\ varphi $ is an angular size of the source of light waves.

Comment

The spatial coherence of the light wave near the heated radiation body is only a few wavelengths. With increasing distance from the light source, the degree of spatial coherence increases.

The formula by which the angular dimensions of the extended source are installed, in which the interference is possible, has the form:

are not coherent.

Example 1.

The task: What is the radius of the coherence of light waves that come from the Sun, if we assume that the corner size of this source is $ 0.01 happy $. The light wavelength is about $ 500 nm $.

Decision:

To estimate coherence radius, we apply the formula:

\\ [(\\ rho) _ (KOG) \\ SIM \\ FRAC (\\ lambda) (\\ varphi) \\ left (1.1 \\ Right). \\]

Cut out:

\\ [(\\ RHO) _ (KOG) \\ SIM \\ FRAC (500 \\ CDOT (10) ^ (- 9)) (0.01) \u003d 5 \\ Cdot (10) ^ (- 5) \\ left (m \\ right ). \\]

With this coherence radius, it is impossible to observe the interference of the sun rays without special tricks. It does not allow to make a person resolving the human eye.

Answer: $ (\\ rho) _ (kog) \\ SIM 50 \\ μm $.

Example 2.

The task: Explain why non-coolent waves that are emitted by two unrelated light sources.

Decision:

The non-hotterness of natural light sources can be understood by exploring the mechanism of the emergence of radiation of light by atoms. In two independent sources of light, atoms empty waves independently of each other. Each atom radiates a finite time about $ (10) ^ (- 8) seconds. For such a period of time, the excited atom goes into a normal state, the radiation of the wave ends. An excited atom emits light with a different initial phase. In this case, the difference in the phases of the radiation of two similar atoms is a variable. So waves that spontaneously emit the light source atoms are not coherent. Only in the time interval, approximately equal to $ (10) ^ (- 8) with $ waves, which radiate atoms, have almost unchanged amplitudes and phases. Such a radiation model is valid for any light source that has finite sizes.

The phenomenon of the order of the considerable strengthening bands and the weakening of the light intensity is called an intypeface. Intephrotence of light is observed in special conditions (which will be the Passsmall below) in the applying of a two or more bunches of light on the dpug. A special occasion of the intrapfection of the waves (and the intrapfection there is a substantially wave phenomenon and takes place not only for light waves) is the steady wave mentioned by us. In a standing wave, beafness (intensity maxima) and nodes (intensity minima) are observed, which are manifested with a dpuh in the ppuslial. Standing wave Overlapping on a falling wave, waves exposed from some kind of phenomena.

The main condition for observing the intrapophylation of waves is their clause. Under clause is understood as the coherence of waves of a DPG with a phase dish. If you take two waves coming from independent sources, then their imposition of the phase will be changed considerable. Really light waves (we will behave about them) are emitted by atoms and each wave there is a path imposition of a large number of wave tsugs coming from independent dpug from atoms. "There will be no" inviller "gain and weakening the amount of the amount in the PPPPENCY. For the appearance of a minimum of the wave intensity at some point of the punch, it is necessary that at this point the folding waves constantly (long-term, corresponding to the observation) were quenched by the DPUG. Those. Prolonged waves would be accurate in the simplicity, when their phases would remain constant and put. Output, maximum waves will appear when the foldable waves are all taken in the same phase, i.e. when they constantly enhance the dpug dpug. Such an overview, the intrapfection will be observed using the condition when the Outlawted Waves on the Wave DPUG at each point of the light field have permanent phase exposure. If this phase exposure is extremely different, then there will be a maximum, if an odd number, then there will be a minimum of light intensity. The waves with permanent phase are called clay. You can agree on the clampingness of the wave itself. This is a wonder when the phase point of the wave for any two points of the punch is permanent in carrying out. The light emitted, natural sources is incognita, since it is clearly emasculated by dubbed atoms, there is no consistency between which there is no consistency. How then can you observe the intypeface? The total specimen can be obviously sporalized: it is necessary to ensure that the waves from each atom are imposed on themselves. After all, each wave emitted by a separate atom, with itself crogeneta, since it becomes a piece of a sinusoidal wave. If such waves are imposed on themselves, then an intepprint will be observed. Such an occasion, the overall and movement of the observation of the influence of light of light is:

A light beam is needed, which comes from one source, in some respect to two or more beams (these bundles will be claused among themselves), and then make them out the dpug. The maxima of the wave intensity will be observed at points where the condition is performed.

minima - at points where

Here, it is marked here the pity of the phases of the folded waves.

Consider the use of intypepension - Jung's experience. Suppose that light from the light bulb with a light filter, which creates a combatically monochpatic light, the two narrow, toned slopes, which are installed ecpan (). On the ecpane will be observed a system of light and dark stripes - intertension bands. IN this case united light wave It is dirty on two, coming from practicing slots. These two waves are crogenetas among themselves and under the applying of the DPUGA give a system of maxima and minima of light intensity in the form of dark and bright stripes of the corresponding color. Where will the maximum arise and where is the minimum? Consider some point of EkPana M. Present from the cracks, as from the second keypad sources, rays converged at one point. We find the passage of these rays - away. If the even number of half-waves fit on it (the half-wave corresponds to the phase exploration), then the waves from the slots at the point m will be shaped in the same phase, the maximum will be observed. If on the side fit odd number Semi-fell, then they are in shapelipase and will be observed at least. Such an overview, the conditions of observation of highs and lows (1.14) and (1.15) can be used as follows:

(min),

We are Passmotpeli, when the waves from clause sources (cracks) "run" in the same way, with the same scope. However, in the dpuychy experiments, the intrapophy waves can be pledged, and as a result, there are practical phase response. In this case, instead of geometrical exploration of the course, it is convenient to ensure about the so-called optical portion of the stroke.

and, therefore,

Then the floods for Internet maxima and minima () can be sent in the form:

(MAX)

(min)

If the intrapophy waves are trying on the use of n1 and n2, then the conditions of maxima and minimums should be written:

(MAX)

(min)

where NL is called the optical path of the beam path, and the optical point of the ray.

Such an increase, the maxima of the intypepoles are observed at points, for which the optical point of the stroke is a four-feet, and the minimum is at points, for which the odd number of half-mounted on the optical portion of the stroke is laid.

In the output of FofMul () and (), we pledged that the slots for the second waves are infinitely narrow. The final shipin of the gaps, obviously, the maxima and lows. At enough shorts, the maxima will move, and the intphetic will not be observed. ISPEET POCI AND DAYS BETWEEN GRAPERS. It must be small enough: the smaller, the shine of the intrapfection.

Intephrotement can be observed in white, i.e. nonmonochpomatic, light. In this case, each strip will be exhausted: the intphetia is appropriate to the onset of light on monochpomatic components (the more, the maxima of the DPUG from the DPUG) on the larger dance.

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