Diffraction (English: diffraction) refers to the physical phenomenon that waves deviate from the original straight line when encountering obstacles.
stayClassical physicsThe wave will bend and spread to different degrees after passing through obstacles such as slits, holes or disks.If an obstacle is placed between the light source and the observation screen, there will be bright areas and dark areas on the observation screen, and the boundaries of these areas are not sharp, which is a complex pattern of light and dark.This phenomenon is called diffraction, which may occur when the wave encounters obstacles in its propagation path.In addition, when light waves pass through media with uneven refractive index, or when sound waves pass throughacoustic impedance(acoustic impedance) A similar effect will occur when the medium is uneven.Under certain conditions, not only water waves and light waves can produce diffraction phenomena visible to the naked eye, but also other types ofelectromagnetic wave(e.gX-rayandradio wavesEtc.) can also be diffracted.becauseatomReal objects of scale have wave like properties, and they will also show diffraction phenomenon, which can be passed throughquantum mechanicsStudy its nature.
In appropriate cases, any wave has the inherent nature of diffraction.However, the degree of wave diffraction varies in different cases.If the obstacle has multiple densely distributed pores, it will result in a more complex diffraction intensity distribution pattern.This is because different parts of the wave propagate to the observer's position in different paths, and the wave occurssuperpositionThe phenomenon formed by.
The form theory of diffraction can also be used to describe finite waves (waves measured as finite size) in thefree spaceCommunication of.For example, the divergent nature of the laser beamradarThe beam shape of antenna and the field of view of ultrasonic sensor can be analyzed by diffraction equation.
Chinese name
diffraction
Foreign name
diffraction
founder
aFrancisco Grimadi/a
Principle
waveDeviation from the original straight line when encountering obstacles
The diffraction effect of light was first caused byFrancisco Grimadi(Francesco Grimaldi) was discovered and described in 1665. He is also the founder of the word "diffraction".The word comes from a Latin worddiffringere, which means "becoming fragments", that is, the original propagation direction of the wave is "broken" and bent to different directions.Grimaldi's observations were not published until 1665, when he died.He proposed that "light can not only travel, refract and reflect along a straight line, but also travel in the fourth way, that is, through diffraction."
British scientistsIsaac NewtonHaving studied these phenomena, he believed that light was bent and that light was composed of particles.Before the 19th century, because of Newton's authority in the academic world, the theory of light particles occupied the mainstream position for a long time.This situation was not changed until several theoretical and experimental results were published in the 19th century.In 1803,Thomas YoungA very famous experiment was carried out, which showed the interference phenomenon caused by two closely adjacent slits, which was later called“Double slit experiment”。In this experiment, a beam of light shines on the light barrier with two adjacent slits, and when the light passes through the slits and shines on the observation screen behind the barrier, it can produce light and dark stripes.He attributed this to the interference phenomenon caused by the diffraction of the light beam after passing through two slits, and further speculated that the light must have the property of wave.Augustine FresnelHe did more authoritative computational research on diffraction, and his results were published in 1815 and 1818 respectively. He said, "In this way, I will show how people can conceive of the continuous propagation of light as a spherical wave..."（ "J'ai donc montré de quelle façon l'on peut concevoir que la lumière s'étend successivement par des ondes sphériques, ..."）
The French Academy of Sciences once held an award-winning debate on diffraction, which was won by Fresnel.As one of the opponents of light wave theory,Simone Denis PoissonIt is proposed that if Fresnel's claimed conclusion is correct, when light strikes a ball, a bright spot will be found in the center of the shadow area behind the ball.As a result, the review committee arranged the above experiment and found a bright spot (later known asArago spot ）。This discovery greatly supports Fresnel's theory.[1]His research isChristian HuygensThe developed wave theory of light provides great support.Together with Yang's theory, he refuted Newton's theory that light is a particle.
In the process of exploring the diffraction phenomenon, people have also accumulated the understanding of diffraction gratings.Scottish mathematician and astronomer in the 17th centuryJames GregoryJames Gregory observed the diffraction of sunlight between the feathers of birds.He was the first to find outdiffraction grating A scientist of principle.He mentioned this discovery in a letter to John Collins on May 13, 1673.In 1786, American astronomerDavid RittenhouseFor the first time, he made a diffraction grating manually with screws and thin lines. The density of thin lines reached 100 lines per inch. He successfully saw the diffraction of sunlight with this device.In 1821,Joseph FraunhoferThomas Young's formula {φ 10 - φ 20=2 π/λ * (R1-R2)} on diffraction is proved by using a similar device (127 lines per centimeter), and many important studies on diffraction have been carried out.In 1867, Lewis Morris Rutherford used a hydraulic turbine as the power to mark lines and make gratings.LaterHenry Augustus RolandImproved the grating marking technology, and invented the concave grating marking on the concave spherical mirror in 1882.Later, Robert William Wood improved the ruling shape of the grating, thus improving the diffraction efficiency of the grating.ModernAlbert MichelsonThe idea of using an interferometric servo system to control the grating marking process was proposed and realized in 1948.In the second half of the 20th century, due to the emergence of new technologies such as laser and photoresist, the grating manufacturing technology has made great progress, the manufacturing cost has been significantly reduced, and the manufacturing cycle has also been shortened.[2]
Diffraction pattern
If using monochromeDirectional lightAs a light source, diffraction will produceinterferenceresult.Coherent waveAfter meeting somewhere in space, due to different phasesInterferenceCausing mutual reinforcement or weakeningphysical phenomenon。 The result of diffraction is to produce light and dark diffraction patterns, representingDiffraction direction(angle) and strength.According to the diffraction pattern, the light source and grating can be inferred in turn.In order to make the light energy produce obvious deviation, the "grating spacing" must have the same order of magnitude as the wavelength of light.The grating used for visible spectrum has about 500 lines per millimeter.
In 1912,LaueIt is thought that if the atoms in the crystal are arranged regularly, the crystal can be regarded as X-rayThree-dimensional diffraction grating。The order of magnitude of the X-ray wavelength is 10 ^ - 8cm, which is roughly the same as the atomic spacing in the solid.As expected, the experiment was successful, which is the earliestX-ray diffraction。 Obviously, under the condition that the X-ray is constant, the properties of the crystal can be analyzed according to the diffraction pattern.For this reason, the corresponding relationship between the direction and intensity of X-ray diffraction and the crystal structure must be established in advance.
Diffraction of light
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Diffraction diagram
In the propagation path, light encounters opaque or transparent obstacles or small holes (narrow slits), bypasses the obstacles, and produces a phenomenon that deviates from the straight line propagation, which is called light diffraction.The light and dark stripes or halos generated during diffraction are calledDiffraction pattern。
definition：light waveIt will deviate more or less after encountering obstaclesgeometrical optics The phenomenon of propagation law.
The conditions for diffraction are:Since the wavelength of light is very short, only a few tenths of a micron, usually objects are much larger than it, but when the light shoots at a pinhole, a slit, or a filament, it can be clearly seenDiffraction of light。The effect is better when the monochromatic light is used. If the polychromatic light is used, the diffraction pattern is colored.
Any obstacle can make light happenDiffraction phenomenonHowever, the conditions for obvious diffraction are "harsh".
When the size of the obstacle is much larger thanlight waveThe light can be seen as propagating along a straight line.be careful,Linear propagation of lightIt is only an approximate rule that when the wavelength of light is much smaller than that of holes or obstacles, light can be seen as propagating along a straight line;When the hole or obstacle can be compared with the wavelength, or even smaller than the wavelength, the diffraction is very obvious.Since the visible light wavelength range is between 4 × 10 ∧ - 7m and 7.7 × 10 ∧ - 7m, it is rare to see obvious light diffraction in daily life.
Huygens Fresnel principle
diffraction
Huygens proposed that,mediumupperWavefrontAll points on can be regarded as emissionwaveletThe wave source of, and the wave trace of these wavelet at any time after, is the new wave front at that time.Huygens Fresnel principle can describe qualitativelyDiffraction phenomenoninPropagation of lightQuestion.Fresnel has enrichedHuygens principle, he proposedwavefrontEach surface element on the can be regarded as the wave source of the wavelet, and the vibration of P at a certain point in space is the superposition of the coherent vibration generated by all these wavelet at that point, which is called Huygens Fresnel principle.
Fresnel diffraction
It refers to the situation where the distance between the light source diffraction screen and the diffraction screen receiving screen is finite, or one of them is finite, or that the Fresnel diffraction field is received at a finite distance when the spherical wave is illuminated.For example: circular aperture diffraction, circular screen diffraction Fresnel diffraction, Poisson bright spot.
Fraunhofer diffraction
Single slit fraunhofer diffraction
It refers to the situation where the distance between the diffraction screen and both is infinite, or that the Fraunhofer diffraction field is received at infinity when the plane wave is illuminated.Generally speaking, Fresnel diffraction is near field diffraction, while Fraunhofer diffraction is far field diffraction.However, in the imaging diffraction system, the diffraction field on the image plane conjugate with the point light source for illumination is also the Fraunhofer diffraction field. At this time, the distance between the diffraction screen and the point light source or the receiving screen is very close in real space.
Circular aperture diffraction pattern of red laser
In theory, Fraunhofer diffraction is obviously a special case of Fresnel diffraction, but in fact, people pay more attention to it, because the theoretical calculation of Fraunhofer diffraction field is relatively easy, the application value is great, and it is not difficult to achieve in experiment.In particular, the rise of Fourier optics in modern transformation optics has given the classical Fraunhofer diffraction a new meaning of modern optics - Fourier optics grew from Fraunhofer diffraction as a branch.
For example: single slit Fraunhofer diffraction, rectangular and triangular Fraunhofer diffraction, circular Fraunhofer diffraction[3]
① Slit diffraction
X-ray diffractometer
When the slit is very wide, the width of the slit is far greater than the wavelength of the light, and the diffraction phenomenon is very unobvious. The light travels along a straight line, producing a bright line on the screen that is equivalent to the slit width;However, when the width of the slit is adjusted to be very narrow, which can be comparable to the light wave, the light will obviously deviate from the straight propagation direction after passing through the slit, and will shine on a relatively wide place on the screen, and there will be light and dark diffraction stripes. The smaller the slit, the larger the diffraction range, and the wider the diffraction stripes.But the brightness is getting darker.
Test: use vernier caliper to adjust to the minimum distance that can be recognized by the naked eye, and then look at the light source through this seam
② Small aperture diffraction
When the hole radius is large, the light propagates along a straight line, and a bright circular spot of the same size calculated according to the straight line propagation is obtained on the screen;Reduce the radius of the hole, and the inverted light source image calculated by linear propagation will appear on the screen, namelypinhole imaging ；Continue to reduce the radius of the aperture, and a circular diffraction ring with light and dark will appear on the screen.
Geometric theory
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The asymptotic theory of diffraction characteristics of electromagnetic waves is analyzed by using the concept of ray, which is called GTD for short.Geometric theory is monochromatic wave fieldSolution of the equationWhen the frequency tends to infinitylimitTherefore, it is also an asymptotic solution suitable for the high frequency case, and the basic idea of this theory is toUniform plane waveReflection and refraction on the infinite plane interfaceconductorThe asymptotic expression of the exact solution of the diffraction on the edge and the creeping wave along the surface of a cylindrical conductor is applied frompoint sourceIssuedspherical waveOr the reflection and refraction of cylindrical wave from a line source on a smooth interface, the diffraction on the edge of an arc conductor, and the creeping along the convex surface of the conductor, and regard it as the zero stage near solution of the problem.
Square aperture diffraction pattern of red laser generated by computer simulation
The geometrical theory of diffraction was first developed by JB. Keller put forward it in 1957, and it has been gradually improved by many people's work. It has been applied in dealing with the scattering problems of many special-shaped objects, as well as the numerical calculation of diffraction and diffraction.However, because the asymptotic expression of the exact solution isShaded areaThe transition area with the lighting area cannot be established, so GTD cannot be applied in this area. In order to make up for this defect, J. Posema and others later proposed the Uniform Asymptotic Theory (UAT).The basic idea of this theory is to multiply the projected wave by an artificial factor, so that this factor is close to 1 in the illumination area and close to 0 in the shadow area, and it will increase infinitely as the field point approaches the boundary of the illumination area in the transition area.The theory of uniformly continuous addition of the asymptotic formula of the projected wave multiplied by the factor and the diffracted wave has also been widely used.However, its basis is only an estimate (ansatzCausticsNear the line, it cannot be applied as GTD.However, ray theory has many advantages, and people are still exploring ways to improve it.
