7주/15주

7주/15주

• 영의 실험

• 빛의 간섭

• 마이켈슨 간섭계

• 위상속도와 군속도

현대물리: 광학 3장

Coherence and Interference

목포해양대학교 기관공학부 김상훈

Ch 3. Coherence and interference

2 * * *

1 2 1 2

2 2

1 1 1 1

( )( )

2 cos

I E EE E E E E

A A A A 

    

   

간섭항 (Interference term)

(k r t 1)

1 1

E  A e

E

 A e

1 2 1 2

( k k ) r

       

빛의 결맞음(coherence)

• Two wave sources are coherent if they have a constant phase difference and the same frequency. It is an ideal property of waves that enables stationary interference.

• It contains several distinct concepts, which are limited cases that never occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics.

• Coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets.

• Interference is nothing more than the addition of wave functions.

In quantum mechanics, a single wave can interfere with itself, but this is due to its quantum behavior and is still an addition of two waves. This implies that constructive or destructive interferences are limit cases, and that waves can always interfere, even if the result of the addition is complicated or not remarkable.

• When interfering, two waves can add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of lesser amplitude than

either one (destructive interference), depending on their relative phase.

• Two waves are said to be coherent if they have a constant relative phase.

• The degree of coherence is measured by the

interference visibility, a measure of how perfectly the

waves can cancel due to destructive interference.

• Spatial coherence describes the correlation between waves at different points in space. Temporal coherence describes the

correlation or predictable relationship between waves observed at different moments in time.

• Both are observed in the Michelson–Morley experiment and Young's interference experiment.

• Once the fringes are obtained in the Michelson–Morley

experiment, when one of the mirrors is moved away gradually, the time for the beam to travel increases and the fringes become dull and finally are lost, showing temporal coherence. Similarly, if in Young's double slit experiment the space between the two slits is increased, the coherence dies gradually and finally the fringes disappear, showing spatial coherence.

FIG. 1. The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by τ(green). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays τ

FIG. 2. The amplitude of a wave whose phase drifts significantly in time τ_c as a function of time t (red) and a copy of the same wave delayed by 2τ_c(green). At any particular time t the wave can interfere perfectly with its delayed copy. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over t any interference disappears at this delay.

Thomas Young’s Experiment

• 간섭이론에 대한 최초의 학술적 실험

• 두 파원의 경로차가 파장의 정수배이면 보강간섭, 파장 의 반정수배이면 소멸간섭.

• 물질의 입자성과 파동성의 차이를 구별하는 기본성질.

• Supposing the light of any given color to consist of undulations of a given breadth, or of a given frequency, it follows that these undulations must be liable to those effects which we have already examined in the case of the waves of water and the pulses of

sound.

• It has been shown that two equal series of waves, proceeding from centers near each other, may be seen to destroy each

other's effects at certain points, and at other points to redouble them; and the beating of two sounds has been explained from a similar interference. We are now to apply the same principles to the alternate union and extinction of colors.

• In order that the effects of two portions of light may be thus combined, it is necessary that they be derived from the same origin, and that they arrive at the same point by different paths, in directions not much deviating from each other.

• This deviation may be produced in one or both of the portions by diffraction, by reflection, by refraction, or by any of these effects combined; but the simplest case appears to be, when a beam of homogeneous light falls on a screen in which there are two very small holes or slits, which may be considered as centers of divergence, from whence the light is diffracted in every

direction.

• In this case, when the two newly formed beams are received on a surface placed so as to intercept them, their light is divided by dark stripes into portions nearly equal, but becoming wider as the surface is more remote from the apertures, so as to subtend very nearly equal angles from the apertures at all distances, and wider also in the same proportion as the apertures are closer to each other.

• The middle of the two portions is always light, and the bright stripes on each side are at such distances, that the light coming to them from one of the apertures, must have passed through a longer space than that which comes from the other, by an

interval which is equal to the breadth of one, two, three, or more of the supposed undulations, while the intervening dark spaces correspond to a difference of half a supposed undulation, of one and a half, of two and a half, or more.

경로차 (path difference) : d sin

sin

d   n 

sin ( 1/ 2)

d   n  

여러

간섭 무늬 형태