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• 광의 기술방법

• 전기장과 자기장의 진동으로 광이 진행한 다.

• 진동에 방향성을 가질 수 있다.

• 빛은 전자기파의 에너지를 전달하는 과정 이다.

• 빛 에너지의 전달방법

• 광자

현대물리: 광학 2장

The Vector Nature of Light

목포해양대학교 기관공학부

김상훈

1radio, 2microwave, 3infrared, 4the visible region,

5ultraviolet, 6X-rays, and 7gamma rays.

Big-7 regions

Ch 2. The vector nature of light

대부분의 파는 아래와 같은 평면조화파다. 코사인이나 사인으로 다루지 않고 지수함수로 다루는 것이 일반적이고 편하다.

i(k r t)

( , )

_{o o}

exp{i(n r t) k}

U r t  U e

^{ }

 U   u

따라서 공간미분 연산자와 시간미분 연산자는 다음과 같은 항을 만들 어 낸다.

  ik

t i 

  



2 2

   k

2

2

t

2



  



균질하고(isotropic) 대전되지 않은(non-conducting) 매질에서의 맥스웰 방정식은 다음처럼 쓸 수 있다.

o

E H

 ^ t

  



0

  E

0

  H

o

H E

 ^ t

 



k E    H

0 k E  

0 k H  

k H     E

(E, H, k)가 E -> H ->k 로 서로 직각임을 알 수 있다.

기계파(압력차로 발생)와 전자기파(전

위차로 발생)

파동의 진행 방향

전기마당 벡터 E와 자기마당 벡터 H와 파동벡터 k는 서로 직각이다.

이들의 상대적인 크기만 보면 다음과 같다.

r o

H E uE n E

k Z

 

   

만일 비자기적인(nonmagnetic) 매질이라면 _r = 1이다.

Z_o는 자유공간 또는 진공의 임피던스로 전기유전률과 자기투자율의 비로써 결정된다.

o

377

o

o

Z 

   

모든 파동은 임피던스가 동일하면 동일한 물질로 인식한다.

전기 임피던스

임피던스의 위상(phase)

광자(photon, light quanta)

• A photon is an elementary particle(내부 구조를 갖지 않는 기본입 자), the quantum of light and all other forms of electromagnetic radiation, and the force carrier for the electromagnetic force, even when static via virtual photons.

• The effects of this force are easily observable at both the

microscopic and macroscopic level, because the photon has zero rest mass; this allows long distance interactions.

• Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality. For

example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured.

• Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–

particle duality. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured.

• The modern photon concept was developed gradually by Albert Einstein to explain experimental observations that did not fit the classical wave model of light.

• In particular, the photon model accounted for the

frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal

equilibrium.

• It also accounted for anomalous observations, including the properties of black-body radiation, that other physicists, most notably Max Planck, had sought to explain using

semiclassical models

, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light do so in amounts of energy that are

quantized

(i.e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way).

• Although these semiclassical models contributed to the

development of quantum mechanics, many further experiments starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that

light

itself

is quantized.

• Although these semiclassical models contributed to the

development of quantum mechanics, many further experiments starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that

light itself

is quantized.

• In 1926 the optical physicist Frithiof Wolfers and the chemist

Gilbert N. Lewis coined the name

photon

for these particles, and after 1927, when Arthur H. Compton won the Nobel Prize for his scattering studies, most scientists accepted the validity that

quanta of light have an independent existence, and the term

photon

for light quanta was accepted.

• In the Standard Model (표준모델, 우주의 물질구성에 관 한 이론) of particle physics, photons are described as a necessary consequence of physical laws having a

certain symmetry at every point in spacetime.

• The intrinsic properties of photons, such as charge, mass and spin, are determined by the properties of this gauge symmetry(게이지 대칭). The photon

concept has led to momentous advances in

experimental and theoretical physics, such as lasers,

Bose–Einstein condensation, quantum field theory, and

the probabilistic interpretation of quantum mechanics.

• It has been applied to photochemistry (광화학), high- resolution microscopy (고해상 분광기), and

measurements of molecular distances.

• Recently, photons have been studied as elements of

quantum computers and for applications in optical

imaging(광영상) and optical communication(광통신)

such as quantum cryptography(양자암호화).

Space-time 좌표

광자의 운동량과 에너지의 관계

Poynting vector

• 포인팅(사람 이름) 벡터는 단위시간당, 단위면적 당 흐르는 전자기 에너지의 양이다. 따라서 단위 는 J/sec.m^2=W/m^2다.

• 포인팅벡터는 다음처럼 정의된다. S=ExH

• 포인팅벡터의 방향은 파동벡터의 방향인 k와 같

다.

E와 H가 두 개의 평면파인 경우 포인팅벡터는 다음처 럼 표현된다. E_o와 H_o는 두 평면파의 진폭들이다.

cos (k r2 t)

o o

S  E  H   

이 값의 시간평균은 진폭의 ½이 된다. 진폭이 복소수인 경우 일반적으로 다음처럼 쓸 수 있다.

1

*

ˆ

2

^{o o}

S E H In

   

I는 파동의 세기(intensity)로써 irradiance 라 한다. 매질이 비자기성의 물질인 경우 다음과 같다. 마당 진폭의 절대치의 제곱에 비례한다.

2 2

1

*

2

^{o o}

2

_{o r} ^o

2

_o ^o

n n

I E H E E

Z  Z

  

원자에서 빛이 나오는 이유 (보어 이론)

Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon

behavior by quantizing only

matter

, as in the Bohr model of the hydrogen atom. Even though these semiclassical models were only a first approximation, they were accurate for simple

systems and they led to quantum mechanics

불확정성의 원리

• Photons, like all quantum objects, exhibit both wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize.

• The photon displays clearly wave-like phenomena such as

diffraction and interference on the length scale of its wavelength.

For example, a single photon passing through a double-slit experiment lands on the screen exhibiting interference

phenomena but only if no measure was made on the actual slit being run across.

• To account for the particle interpretation that phenomenon is

called probability distribution but behaves according to Maxwell's equations.

• However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.

• Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by

arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10 ⁻¹⁵ m

across) or even the point-like electron.

• Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the

photon-correlation experiments cited above.

• According to our present understanding, the

electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second

quantization and Gauge boson sections below).

Heisenberg's thought experiment for locating an electron (shown in blue) with a high-resolution gamma-ray microscope.

The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma ray is shown in red.

Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the