Electromagnetic Waves, Photons and Light

Other sources of reference :

http://microscopy.fsu.edu/primer/java/polarizedlight/filters/
http://abalone.cwru.edu/tutorial/enhanced/files/lc/light/light.htm

References:

1. Waldman, G. 1983. Introduction to Light: The Physics of Light, Vision, and Color. Englewood Liffs, New Jersey: Prentice-Hall, Inc.
2. Shimoda, K. 1984. Introduction to Laser Physics. New York, NY: Springer-Verlag
3. Svelto, O. 1998. Principles of Lasers, 4th Edition. New York, NY: Plenum Press
4. Hecht, E. 1990. Optics. Addison Wesley Educational Pubs., Inc.

WHAT IS LIGHT?

Light exhibits both wave and particle properties. It behaves like a wave in its propagation and in the phenomena of interference and diffraction. It behaves like a collection of tiny particles (photons) when it interacts with matter.

A wave is characterized by its amplitude, the displacement above or below the equilibrium position; its frequency, the number of oscillations per second; its wavelength, the distance between crest of the wave; and its velocity, the speed at which the wave moves through the medium. The velocity of a wave is the product of its wavelength and frequency. Remember: displacement is a vector quantity, and since waves have displacement they are treated as vectors. When describing light as a wave phenomenon, the classical electromagnetic approach is used. Ultimately light can be described by Maxwell's equations in this approach.

Certain properties of light can not be described by the wave approach. For example, propagation of light in a vacuum (i.e. without a medium to sustain the waves) is inconsistent with the wave nature of light. Hence, these properties are better explained when considering light to have a particle nature. When considered as particles, also known as photons, these particles have no mass but do have energy.

Wave properties of light are used to describe:

1. diffraction
2. reflection
3. refraction
4. transmission/propagation
5. coherence/interference
6. polarization

Particle properties of light are used to describe:

1. propagation in vacuum / space
2. discrete energy levels (for both absorption and emission): energy packages
3. light distribution in matter (tissue)

Classical Description of Light Propagation

• Basics of wave motion

Definition: A propagating wave is a self-sustaining disturbance of medium through which it travels - "wave in a rope" that is a function of position and time

 

• Basic EM Theory

  E: electric field caused by:

  1) electric charge
  2) time-varying B-field

  B: magnetic field caused by:

  1) electric current
  2) time-varying E-field

*The electric and magnetic fields are always orthogonal to each other and can be solved using the right-hand rule.

Electric and magnetic fields are two aspects of a single phenomena (EM field). An accelerated charge produces an E-field that varies over time. A time-varying E-field creates a time-varying B-field which in turn sustains the time-varying E-field. As you can see, this phenomena produces a wave that is capable of sustaining itself forever.

James Maxwell developed four equations to describe electromagnetism and the propagation of electromagnetic waves:

• Polarization

The electric field defines the polarization orientation of the EM field.

The plane of polarization of the wave is defined as the electric field vector and the direction of wave propagation.

Every single atom or molecule that emits light is emitting plane-polarized light instantaneously. However, any sample of light we might examine is made up from the contributions of billions of atoms, all of which are changing the polarization of their emitted waves quite rapidly. Therefore, unless we had some way of making the atoms behave cooperatively with each other (such as a laser), we would expect to find all possible wave orientations or polarization in equal amounts. Laser light is polarized.

Linear polarization

In linearly polarized light the orientation of the electric (or magnetic) field is constant.
For two sources that are colinear, i.e. oscillate in the same plane, the sum is linearly polarized regardless of phase.
For two sources that are not colinear, one has to consider the phase. When in phase - linearly polarized; when p/2 out of phase - circularly polarized; otherwise - elliptically polarized.

A polarizer is a material that allows only light with a specific orientation to pass through.

If two polarizers are set up in series so that their optical axes are parallel, light passes through both. However, if the polarization axes are orthogonal, the polarized light from the first is extinguished by the second (also called an analyzer). As the angle rotates from 0 to 90 degrees, the amount of light that is transmitted decreases. The relationship between polarization angles and transmitted light intensity is given by Malus' Law.

I(q) = I(0) cos2q

Where I = intensity (W/m2)

Other sources of reference:

http://microscopy.fsu.edu/primer/java/polarizedlight/filters/
http://abalone.cwru.edu/tutorial/enhanced/files/lc/light/light.htm

Some substances have two different light bending powers (indexes of refraction) that depend on the polarization of the light entering the substance. These substances, usually crystals, are called BIREFRINGENT.

It was noted that an incident ray of light perpendicular to the principal plane can be thought of as two rays, one for vertical polarization and one for horizontal polarization. Within the birefringent material, the atoms are arranged in a regular way and held in place by strong forces. These materials are said to be non-isotropic, i.e. there is directionality to their properties. Since any light passing through the birefringent material is passed from atom to atom, it is not too surprising that the material behaves differently in response to electric field vibrations in one direction than it does in response to those which are perpendicular to the first direction. The two perpendicular polarizations of light have, in general, different indices of refraction within the material.
The next effect of this phenomenon is that birefringent materials are characterized by their ability to rotate the angle of polarization of the light that goes through them. Biological examples of birefringent materials are tissues that have fibril structures such as collagen (a triple helix) and the actin-myosin structure of muscle fibers.

Thermally-induced partial and complete loss of native birefringence in muscle and collage are objective histologic markers of thermal damage. The birefringence of muscle is due to the regular, crystalline-like array of actin and myosin molecules within the sarcomere of striated muscle and the longitudinal fascicles of the same contractile proteins in the cytoplasm of smooth muscle cells. Loss of birefringence in striated muscle is due to the destruction of the regular relationship of the contractile proteins of the sarcomere by thermal denaturization of the contractile proteins. The birefringence in collagen is related to the regular arrangement of molecules forming the collagen fibrils. Thermally damaged collagen reveal unraveling of collagen fibrils with loss of the unique striations of collagen and an increase in fibrillar diameters.

How is light produced?

• Classically

  An accelerating charge radiated electromagnetic waves. This is known as dipole radiation

  The outermost weakly bound electrons in atoms form and oscillating dipole. Think of this as the classic electron oscillation around a positive nucleus.

  The dipole moment is described by:

  P(t) = P0 cos wt

  At t=0, P = P0 = q d

  • With d the initial maximum distance between the centers of charge
  • Near the atom the electric field is very complex in shape. However, far away in what is called the radiation zone, the electric field is simple and has a wavelength.
  • It is important to remember that EM waves carry energy

• Quantum Mechanical

In 1913, Niels Bohr offered an explanation that correctly predicted the spectral lines of hydrogen by incorporating the ideas of quantum theory. Bohr's theory was basically classical but incorporated with quantum ideas at certain key points.
His assumptions contrary to classical physics were:

1. e- exist in certain orbits/energy levels
2. transitions between the levels are achieved with either energy emission or absorption.
3. only certain transitions between energy levels are allowed.

In each case the wavelength of the emitted or absorbed light is exactly such that the photon carries the energy difference between the two orbits. This energy may be calculated by dividing the product of the Planck constant and the speed of light, hc, by the wavelength of the light. Thus, an atom can absorb or emit only certain discrete wavelengths/frequencies.

k = Boltzman constant = 1.38x10-23 J/K
T is in Kelvin

Bohr established the radii and energies of his discrete orbits. He realized that the units of Planck's constant h were the same as the units of angular momentum. The angular momentum of a point mass m traveling at constant speed v in a circle of radius r is mvr. Bohr theorized that the electron in an atom might just have whole numbers of a basic chunk of angular momentum which was h/2p. In other words, the electron could only have an angular momentum of 2h/2p, 3h/2p, 4h/2p, and so on.