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Users download and print one copy of any publication from the public portal for the purpose of private study or Publisher's PDF, also known as Version of record Chapter 1 The Fundamental Physics of Electromagnetic Waves 3. Raghunath K. Shevgaonkar, Ph. D., Fellow IEEE A textbook on ' Electromagnetic waves' and a monograph on 'Transmission lines' published by McGraw Hill. on electromagnetic waves, which covers propagation, reflection, and . The MATLAB functions as well as other information about the book be downloaded.
What is usually measureable is the reflected and transmitted average energy fluxes per unit area a. This is an expression of energy conservation at the interface.
The discussion will lead to three well-known optical laws: Snell s law, the law of reflection, and Brewster s law governing polarization by reflection. The media for and have the indices of refraction, and, respectively. The unit normal to the boundary is. The plane defined by and is called the plane of incidence, and its normal is in the direction of.
Incident wave strikes plane interface between different media, giving rise to a reflected wave and refracted wave. The three plane waves are: Incident 7. Using the vector identity and on the boundary, we obtain We substitute this into Eq. The boundary conditions at are [ ] [ ] [ ] [ ] In applying the boundary conditions it is convenient to consider two separate situations: the incident plane wave is linearly polarized with its polarization vector a perpendicular spolarization and b parallel p-polarization to the plane of incidence see Fig.
For simplicity, we assume the dielectrics are nonmagnetic.
With Eqs and 7. Using the Snell s law,, we can write then Similarly, 7. Brewster angle We see that in Eq vanishes when.
Using Snell s law, we can determine Brewster s angle or at which the p-polarized reflected wave is zero: 7. If a plane wave of mixed polarization is incident on a plane interface at the Brewster angle, the reflected radiation is completely s-polarized.
The generally lower reflectance for p-polarized lights accounts for the usefulness of polarized sunglasses. Since most outdoor reflecting surfaces are horizontal, the plane of incidence for most reflected glare reaching the eyes is vertical.
The polarized lenses are oriented to eliminate the strongly reflected s-component. The Brewster angle is for this case. Brewster s angle is Total internal reflection There is another case in which. Eqs and 7. The incident angle for which is called the critical angle,. From Snell s law 7. Brewster s angle is and the critical angle is 15 16 For waves incident at, the refracted wave is propagated parallel to the surface.
There can be no energy flow across the surface. Hence at that angle of incidence there must be total reflection. For incident angles greater than the critical angle, Snell s law gives This means that is a complex angle with a purely imaginary cosine.
This perfect reflection is called total internal reflection. The meaning of this total internal reflection becomes clear when we consider the propagation factor for the refracted wave: 7. This shows that, for, the refracted wave is propagating only parallel to the surface and is attenuated exponentially beyond the interface.
The attenuation occurs within a few wavelengths of the boundary except for. Essentially, even though the entire incident wave is reflected back into the originating medium, there is some penetration into the second medium at the boundary. The evanescent wave appears to travel along the boundary between the two materials.
We can estimate the displacement. Rigorous calculation shows that depends on the polarization of the incident radiation: 7. In general, and depend on the frequency of the wave, varying widely in the range from d-c to x-rays. Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.
Media having such a property are termed dispersive media. The dispersion relation of an EM wave in a dispersive medium is expressed as 7.
The bound electrons can be treated as harmonic oscillators. For generality we make it a damped harmonic oscillator. When an EM wave is present, the oscillator is driven by the electric field of the wave. The response of the medium is obtained by adding up the motions of the electrons. The equation of motion for an electron of charge and acted on by an electric field is 7. The amplitude of oscillation is small compared to the spatial variation of the field e.
Assuming that the field varies harmonically in time with frequency as, the dipole moment contributed by one electron is 7.
The intensity of the wave falls off as. The relation between and is 7. The region of anomalous dispersion is the frequency interval where absorption occurs. However, in the immediate neighborhood of a resonance drops sharply. Because this behavior is atypical, it is called anomalous dispersion. Notice that the region of anomalous dispersion coincides with the region of maximum absorption. Drude model: Electric conductivity at low frequencies If the density of free electrons i.
With the Ohm s law and where the fields are harmonic in terms of, the Maxwell-Ampere equation 7. High-frequency limit: plasma frequency At frequencies far above the highest resonant frequency Eq becomes where the plasma frequency is defined as 7. Metal Semiconductor doped Semiconductor pure Ionosphere The dispersion relation is 7.
The plasma frequencies of common metals are in the UV, and hence the visible light is almost entirely reflected from metal surfaces and the metals suddenly become transparent in UV. Weber observed that electromagnetic waves travel at a slower speed in tubes than in free space, and deduced the reason; that the waves travel in a "zigzag" path as they reflect from the walls.
In a June 1, lecture, "The work of Hertz", before the Royal Society , Oliver Lodge demonstrated the transmission of 3 inch radio waves from a spark gap through a short cylindrical copper duct.
It was discovered that transmission lines used to carry lower frequency radio waves, parallel line and coaxial cable , had excessive power losses at microwave frequencies, creating a need for a new transmission method. Barrow at the Massachusetts Institute of Technology , who worked without knowledge of one another.
EM Waves R S Shevgaonkar
He found that if he removed the Lecher line, the tank of water still showed resonance peaks, indicating it was acting as a dielectric waveguide. By March he observed waves in water-filled copper pipes. Rayleigh's previous work had been forgotten, and Sergei A. Schelkunoff , a Bell Labs mathematician, did theoretical analyses of waveguides   and rediscovered waveguide modes. In December it was realized that with a metal sheath the dielectric is superfluous and attention shifted to metal waveguides.
Barrow had become interested in high frequencies in studying under Arnold Sommerfeld in Germany. He invented a horn antenna and hit on the idea of using a hollow pipe as a feedline to feed radio waves to the antenna.
EM Waves R S Shevgaonkar
The development of centimeter radar during World War 2 and the first high power microwave tubes, the klystron and cavity magnetron , resulted in the first widespread use of waveguide.
After the war in the s and 60s waveguides became common in commercial microwave systems, such as airport radar and microwave relay networks which were built to transmit telephone calls and television programs between cities. Analysis[ edit ] Electromagnetic waveguides are analyzed by solving Maxwell's equations , or their reduced form, the electromagnetic wave equation , with boundary conditions determined by the properties of the materials and their interfaces.
These equations have multiple solutions, or modes, which are eigenfunctions of the equation system. Each mode is characterized by a cutoff frequency below which the mode cannot exist in the guide. Waveguide propagation modes depend on the operating wavelength and polarization and the shape and size of the guide.Boreman, Lithographic antennas at visible frequencies, Optics Letters, 24, Further, suppose varies in only one dimension, say the -direction, and is independent of and.
Corkish, M. TM modes transverse magnetic have no magnetic field in the direction of propagation. The pulse energy is preserved during the propagation.
Kasemo, Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons, Applied Physics Letters, 92, Kurs, A. Rees, Planar antennas on a dielectric surface, Electron. Figure What is usually measureable is the reflected and transmitted average energy fluxes per unit area a.