Metal waveguide modeling of tapered quadratic index media

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:

Biasing metal-semiconductor junctions involves applying a voltage across the junction. Specifically, the metal is connected to a voltage source, while the semiconductor is grounded. This technique is essential for controlling the direction and magnitude of current flow in electronic devices, including diodes, transistors, and photovoltaic cells.
In Schottky junctions, where the semiconductor is n-type, applying a positive voltage to the metal relative to the semiconductor reduces its Fermi...

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...

Understanding the behavior of diodes when forward-biased is a fundamental aspect of electronic circuit design and analysis. This analysis primarily utilizes two models: the exponential diode model and the constant-voltage-drop model. The exponential model comes into play when the source voltage exceeds 0.5 volts, pushing the diode current to rise exponentially above the saturation current. This relationship is graphically depicted in the current-voltage (I-V) curve, illustrating the diode's...

In electronic circuits, reverse-biased diode configurations are critical for regulating voltage levels. Zener diodes exploit the reverse breakdown phenomenon and exhibit a controlled breakdown at a specific Zener voltage (VZ). They are designed to maintain a constant voltage across their terminals and are commonly used for voltage regulation in circuits.
When a reverse voltage applied to a Zener diode exceeds its breakdown voltage, the diode enters the breakdown region. At this point, the...

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...