Electromagnetic Waves -EC501- Module2( MAKAUT-Syllabus)

Today Our communication elements: -Uniform Plane Wave, Propagation of wave, Wave Polarisation, Poincare’s Sphere, Wave spread in a leading medium, Phase and Group Velocity, Surface current and electricity loss in a conductor, Plane Waves at a Media Interface – Plane Wave in Arbitrary Direction, Reflection and Refraction at a Dielectric Interface,  Total internal reflection, Wave Polarisation in a Media Interface, Reflection from a Conducting Boundary.

Uniform Plane Wave: - 

A similar airwave (UPW) is a basic concept in electromagnetic (EM) wave principles, representing an ideal wave where the electric field (E) and magnetic field (H) are similar in vertical aircraft to spread. This means that at any time, all points for the normal aircraft in the direction of the journey's strength and phase are in the same area.

In an upwelling, the fronts of the wave are endless, completely flat aircraft, and the wave spreads in the same direction without deformity. Electrical and magnetic fields are perpendicular to each other and are also perpendicular to the wave direction, and satisfy the rule for the right hand. The relationship between E and H is given by the internal impedance of the medium:

The equations of uniform plane waves of Maxwell are in a source-free, homogeneous medium. They can travel in free space, dignity or a conductor at the speed determined by the medium permeability and permeability.

Although real UPWs do not exist in reality due to final restrictions, they are a useful estimate to analyse many practical EM problems, such as antenna radiation and wired and wireless communication systems.

They form the basis for the real-world electromagnetic wave behavior.

Propagation of wave: -

Wave proliferation refers to the way waves travel from one point to another or from a free place. This concept is used on different types of waves, such as sound waves, water waves, and electromagnetic (EM) waves. The process depends on the nature of the waves and the properties of the medium that moves through.

In electromagnetic waves, waves contain mutually vertical electric (s) and magnetic (H) fields that swing in phase and also perpendicular to the direction of travel. These waves can continue through free space, diet or conductive materials. The speed of the scattered medium is determined by the permeability (ε) and the permeability (µ), with the speed given by:

Waves can occur in different modes, including guided spread (in waves or optical fibres) and uncontrolled spread (in free space). For radio waves, atmospheric conditions, frequency, and terrain affect how far and efficiently the waves travel. The general mechanism includes ground wave, sky wave, and the spread of the line of sight.

Functions of wave spread – such as reflection, refraction, diffraction, and resolution – play an important role in communication systems, radars, and remote measurement. In long-distance communication, understanding how waves interact with obstacles and environmental and ion shares, engineers help design reliable systems.

Overall, wave spread is a basic concept in physics and engineering, which provides the basis for techniques ranging from wireless networks to satellite communication and optical data transfer.

Wave Polarization: -

Wave polarisation refers to the orientation of the electric field vector in an electromagnetic (EM) wave as it spreads through the room. Since the EM waves contain electric and magnetic fields that are perpendicular to each other and are against spread, polarisation is mainly determined from the direction of the electric field.

In linear polarisation, the electrical field maintains a continuous orientation. For example, if the electric field always indicates vertical while the wave moves forward, it is vertically polarised. Similarly, horizontal polarisation occurs when the area remains horizontal. Linear polarisation is widely used in radio transmission, antennas, and optical systems.

In circular polarisation, the electric field vector rotates in a circle because the wave is scattered. This occurs when two vertical components in the electric field have the same dimensions and a difference of 90°. Depending on the direction of rotation, it may be the spherical polarisation of the right hand (RHCP) or spherical polarisation (LHCP) on the left hand. Circular polarisation is common in satellite communication, as this wave reduces the indication drops due to orientation changes.

Elliptical polarisation is the most common form, where an ellipse detects an ellipse under the electric field spread. Linear and circular polarisation are special cases of elliptical polarisation.

The polarisation type in communication systems is important because non-sampling polarisation between the transmitter and the receiver can cause significant signal loss. In optics, polarisation plays an important role in dazzling, 3D imaging, and material analysis.

Polarisation can be replaced by reflection, refraction, resolution, or some materials such as polarisation.

Poincare’s Sphere: -

The Poincaré area is a powerful missed device used to represent the position of light polarisation. In the name of the French physicist Henri Poincaré, it offers a simple yet comprehensive way to imagine all possible polarisation states in the three-dimensional coordinate system.

In polarisation theory, light can be linear, circular, or elliptically polarised. The Poincaré area maps these conditions at points on the surface of a shell. The horizontal axis represents the relative phase between two orthogonal polarisation components, while the vertical axis indicates the degree of polarisation type.

In the region are linear polarisation states along the equator. For example, horizontal and vertical polarisations are displayed at opposite points at the equator, while 45° linear polarisations are located on other equatorial points. Circular polarisation conditions (right and left) are found on the north and south poles, respectively. Elliptical polarisation occupies the state coils and other points between the equator, with their positions determined by the polarisation of the ellipse and orientation.

The area of Poincaré is closely connected to the Stokes parameters, a set of four values (S0, S1, S2, S3) describing the location of the polarisation of light. Generalised parameters (S1/S0, S2/S0, S3/S0) correspond to the coordinates of the surface of the region, which is a practical way to interpret experimental polarisation data.

This representation is widely used in optics, telecommunications, and remote measurement. In the optical fibre system, it helps engineers imagine polarisation mode spread and control. In quantum optics, this photon plays a role in studying polarisation states.

In summary, the field of Poincaré converts complex polarisation concepts into a spontaneous geometric form, making it an essential tool for both theoretical analysis and practical applications in modern photonics and communication technologies.

Wave spread in a leading medium: -

The wave spread in a management medium refers to the transmission of electromagnetic (EM) waves, which contain electroculation, such as metals, seawater, or ionised gases. Unlike free space or a proper diet, you absorb media due to the presence of free electrons that interact with the electric field in the wave and lead to electromagnetic waves.

When an EM wave enters a conductor medium, the electric field causes a free fee and produces currents. These currents cause energy loss in the form of heat, an event known as Ohm's law. As a result, the dimension of the wave is quickly reduced along the distance, a process described by the decay constant (α).

The spreading constant in a medium is complicated, including both the decay constant (α) and the phase constant (β). Huddy Depth (Δ) is an important parameter that represents the distance as the dimension of the wave falls to 1/e of its original value. The depth of the skin is proportional to the conductivity (σ) of the wave (σ) and the frequency (F). Thus, signs of high existing in good leaders only enter very shallow depths.

Conducting media appreciably adjusts wave behaviour. In correct conductors like copper or aluminium, excessive-frequency waves can't propagate very way and are basically confined to the surface, which is why metals are brilliant electromagnetic shields. In negative conductors, such as seawater, waves can propagate; however, with significant attenuation, which is a major undertaking for underwater communication structures.

Applications of wave propagation in accomplishing media include electromagnetic defence, underground communication, geophysical exploration, and induction heating. Understanding the interaction between waves and conductive materials is crucial for designing antennas, cables, and Wi-Fi structures that perform in such environments.

In summary, EM wave propagation in lossy media is characterised by attenuation, restricted penetration, and power loss, making it a crucial consideration in engineering and communication technologies.

The operation of the media changes wave behaviour significantly. In good leaders such as copper or aluminium, high existing waves cannot propagate far and are mostly reflected on the surface, which is why metals are excellent electromagnetic shields. In poor leaders, such as seawater, waves can propagate, but with noticeable loads, which is a major challenge for communication systems underwater.

The operation of the media includes electromagnetic conservation, underground communication, geopolitical exploration, and induction heating. Understanding the interaction between waves and conductive materials is necessary to design antennas, cables, and wireless systems that work in such an environment.

In summary, media operations are characterised by ignorance, limited penetration, and energy loss to the EM wave spread, which is an important idea in engineering and communication technologies. The operation of the media changes significantly wave behaviour. In good leaders such as copper or aluminium, high existing waves cannot propagate far and are mostly reflected on the surface, which is why metals are excellent electromagnetic shields. In poor leaders, such as seawater, waves can propagate, but with noticeable loads, which is a major challenge for communication systems underwater.

Phase and Group Velocity: -

In wave theory, phase speed and group speed are two important concepts that explain how different aspects of a wave move through the room. Although they make the same sound, they represent different physical volumes.

The phase speed (Vₚ) is the speed at a point in a constant phase, such as a comb, trough or a certain point on the wave. It is given by:

Where the angular frequency is and k is the wave number. The phase speed tells us how fast the wave pattern is moving. In a non-faced medium, it also represents the speed at which the energy is travelling. However, the phase speed in the spread media may vary from the real signal speed.

The group speed (V𝗀) describes the movement as the general shape of the wave amplitude - the wave package - transmits. It is given by:

The group speed often matches the speed at which energy or information is sent. In many practical systems, especially in telecommunications and optics, group speed is more relevant than speed.

In a non-sequential medium, phase speed and group speed are similar. But in a scattered medium, where the speed of the wave depends on the frequency, they vary. This leads to pulses that spread in optical fibres, where different frequency components move at different speeds.

Interestingly, in some special cases - for example, anomal spread - the speed of the rumb may be greater than the speed of light or even negative. It does not violate relativity because it does not represent the actual transmission of information faster than light.

In summary, the phase speed describes the movement of individual waves, while the group speed represents the spread of envelopes and energy in the wave. Both physics, engineering and communication technology are important for understanding wave behaviour.

Surface current and electricity loss in a conductor: -

When an alternating current (AC) flows through a conductor, it does not distribute equally in the entire cross-section at high frequencies. Instead, due to the effect of the skin, the current focuses near the surface of the conductor. This phenomenon gives rise to the concept of surface stream density, which represents current density per unit width along the conductor.

The surface current is important because it directly affects the effective resistance of the conductor. At high frequencies, skin depth (Δ) - depth as the current density falls to 1/e of the surface value - becomes smaller. This means that the current is limited to a thin outer layer, reducing the effective operating field and increasing alternating resistance compared to the DC resistance.

As resistance increases, the loss of electricity in the conductor also increases. The shape of heat is given by the disintegrated force:

Where I is the current and R is the AC resistance. This deficit, known as I gross loss or ohmic loss, results in broken electrical energy and unwanted heating of the conductor.

Power loss is especially important in high-frequency applications such as radio frequency (RF) transmission lines, antennas and transformers. Engineers often reduce this damage by using large surface areas, such as the Litz line (made of many thin, pristine threads) or by offering leads with severely condensed metals, such as silver, to improve the conductivity of the surface.

In summary, the surface current plays an important role in determining the AC resistance of high-frequency conductors. Increased surface companies lead to high resistance and high power loss, causing careful designs in electrical and communication systems to ensure efficiency and reduce the heat effect.

Plane Waves at a Media Interface – Plane Wave in Arbitrary Direction: -

When an electromagnetic (EM) waves face an area with two different media, its behaviour is determined by the electrical properties (ε), permeability (µ) and conductivity (σ) of the media. In the simplest case, the wave is normally on the surface. In many practical scenarios, however, the wave transfers the interface to any angle.

In such cases, the phenomenon wave can be dissolved into components: the event wave vector (Kᵢ), reflected wave vector (Kᵣ) and transmitted or broken wave vector (Kₜ). The instructions for these vectors are governed by the reflection and the law of Snell:

Reflection Rule: The angle of reflection is equal to the angle of incidence.

Snell's law:

Here, θᵢ is the incident angle, θₜ is the transmission angle, and v₁, v₂ are wave velocities in the two media.

The polarisation of the wave plays an important role in determining reflection and transmission. There are two common cases:

• Parallel (P-) Polarisation: Parallel to the aircraft in the electric field phenomenon.
• Vertical (s-) polarisation: vertical field for the aircraft's aircraft.

For some direction, the location of the boundaries in the interface requires continuity of key components in both electric and magnetic regions. It leads to frazel equations, which suggest how reflected and transferred to the wave for each polarisation.

Applications of aircraft wave analysis in arbitrary directions include optical coatings, radar wave spread, antenna design and fibre optic communication.

In summary, a media interface for arbitrary directions involves understanding the air waves in a media interface, involving wave vector geometry, polarisation effects and positions of wave vector geometry, polarisation effects and limits to predict reflection and transmission behaviour in design behaviour.

Reflection and Refraction at a Dielectric Interface:-

When an electromagnetic (EM) wave passes into another medium with another refractive index through one dielectric medium, it undergoes reflection and refraction. A dielectric is an insulating material with low conductivity, which means that it does not significantly absorb EM energy, but can change speed and direction.

At the interface, the law of reflection states that the angle of reflection equals the angle of incidence      ($\theta_i = \theta_r$). The refracted wave direction is determined by Snell’s Law:   n1​sinθi​=n2​sinθt

​where n1​ and n2​ are the refractive indices of the two media, and θt​ is the transmission angle.

The behaviour of the waves also depends on polarisation:

• Vertical (s-) polarisation: vertical field for the aircraft's aircraft.
• Parallel (P-) Polarisation: Parallel to the aircraft in the electric field phenomenon.

Fresnel equations provide reflection and transmission coefficients for both polarisations, showing how dimensions and phase phenomena vary with angle and physical properties.

A special case is the angle of crime, where the reflection of the P-polarised light is zero, resulting in complete transmission. This theory is used in anti-reflective coatings and optical devices.

Reflection and wrestling lenses on the dielectric interface are fundamental in fibre optics and radar systems, where accurate control of wave direction and intensity is necessary.

In summary, these interactions are controlled by geometric laws and polarisation effects, making them important to design effective optical and communication systems.

Total internal reflection: -

The total internal reflection (TIR) is a phenomenon where a wave travelling in a medium with a high refractive index affects the area through a low refractive index at an angle more than a specific value, which is known as a critical angle. Instead of refracting into the second medium, the wave is completely reflected back to the first medium.

The critical angle (θc) is determined using Snell’s law:

where $n_1$ is the refractive index of the denser medium and $n_2$ is the refractive index of the rarer medium ($n_1 > n_2$). When the incident angle ($θ_i$) exceeds $θ_c$, no refracted wave exists, and all the energy is reflected.

In optics, TIR is widely used as it enables effective light guides without loss through refraction. This theory is the basis for optical fibre, where light signals long distances with minimal damage, making high-speed internet and telecommunications possible. It is also used in prisms for binoculars, periscope and other precise optical devices to achieve high reflection without the need for a mirror.

Although no energy is transferred to another medium, it is formed in an exclusive wave area, which is quickly decays in the rare medium. This property is used to detect changes near the interface in optical sensing technologies.

Tue is beneficial, as it ensures about 100% reflection efficiency, opposite to the mirror suffering from surface damage. However, this only happens under specific circumstances - the light should travel from a dense medium to a rare medium, and the angle of events should be greater than the critical angle.

In summary, the total internal reflection is a powerful concept in wave physics and optical engineering science, which enables flawless light guides in applications from telecom to the exact image system.

Wave Polarisation in a Media Interface: -

When an electromagnetic (EM) wave faces the area between two separate media, there are both reflections and wrestling. The way the wave behaves in this media interface depends not only on physical properties - such as permeability (ε) and permeability (µ) - but also on the polarisation of the wave.

Polarisation refers to the orientation of the electric field vector to the EM wave. In one interface, two main polarisation cases are considered:

Vertical (s-) polarisation: The electric field is perpendicular to the aircraft's aircraft.

Parallel (P-) Polarisation: The electric field is parallel to the aircraft in the phenomenon.

The reflection and transmission properties for these polarisations are described by Fresnel equations, which provide reflection coefficients (s) and transmission coefficients (T) for each case. These coefficients depend on the angle of the phenomenon and the refractive indices in the two media.

For S-polarised waves, the reflection is usually stronger than the P-polarised waves. The interesting thing is that for the P-polarised light, there is a bridge angle, as the reflection coefficient is zero-something, which means that the wave is completely transmitted without reflection. This occurs when the broken beam occurs at the right angle for reflected rays.

In oblique events, the polarisation status can turn the reflection, especially if the material is harmful or operates. This can lead to a phase change between vertical and parallel components and cause elliptical polarisation to the reflected wave.

Understanding polarisation behaviour on media interfaces is essential in optics, telecommunications, antenna design and radar systems. This allows engineers to reduce the reflection deficit, reduce anti-reflective coatings and transmission of control signal.

In summary, wave polarisation in a media interface controls how EM waves are reflected, sent and shifted, making it an important factor in effective wave-based system design.

Reflection from a Conducting Boundary: -

When an electromagnetic (EM) wave affects a behavioural area, such as the metal surface, it passes through almost complete reflection. Managers have high electrical conductivity, which means that they contain a large number of free electrons that strongly react to the electric field in the wave. These electron managers are moving to cancel the Electric Field, which prevents the input into the wave and leaves a very thin area known as the head of the skin.

Hudd depth (Δ) is the distance in the conductor as the dimension of the waves falls to 1/e of its value on the surface. For good conductors such as copper or aluminium, with high frequencies, the conductor behaves like an ideal reflector.

When the wave indicates, the phase may change by the basis of polarisation and the angle of events. For an ideal conductor, the electric field of the reflected wave is the same in order of magnitude, but the opposite in the wave phenomenon on the surface, making sure the total tangent electric field on the border is zero - it satisfies the electromagnetic limits.

The reflection coefficient in an ideal operating area is about 1 (or 100%), which means that almost all the phenomenon's energy is reflected, with insignificant transmission. However, in actual conductors with final conductivity, a small part of the wave is absorbed, causing some damage and heating of the surface.

This phenomenon is widely used in antennas, wave propagation and prescription applications, where managers are employed to limit or redirect EM waves. For example, waves depend on reflections from the walls of the operation to correct the signals with minimum damage.

In summary, reflection from a behavioural area is an almost correct process due to high conductivity, minimal penetration and strong border -inspired phase changes, making it necessary in many RF, microwave and optical systems.

-------------------------------------------MODULE-3 NEXT PAGE-------------------------------------------