P Polarized:Detailed Analysis and Facts

When light strikes on a medium, it has to trace a path parallel to the propagation medium or perpendicular to it.

In the previous post, we have given a brief introduction about s polarized waves, which are perpendicular to the direction of propagation. P polarization is the direction of the polarized wave parallel to the propagating medium. Generally, the alignment of the incident wave and the p polarized waves is the same, i.e., both are in the same direction.

Let us discuss how can we achieve p polarization and the cause of p polarized wave in detail.

What is p polarization?

Assume electromagnetic radiation is incident on a dielectric medium such as glass. A part of radiation transmitted through the medium and part of the light reflects due to surface effect, the general polarization process.

Electromagnetic radiation is said to be p polarized when the transmitted radiation is well defined in a single direction parallel to the propagation medium. We can observe the vanishing Brewster’s angle in p polarization.

We know that the transmitted waves are in parallel to the propagating medium; hence the incident wave is also in the exact direction parallel to the medium of propagation.

p polarized light

Light is electromagnetic radiation; hence it can easily undergo polarization when it passes through a polarizing medium.

The orientation of the polarized light is characterized to lay parallel to the plane of incidence. The orientation depends on Brewster’s angle as the p polarized light is harder to achieve at Brewster’s angle.

What is p polarized light?

Incident lights are un-polarized; they are randomly distributed in all directions, leading us to the loss of light energy due to certain surface phenomena. To avoid such loss, we use the technique of polarization by bringing the shattered light into one path.

The confinement of the random light into a well-defined direction parallel to the plane of incidence and hence the electric fields are also pointed parallel to the incident plane.

Let us assume that an un-polarized light is randomly distributed on a plane is made to fall on the dielectric medium. As usual, a part gets reflected and partly gets transmitted, resulting in random light radiation tracing a single path. If the interface is perpendicular to the transmitted light direction, the transmitted light traces a path parallel to the propagating medium; this gives the p polarized light.

p polarized wave

We know that all waves cannot undergo polarization; only transverse waves can. One such example of a transverse wave is an electromagnetic wave. Now let us discuss how the p polarization happens in these waves.

Electromagnetic waves combine both electric and magnetic fields laying perpendicular to one another. Since electric fields and magnetic fields are not in phase, we can bring them in phase by polarization. During the process, the unwanted random waves are reflected, and only the waves which can be confined are allowed to transmit. Generally, the p polarization of a wave is referred to as the transverse magnetic polarized wave because, in an electromagnetic wave, magnetic fields are perpendicular to the interface. Hence, they polarized parallel to the meridional plane.

Suppose the electromagnetic wave strikes the medium and get polarized and transmitted through the medium parallel to the plane of incidence, and some of the waves are reflected. The phenomenon takes place between the two mediums of different refractive indices. The tangential component of the electric field and the magnetic field can be resolved as follows;

Let us assume that the electromagnetic wave is transmitting from the medium of refractive index η₁ to η₂ and θ_i be the angle of incidence, θ_r be the angle of reflection and θ_t be the angle transmission.

The tangential component of the electric and magnetic field at the interface of both the medium is

E_tan,1 = E_tan,2

H_tan,1 = H_tan,2

For the magnetic field, all the components are tangential, and hence we can write them as

H_i = H_r + H_t

Where Hi is the incident magnetic field, Hr is the reflected magnetic field, and Ht is the transmitted magnetic field.

The tangential vector for the electric field is a bit complicated because all the components are oriented in different directions. They can be written as

E_i cosθ_i – E_r cosθ_r = E_t cosθ_t

Where E_i, E_r and E_t are the incidents, reflected, and transmitted electric fields, respectively.

For electric field, the angle of incidence and angle of reflection are same, i.ie., θ_i=θ_r; hence the equation can be written as

E_i cosθ_i – E_r cosθ_i = E_t cosθ_t (1)

The magnetic fields components can be written in terms of electric field as

E_i/η₁+E_i/η₁=Et/η₂ (2)

The ratio of the reflected and transmitted wave with the incident wave gives the required p polarized reflected and transmitted wave as

E_r/E_i=r

and E_t/E_i = r

Now divide the equations (1) and (2) by E_i we get

Cosθ_i – r cosθ_i = t cosθ_t

1/η_i+r/η₁=t/η₂

The refractive index can be written in terms of ratio of wave in free space and standard value of refractive index in the medium as

η₁=η₀/η

Comparing and resolving the equations obtained above we can write the p polarized reflective wave as

r_p=η₂ cos θ_i-η₁ cos θt/η₂ cos θ+η₁ cos θt

And the transmitted p polarized wave as

tp=2η₂ cos θ_i/ η₂ cos θ_i+η₁ cos θt

The equation obtained above gives the p polarized electromagnetic wave transmitting through a medium. The equations are also called as “Fresnel’s equations for p polarized wave.”

p-polarized incidence

P polarization depends on the wave’s angle of incidence on the interface. As Brewster’s angle vanishes at the interface during the p polarization, the angle of incidence should not be equal to Brewster’s angle.

P polarized waves can be used as an incident wave; this means that p polarized waves are mostly linearly polarized.

If a linearly polarized light wave is incident on the interface of the dielectric medium at Brewster’s angle parallel to the direction of propagating medium, then there would be no reflection taking place on the medium because Brewster’s angle refers to the angle at which no reflection is possible. Hence we can observe complete refraction and transmission of the light wave through the medium when the p polarized wave is used as the incident wave, and thus reflection coefficient will be zero.

p-polarized emission

The emission of the polarized wave is most commonly observed in plasmons. With the help of the photoelectric emission microscope, we can observe the emission of polarized light. The emission of the linearly polarized optical waves is observed in a nanoscale.

Young’s double-slit experiment for high-intensity lasers gives a good account for the p polarized emission. The intensity of the p polarized emission as the function of angle of emission is observed around 597 nm. The electrons with the high energy state emit more rapidly than the lower-energy electrons. For the p polarized emission, the incident p polarized laser should be oblique. The higher energy emitted electrons are accelerated in the polarized direction of the incident laser beam.

Can you see circularly polarized light?

Most of us are unaware of our sensitivity towards polarization. Polarization is nothing but the orientation of the light oscillating in a particular direction. We see the pattern of the polarization in the sky, but we cannot recognize them as polarization. Humans can also perceive circularly polarized light with bare eyes.

Human eyes have the ability to detect polarized light. The polarization angle can be detected using a phenomenon called Haidinger’s brushes.

Is p polarization vertical?

Yes, p polarization is vertical. A vertical polarization is corresponds to some arbitrary frame of reference. By considering the direction of gravity, we can say vertical polarization and p polarization are the same.

If we consider the direction of gravity as the propagation medium, then vertically polarized light has the electric field parallel to the direction of the gravity; this means that p polarization is vertical as the polarized wave is parallel to the direction of propagation along with the medium.

However, in some cases the above statement is contradicts what we have assumed. If we choose the propagation of light on the medium considering the gravity direction, p polarization is not vertical, as the electric field is perpendicular to the propagation of the wave.

Thus p polarization is vertical or not depending on the frame of reference. In the laboratory frame we use horizontal direction as the parallel to the propagation.

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