Polarization of Electromagnetic Waves, Study notes of Physics

Download Polarization of Electromagnetic Waves and more Study notes Physics in PDF only on Docsity! ELECTROMAGNETIC THEORY Polarization of Electromagnetic Waves Author of this note Mr. K. Prasad BSc from University of Calicut, MSc from university of Delhi, and M.B.A from IGNOU Delhi, These notes were prepared during my teaching session for under graduate students (11 Th and 12 Th class) of my school physics department. This note is helpful for under graduate students and junior level graduates. I declare that these notes are my original works based on my knowledge in physics and the books mentioned below are the reference books I used for preparing these notes. Table of contents, (1) Description of Linear, Circular and Elliptical Polarization, (2) Linear Polarization, (3) Circularly polarized light, (4) Elliptically polarized light, (5) Polarization Methods, (6) Polarization by Scattering, (7) Polarization by Reflection, (8) Polarization by Refraction, (9) Polarization by Transmission, (10)Diagrammatic representation of polarized light, (11)Propagation of E.M. Waves in An-isotropic Media, (12)Types of Propagation of Electromagnetic Waves, (13)Electromagnetic waves Properties, (14)The dielectric tensor, (15)Fresnel’s half period zone, (16)Area of half period zone, (17)Uniaxial and Biaxial Crystals, (18)Double Refraction, (Birefringence), (19)Types of Birefringence and its measurement, (20)Double Refraction Explanation, (21)Double Refraction Phenomenon explanation of Calcite crystal, (22)Nicol prism, (23)Retardation plates, (24)Application of retardation plates, (25)Common Types and Applications, (26)Different kinds of wave plates, (27)Multiple-order waveplates (multi-order plates), (28)Low-order waveplates, (29)Effective zero-request wave-plates, (30)Babinet compensator, (31)Refractive Index Elliptically polarized light, Elliptical polarization is the polarization of electromagnetic radiation to such an extent that the tip of the electric field vector portrays an ellipse in any fixed plane intersecting, and normal to, the course of propagation. A circularly polarized wave might be settled into two directly polarized waves in phase quadrature, with their polarization planes at right angles to one another. Since the electric field can turn clockwise or counterclockwise as it propagates, elliptically polarized waves show chirality. Polarization Methods, The most popular methods of polarization of light By scattering, By Reflection, By Refraction, By Transmission, Polarization by Scattering, At the point when light goes through a medium, molecules of the medium (likewise the residue present in the medium) vibrate and deliver electromagnetic waves. These waves are emitted outwards and in this way the light is scattered. In this whole cycle, retention and re emission of light waves happen all through the material. The scattered light is otherwise called as partially polarized. Transmission of these partially polarized lights causes glare. Polarization by Reflection, When unpolarized light is made to fall on a non-metallic surface, at a specific point, the surface reflects the polarized light. In this cycle, the angle of incidence and the non-metallic surface assumes a significant role to direct the magnitude of polarization. Polarization by Refraction, Refraction is the point at which a light wave makes a trip starting with one medium then onto the next, it alters its course and speed. This refracted beam achieves some level of polarization. In most of the cases, polarization by refraction happens in the plane which is opposite to the surface. Polarization by Transmission, In this type, includes the utilization of channel materials that have exceptional chemical composition. They are known as Polaroid filters These Polaroid filters can block one of the two planes of electromagnetic waves. When the unpolarized light is passed through these Polaroid channels, it cuts one-half of the vibrations of the light in a single plane. This polarized light has one half of the intensity. Diagrammatic representation of polarized light, Propagation of E.M. Waves in An-isotropic Media An-isotropic media yield characteristics such as conformal surfaces, focusing and refraction of electromagnetic waves as they propagate through a material, high impedance surfaces for artificial magnetic conductors as well as high index, low loss, and lightweight materials. An-isotropic medium is the medium in which the properties are different in all directions. Crystalline solids are anisotropic in nature. resultant intensity at point P due to wavefront, we divide the wavefront into a concentric Half period zone, these period zone are known as Fresnel’s half period zone. Now we make zone with consider a point P as a center then the radii equal to (b + 𝜆/2), (𝑏 + 2𝜆/2), (𝑏 + 3𝜆/2)… (b+n 𝜆/2) A series of spheres on the wavefront thus cutting the wavefront into zone When wavefront having a common center O then radii OM1= r1 , OM2 = r2 ……………….. OMn = rn ……. The secondary wavelets from any two consecutive zones reach P with path difference 𝜆/2 or Time difference T/2 half period. That is why the zone is called Fresnel’s half period zone. The area of the first circle (radius = r1) is called ‘first half period zone’. The annular area Between first and second circle is known as a second half period zone and so on. Thus, The annular area between (n-1) nt and nth circle is the nth half period zone. Radius of nth half period zone: ΔMnOP MnP2 = OMn square + OP2 ( b + n𝜆/2) 2 = rn2+ b2 rn2= ( b + n𝜆/2)2- b2= b2+ nb𝜆+ n2𝜆2 /4 – b2 rn2 = nb𝝀+ n2𝝀2/4 ≈ nb𝜆 ( n2𝜆2 /4 term can be ignored as compared to nb𝝀 𝑟n = √nb𝜆 𝒓n ∝ √𝐧 here n = 1, 2, 3… Thus we see that the radii of half period zone are proportional to the square root of the natural numbers Average distance n of n Th half period zone from point P and consecutive zone of the path difference of wave at point P. The annular area of concentric circles of radii nth and (n-1) Th is rn and rn-1 respectively. The Average distance of zone from point P Xn = 𝑃𝑀𝑛+𝑃𝑀𝑛−1/2 Xn = 1/ 2 (𝑏 + 𝑛𝜆/ 2 + 𝑏 + (𝑛−1)/ 2 ) =(𝑏 + 𝑛𝜆/ 2 – 𝜆/ 4 ) = b+ (2𝑛−1)/4 Similarly Xn-1 = 𝑏 + (2𝑛−3)/ 4 Path difference of the secondary waves at point P from nth and (n-1) Th zone Xn - Xn-1 = 𝜆/4 So the path difference is equivalent to phase difference 𝜋 as time difference T/2. Area of half period zone, If A n is area of nth half period zone then An = 𝜋r n 2 – 𝜋rn-1 2 Put the value of radius rn and rn-1 from equation (1) rn 2 = nb𝜆+ n2𝜆 2 /4 , rn-1 2 = (n-1)b𝜆+ (n-1)2𝜆 2 /4 An = [ +𝑛2𝜆24 − (n−1)b𝜆−(𝑛−1)2𝜆2/4 ] = 𝜋 [b𝜆+𝑛𝜆2/2−𝜆2/4 An = b𝝀+ (2n-1) 𝝀𝟐/𝟒 If b>>𝜆 then 𝜆2 can be ignored An = 𝝅𝒃𝝀 The area of nth zone is independent of n, thus the area of each half period zone is approximately the same If the value of 𝜆2 is not negligible, then the area of zone increases slightly with increase of n. Resultant amplitude of the disturbance at point due to half period zone, Uniaxial and Biaxial Crystals, A uniaxial crystal is an optical element that has a single optic axis. A biaxial crystal is an optical element that has two optic axes. A negative uniaxial crystal has the refraction index of o-ray (no) larger than that of the e-ray (ne). Examples of biaxial Crystals are mica, lead oxide, topaz etc. These crystals are also known as birefringent crystals. When light beam passed through this crystal, it splits into two parts. Both the fractions are e-rays. Examples of uniaxial Crystals are calcite, KDP, quartz, rutile etc. When light beam passes through such crystal, it splits into o-ray and e-ray, Double Refraction, (Birefringence) Double refraction is the peculiarity of birefringence. It is an optical property where a single ray of unpolarized light enters an anisotropic medium and parts into two beams, each going somewhere unexpected. We can consider twofold refraction the end what partitions into two streets. Here, the end is the anisotropic medium; the individual traveling is the unpolarized light, while the two streets are the two rays, each traveling their ways. Birefringence is described by crystallographic materials with various different recurrence concerning different crystallographic directions. Birefringence happens when light goes through transparent objects ordered by particles, demonstrating a differential difference in reception at refractive indices. Types of Birefringence and its measurement Intrinsic Birefringence The anisotropy in crystals causes this kind of birefringence. Birefringence is brought about by the nuclear plan of the crystal Calcite, tourmaline, and different minerals are models. Stress-Induced or Pressure-induced birefringence This sort of birefringence is caused by applying pressure to the property. Glass and polymers, for example, exhibit a combination of strain birefringence. The planned value of optical retardance (contrast in stage delay for the two polarization directions) is accomplished exclusively in a limited frequency range (see underneath) and in a restricted scope of incidence angles. Common Types and Applications The most well-known sorts of wave plates are quarter-wave plates (λ/4 plates) and half-wave plates (λ/2 plates), where the distinction of phase delays between the two straight polarization directions is π/2 or π, individually, relating to propagation phase shifts over a distance of λ/4 or λ/2, respectively. Some important cases are At the point when a light beam is linearly polarized, and the polarization course is along one of the axis of the wave plate, the polarization stays unchanged At the point when the incident polarization doesn't correspond with one of the axes, and the plate is a half-wave plate, then the polarization stays linear, however the polarization direction is rotated. For instance, for a point of 45° to the axes, the polarization course is rotated by 90°. At the point when the incident polarization is at a point of 45° to the axes, a quarter-wave plate produces a condition of round polarization. (Other input polarizations lead to elliptical polarization states.) Conversely, circularly polarized light is changed over into linearly polarized light. Different kinds of wave plates Genuine zero-order wave plates are thin to such an extent that the overall optical phase postpones between the two polarization directions is only π, for instance, for a half-wave plate. The vital benefit of genuine zero-request waveplates is that they can be utilized in a significant frequency range and range of occurrence angles. What's more, their temperature responsiveness is very week. While zero-request waveplates offer best execution, the gadget thickness can be inconveniently small, especially for strongly birefringent materials like calcite, with the goal that the optical fabrication becomes difficult and the handling delicate. The last issue can be dispensed with by solidifying (or holding) a zero- request plate to a thicker glass plate, which isn't birefringent however gives mechanical adjustment. The subsequent interference point, be that as it may, prompts a lower damage limit like 10 MW/cm2. Multiple-order waveplates (multi-order plates), Multiple order wave plates are made with the goal that the general stage change is bigger than the necessary value by a whole number multiple of 2π. Although the performance at the plan frequency can be basically something similar, the optical bandwidth in which the plate has generally the right relative phase change is very restricted, for example to a couple of nanometers. Likewise, the permitted range of incidence angles can be very small. Likewise, the retardance has higher temperature sensitivity. Low-order waveplates Are multiple-order plates with a relatively small order, keeping the mentioned detrimental effects low. Effective zero-request wave-plates, Effective zero-request wave-plates (or net zero-request wave-plates) can be produced using two multiple order plates with somewhat various thicknesses, which are solidified or optically reached, or air-dispersed for application with higher optical power levels. The slow axis of one plate is lined up with the quick axis of the other plate, so the birefringence of the two plates is almost cancelled. The distinction in thickness should be acclimated to get the necessary net phase change. Such gadgets can work in a broad frequency range, since frequency prompted changes of retardance in one plate are compensated by the other plate. In any case, the issue of a little usable precise reach and temperature range remains. Babinet compensator A Babinet compensator is construction from two pieces of birefringent optical material (quartz prism) with indices n0 and ne for light polarized perpendicular and parallel to the optic axis respectively. This device can be inclined towards positive value or negative value as per adjustment. Reorientation of the optical elements in a standard experimental setup that utilizes a Babinet compensator to measure the anomalous dispersion of a birefringent medium results in a useful trade-off between the intensity and visibility of the polarization fringes produced by the apparatus. Refractive Index The proportion between the speeds of light in medium to speed in a vacuum is the refractive index. At the point when light goes in a medium other than the vacuum, the molecules of that medium ceaselessly absorb and again emit the particles of light, which reduces the speed light. In this article, let us examine the refractive index of water and other different mediums. Refractive list is additionally alluded to as refraction index or index of refraction. The speed of light in a medium relies upon the properties of the medium. In electromagnetic waves, the speed is subject to the optical density of the medium. Optical density is the tendency of the molecules in a material to reestablish the absorbed electromagnetic energy. The more optically thick material is the slower is the speed of light. One such mark of the optical density of a medium is the refractive index. Ordinary and extraordinary refractive indices In a birefringent crystal, the incident light gets split into two beams. One is ordinary and the other is extraordinary rays. The ordinary ray experiences constant refractive index n_o but the extraordinary ray experiences refractive index that varies with the direction of propagation of the light in the crystal. ***************************************************************