Physics
Polarization Vector
In physics, the polarization vector represents the orientation and magnitude of the electric field in an electromagnetic wave. It is a vector quantity that describes the direction in which the wave oscillates. The polarization vector is crucial for understanding the behavior of light and other electromagnetic waves in various mediums and applications.
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11 Key excerpts on "Polarization Vector"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction. This is important in seismology. Polarization is significant in areas of science and technology dealing with wave propagation, such as optics, seismology, telecommunications and radar science. The polarization of light can be measured with a polarimeter. ________________________ WORLD TECHNOLOGIES ________________________ Theory Basics: plane waves The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and wide wavefronts). For plane waves Maxwell's equations, specifically Gauss's laws, impose the transversality requirement that the electric and magnetic field be per-pendicular to the direction of propagation and to each other. Conventionally, when considering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular com-ponents labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner in time, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. Mathematically, the electric field of a plane wave can be written as, or alternatively, where A x and A y are the amplitudes of the x and y directions and φ is the relative phase between the two components.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction. This is important in seismology. Polarization is significant in areas of science and technology dealing with wave propagation, such as optics, seismology, telecommunications and radar science. The polarization of light can be measured with a polarimeter. ________________________ WORLD TECHNOLOGIES ________________________ Theory Basics: plane waves The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and wide wavefronts). For plane waves Maxwell's equations, specifically Gauss's laws, impose the transversality requirement that the electric and magnetic field be per-pendicular to the direction of propagation and to each other. Conventionally, when con-sidering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner in time, the two components have exactly the same frequency. However, these com-ponents have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. Mathe-matically, the electric field of a plane wave can be written as, or alternatively, where A x and A y are the amplitudes of the x and y directions and φ is the relative phase between the two components.
eBook - PDF- Charles A. Bennett(Author)
- 2022(Publication Date)
- Wiley(Publisher)
We will generally use the electric field to specify the complete electromag- netic wave. An electromagnetic wave with an electric field vector ⃗ E that oscillates back and forth along a fixed direction is said to be linearly polarized. In this case, the electric field oscillates within the plane of polarization, as shown in Figure 6.2. The plane of polarization for the wave illus- trated is inclined between the x–z and y–z planes. At any instant, the electric field vector has Principles of Physical Optics, Second Edition. Charles A. Bennett. © 2022 John Wiley & Sons, Inc. Published 2022 by John Wiley & Sons, Inc. 186 6 Polarization E B k λ Figure 6.1 A linearly polarized transverse electromagnetic wave. E (a) (b) E y E x x y k E x y z k Figure 6.2 (a) Linear polarization in the x–y plane. (b) The electric field vector may be resolved into components along the x and y axes. x and y components given by E 0x and E 0y . The corresponding forward traveling electromag- netic wave is determined by ⃗ E = ⃗ E 0 e i(kz−𝜔t+𝜑) = ( E 0x î + E 0y ̂ j ) e i(kz−𝜔t+𝜑) (6.1) where we have used the complex representation discussed in Section 1.6. Equation 6.1 repre- sents a linearly polarized electromagnetic wave traveling in the positive-z direction, as illus- trated in Figure 6.2. The initial phase angle 𝜙 represents the phase of the wave when z and t both equal zero. 6.2.1 Linear Polarizers A linear polarizer selectively removes light that is linearly polarized along a direction that is perpendicular to its transmission axis, as illustrated in Figure 6.3. In an ideal linear polar- izer, the transmission is zero for electric field components perpendicular to the transmission axis and 100% for electric field components parallel to the transmission axis. The light that is transmitted by the polarizer is linearly polarized along an axis that is parallel to the trans- mission axis, as shown.
eBook - PDF- Andri M. Gretarsson(Author)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
8 Polarization 8.1 Polarized Light Electromagnetic waves traveling in vacuum or any linear medium 1 are transverse waves. The electric and magnetic fields are perpendicular to the wave’s direction of travel and perpendicular to each other. The direction of travel of the wave is E × B. The electric and magnetic fields are in phase with each other and the magnetic field and electric field vector amplitudes are related by the speed of light v in the medium B 0 = ˆ z × E 0 v . (8.1) In vacuum or linear media then, one can always find the magnetic field from the electric field and vice versa so it’s enough to specify one or the other. The usual choice is to specify the electric field. Therefore, the language of polarization always refers to the properties of the electric field vector. For example, a plane-polarized electromagnetic wave traveling in the +z direction with polarization in the ˆ y direction would be written E (z, t) = ˆ yE 0 cos (kz − ωt) (8.2) B (z, t) = − ˆ xB 0 cos (kz − ωt) . (8.3) If the ˆ y direction corresponds to the vertical axis, we would call this a “vertically polar- ized” plane wave even though the magnetic field (which carries just as much energy as the electric field) is oriented horizontally. In general, an electromagnetic wave consists of two polarization components that can be expressed with respect to a transverse set of basis vectors, such as ˆ x and ˆ y. With respect to this basis, E x (z, t) is the x-component of polarization and E y (z, t) is the y-component. The general expression for the electric field of a plane wave traveling in the ˆ z direction incorporates both of these components E (z, t) = ˆ xE x (z, t) + ˆ yE y (z, t) (8.4) = ˆ xu x cos (kz − ωt − φ x ) + ˆ yu y cos kz − ωt − φ y . (8.5) where the fields of the polarization components have been expanded to correspond to plane waves. The amplitudes u x and u y are constant and the components may have different phase leads φ x and φ y .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction. This is important in seismology. Polarization is significant in areas of science and technology dealing with wave propa-gation, such as optics, seismology, telecommunications and radar science. The polar-ization of light can be measured with a polarimeter. Theory Basics: plane waves The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and ________________________ WORLD TECHNOLOGIES ________________________ wide wavefronts). For plane waves Maxwell's equations, specifically Gauss's laws, im-pose the transversality requirement that the electric and magnetic field be perpendicular to the direction of propagation and to each other. Conventionally, when considering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner in time, the two com-ponents have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. Mathematically, the electric field of a plane wave can be written as, or alternatively, where A x and A y are the amplitudes of the x and y directions and φ is the relative phase between the two components.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 8 Circular Polarization The electric field vectors of a traveling circularly polarized electromagnetic wave In electrodynamics, circular polarization of an electromagnetic wave is a polarization where the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. If the wave is frozen in time the electric field vectors describe a helix along the direction of propagation. Circular polarization is a limiting case of the more general condition of elliptical polarization. The other special case is the easier-to-understand linear polarization. ________________________ WORLD TECHNOLOGIES ________________________ General description Right-handed/Clockwise circularly polarized light displayed with and without the use of components. On the right is an illustration of the electric field vectors of a circularly polarized electromagnetic wave. The electric field vectors have a constant magnitude but their direction changes in a rotary manner. Given that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis. Specifically, given that this is a circularly polarized plane wave, these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates. Using the convention of the physics community, it is considered to be right-hand, clockwise circularly polarized. Notice that the helix forms a right-handed screw in space. Since this is an electromagnetic wave each electric field ________________________ WORLD TECHNOLOGIES ________________________ vector has a corresponding, but not illustrated, magnetic field vector that is at a right angle to the electric field vector and proportional in magnitude to it. As a result, the magnetic field vectors would trace out a second helix if displayed.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Circular Polarization The electric field vectors of a traveling circularly polarized electromagnetic wave In electrodynamics, circular polarization of an electromagnetic wave is a polarization where the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. If the wave is frozen in time the electric field vectors describe a helix along the direction of propagation. Circular polarization is a limiting case of the more general condition of elliptical polarization. The other special case is the easier-to-understand linear polarization. ________________________ WORLD TECHNOLOGIES ________________________ General description Right-handed/Clockwise circularly polarized light displayed with and without the use of components. On the right is an illustration of the electric field vectors of a circularly polarized electromagnetic wave. The electric field vectors have a constant magnitude but their direction changes in a rotary manner. Given that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis. Specifically, given that this is a circularly polarized plane wave, these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates. Using the convention of the physics community, it is considered to be right-hand, clockwise circularly polarized. Notice that the helix forms a right-handed screw in space. Since this is an electromagnetic wave each electric field vector has a corresponding, but not illustrated, magnetic field vector that is at a right ________________________ WORLD TECHNOLOGIES ________________________ angle to the electric field vector and proportional in magnitude to it. As a result, the magnetic field vectors would trace out a second helix if displayed.
eBook - ePub- Grant R. Fowles(Author)
- 2012(Publication Date)
- Dover Publications(Publisher)
y directions, respectively. Accordingly, the component electric fields areFigure 2.4 . Illustrating polarization in the molecular scattering of light. The E vectors for the incident and scattered waves are indicated.The total electric field E is the vector sum of the two component fields, namely,(2.28)Now the above expression is a perfectly good solution of the wave equation. It can be interpreted as a single wave in which the electric vector at a given point is constant in magnitude but rotates with angular frequency ω. This type of wave is said to be circularly polarized. A drawing showing the electric field and associated magnetic field of circularly polarized waves is shown in Figure 2.5 .The signs of the terms in Equation (2.28) are such that the expression represents clockwise rotation of the electric vector at a given point in space when viewed against the direction of propagation. Also, at a given instant in time, the field vectors describe right-handed spirals as illustrated in Figure 2.5 . Such a wave is said to be right circularly polarized .Figure 2.5 . Electric and magnetic vectors for right circularly polarized light. (a) Vectors at a given instant in time; (b) rotation of the vectors at a given position in space.If the sign of the second term is changed, then the sense of rotation is changed. In this case the rotation is counterclockwise at a given point in space when viewed against the direction of propagation, and, at a given instant in time the fields describe left-handed spirals. The wave is then called left circularly polarized.It should perhaps be pointed out here that if one “rides along” with the wave, then the field vectors do not change in either direction or magnitude, because the quantity kz –ωt remains constant. This is true for any type of polarization.Let us now return to the complex notation. The electric field for a circularly polarized wave can be written in complex form as
eBook - PDF- Md Nazoor Khan, Simanchala Panigrahi(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
The plane passing through the direction of propagation, on which the light vectors of the light wave are confined, is called the plane of vibration . The plane passing through the direction of propagation and perpendicular to the plane of vibration is called the plane of polarization . Therefore, we can define the plane of polarization as the plane passing through the direction of propagation on which magnetic vectors of the light wave are confined. The plane of vibration and the plane of polarization are shown in Fig. 4.4. The plane passing through the incident ray and the the normal drawn at the point of incidence is called the plane of incidence . The plane passing through the reflected ray and the normal drawn at the point of incidence is called the plane of reflection . The plane passing through the refracted ray and the normal drawn at the point of incidence is called the plane of refraction . The electric vectors of the light wave which are vibrating in the plane of incidence are called parallel vibrations and the light vectors which are vibrating perpendicular to the plane of incidence are called perpendicular vibrations . 4.3 Classification of Polarized Light Generally, there are three different types of polarization states: linear, circular and elliptical. Each of these commonly encountered states is characterized by differing motion of the electric field vector with respect to the direction of propagation of the light wave. 276 Principles of Engineering Physics 1 Figure 4.4 Unpolarized light after passing through tourmaline crystal become plane polarized. The EFGH plane along the vertical axis of the tourmaline crystal is the plane of vibration and the ABCD plane is the plane of polarization 4.3.1 Plane polarized light Plane polarized light is also called linearly polarized light.
eBook - PDFPolarized Light and Optical Measurement
International Series of Monographs in Natural Philosophy
- D. N. Clarke, J.F. Grainger, D. Clarke, D. Ter Haar(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
Mathematical methods have been developed to express the degree of coherence between vibrations and the connection between this and the degree of polariza-tion (defined below) has been established (see, for example, Born and Wolf, 1959). Any discussion of this approach is outside the scope of this book. We have now taken our conceptual analysis of the phenomenon of polarization as far as we can without the introduction of mathe-matical methods. In the next section, we shall consider some of these methods of describing the various types of polarization and the ways of calculating the effects of optical devices. 1.3. Mathematical Methods 1.3.1. INTRODUCTION For the purposes of manipulation, it is convenient to split any par-tially polarized light into completely polarized and unpolarized com-ponents. As we have seen, the form of the polarization ellipse for any beam of completely polarized light is preserved over the experimental 17 P O L A R I Z E D L I G H T A N D O P T I C A L M E A S U R E M E N T time. In order to describe the polarization characteristics, we need to know the geometry of the ellipse. Consider a beam of quasi-monochromatic light travelling along the z-axis, in the direction of increasing z, of a right-handed Cartesian frame. Over a time period of a few cycles, the resultant components along the x-and j-axes may be expressed as : _ _ / 2πζ c E x = E XQ COS Ιωί — + o x or the real part of E XQ e*»'-<*«M>+**], Ey = Ey Q COS ^COt — + Oy or the real part of E yo ^ < * < -< 2 * z M > + M , where E x , E y are the values of the electric field in the x-and j-direc-tions at the position ζ and at time t; E Xo , E yo are the amplitudes of the x-and ^-vibrations; ô X9 ô y are the phases of the x-and ^-vibrations at ζ = 0 ; ω is the angular frequency, λ is the wavelength and y is the square root of minus 1. The form of the ellipse is obtained by considering the locus of the tip of the electric vector at a particular value of z, say ζ = 0.
eBook - PDFSneaking a Look at God's Cards
Unraveling the Mysteries of Quantum Mechanics - Revised Edition
- Giancarlo Ghirardi, Gerald Malsbary(Authors)
- 2021(Publication Date)
- Princeton University Press(Publisher)
25 C H A P T E R T W O The Polarization of Light We begin with some simple experiments with a beam of light and three identical transparent disks of a rather special kind ... which can be acquired by purchasing two sets of polarizing sunglasses. ... The effect is particularly dramatic if, instead of shining light through the three disk sandwich, you look through it. After the middle disk is removed nothing at all can be seen. Conversely if the middle disk is reintroduced the sandwich again becomes transparent. By adding a disk to the pile you have succeeded in letting through more light ... this behavior, like a good magic trick, remains very striking to observe, no matter how long or how well you have understood the explanation. —David Mermin W hy would a book on the history and philosophical implications of quantum mechanics need to devote an entire chapter to the single phe-nomenon of light polarization? For a very good reason: polarization phe-nomena—especially, the behavior of polarized states when combined— present a very close analogy to the combination of quantum states in general, giving us a clear and simple way to illustrate the principles of quantum formalism. And this is not all: nearly all quantum experiments with major rele-vance for the debate directly involve either polarization states of photons or certain properties of material particles, such as spin , which present a formally perfect analogy with properties of the electromagnetic field. In the next chapter, we will supplement the classical analysis presented in this chapter, by adding Planck’s hypothesis about quanta of light; after that, we will be ready to understand some important aspects of quantum formalism. 2.1. Polarization States of the Electromagnetic Field In the preceding chapter we discussed states of the electric field that cor-respond to certain polarization states—that is, linear polarization.
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