Propagation of Light

11 Key excerpts on "Propagation of Light"

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  eBook - ePub

  Essentials of Photonics

  • Alan Rogers(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Emission, Propagation, and Absorption Processes

  4.1 Introduction

  In this chapter, we shall deal with the various processes by which light and matter interact. It is impossible to overestimate the importance of this subject, because it is only via this interaction that we can even become aware of the existence of light, and certainly we need to understand well the processes of interaction in order to study and to use light.

  The detailed understanding of the interactive processes requires a deep knowledge of quantum theory, which is beyond the purpose of this book. Much insight can be gained, however, from a combination of classical (i.e., quasi-intuitive) ideas and elementary quantum physics. This is the approach that will be adopted.

  A familiarity with the ideas in this chapter will ease the path for appreciation of most of the later chapters in the book, but especially Chapters 7 and 9 .

  We shall begin by considering the nature of light propagation in an optical medium. This uses the classical wave theory of Chapter 2 , which provides a useful picture of the processes involved. The following sections, on optical dispersion and the emission and absorption processes, develop further the ideas introduced in the first section and also provide the groundwork for the more comprehensive treatments in later chapters.

  4.2 Classical Theory of Light Propagation in Uniform Dielectric Media

  Consider the standard expression for the electric field component of an electromagnetic wave (of arbitrary polarization) propagating in the Oz direction in an optical medium of refractive index n :

  E = E 0 exp [i (ωt − kz )]

  We know that

  ω k

  = c =

  c 0

  n

  and hence may write

  E =

  E 0

   exp 

  [ i ω

  ( t -

  n z

  c 0

  )

  ]

  We may conveniently include both the amplitude attenuation and the phase behaviour of the wave in this expression by defining a complex refractive index:

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  The Manual of Photography

  • Elizabeth Allen, Sophie Triantaphillidou(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  ray and many optical effects assume light as rays (as in geometric optics).

  Figure 2.7    Propagation of Light as wavefronts and wavelets.

  The plane wave is the simplest representation of a three-dimensional wave (Figure 2.8a ), where wavefronts are parallel to each other and perpendicular to the direction of propagation. Light propagating in plane wavefronts is referred to as collimated light. Far enough from the source a small area of a spherical wavefront – described above – resembles a part of a plane wave, as illustrated in Figure 2.8b .

  The mathematical description of a monochromatic (i.e. single constant frequency) plane wave is the vector equivalent of the expressions describing the simple harmonic motion (see definition in Appendix A ).

  Light intensity

  In practice, the wave oscillations are not usually observed, as their frequency is too high. We observe the power transmitted by the light beam, averaged over some millions of oscillations. The instantaneous light power is proportional to Ψ2 (x, t):

  The average of this over a long time is equal to the light intensity, or irradiance, I, which is proportional to the square of the amplitude, a, of the electric field:

  This is the quantity measured by light detectors.

  Refraction and dispersion

  As mentioned in the introduction to wave theory, electromagnetic waves slow down when travelling through media denser than vacuum. A measure of this reduction in speed in transmitting materials such as air, glass and water is the refractive index n

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  University Physics Volume 3

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  1 | THE NATURE OF LIGHT Figure 1.1 Due to total internal reflection, an underwater swimmer’s image is reflected back into the water where the camera is located. The circular ripple in the image center is actually on the water surface. Due to the viewing angle, total internal reflection is not occurring at the top edge of this image, and we can see a view of activities on the pool deck. (credit: modification of work by “jayhem”/Flickr) Chapter Outline 1.1 The Propagation of Light 1.2 The Law of Reflection 1.3 Refraction 1.4 Total Internal Reflection 1.5 Dispersion 1.6 Huygens’s Principle 1.7 Polarization Introduction Our investigation of light revolves around two questions of fundamental importance: (1) What is the nature of light, and (2) how does light behave under various circumstances? Answers to these questions can be found in Maxwell’s equations (in Electromagnetic Waves (http://cnx.org/content/m58495/latest/) ), which predict the existence of electromagnetic waves and their behavior. Examples of light include radio and infrared waves, visible light, ultraviolet radiation, and X-rays. Interestingly, not all light phenomena can be explained by Maxwell’s theory. Experiments performed early in the twentieth century showed that light has corpuscular, or particle-like, properties. The idea that light can display both wave and particle characteristics is called wave-particle duality, which is examined in Photons and Matter Waves. In this chapter, we study the basic properties of light. In the next few chapters, we investigate the behavior of light when it interacts with optical devices such as mirrors, lenses, and apertures. Chapter 1 | The Nature of Light 7

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  Information Photonics

  Fundamentals, Technologies, and Applications

  • Asit Kumar Datta, Soumika Munshi(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  For θ 1 > θ c , the wave undergoes total internal reflection accompanied by a phase shift. 2.6 Interaction of light and matter Light, like any other kind of electromagnetic radiation, interacts with medium in mainly two different ways: absorption, where the photons dis-appear, and scattering, where the photons change their direction. A third way of interaction also exists, when the light can change its state of polarisa-tion. In the case of absorption it may happen that light is being re-emitted at a different wavelength, i.e., as fluorescence or phosphorescence. Classically, light-matter interactions are a result of an oscillating electromagnetic field res-onantly interacting with charged particles. Quantum mechanically, light fields will act to couple quantum states of the matter. 2.6.1 Absorption Absorption is a transfer of energy from the electromagnetic wave to the atoms or molecules of the medium. Energy transferred to an atom can excite electrons to higher energy states, and energy transferred to a molecule can excite vibrations or rotations. The wavelengths of light that can excite these energy states depend on the energy-level structures and therefore on the types of atoms and molecules contained in the medium. The spectrum of the light after passing through a medium appears to have certain wavelengths removed because they have been absorbed. This is called an absorption spectrum. Se-lective absorption is also the basis for objects having colour. The colour red 76 Information Photonics: Fundamentals, Technologies, and Applications is red because it absorbs the other colours of the visible spectrum and reflects only red light. The intensity of the light beam is weakened by absorption, and the trans-mitted intensity decreases exponentially with the thickness x of the layer of material through which the light has to pass.

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  An Introduction to the Atomic and Radiation Physics of Plasmas

  • G. J. Tallents(Author)
  • 2018(Publication Date)
  • Cambridge University Press

    (Publisher)

  2 The Propagation of Light To achieve a plasma with free electrons requires elevated temperatures and hence light emission, propagation and absorption can be important. The Propagation of Light, unlike many other familiar waves, does not need a medium in which to oscillate. 1 Light propagates in plasma and the free electrons are driven to oscillate, but the electrons generally impede the wave oscillation rather than aid the process. It becomes impossible for light to travel through an unmagnetised plasma if the frequency of the radiation is less than the plasma’s natural oscillation frequency: the plasma frequency is discussed in Section 1.1. At low frequencies, the electron oscillations relative to the ions dampen the electromagnetic oscillation of light. Light of all frequencies passes with no absorption or alteration in phase in vacuum, though the intensity from any finite-sized source ultimately falls proportionally to the inverse of the square of distance from the source. In this chapter, we show how Maxwell’s equations describing the relationships between electric and magnetic fields (and electric current and electric charge) are consistent with oscillating electric and magnetic fields propagating in vacuum at the velocity of light c. The oscillating fields are solutions of Maxwell’s equations. We treat the electric currents generated in a plasma by light to show how the currents affect electromagnetic waves. The acceleration of any charge is shown to produce transverse electric field oscillations, thus providing a mechanism for the production of electromagnetic waves. The electromagnetic spectrum of interest in plasma physics ranges from radio waves to X-rays and gamma rays (see Figure 2.1). The propagation of the different 1 The aether was a construct in which light was supposed to propagate. Its existence was negated by the Michelson–Morley experiment in 1887 which showed that light always propagates at the same velocity in vacuum.

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  Understanding Light Microscopy

  • Jeremy Sanderson(Author)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  very close to the first so that the colours exit the second prism parallel and recombine to form white light.

  Source: (top left) Apic / Contributor. Reproduced with permission from Getty Images. (top right) Spigget (Own work) Reproduced under the terms of the Creative Commons Attribution Share-Alike licence, CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0 ).

  It was the work of the polymath Thomas Young from 1803 onwards, who demonstrated the effects of the interference of coherent light rays, that truly marked the beginning of humankind’s significant understanding of the nature of light. Building upon Young’s investigation of diffraction and also on the earlier work of Christiaan Huygens, Augustin-Jean Fresnel showed that light propagated entirely as a transverse wave, with no longitudinal vibration whatsoever. He also explained both the rectilinear Propagation of Light and diffraction effects. Later in the mid-19th century, from the data of simple electrical experiments, James Clerk Maxwell formulated his equations to describe electromagnetic waves that could travel at approximately the known speed of light. Maxwell considered this fact more than a coincidence. In a key paper published in 1865 he wrote:

  ‘The … results seem to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated … according to electromagnetic laws.’

  Towards the end of the 19th century, in a successful attempt to prove Maxwell’s equations, Heinrich Hertz demonstrated the existence of radio waves. He showed that these belonged to the electromagnetic spectrum, of which light was part.

  2.3 The Nature of Waves

  Energy is carried from one place to another by two means. Either it is transferred directly by the movement of matter or is carried by a wave. In the former case, two boats may ram one another, causing a transport, or displacement, of mass. Conversely, a boat may be rocked by an approaching wave. It will bob up and down (or oscillate) in unison with that wave, but not necessarily be displaced. Waves can therefore transfer energy without

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  Making Physics Fun

  Key Concepts, Classroom Activities, and Everyday Examples, Grades K?8

  • Robert Prigo(Author)
  • 2015(Publication Date)
  • Skyhorse

    (Publisher)

  So the particle picture of light was back on the scene. Indeed, the nature of light turned out to be much more interesting than an either-or particle or wave reality. Both descriptions are needed for a full picture of light. This complementary picture is known as the wave-particle duality for light. The dual nature of light, propagating as an electromagnetic wave while interacting with matter through particle-like photons, sums up our present understanding of light. This wave-particle duality is now known to be a universal property of nature. Based on an analogy with the dual nature of light, Louis de Broglie (1892–1987) proposed that matter itself (electrons, atoms, etc.) might show the same duality. He proposed that particles such as electrons might have wave-like features. His ideas were soon put to the test and vindicated when experiments revealed the diffraction and superposition of electrons! All forms of light, both visible and nonvisible, share many fascinating characteristics and properties. Light does not need a medium through which to propagate. It can propagate in a vacuum. Light is made up of oscillating and self-sustaining electric and magnetic fields that interact with matter in a particle-like way (photons). Light travels at a constant speed in a vacuum (299,792,458 meters per second). In a transparent material, light travels at a slower speed, with different frequencies traveling at slightly different speeds. In a vacuum and in uniform transparent materials, light travels in straight lines. Some objects reflect light, some absorb light, and some do both. Light bends— refracts —when it propagates from one transparent medium into another. Visible light comes in a narrow but continuous spectrum of frequencies that we detect as different colors (red to violet). “White” light is composed of light of different colors (red to violet). “Black” is the absence of light

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  Physics of Photonic Devices

  • Shun Lien Chuang(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Part Propagation of Light 5 Electromagnetics and Light Propagation In this chapter, we discuss a few important results using electromagnetic theory. First, the time-harmonic fields and the duality principle, which will be useful in studying the Propagation of Light in waveguides and laser cavities, will be presented in Section 5.1. The duality principle allows us to obtain the solutions for plane wave reflection and guidance for the transverse magnetic (TM) polarization of light once we obtain the solutions for the transverse electric (TE) polarization. We then present Poynting's theorem and the reciprocity theorem in Section 5.2, followed by plane wave solutions in homogenous media in Section 5.3. We then consider the simplest case, isotropic media, in Section 5.4. The complex permittivity functions for res-onant dielectric media and conducting media are presented in Section 5.5. Plane wave reflection from a planar surface and a multilayered medium is then investigated in Sections 5.6 to 5.8, which include matrix optics, a convenient tool to investigate forward and backward propagation plane waves. An important case of plane wave reflection from a distributed Bragg reflector (DBR) is presented in Section 5.9. DBR structures provide extremely high reflectivity and are used in vertical-cavity surface-emitting lasers (VCSELs) as well as microcavity lasers. In Appendix 5A, we discuss me Kramers-Kronig relations, which relate the real part and imaginary part of a permittivity function to each other. These relations are useful in optical materials because if the absorption coefficients of the semiconductors are measured, the real parts of the refractive indices are calculated based on the Kramers-Kronig relation or vice versa. 5.1 TIME-HARMONIC FIELDS AND DUALITY PRINCIPLE 5.1.1 Time-Harmonic Fields Very often, the excitation sources described by real functions J(r, t) and p(r, t) depend on time sinusoidally.

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  Fundamentals of Liquid Crystal Devices

  • Deng-Ke Yang, Shin-Tson Wu(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  2 Propagation of Light in Anisotropic Optical Media 2.1 Electromagnetic Wave In wave theory, light is electromagnetic waves propagating in space [1–3]. There are four fundamental quantities in electromagnetic wave: electric field, electric displacement, magnetic field, and magnetic induction. These quantities are vectors. In the SI system, the unit of electric field is volt/meter ; the unit of electric displacement is coulomb/meter 2, which equals newton/volt · meter ; the unit of magnetic field is ampere/meter, which equals newton/volt · second, and the unit of magnetic induction is tesla, which equals volt · second/meter 2. In a medium, the electric displacement is related to the electric field by (2.1) where ε o = 8.85 × 10 −12 farad/meter = 8.85 × 10 −12 newton/volt 2 and is the (relative) dielectric tensor of the medium. The magnetic induction is related to the magnetic field by (2.2) where μ o = 4 π × 10 −7 henry/meter = 4 π × 10 −7 volt 2 · second 2 /newton · meter 2 is the permeability of vacuum and is the (relative) permeability tensor of the medium. Liquid crystals are non-magnetic media, and the permeability is close to 1 and approximately we have, where is the identity tensor. In a medium without free charge, the electromagnetic wave is governed by the Maxwell equations: (2.3) (2.4) (2.5) (2.6) When light propagates through more than one medium, at the boundary between two media, there are boundary conditions: (2.7) (2.8) (2.9) (2.10) At the boundary, the normal components of and and the tangential components of and are continuous. These boundary condition equations are derived from the Maxwell equations. Figure 2.1 Schematic diagram showing the electromagnetic fields at the boundary between two media; represents,,, and ; is a unit vector along the normal direction of the interface; n: normal component and t: tangential component. We first consider light propagating in an isotropic uniform medium where and

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  eBook - ePub

  Wireless Optical Communications

  • Olivier Bouchet(Author)
  • 2013(Publication Date)
  • Wiley-ISTE

    (Publisher)

  Chapter 5

  Propagation in the Atmosphere

  “Look at the light and consider its beauty.

  Closes and opens the eyes quickly: what you see is already passed and what you saw is gone Leonardo da Vinci, Codex Forster, 1493–1505

  5.1. Introduction

  Laser beams, used to operate free-space optical (FSO) links, involve the transmission of an optical signal (visible or infrared) in the atmosphere. They interact with various components (molecules, aerosols, etc.) of the propagation medium. This interaction is at the origin of many phenomena such as absorption, diffusion, refraction, and scintillation. The only limitation known is heavy fog and they cannot cover distances more than a few kilometers. They are therefore suitable for the construction of networks between nearby buildings. The laser beams generally used have low power; and the environmental impact is negligible.

  One of the challenges to take up is a better understanding of atmospheric effects on propagation in this frequency spectrum, to better optimize wireless broadband communications systems, and to evaluate their performance. It is a prerequisite to test communication equipments.

  Atmospheric effects on propagation, such as absorption and molecular and aerosol diffusion, scintillation due to the change in the air index under the effect of temperature variation, hydrometeors attenuation (rain, snow), and their different models (Kruse and Kim, Bataille, Al Naboulsi, Carbonneau, etc.) are presented and confronted against experimental results.

  The runway visual range (RVR), a parameter for characterizing the transparency of the atmosphere, is defined and various measuring instruments such as transmissometer and scatterometer are described.

  5.2. The atmosphere

  In the context of FSO links, the propagation medium is the Earth’s atmosphere. It may be regarded as a series of concentric gaseous layers around the Earth. From 0 to approximately 80–90 km in altitude, we have the homosphere and, extending beyond these altitudes, the heterosphere. When considering the temperature gradients as a function of the altitude, homosphere can be seen with three layers: the troposphere, the stratosphere, and the mesosphere.

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  Nonlinear Photonics

  • Jia-Ming Liu(Author)
  • 2022(Publication Date)
  • Cambridge University Press

    (Publisher)

  4 Propagation of Optical Waves 4.1 OPTICAL ENERGY FLOW ............................................................................................................................................................................. The propagation of an optical wave is governed by Maxwell’s equations. The flow of optical power and energy is a consequence of wave propagation and is thus also governed by Maxwell’s equations. For generality, we begin our discussion with the general form of Maxwell’s equations given in (1.1)–(1.4). By using (1.1) and (1.2) with the vector identity Δ  ðE  HÞ ¼ H  ð Δ  EÞ  E  ð Δ  HÞ, we obtain the relation: Δ  ðE  HÞ ¼ H  ∂B ∂t  E  ∂D ∂t  E  J: (4.1) By using the relations D ¼ ϵ 0 E þ P from (1.5) and B ¼ μ 0 H þ μ 0 M from (1.6), we can rearrange (4.1) as E  J ¼  Δ  ðE  HÞ  ∂ ∂t ϵ 0 2   E    2 þ μ 0 2   H    2    E  ∂P ∂t þ μ 0 H  ∂M ∂t   : (4.2) Each term in (4.2) has the unit of power density (i.e., power per unit volume). The term on the left-hand side, E  J, is the power expended by the field E to drive the current J. It is similar to the resistive power loss in an electric circuit. This power is lost as heat to the surroundings. The vector quantity S ¼ E  H (4.3) is called the Poynting vector of the optical field. It represents the instantaneous magnitude and direction of the power flow of the field. The scalar quantity u 0 ¼ ϵ 0 2   E    2 þ μ 0 2   H    2 (4.4) has the unit of energy per unit volume and is the energy density that is stored in the propagating field. It consists of two components, thus accounting for the energies stored in both the electric field and the magnetic field at any instant of time. The last term in (4.2) also has two components that are associated with the electric field and the magnetic field, respectively. The quantity W p ¼ E  ∂P ∂t (4.5) is the power density that is expended by the electromagnetic field on the polarization.

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