Appendices appendix a derivation of the evanescent wave. This will result in a linearly polarized plane wave travelling. Relation between displacement and slope before and after the reflection. New approach to optical diffraction tomography yielding a.
We propose and experimentally demonstrate singlesideband ssb photonic vector millimeterwave mmwave signal generation enabled by optical dualssb modulation and a single pushpull machzehnder modulator mzm. Galerkins method is employed to analyze the quasivector wave equation for optical waveguides with arbitrary refractive index profile in a mapped infinite domains. Calculation of vectorial diffraction in optical systems. Energy, power, and photons energy in a light wave why we can often neglect the magnetic field poynting vector and irradiance the quantum nature of light photon energy and photon momentum. Ray optics geometrical optics covered by lecture introduction to optical modeling the topic of ray optics geometrical optics is not covered in the course fundamentals of modern optics.
Furthermore, we have a plane wave, by which we mean that a. Classical electromagnetism within such a region is governed by the sourcefree version of maxwells equations with the. Max born institute for nonlinear optics and ultrashort laser pulses, berlin. Script fundamentals of modern optics, fsu jena, prof. Solid state physics part ii optical properties of solids. The ray matrices along the optical axis can be written in. Now consider solutions to the wave equation, say for electric field ex. This equation determines the properties of most wave phenomena, not only light waves. It is a threedimensional form of the wave equation. Description of optical vortices in general, the vector wave equation admits cylindrical wave solutions that are characterized by a separable phase term, expimu, where uis the azimuthal coordinate in the transverse plane and m is a signed integer called.
The phase and group velocities are given by 2 2 1 pz z c c v f f and 2 2 1 c g z f vc f the effective guide impedance is given by. Wave functions waveguides and cavities scattering separation of variables the special functions vector potentials the spherical bessel equation each function has the same properties as the corresponding cylindrical function. Sph 618 optical and laser physics university of nairobi. University of calgary seismic imaging summer school august 711, 2006, calgary abstract abstract. The agrees with the general expectation for a traveling wave that the energy current flux j. Results are presented for a range of waveguide structures which include rectangular core, circular core, rib, and multiple quantum well. Chapter 2 classical electromagnetism and optics the classical electromagnetic phenomena are completely described by maxwells equations. In particular, we examine questions about existence and. From maxwells equation to the wave equation consider a region of empty space in which there is no charge density and no current density, i. Optics of gaussian beams department of electrical and. Solutions are compared favorably to exact vector solution and numerical results using fourier.
The field is often observed or measured at a planar surface along the optical axis z. It is customary in the theory of optical fibers to make the weakly guiding approximation n. Simple derivation of electromagnetic waves from maxwells. Physics study center now staffed by tas an hour later on. We now turn to a monochromatic single color optical field. Solid state physics part ii optical properties of solids m. The direction the plane wave is traveling is given by the wave vector k. The book discusses digital fourier transforms ft, ftbased operations, multiple methods of waveoptics simulations, sampling requirements, and simulations in atmospheric turbulence. Optical wave is a special category of electromagnetic waves which can propagate in free space as well as been guided with dielectric waveguides. An electromagnetic em wave has both electric e fields and magnetic i.
However, vector calculus is invoked frequently throughout this book, and students will more fully appreciate the connection between electromagnetic principles and optical phenomena when they are comfortable with vector calculus. We use softwarebased digital signal processing to generate the dualssb driving signal for the pushpull mzm. In the absence of free charge and current densities the maxwell equations are. The change to vector notation produced a symmetric mathematical representation. In electromagnetic wave theory, the conventional maxwells equations are formulated via vector notation in two forms of integral equations and differential forms. We shall see that special solutions to the electromagnetic wave equation exist that take the form of narrow beams called gaussian beams. The simplest case we may consider is that of electrodynamics of isotropic media 2. Maxwells equations and derivation of the wave equation for light. New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope. The wave equation in one dimension later, we will derive the wave equation from maxwells equations.
Winter college on fibre optics, fibre lasers and sensors. Derivation of the onedimensional wave equation for a string x x y ux, t y u x, t. D represents the electric displacement and b the magnetic induction vector. On the natures of the spin and orbital parts of optical. Lectures on theory of microwave and optical waveguides. Simple derivation of electromagnetic waves from maxwells equations. Osa photonic vector mmwave signal generation by optical. In the derivation of the wave equation for the pulse envelope 2. Hence, it transmits signals with very good shielding and very little interference from other signals. Physical optics lecture notes pdf 44p this note covers the following topics. Therefore, optoelectronic detectors only register the average energy flux this referred to as irradiance or intensity of the optical field. The third spherical vector wave f 3lmr 1 k rfr lkry lmrg spherical vector waves lecture 3.
In many realworld situations, the velocity of a wave. The only way to gain access to the energy is to tap holes in the waveguide wall. Fullwave vector maxwell equation modeling of the selffocusing of ultrashort optical pulses in a nonlinear kerr medium exhibiting a finite response time richard w ziolkowski and justin b. The strattonchu integral 18 derived from a vector analog of greens theorem 2 is one for any arbitraryshaped surface of diffraction aperture geometry as e x 1 4. Transverse waves motion is along the direction of propagation motion is. Introduction classical electromagnetic waves in free space.
This appendix presents a derivation of the evanescent wave equation and discussion of the origin of optical evanescence. The electromagnetic wave equation is a secondorder partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. Simple derivation of electromagnetic waves from maxwells equations by lynda williams, santa rosa junior college physics department assume that the electric and magnetic fields are constrained to the y and z directions, respectfully, and that they are both functions of only x and t. The two forms are mathematically equivalent and useful in. Optical diffraction is often described by an integral solution of the timeindependent helmholtz wave equation. Solutions of the quasivector wave equation for optical. Chapter maxwells equations and electromagnetic waves. A solution of the wave equation longitudinal plane wave ux,t aeiqx t where q wave vector. Lecture notes optics pdf 57p this note covers the following topics. Fullwave vector maxwell equation modeling of the self. Optical trapping of tiny objects by a focused laser.
The wave vector represents the momentum of the wave. The nonlinearity is typically observed only at very high light intensities values of atomic electric fields, typically 10 8 vm such as those provided by lasers. The wave equation handbook of optical systems wiley. We will derive the wave equation from maxwells equations in free space. Chapter 1 optical properties of plasmonic materials. Numerical simulation of optical wave propagation with. Physics 116 lecture 20 optical instruments nov 1, 2011.
The 3d wave equation plane wave spherical wave mit 2. Nonlinear optics nlo is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density p responds nonlinearly to the electric field e of the light. The mathematics of pdes and the wave equation michael p. Here it is, in its onedimensional form for scalar i. The course modern optics has the prime focus for light matter. The electromagnetic wave from maxwells equations contd 2 2 t e e w w u u 2 2 2 t e e e o o w w x ph xe 0 using the vector identity becomes, in free space and. Vector field representation by spatial frequencies. Application of the manakovpmd equation to studies of. Energy density and the poynting vector overview and. Approximative solutions to the wave equation geometrical optics and the eikonal equation.
Irradiance aka intensityfrom the definition of the poynting vector and the k, e, b relationship, for a harmonic sinusoidal wave propagating along z recall at optical frequencies, the field oscillates very rapidly, 10 14 1015 hz. Plane electromagnetic waves and wave propagation 7. Vector magnetic potential page 5 under this condition, a z a y 0, since there is no term to drive these components of the equations, hence yielding trivial solutions to the scalar helmholtz equations for those components. Maxwells equations and electromagnetic waves nptel. We can use this to see how optical components affect the intensity. E0, that is, the magnetic field vector is perpendicular to the electric field vector and the wavevector k. The homogeneous form of the equation, written in terms of either the electric field e or the magnetic field b, takes the form.
Fundamentals of modern optics institute of applied physics. Judkins department of electrical and computer engineering, university of arizona, tuscon, arizona 85721. Photonics communications engineering, opti 500b, lectures 17 and 18. Optical fiber is enabled by the optical field confinement mechanism of the waveguide. View the article pdf and any associated supplements and figures for a period of 48 hours. Numerical simulation of optical wave propagation is solely dedicated to waveoptics simulations. Solve maxwells equation with lateral dielectric boundary conditions of the waveguide using the. The wave equation derived from the maxwell equations describes propagation of. Consistent with geometrical optics, its magnitude is constrained to be proportional to. The angular dependence of the solutions will be described by spherical harmonics.