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  • mbenkerumass 9:00 am on January 14, 2020 Permalink | Reply
    Tags: , Optics   

    Ray Optics – Graded-Index Fibers, Matrix Optics 

    Graded-Index Fibers

    Guiding light rays with multiple lenses or mirrors is possible, however this may result in great loss of optical power due to refraction in a system if there are many lenses or mirrors. Using total internal reflection however, rays may be transmitted over long distances without these losses. Glass fibers are the primary choice for guiding light in this manner using total internal reflection. Glass fibers consist of a glass wire with a cladding. The refractive index of the outer cladding will be smaller than the glass core. This allows for a consistent total internal reflection throughout the wire.

    fiber

    A graded-index material (GRIN) has a refractive index that varies throughout the material. When a ray moves through a graded-index material, the variance in refractive index causes the ray to bend and curve according to how the graded index is laid out.

    grinparax

    The path of an optical ray in graded-index material is determined by Fermat’s principle, which states that the path of a ray is the integral of the refractive index (a function of position on the material) between two points, equated to zero. The ray equation can solve this problem, however for simplification, a paraxial approach is taken to give the paraxial ray equation.

    Ray Equation:

    rayeq

    Paraxial Ray Equation:

    rayeqpar

    A graded index glass fiber is modeled below:

    gribfiber


     

    Matrix Optics

    A paraxial ray is described by a coordinate and angle. Using this approximation, the output paraxial ray going through a system can be written in matrix form:

    abcd          ,            abcd1

    An optical system can be modeled using the 2×2 ABCD matrix. Matrices of systems may also be cascaded to describe the effect of many systems on a ray.

    abcdmatricies

     
  • mbenkerumass 9:00 am on January 7, 2020 Permalink | Reply
    Tags: , Optics   

    Planar Boundaries, Total Internal Reflection, Beamsplitters 

    Refraction is an important effect in ray optics. The refractive index of a material influences how rays react when entering or leaving a boundary. For instance, if the ray is exiting a medium of smaller refractive index and entering a medium with a higher refractive index, the angle will tend towards being perpendicular to the boundary line. The angle of refraction is also greater than the angle of incidence. This case is called external refraction (n1 < n2) and (θ1 > θ2). If the ray is exiting a medium of higher refractive index into a medium with a lower refractive index, the rays will tend towards being closer to parallel with the medium boundary. This case is referred to as internal refraction (n1 > n2) and (θ2 > θ1). Both of these situations are governed by Snell’s Law:

    n1*sin(θ1) = n2*sin(θ2)

    When the rays are paraxial, the relation between θ1 and θ2 is linear (n1*θ1 = n2*θ2).

    refraction

    The critical angle occurs when n1*sin(θ1) = n2*sin(pi/2) = n2. θ1 in this case is then equal to the critical angle. If θ1 is greater than the critical angle θC, refraction cannot occur and the situation is characterized by a phenomenon known as total internal reflection (TIR). Total internal reflection is the basis for many optical systems and devices. Systems with total internal reflection are understood to be highly efficient even under more rigorous approaches to optics such as electromagnetic optics.

    tir

     

    Prisms are common applications of refraction. A prism of apex angle α and refractive index n deflects a ray incident at an angle of θ:

    prism2

    This is taken by using Snell’s law twice along two planar boundaries.

    prism1

     

    A beamsplitter is an optical component that divides a ray into a reflected and refracted (or transmitted) ray. The proportions of reflected to refractive light is a problem dealt with in electromagnetic optics. Beamsplitters are also used to combine two rays.

    beamsplit

    Beam directors apply Snell’s law and the rules governing refraction to direct rays in different directions. Three methods of directing waves are the biprism, the Fresnel biprism and the axicon.

     

     

     
  • mbenkerumass 9:00 am on December 31, 2019 Permalink | Reply
    Tags: , Optics   

    Mirrors in Geometrical Optics, Paraxial Approximation 

    The main types of mirrors used as simple optical components are planar mirrors, paraboloidal mirrors, spherical mirrors and elliptical mirrors.

    Planar Mirrors reflect rays in a manner that the apparent object location reflects rays from a position that forms a reflected angle (Snell’s law) with the angle between the point of reference and the mirror.

    mirror1

    Paraboloidal Mirrors focus all incident rays to a single point, the focus or focal point. The distance from the end of the paraboloidal mirror to the focal point is the focal length. Paraboloidal mirrors are used in telescopes to collect light. Paraboloidal mirrors are also used in flashlight bulbs and light-emitting diodes to direct rays in one direction from a source of light.

    Elliptical Mirrors reflect all rays from one source point to another point. Hero’s principle concludes that any path traveled from either point to another will be equal in distance, no matter the direction.

    ellipticalmirror

    Spherical Mirrors will direct all rays in varying directions. Spherical mirrors may be concave and convex. A spherical mirror acts like a paraboloidal mirror of focal length f = radius/2.

    spmirror

    Rays that make small angles with the mirrors axis are called paraxial rays. For paraxial rays, a spherical mirror exhibits a focusing property similar to an elliptical mirror and an imaging property as present in elliptical mirrors. The paraxial approximation considers only paraxial rays and therefore allows spherical mirrors to be considered for the above tendencies. Paraxial Optics is an approach to optics which operates under a set of rules derived from the paraxial approximation. Paraxial Optics is also referred to as first-order optics or Gaussian optics.

    In spherical mirrors, considering the paraxial approximation, a focal point is assigned for each source point. All rays that are emitted from a a very far distance (approaching infinite distance) are focused to a point at distance f = (-R)/2.

    spmir2

    The following is an example of a use of a paraxial approximation for an image formation using a spherical mirror:

    sp

    Images are credit of Fundamentals of Photonics, Wiley Series in Pure and Applied Optics

     
  • mbenkerumass 9:00 am on December 24, 2019 Permalink | Reply
    Tags: , Optics   

    Postulates of Ray Optics 

    The following principles of ray optics may be used to describe many optical systems. The numbering system is of no significance.

    1. Light travels in the form of a ray. This means that light will travel from a source and is observed when reaching a detector.

    2. Optical rays are vector which point in the direction of energy flow.

    3. An optical medium is characterized by a refractive index, n = c0 / c, where c0 is the speed of light in free space and c is the speed of light in the medium. The time taken by light to travel a distance d is d/c = nd/c0. The optical pathlength is n*d.

    4. In an inhomogeneous medium, the refractive index n(r) is a function of the position r(x,y,z). The optical pathlength along a path between A and B is the integral of A to B of n(r)*ds.

    5. Fermat’s Principle states that optical rays travel from A to B following the path that requires the least amount of travel time.

    6. Hero’s Principle states that light travels in straight lines in a homogeneous medium. A homogeneous medium means that the refractive index is consistent throughout.

    7. Light reflects from mirrors in accordance with the law of reflection: The angle of reflection equals the angle of incidence and the reflected ray lies in the plane of incidence. This may be proven using Hero’s principle.

    planeofincidence

    8. At a boundary between two mediums of different refracting indexes, a ray is split in two. One resulted ray is a reflected ray and the other is a refracted or transmitted ray. The reflected ray is shown in figure (b) above as vector C, while the refracted ray is C’.

    9. The refracted ray lies in the place of incidence. The angle of refraction is related to the angle of incidence by Snell’s Law:

    snell

    10. The proportion of reflected light to refracted light is not dealt with in ray optics.

    ray1

     
  • mbenkerumass 9:00 am on December 19, 2019 Permalink | Reply
    Tags: , Optics   

    Ray Optics & Geometrical Optics (Introduction) 

    Ray Optics

    In describing the nature of light, numerous theories have been described. One of the oldest and most simplest of explanations of the nature of light is Ray Optics. In variable contrast to Wave Optics, Electromagnetic Optics or Quantum Optics, the theory of Ray Optics describes light as obeying a set of geometrical rules. Ray Optics assumes that the wavelength of light is infinitesimally smaller than the objects that light “rays” interact with. Ray Optics is also referred to as Geometrical Optics due to the geometrical nature of the understanding of the theory and the manner of calculations involved.

    2

    Ray Optics has limitations and does not describe many phenomenon. However, Ray Optics or Geometrical Optics is is useful in determining the conditions in which light travels and is guided within various mediums, such as in relation to a lens, mirror or glass fiber. Optical rays may also be described as vectors which point in the direction of travel of a light ray.

    optics1

    The above diagram describes the relationship between Ray Optics to other important theories regarding the nature of light. Electromagnetic Optics describes light as an electromagnetic wave phenomenon and therefore assesses light using concepts applied to electromagnetic radiation, such as the form of electric field waves and magnetic field waves coupled. Wave Optics approximates this wave phenomenon as a scalar wave. Electromagnetic Optics, Wave Optics and Ray Optics encompass what is known as Classical Optics. To describe the nature of light in a manner consistent with quantum mechanics, the theory of Quantum Optics meets these purposes.

     

     
  • mbenkerumass 9:00 am on December 17, 2019 Permalink | Reply
    Tags: Optics, Optoelectronics,   

    Optics, Optoelectronics, Electro-Optics and Photonics 

    Optics vs. Photonics

    What is the difference between Optics and Photonics? These words are sometimes used interchangeably. A distinction may be made however. Optics, on one hand is a very old subject, whereas Photonics is a term that has only recently been used. Photonics is a word which refers to devices that primarily involve the flow of photons as opposed to electronics, which deals with the flow of electrons. The main inventions that lead to the use of the word Photonics are the laser, fabrication of low-loss optical fibers and semiconductor optical devices. Other terms that are often used to refer to these inventions and their various applications are electro-optics, optoelectronics, quantum electronics, quantum optics and lightwave technology. Many of these terms may be used interchangeably, although some of them refer to specific technologies.

    The first figure below may be viewed as an optical system, while the second figure may be referred to as a photonic system. The first figure features a light beam that is modulated, reflected and reflacted through a medium. The second figure is of a photonic integrated circuit device.

    optics2

    photonics1

     

    Electro-Optics is term for devices that incorporate both an optical and electrical properties, however are primarily optical devices. Examples of electro-optical devices are lasers and electro-optic modulators and switches.

    laser1

     

    Optoelectronics refers on the other hand to devices that are primarily electronic, but involve light, such as light-emitting diodes, photodetectors or liquid-crystal display devices.

    led

     

    Quantum Optics refers to the study of the quantum mechanical and coherence properties of light. Lightwave Technology typically is used to describe optical communications and optical signal processing devices and systems. Quantum Electronics is the study of technology concerned with the interaction of light and matter, such as lasers, optical amplifiers and optical wave mixing devices.

     
  • mbenkerumass 4:01 pm on December 15, 2019 Permalink | Reply
    Tags: Optics   

    Branches of Optics 

    Optics is a broad subject that has been studied and renovated over a long period of time. The following is a quick list of the different branches, theories and studies of optics. This list does not cover all concepts related to Optics by any means, however when discussing a topic related to Optics, it will be important to know which type of Optics is being discussed.

    Optics

    Ray Optics

    Geometrical Optics

    Wave Optics

    Electromagnetic Optics

    Quantum Optics

    Paraxial Optics

    Matrix Optics

    Classical Optics

    Beam Optics

    Gaussian Optics

    Fourier Optics

    Physical Optics

    Polarization Optics

    Magneto-Optics

    Electro-Optics

    Metal Optics

    Metamaterial Optics

    Transformation Optics

    Fiber Optics

    Micro-Optics

    Nano-Optics

    Guided-Wave Optics

    Resonator Optics

    Photonic-Crystal Optics

    Statistical Optics

    Photon Optics

    Spatial Optics

    Acousto-Optics

    Semiconductor Optics

    Nonlinear Optics

    Ultrafast Optics

    Atom Optics

     

     

     
  • mbenkerumass 10:08 am on November 22, 2019 Permalink | Reply
    Tags: , Optics,   

    Interferometry – Introduction 

    RF/Photonics Lab
    Jared Alves
    November 2019

    Interferometry – Introduction

                    Interferometry is a family of techniques in which waves are superimposed for measurement purposes. These waves tend to be radio, sound or optical waves. Various measurements can be obtained using interferometry that portray characteristics of the medium through which the waves propagate or properties of the waves themselves. In terms of optics, two light beams can be split to create an interference pattern when the waves combine (superimpose). This superposition can lead to a diminished wave, an increased wave or a wave completely reduced in amplitude. In an easily realizable physical sense, tossing a stone into a pond creates concentric waves that radiate away from where the stone was tossed. If two stones are thrown near each other, their waves would interfere with each other creating the same effect described previously. Constructive interference is the superposition of waves that results in a larger amplitude whereas destructive interference diminishes the resultant amplitude. Normally, the interference is either partially constructive or partially destructive, unless the waves are perfectly out of phase. The following image displays total constructive and destructive interference.

    interferrometry1

    A simple way to explain the operation of an interferometer is that it converts a phase difference to an intensity. When two waves of the same frequency are added together, the result depends only on the phase difference between them, as explained previously.

    interferrometry2The image above shows a Michelson interferometer which uses two beams of light to measure small displacements, refractive index changes and surface irregularities.  The beams are split using a mirror that is not completely reflective and angled so that one beam is reflected, and one is not. The two beams travel in separate paths which combine to produce interference. Whether the waves combine destructively or constructively depends on distancing between the mirrors. Because the device shows the difference in path lengths, it is a differential device. Generally, one leg length is kept constant for control purposes.

     
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