By Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva
ISBN-10: 143986960X
ISBN-13: 9781439869604
Going past regular introductory texts, Mathematical Optics: Classical, Quantum, and Computational tools brings jointly many new mathematical thoughts from optical technological know-how and engineering examine. Profusely illustrated, the e-book makes the fabric available to scholars and novices to the sphere. Divided into six elements, the textual content provides state of the art mathematical tools and functions in classical optics, quantum optics, and photo processing. half I describes using part house thoughts to symbolize optical beams and the appliance of dynamic programming in optical waveguides. half II explores recommendations to paraxial, linear, and nonlinear wave equations. half III discusses state-of-the-art components in transformation optics (such as invisibility cloaks) and computational plasmonics. half IV makes use of Lorentz teams, dihedral workforce symmetry, Lie algebras, and Liouville house to research difficulties in polarization, ray optics, visible optics, and quantum optics. half V examines the function of coherence features in smooth laser physics and explains how one can observe quantum reminiscence channel versions in quantum desktops. half VI introduces super-resolution imaging and differential geometric tools in photograph processing. As numerical/symbolic computation is a crucial software for fixing quite a few real-life difficulties in optical technological know-how, many chapters contain Mathematica® code of their appendices. The software program codes and notebooks in addition to colour types of the book’s figures can be found at www.crcpress.com.
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Extra resources for Mathematical Optics: Classical, Quantum, and Computational Methods
Sample text
The partially coherent beams have higher divergence than the coherent one, as can be observed projecting the corresponding WD onto the u axis. 1. 3 WD of a one-dimensional GSM beam with parameters h = 0, g1 = w−2 , and different degrees of coherence: (a) the coherent case g2 = g1 , (b) g2 = 10g1 , (c) g2 = 100g1 , and (d) g2 = 1000g1 . Note that w = 1 mm defines the waist of the Gaussian intensity profile and the scale normalization parameter s = w. 1 MI and WD of Some Simple Two-Dimensional Example Signals f (r) δ (r − ro ) exp i2πpto r exp (iπart r) Signal type Point Plane wave Quadratic phase (r1 , r2 ) δ (r1 − r◦ ) δ (r2 − r◦ ) exp i2πpt◦ (r1 − r2 ) exp iπa rt1 r1 − rt2 r2 W (r, p) δ (r − ro ) δ (p − po ) δ (p − ar) The two-dimensional HG beam is separable in Cartesian coordinates as HGm,n r; wx , wy ≡ HGm (x; wx ) HGn y; wy .
The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proceedings of the Royal Society of London Series A—Containing Papers of a Mathematical and Physical Character, 82, 560–567. Simpson, N. , 1997. Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner. Optics Letters, 22(1), 52–54. , 1988. Frequency locking of 2 transverse optical modes of a laser. Physical Review A, 38(11), 5960–5963. A. , 1996.
1 First-Order Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Second-Order Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Beam Representation on the Poincaré Sphere . . . . . . . . . . . . . . . . . . . . . . . . . 8 Moments Expressed in Terms of Beam Mode Expansion Coefficients . . . . . . . . . . . 9 Signal Analysis and Comparison .