part iii - snvhomesnvhome.net/ee-braude/introduction2eo/figures/figures 2... · spherical waveform...
TRANSCRIPT
Dr. Vladislav Shteeman Page 34
Part III
Dr. Vladislav Shteeman Page 35
Figure 45. Sketch of a transverse amplitude and phase variation of a paraxial wave (after [1]).
Dr. Vladislav Shteeman Page 36
Figure 46. A plane wave traveling at a small angle θ to the optic axis (after [1])
Dr. Vladislav Shteeman Page 37
Figure 47. Spherical waveform coming from a real point source (after [1]).
Figure 48. Gaussian-spherical wave from a complex point source (after [1], p. 658).
Dr. Vladislav Shteeman Page 38
Figure 49. Notation for a lowest-order gaussian beam diverging away from its waist (after [1], p. 664).
Dr. Vladislav Shteeman Page 39
Analogy between the lowest-order and higher order solutions for Paraxial wave equation and Schrodinger equation for Hydrogen atom
Paraxial wave equation Schrödinger equation
for resonator of cylindrical symmetry
for resonator of square symmetry
for 3D Hydrogen atom of spherical symmetry
lowest-order solution lowest-order solution lowest-order solution
higher order solutions higher order solutions higher order solutions
Dr. Vladislav Shteeman Page 40
Figure 50. Gaussian beam in a two-mirror resonator.
Dr. Vladislav Shteeman Page 41
Figure 51. Example of an optical resonator or lensguide containig arbitrary paraxial elements.
Dr. Vladislav Shteeman Page 42
Figure 52. Explanation to connection between the parameters of complex Gaussian beams at the input ( 1z ) and output ( 2z ) of an arbitrary ABCD system.
Dr. Vladislav Shteeman Page 43
Figure 53. Sketches of 2D hard aperture and 2D Gaussian aperture. ( )yxt ,~ is 2D amplitude transmission function; 0Re, 22 >∈ aa (after
Error! Reference source not found.).
Dr. Vladislav Shteeman Page 44
Figure 54. A gaussian aperture with transversely varying amplitude transmission ( 0Re, 22 >∈ aa ).
Dr. Vladislav Shteeman Page 45
Figure 55. Explanation to confined Gaussian eigenbeams of resonators / lensguides.
Figure 56. Propagation of Gaussian beam ( λ= 30 mm) in air (after [5]).
Dr. Vladislav Shteeman Page 46
Figure 57. Fractional power transfer of a cylindrical gaussian beam through a circular aperture.
Dr. Vladislav Shteeman Page 47
Figure 58. Explanation to the Rayleigh range & collimated range.
Dr. Vladislav Shteeman Page 48
Figure 59. A gaussian beam spreads with a constant diffraction angle in the far field.
Figure 60. Illustration to the cone, corresponding to the solid angle
e1Ω .
Dr. Vladislav Shteeman Page 49
Figure 61. Intensity distribution for the first 12 Hermite-Gaussian modes (TEMnm modes for n = 0,…,3 & m = 0,…,3 ) (after [5]).
Dr. Vladislav Shteeman Page 50
Figure 62. Intensity distribution for the first 12 Laguerre-Gaussian modes (after [5]).
Dr. Vladislav Shteeman Page 51
Figure 63. Illustration to analysis of a guided gaussian beam in a two-mirror cavity (Problem III - 1).
Figure 64. Explanation to the Problem III - 2.
Dr. Vladislav Shteeman Page 52
Figure 65. Cavity sketch (Problem III - 3).
Figure 66. Hard aperture inserted into the cavity (Problem III - 3).
Dr. Vladislav Shteeman Page 53
References : [1]. A. Siegman. Lasers.(University Science books 1986) [2]. A. Yariv. Quantum electronics (3rd edition, Wiley, 1989) [3]. T. Gavlin, G.Eden (ECE Illinois) Optical Resonator Modes ECE 455 Optical Electronics.
https://courses.engr.illinois.edu/ece455/Files/Galvinlectures/02_CavityModes.pdf [4]. A. Fox, T. Li, Resonant modes in a maser interferometer, Bell Labs 1961. [5]. http://en.wikipedia.org/wiki/Gaussian_beam (as of the date 18.03.2015) [6]. https://ashtriferous.wordpress.com/2012/06/19/activity-2-scilab-basics/ (as of the date
1.03.2017)