• Acta Optica Sinica
  • Vol. 38, Issue 9, 0905001 (2018)
Changcheng Xiang1、2、* and Changhe Zhou1、*
Author Affiliations
  • 1 Laboratory of Information Optics and Optoelectronic Technology, Shanghai Institute of Optics and Fine Mechanics, Shanghai 201800, China
  • 2 University of Chinese Academy of Sciences, Beijing 100049, China
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    DOI: 10.3788/AOS201838.0905001 Cite this Article Set citation alerts
    Changcheng Xiang, Changhe Zhou. Dispersion Equation and Symmetry of Grating Modes[J]. Acta Optica Sinica, 2018, 38(9): 0905001 Copy Citation Text show less
    Rectangular grating and attached coordinate system
    Fig. 1. Rectangular grating and attached coordinate system
    Four types of symmetric mode profiles with grating parameters of d=1965 nm, c=g=932.5 nm, nc=1.4496, ng=1 and λ=1310 nm. (a) (b) First two modes under incidence of the first order Bragg angle; (c) (d) first two modes under incidence of the second order Bragg angle
    Fig. 2. Four types of symmetric mode profiles with grating parameters of d=1965 nm, c=g=932.5 nm, nc=1.4496, ng=1 and λ=1310 nm. (a) (b) First two modes under incidence of the first order Bragg angle; (c) (d) first two modes under incidence of the second order Bragg angle
    Graphs of four functions under grating parameters of d=1979 nm, c=1385 nm, g=594 nm, nc=1.4496, ng=1 and λ=1064 nm. (a) f1(neff2); (b) f2(neff2); (c) f3(neff2); (d) f4(neff2)
    Fig. 3. Graphs of four functions under grating parameters of d=1979 nm, c=1385 nm, g=594 nm, nc=1.4496, ng=1 and λ=1064 nm. (a) f1(neff2); (b) f2(neff2); (c) f3(neff2); (d) f4(neff2)
    Effective refractive index of the first three modes obtained by two methods versus duty ratio under grating parameters of d=1500 nm, nc =1.4496, ng=1 and λ=1064 nm
    Fig. 4. Effective refractive index of the first three modes obtained by two methods versus duty ratio under grating parameters of d=1500 nm, nc =1.4496, ng=1 and λ=1064 nm
    Method12345Average
    Scanning method36.0335.2735.4235.1535.0635.39
    Method using symmetric mode equation0.410.420.430.420.400.42
    Table 1. Computation time of effective index by two methodss