The normal-mode transmission direction perpendicular to the substrate is used for developing an alternative equivalent-network formulation for the analysis of optical strip waveguides (e.g., strip-loaded waveguides and rib waveguides). Our choice of transmission direction permits simple forms of normal modes, symmetric slab-waveguide modes, and plane waves. Our approach becomes simple when the thickness of the uniform-slab waveguide is small.
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Normalized Guide Index of the Structures of Type A in the Present Methoda
h (μm)
(9 + 0)
4λ, (9 + 21)
4λ, (9 + 31)
7λ, (9 + 26)
7λ, (9 + 31)
VFE
0.1
0.3010
0.3007
0.3008
0.3004
0.3005
0.3038
0.2
0.3056
0.3047
0.3048
0.3042
0.3044
0.3075
0.3
0.3137
0.3103
0.3105
0.3096
0.3100
0.3125
0.4
0.3199
0.3176
0.3179
0.3164
0.3166
0.3200
0.5
0.3247
0.3256
0.3257
0.3253
0.3256
0.3275
0.6
0.3260
0.3350
0.3353
0.3358
0.3359
0.3399
0.7
0.3218
0.3508
0.3517
0.3496
0.3503
0.3512
0.8
0.3121
0.3658
0.3661
0.3654
0.3656
0.3674
0.9
0.2996
0.3871
0.3873
0.3871
0.3872
0.3886
4λ denotes that the conductor spacing s = 4λ. (m + n) denotes that m-guided modes and n-radiation modes are used in the analysis; VFE, vector H finite element.
Table 4
Comparison of the Normalized Guide Index with Other Resultsa
Normalized Guide Index of the Structures of Type A in the Present Methoda
h (μm)
(9 + 0)
4λ, (9 + 21)
4λ, (9 + 31)
7λ, (9 + 26)
7λ, (9 + 31)
VFE
0.1
0.3010
0.3007
0.3008
0.3004
0.3005
0.3038
0.2
0.3056
0.3047
0.3048
0.3042
0.3044
0.3075
0.3
0.3137
0.3103
0.3105
0.3096
0.3100
0.3125
0.4
0.3199
0.3176
0.3179
0.3164
0.3166
0.3200
0.5
0.3247
0.3256
0.3257
0.3253
0.3256
0.3275
0.6
0.3260
0.3350
0.3353
0.3358
0.3359
0.3399
0.7
0.3218
0.3508
0.3517
0.3496
0.3503
0.3512
0.8
0.3121
0.3658
0.3661
0.3654
0.3656
0.3674
0.9
0.2996
0.3871
0.3873
0.3871
0.3872
0.3886
4λ denotes that the conductor spacing s = 4λ. (m + n) denotes that m-guided modes and n-radiation modes are used in the analysis; VFE, vector H finite element.
Table 4
Comparison of the Normalized Guide Index with Other Resultsa