TABLE I
Electromagnetic properties of the different domains in a cross sectional plane.
Domain | Permittivity | Permeability | Profile |
---|
| ∊0 | μ0 | homogeneous, isotropic |
| ∊xx, ∊yy = ∊(o)(rT) | μxx, μyy = μ(o) (rT) | inhomogeneous, uniaxial |
| ∊zz = ∊(e) (rT) | μzz = μ(e) (rT) | |
TABLE II
Even and odd field distributions in a configuration with x = 0 as a plane of symmetry (dependences on irrelevant parameters are omitted).
Even modes | Odd modes |
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|
|
|
|
|
|
|
|
TABLE III
Definitions of the components πE and πM for odd and even modes to be used in Eqs. (11) and (12); g−(x,x′,kz) = g(x,x′,kz) −g(−x,x′,kz) and g+ (x,x′,kz) = g(x,x′,kz) + g(−x,x′,kz) (dependences on irrelevant parameters are omitted).
Even modes | Odd modes |
---|
|
|
|
|
|
|
|
|
TABLE IV
Some values of kz/k0 for the step-index, ∊r = 1.01 symmetrical slab waveguide, obtained by the integral-equation method with 8 and 16 matching points; values from the analytical expression for comparison. Average C.P.U. time was 10 s for N = 8 matching points, and 35 s for n = 16 matching points.
k0a | Mode | kz/k0 | Mode | kz/k0 |
---|
Int. eq. N = 8 | Int. eq. N = 16 | Exact | Int. eq. N = 8 | Int. eq. N = 16 | Exact |
---|
3.142 × 100 | TE0 (even) | 1.000 437 0 | 1.000 436 9 | 1.000 436 9 | TM0 (odd) | 1.000 429 8 | 1.000 429 7 | 1.000 429 7 |
1.101 × 102 | TE0 (even) | 1.004 898 7 | 1.004 901 4 | 1.004 902 5 | TM0 (odd) | 1.004 898 4 | 1.004 901 2 | 1.004 902 3 |
1.885 × 101 | TE1 (odd) | 1.000 312 9 | 1.000 314 6 | 1.000 315 2 | TM1 (even) | 1.000 308 8 | 1.000 310 6 | 1.000 311 2 |
1.101 × 102 | TE1 (odd) | 1.004 632 7 | 1.004 643 2 | 1.004 647 7 | TM1 (even) | 1.004 631 4 | 1.004 642 5 | 1.004 647 2 |
8.168 × 101 | TE5 (odd) | 1.000 051 2 | 1.000 131 7 | 1.000 161 4 | TM5 (even) | 1.000 055 1 | 1.000 129 7 | 1.000 160 2 |
1.101 × 102 | TE5 (odd) | 1.001 848 5 | 1.001 948 7 | 1.001 991 4 | TM5 (even) | 1.001 838 8 | 1.001 944 0 | 1.001 988 4 |
TABLE V
Some values of kz/k0 for the step-index ∊r = 2.25 symmetrical slab waveguide, obtained by the integral-equation method with 8 and 16 matching points; values from the analytical expression for comparison. Average C.P.U. times as in Table IV.
k0a | Mode | kz/k0 | Mode | kz/k0 |
---|
Int. eq. N = 8 | Int. eq. N = 16 | Exact | Int. eq. N = 8 | Int. eq N = 16 | Exact |
---|
2.811 × 10−1 | TE0 (even) | 1.053 23 | 1.053 23 | 1.053 23 | TM0 (odd) | 1.012 43 | 1.012 43 | 1.012 43 |
9.848 × 100 | TE0 (even) | 1.492 55 | 1.492 77 | 1.492 86 | TM0 (odd) | 1.489 67 | 1.491 48 | 1.492 15 |
1.686 × 100 | TE1 (odd) | 1.038 36 | 1.038 57 | 1.038 64 | TM1 (even) | 1.010 86 | 1.011 18 | 1.011 28 |
9.848 × 100 | TE1 (odd) | 1.470 00 | 1.470 89 | 1.471 27 | TM1 (even) | 1.458 60 | 1.465 75 | 1.468 41 |
8.061 × 100 | TE5 (odd) | 1.006 93 | 1.016 42 | 1.094 92 | TM5 (even) | | 1.003 61 | 1.064 82 |
9.848 × 100 | TE5 (odd) | 1.209 43 | 1.219 75 | 1.224 13 | TM5 (even) | 1.128 94 | 1.179 64 | 1.198 76 |
TABLE VI
Some values of kz/k0 of the TM0 mode for the negatively and positively uniaxial symmetrical step-index slab waveguide with
. The extraordinary direction is along the z axis. Values are obtained by the integral-equation method with eight matching points, and from the analytical expression. Average C.P.U. time as in Table IV.
k0a | kz/k0,
| kz/k0,
|
---|
Int. eq. N = 8 | Exact | Int. eq. N = 8 | Exact |
---|
2.811 × 10−1 | 1.012 08 | 1.012 08 | 1.012 79 | 1.012 79 |
2.096 × 100 | 1.319 86 | 1.320 05 | 1.396 14 | 1.398 22 |
6.288 × 100 | 1.468 55 | 1.469 68 | 1.483 66 | 1.486 74 |
9.848 × 100 | 1.485 45 | 1.487 00 | 1.491 43 | 1.494 44 |
TABLE VII
Some values of kz/k0 for a graded-index symmetrical slab waveguide having a quadratic permittivity profile with ∊r,max = 1.01, A = 2.475 × 10−3, obtained by the integral-equation method with N = 8 and N = 16 matching points. Average C.P.U. times as in Table IV.
k0a | Mode | kz/k0 | Mode | kz/k0 |
---|
N = 8 | N = 16 | N = 8 | N = 16 |
---|
6.288 × 10−1 | TE0 | 1.000 013 7 | 1.000 013 7 | TM0 | 1.000 013 5 | 1.000 013 4 |
1.101 × 102 | TE0 | 1.004 655 9 | 1.004 664 5 | TM0 | 1.004 655 4 | 1.004 664 2 |
2.620 × 101 | TE1 | 1.000 783 4 | 1.000 785 0 | TM1 | 1.000 780 8 | 1.000 782 6 |
1.101 × 102 | TE1 | 1.003 992 6 | 1.004 017 1 | TM1 | 1.003 991 4 | 1.004 016 6 |
TABLE VIII
Some values of kz/k0 for a graded-index symmetrical slab waveguide having a quadratic permittivity profile with ∊r,max = 1.01, Δ = 4.950 × 10−3, obtained by the integral-equation method with N = 8 and N = 16 matching points. Average C.P.U. times as in Table IV.
k0a | Mode | kzk0 | Mode | kz/k0 |
---|
N = 8 | N = 16 | N = 8 | N = 16 |
---|
6.288 × 10−1 | TE0 | 1.000 008 8 | 1.000 008 8 | TM0 | 1.000 008 7 | 1.000 008 6 |
1.101 × 102 | TE0 | 1.004 518 6 | 1.004 530 8 | TM0 | 1.004 517 7 | 1.004 530 3 |
2.620 × 101 | TE1 | 1.000 155 7 | 1.000 155 3 | TM1 | 1.000 156 5 | 1.000 156 2 |
1.101 × 102 | TE1 | 1.003 584 1 | 1.003 618 0 | TM1 | 1.003 582 3 | 1.003 617 3 |