Table 1.
Effective indices for the two modes of interest for the wavelength λ = 1.1 Λ.
n
_{1}
 1.391278278 + 1.262 × 10^{6}
i

n
_{2}
 1.387085741 + 1.961 × 10^{6}
i

Table 2.
Finite difference calculation of third derivative of effective indices with respect to diameter of holes 1 and 11.
hole number 
$\frac{{\partial}^{3}{n}_{1}}{\partial {d}^{3}}$

$\frac{{\partial}^{3}{n}_{2}}{\partial {d}^{3}}$


1  5.58 × 10^{1}  5.38 × 10^{4}
i
 5.62 × 10^{1}  6.98 × 10^{4}
i

11  1.99 × 10^{4}  1.68 × 10^{4}
i
 2.81 × 10^{4}  2.58 × 10^{4}
i

Table 3.
Sensitivity of modal effective indices to the diameters of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The units of the derivative are Λ^{1}.
hole number 
$\frac{\partial {n}_{1}}{\partial d}$

$\frac{\partial {n}_{2}}{\partial d}$


1  4.8 × 10^{2}  1.7 × 10^{6}
i
 6.2 × 10^{2}  1.9 × 10^{6}
i

2  1.3 × 10^{2}  2.9 × 10^{6}
i
 1.8 × 10^{2}  4.1 × 10^{6}
i

3  1.4 × 10^{2}  2.3 × 10^{6}
i
 1.1 × 10^{2}  2.6 × 10^{6}
i

9  1.4 × 10^{5}  1.2 × 10^{6}
i
 1.2 × 10^{5}  1.4 × 10^{6}
i

10  1.1 × 10^{4}  2.3 × 10^{6}
i
 1.0 × 10^{4}  2.8 × 10^{6}
i

11  1.4 × 10^{5}  1.4 × 10^{6}
i
 2.1 × 10^{5}  2.2 × 10^{6}
i

12  1.4 × 10^{4}  4.7 × 10^{6}
i
 3.0 × 10^{4}  8.8 × 10^{6}
i

Table 4.
Sensitivity of modal effective indices to the xcoordinate of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The units of the derivative are Λ^{1}.
hole number 
$\frac{\partial {n}_{1}}{\partial x}$

$\frac{\partial {n}_{2}}{\partial x}$


1  3.8 × 10^{2}  3.4 × 10^{6}
i
 4.3 × 10^{2}  6.4 × 10^{6}
i

2  9.7 × 10^{3}  2.6 × 10^{7}
i
 1.1 × 10^{2}  9.2 × 10^{7}
i

3  10^{10} + × l0^{12}
i
 10^{10} + 10^{12}
i

9  10^{12}  10^{l3}
i
 10^{12} + 10^{13}
i

10  5.4 × 10^{5} + 1.2 × 10^{7}
i
 2.9 × 10^{5}  8.4 × 10^{8}
i

11  9.8 × 10^{6} + 3.6 × 10^{7}
i
 1.3 × 10^{5} + 3.9 × 10^{7}
i

12  1.1 × 10^{4} + 5.0 × 10^{8}
i
 2.3 × 10^{4} + 2.1 × 10^{7}
i

Table 5.
Sensitivity of modal effective indices to the ycoordinate of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The units of the derivative are Λ^{1}.
hole number 
$\frac{\partial {n}_{1}}{\partial y}$

$\frac{\partial {n}_{2}}{\partial y}$


1  10^{10}  10^{l2}
i
 10^{10}  10^{l2}
i

2  5.1 × 10^{3} + 2.5 × 10^{7}
i
 9.0 × 10^{3} + 5.1 × 10^{7}
i

3  1.1 × 10^{2}  1.3 × 10^{7}
i
 9.0 × 10^{3}  1.9 × 10^{7}
i

9  9.9 × 10^{6}  3.1 × 10^{7}
i
 1.0 × 10^{5}  4.6 × 10^{7}
i

10  7.5 × 10^{6}  9.3 × 10^{8}
i
 7.7 × 10^{5}  2.7 × 10^{7}
i

11  5.7 × 10^{6}  2.7 × 10^{7}
i
 9.2 × 10^{6}  6.8 × 10^{7}
i

12  1.6 × 10^{5}  8.7 × 10^{7}
i
 2.7 × 10^{5}  1.8 × 10^{6}
i

Table 6.
Sensitivity of modal effective indices to the oblateness of individual holes. Only two significant figures are shown, although the real parts are known more accurately. The derivative is dimensionless.
hole number 
$\frac{\partial {n}_{1}}{\partial \epsilon}$

$\frac{\partial {n}_{2}}{\partial \epsilon}$


1  7.7 × 10^{3} + 5.1 × 10^{7}
i
 4.5 × 10^{3} + 1.3 × 10^{6}i 
2  1.4 × 10^{3}  2.6 × 10^{8}
i
 2.7 × 10^{4} + 4.2 × 10^{7}
i

3  1.9 × 10^{3}  3.0 × 10^{7}
i
 2.1 × 10^{3}  8.1 × 10^{8}
i

9  1.1 × 10^{6}  1.2 × 10^{7}
i
 2.3 × 10^{6}  2.7 × 10^{9}
i

10  4.5 × 10^{6}  1.0 × 10^{7}
i
 1.5 × 10^{5} + 1.4 × 10^{7}
i

11  1.1 × 10^{6}  7.5 × 10^{9}
i
 2.9 × 10^{7} + 2.0 × 10^{7}
i

12  2.1 × 10^{5}  1.6 × 10^{7}
i
 3.9 × 10^{5} + 5.2 × 10^{7}
i
