Table 1
Required Run Times of the DM, RCWA, and LPEM to Achieve an Accuracy of 1% in the Largest Diffraction Efficiency of Both Major Polarizations
Approach | Required Run Time (s) |
---|
DM [11] | RCWA [5] | LPEM |
---|
Case A | | | |
TE polarization | 0.042 | 0.008 | 0.004 with
|
TM polarization | 0.063 | 0.031 | 0.015 with
|
Case B | | | |
TE polarization | 0.117 | 0.100 | 0.039 with
|
TM polarization | 3.08 | Very large | 0.62 with
|
Table 2
Transmitted Diffraction Efficiencies of the
, 0th, and
Orders, Together with the Total Diffracted Energy of the Dielectric Surface Relief Grating in Case A, Are All Calculated Using the LPEM with
and
and for Different Values of L
L
| Transmitted Efficiency | Total Diffracted Energy |
---|
Order | 0th Order |
Order |
---|
TE | | | | |
1 | 0.1280789 | 0.6966239 | 0.1588289 | 1.000063246582 |
2 | 0.1281937 | 0.6963942 | 0.1588820 | 1.000001134920 |
3 | 0.1281940 | 0.6963924 | 0.1588828 | 1.000000192145 |
5 | 0.1281939 | 0.6963922 | 0.1588828 | 1.000000002966 |
10 | 0.1281939 | 0.6963922 | 0.1588828 | 0.999999999649 |
20 | 0.1281939 | 0.6963922 | 0.1588828 | 0.999999999985 |
| | | | |
TM | | | | |
1 |
| 0.8439878 |
| 1.000178730737 |
2 |
| 0.8426590 |
| 0.999942117523 |
3 |
| 0.8426111 |
| 0.999940711633 |
5 |
| 0.8426233 |
| 0.999936680417 |
10 |
| 0.8426197 |
| 0.999939591549 |
20 |
| 0.8426203 |
| 0.999939765866 |
50 |
| 0.8426203 |
| 0.999939766240 |
Table 3
Required Run Times of the C-Method and LPEM to Achieve an Accuracy of 1% in the Largest Diffraction Efficiency of Both Major Polarization in Cases A and B
Approach | Required Time (s) |
---|
C-Method | Single-Layer LPEM [18] | Multilayer LPEM |
---|
Case A | | | |
TE polarization | 0.008 with
| 0.004 with
,
| 0.004 with
,
,
|
TM polarization | 0.008 with
| 0.007 with
,
| 0.015 with
,
,
|
| | | |
Case B | | | |
TE polarization | 0.008 with
| 0.043 with
,
| 0.039 with
,
,
|
TM polarization | 0.005 with
| Very large | 0.62 with
,
,
|
Table 4
Required Run Rimes of the C-Method and LPEM to Achieve and Accuracy of 1% in the Largest Diffraction Efficiency of Both Major Polarizations in Cases C and D
Approach | Required Time (s) |
---|
C-Method | Single-Layer LPEM [18] | Multilayer LPEM |
---|
Case C | | | |
TE polarization | 0.051 with
| 0.004 with
,
| 0.004 with
,
,
|
TM polarization | 0.045 with
| 0.004 with
,
| 0.006 with
,
,
|
| | | |
Case D | | | |
TE polarization | 0.011 with
| 0.007 with
,
| 0.007 with
,
|
TM polarization | 6.61 with
| 58 with
,
| 1.77 with
,
,
|
Table 5
Incurred Reciprocity Error in Applying the LPEM for the Analysis of Different Surface Relief Gratings in Cases A–D
Case | Reciprocity Error, e
| Parameters |
---|
Case A | | |
TE polarization |
|
,
,
|
TM polarization |
|
,
,
|
| | |
Case B | | |
TE polarization |
|
,
,
|
TM polarization |
|
,
,
|
| | |
Case C | | |
TE polarization |
|
,
,
|
TM polarization |
|
,
,
|
| | |
Case D | | |
TE polarization |
|
,
,
|
TM polarization |
|
,
,
|