Table 1
Fraction of Reflected and Transmitted Incident Power, Total Power, and Diffraction Efficiency for Rectangular Window Function
Power | Lens |
---|
|
---|
Continuous | 32-Level | 8-Level | 2-Level |
---|
TE Polarization | | | | |
Reflected Power Pr/Pinc | 0.05821 | 0.06090 | 0.08692 | 0.06810 |
Transmitted Power Pt/Pinc | 0.93384 | 0.93073 | 0.90603 | 0.93173 |
Total Power (Pr + Pt)/Pinc | 0.99205 | 0.99162 | 0.99295 | 0.99983 |
Diffraction Efficiency DE (%) | 73.2 | 72.9 | 68.4 | 35.3 |
TM Polarization | | | | |
Reflected Power Pr/Pinc | 0.03459 | 0.03331 | 0.04978 | 0.05383 |
Transmitted Power Pt/Pinc | 0.95921 | 0.95592 | 0.94109 | 0.94438 |
Total Power (Pr + Pt)/Pinc | 0.99380 | 0.98923 | 0.99087 | 0.99821 |
Diffraction Efficiency DE (%) | 74.4 | 74.0 | 70.4 | 35.1 |
Table 2
Diffraction Efficiency Dependence on Detection Slit Width at Focal Point
| Lens |
---|
|
---|
Continuous | 32-Level | 8-Level | 2-Level |
---|
TE Polarization | | | | | | | | |
Slit Width (μm) | 8/π | 5.0 | 8/π | 5.0 | 8/π | 5.0 | 8/π | 5.0 |
Pf/Pinc (%) | 73.2 | 79.3 | 72.9 | 79.0 | 68.4 | 74.3 | 35.3 | 39.1 |
Pf/Pt (%) | 78.4 | 84.9 | 78.3 | 84.9 | 75.5 | 82.0 | 37.9 | 42.0 |
TM Polarization | | | | | | | | |
Slit Width (μm) | 8/π | 5.0 | 8/π | 5.0 | 8/π | 5.0 | 8/π | 5.0 |
Pf/Pinc (%) | 74.4 | 80.4 | 74.0 | 80.1 | 70.4 | 76.4 | 35.1 | 39.1 |
Pf/Pt (%) | 77.6 | 83.8 | 77.4 | 83.8 | 74.8 | 81.2 | 37.2 | 41.4 |
Table 3
Fraction of Reflected and Transmitted Incident Power, Total Power, and Diffraction Efficiency for Cosine-Squared-Edged Window Function
| Polarization |
---|
|
---|
TE | TE | TE | TM | TM | TM |
---|
Continuous Lens | | | | | | |
l of Window Function (μm) | 5 | 1 | 0 | 5 | 1 | 0 |
Reflected Power Pr/Pinc | 0.05396 | 0.05721 | 0.05821 | 0.03474 | 0.03523 | 0.03459 |
Transmitted Power Pt/Pinc | 0.94547 | 0.94128 | 0.93384 | 0.96472 | 0.96369 | 0.95921 |
Total Power (Pr + Pt)/Pinc | 0.99944 | 0.99850 | 0.99205 | 0.99946 | 0.99892 | 0.99380 |
Diffraction Efficiency DE (%) | 73.2 | 73.6 | 73.2 | 74.1 | 74.7 | 74.4 |
8-Level Lens | | | | | | |
l of Window Function (μm) | 5 | 1 | 0 | 5 | 1 | 0 |
Reflected Power Pr/Pinc | 0.08174 | 0.08650 | 0.08692 | 0.04811 | 0.05039 | 0.04978 |
Transmitted Power Pt/Pinc | 0.91861 | 0.91218 | 0.90603 | 0.95205 | 0.94855 | 0.94109 |
Total Power (Pr + Pt)/Pinc | 1.00035 | 0.99868 | 0.99295 | 1.00016 | 0.99894 | 0.99087 |
Diffraction Efficiency DE (%) | 68.2 | 68.7 | 68.4 | 70.2 | 70.7 | 70.4 |
Table 4
Fraction of Reflected and Transmitted Incident Power, Total Power, and Diffraction Efficiency for Gaussian Window Function
| Polarization |
---|
|
---|
TE | TE | TM | TM | TM | TM |
---|
Continuous Lens | | | | | | |
Standard Deviation σ (μm) | 25 | 12.5 | 8.33 | 25 | 12.5 | 8.33 |
Reflected Power Pr/Pinc | 0.05120 | 0.04527 | 0.04210 | 0.03659 | 0.03747 | 0.03856 |
Transmitted Power Pt/Pinc | 0.94835 | 0.95454 | 0.95781 | 0.96305 | 0.96239 | 0.96138 |
Total Power (Pr + Pt)/Pinc | 0.99955 | 0.99981 | 0.99991 | 0.99965 | 0.99986 | 0.99994 |
Diffraction Efficiency DE (%) | 64.9 | 72.4 | 60.2 | 65.8 | 73.0 | 60.5 |
8-Level Lens | | | | | | |
Standard Deviation σ (μm) | 25 | 12.5 | 8.33 | 25 | 12.5 | 8.33 |
Reflected Power Pr/Pinc | 0.07210 | 0.05990 | 0.05216 | 0.04648 | 0.04279 | 0.04131 |
Transmitted Power Pt/Pinc | 0.92853 | 0.94068 | 0.94821 | 0.95366 | 0.95741 | 0.95882 |
Total Power (Pr + Pt)/Pinc | 1.00063 | 1.00058 | 1.00037 | 1.00014 | 1.00020 | 1.00012 |
Diffraction Efficiency DE (%) | 60.7 | 67.9 | 56.9 | 62.3 | 69.4 | 57.8 |
Table 5
Focal Position and Diffraction Efficiency of Continuous Lens for TE and TM Polarizations
Incident Angle θ (deg) | Estimated | BEM | Diffract Efficiencyion DE (%) |
---|
|
|
|
---|
x (μm) | f =−y (μm) | x (μm) | f =−y (μm) | TE | TM |
---|
0 | 0.0 | 100 | — | — | 73.2 | 74.4 |
0 | — | — | 0.0 | 97 | 74.3 | 75.3 |
2.5 | 6.5 | 100 | — | — | 71.0 | 72.0 |
2.5 | — | — | 6.5 | 96 | 73.9 | 74.7 |
5 | 13.1 | 100 | — | — | 64.8 | 65.7 |
5 | — | — | 12.8 | 94 | 72.7 | 73.7 |
10 | 26.1 | 100 | — | — | 32.7 | 32.2 |
10 | — | — | 24.3 | 87 | 68.2 | 69.7 |
Table 6
Change of Solution with Number of Quadratic Elements
| Polarization |
---|
|
---|
TE | TE | TE | TM | TM | TM |
---|
Continuous Lens | | | | | | |
Number of Elements | 294 | 444 | 582 | 294 | 444 | 582 |
Reflected Power P/Pinc | 0.05731 | 0.05821 | 0.05846 | 0.03448 | 0.03459 | 0.03466 |
Transmitted Power Pt/Pinc | 0.93296 | 0.93384 | 0.93389 | 0.95751 | 0.95921 | 0.95956 |
Total Power (Pr + Pt)/Pinc | 0.99027 | 0.99205 | 0.99236 | 0.99199 | 0.99380 | 0.99422 |
Diffraction Efficiency DE (%) | 73.2 | 73.2 | 73.1 | 74.4 | 74.4 | 74.3 |
8-Level Lens | | | | | | |
Number of Elements | 310 | 456 | 594 | 310 | 456 | 594 |
Reflected Power Pr/Pinc | 0.09127 | 0.08692 | 0.08521 | 0.05063 | 0.04978 | 0.04914 |
Transmitted Power Pt/Pinc | 0.90919 | 0.90603 | 0.90109 | 0.93942 | 0.94109 | 0.93718 |
Total Power (Pr + Pt)/Pinc | 1.00046 | 0.99295 | 0.98630 | 0.99005 | 0.99087 | 0.98633 |
Diffraction Efficiency DE (%) | 68.5 | 68.4 | 68.0 | 70.2 | 70.4 | 70.0 |
Table 7
Change of Solution with Calculational Radius R for Continuous Lens
TE Polarization | Calculation Radius R (μm) |
---|
|
---|
30 | 40 | 50 | 60 |
---|
Number of Elements | 354 | 444 | 534 | 624 |
Reflected Power Pr/Pinc | 0.05815 | 0.05821 | 0.05821 | 0.05821 |
Transmitted Power Pt/Pinc | 0.93382 | 0.93384 | 0.93385 | 0.93385 |
Total Power (Pr + Pt)/Pinc | 0.99197 | 0.99205 | 0.99206 | 0.99205 |
Diffraction Efficiency DE (%) | 73.2 | 73.2 | 73.2 | 73.2 |
TM Polarization | | | | |
Number of Elements | 354 | 444 | 534 | 624 |
Reflected Power Pr/Pinc | 0.03436 | 0.03459 | 0.03461 | 0.03461 |
Transmitted Power Pt/Pinc | 0.95926 | 0.95921 | 0.95921 | 0.95921 |
Total Power (Pr + Pt)/Pinc | 0.99362 | 0.99380 | 0.99382 | 0.99382 |
Diffraction Efficiency DE (%) | 74.4 | 74.4 | 74.4 | 74.4 |