1. Preliminary Design Review (PDR)‏ USP-IAG Universidade de São Paulo 18-19th June 2008 Volume-Phase Holographic Gratings Modelling Brazilian Tunable Filter Imager (BTFI)‏ Bruno Corrêa Quint

2. Jun 19, 2008 BTFI PDR – 18-19 June 2008 VPH Modeling Required modes Operating Modes: Reflection Mode (RX)‏ Transmission Mode (TX)‏ Available materials: Dichromate gelatin (DCG)‏ High refractive index modulation Thin films Low spectral resolution (LR)‏ Doped glass (D-G)‏ Low refractive index modulation Thick films High spectral resolution (HR)‏

3. VPH Modeling Kogelnik Model Reference Wave Signal Wave Main caracteristics Two coupled waves Two coupled equations Second order derivatives ignored It works only for D-G gratings Jun 19, 2008 BTFI PDR – 18-19 June 2008

4. Marc Verhaegen’s Results VPH Modeling Kogelnik Model KoMoPy’s Results Jun 19, 2008 BTFI PDR – 18-19 June 2008

5. Marc Verhaegen’s Results KoMoPy’s Results VPH Modeling Kogelnik Model Jun 19, 2008 BTFI PDR – 18-19 June 2008 VPG parameters: Grating period Λ: 780 nm Grating thickness D: 0.3 mm Refractive index modulation Δn: 0.00125 Incident angle in the air θ air : 24º Incident angle within the grating θ i : 15.75º Bragg Wavelength λ B : 635 nm Spectral Resolution R λ : 141

6. VPH Modeling Multiple-Layer Model Main caracteristics OpenFilters Big number of layers Modulated refractive index Very thin layers Fresnell reflectivity Slow calculation Closed black box Only for reflection mode Jun 19, 2008 BTFI PDR – 18-19 June 2008

7. VPH Modeling Multiple-Layer Model Vs. Kogelnik Model Jun 19, 2008 BTFI PDR – 18-19 June 2008

8. VPH Modeling Multiple-Layer Model Vs. Kogelnik Model KoMoPy Jun 19, 2008 BTFI PDR – 18-19 June 2008

9. VPH Modeling Multiple-Layer Model Vs. Kogelnik Model Jun 19, 2008 BTFI PDR – 18-19 June 2008 VPG parameters: Grating period Λ: 198 nm Grating thickness D: 1 mm Refractive index modulation Δn: 0.00035 Incident angle in the air θ air : 35º Incident angle within the grating θ i : 22.45º Bragg Wavelength λ B : 550 nm Spectral Resolution R λ : 3000

10. 0 +1 +2 0 +1 -2 Incident Wave Backward – Diffracted Waves Forward – Diffracted Waves VPH Modeling Rigorous Coupled-Wave Analysis Main characteristics N coupled waves 2N coupled equations Second order derivatives considered For DCG or D-G S polarization (coupled constant?)‏ Jun 19, 2008 BTFI PDR – 18-19 June 2008

11. VPH Modeling Simulated Modes Jun 19, 2008 BTFI PDR – 18-19 June 2008

12. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 TX-HR Gratingwl500a35R1200 Grating #1 Grating thickness D: 1 mm Incident angle in the air θ: 35º Grating period Λ: 436 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.00025 Bragg Wavelength: 500 nm Slant angle φ: 90º Frequency lines: 2294 lines/mm Efficiency for unpolarized light η: 92.80% Spectral resolution for unpolarized light R:1168 Efficiency for S-Polarized light S-η: 98.38% Spectral resolution for S-Polarized light S-R:1205 Efficiency for P-Polarized light P-η; 87.21% Spectral resoltution for P-Polarized light P-R:1229 Jun 19, 2008 BTFI PDR – 18-19 June 2008

13. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 TX-MR Gratingwl500a35R340 Grating #2 Grating thickness D: 0.3 mm Incident angle in the air θ: 35º Grating period Λ: 436 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.0007 Bragg Wavelength: 500 nm Slant angle φ: 90º Frequency lines: 2294 lines/mm Efficiency for unpolarized light η: 84.90% Spectral resolution for unpolarized light R:341 Efficiency for S-Polarized light S-η: 97.91% Spectral resolution for S-Polarized light S-R:347 Efficiency for P-Polarized light P-η; 71.89% Spectral resoltution for P-Polarized light P-R:438 Jun 19, 2008 BTFI PDR – 18-19 June 2008

14. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 TX-HR Gratingwl450a35R1300 Grating #3 Grating thickness D: 1.0 mm Incident angle in the air θ: 35º Grating period Λ: 392 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.00025 Bragg Wavelength: 450 nm Slant angle φ: 90º Frequency lines: 2551 lines/mm Efficiency for unpolarized light η: 92.58% Spectral resolution for unpolarized light R:1326 Efficiency for S-Polarized light S-η: 90.28% Spectral resolution for S-Polarized light S-R:1392 Efficiency for P-Polarized light P-η; 94.89% Spectral resoltution for P-Polarized light P-R:1225 Jun 19, 2008 BTFI PDR – 18-19 June 2008

15. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 RX-HR Gratingwl550a35R3300 Grating #4 Grating thickness D: 1.0 mm Incident angle in the air θ: 35º Grating period Λ: 198 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.0003 Bragg Wavelength: 550 nm Slant angle φ: 0º Frequency lines: 5050 lines/mm Efficiency for unpolarized light η: 82.75% Spectral resolution for unpolarized light R:3313 Efficiency for S-Polarized light S-η: 90.65% Spectral resolution for S-Polarized light S-R:3021 Efficiency for P-Polarized light P-η; 74.85% Spectral resoltution for P-Polarized light P-R:4166 Jun 19, 2008 BTFI PDR – 18-19 June 2008

16. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 RX-HR Gratingwl550a35R1580 Grating #5 Grating thickness D: 0.5 mm Incident angle in the air θ: 35º Grating period Λ: 198 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.00067 Bragg Wavelength: 550 nm Slant angle φ: 0º Frequency lines: 5051 lines/mm Efficiency for unpolarized light η: 86.14% Spectral resolution for unpolarized light R:1580 Efficiency for S-Polarized light S-η: 93.04% Spectral resolution for S-Polarized light S-R:1436 Efficiency for P-Polarized light P-η; 79.24% Spectral resoltution for P-Polarized light P-R:1937 Jun 19, 2008 BTFI PDR – 18-19 June 2008

17. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 RX-HR Gratingwl500a35R3450 Grating #6 Grating thickness D: 1.0 mm Incident angle in the air θ: 35º Grating period Λ: 180 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.0003 Bragg Wavelength: 500 nm Slant angle φ: 0º Frequency lines: 5556 lines/mm Efficiency for unpolarized light η: 86.77% Spectral resolution for unpolarized light R:3448 Efficiency for S-Polarized light S-η: 93.44% Spectral resolution for S-Polarized light S-R:3144 Efficiency for P-Polarized light P-η; 80.11% Spectral resoltution for P-Polarized light P-R:4202 Jun 19, 2008 BTFI PDR – 18-19 June 2008

18. VPH Modeling Modeled Gratings – KoMoPy 2.4.0 TX-LR Gratingwl550a35R10 Grating #7 Grating thickness D: 0.01 mm Incident angle in the air θ: 35º Grating period Λ: 429 nm Incident angle within the grating θ':22.44º Refractive Index Modulation Δn:0.025 Bragg Wavelength: 550 nm Slant angle φ: 0º Frequency lines: 2331 lines/mm Efficiency for unpolarized light η: 92.80% Spectral resolution for unpolarized light R:12 Efficiency for S-Polarized light S-η: 98.40% Spectral resolution for S-Polarized light S-R:12 Efficiency for P-Polarized light P-η; 92.80% Spectral resoltution for P-Polarized light P-R:12 Jun 19, 2008 BTFI PDR – 18-19 June 2008