Preliminary Design Review (PDR)Preliminary Design Review (PDR)

USP-IAG Universidade de São PauloUSP-IAG Universidade de São Paulo

18-19th June 200818-19th June 2008

Volume-Phase Holographic Gratings Volume-Phase Holographic Gratings ModellingModelling

Brazilian Tunable Filter Imager (BTFI)Brazilian Tunable Filter Imager (BTFI)

Bruno Corrêa Quint

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)

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

Marc Verhaegen’s Results

VPH Modeling

Kogelnik Model

KoMoPy’sResults

Jun 19, 2008 BTFI PDR – 18-19 June 2008

Marc Verhaegen’s Results

KoMoPy’sResults

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 θair: 24º

Incident angle within the grating θi: 15.75º

Bragg Wavelength λB: 635 nm

Spectral Resolution Rλ: 141

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

VPH Modeling

Multiple-Layer ModelVs.

Kogelnik Model

Jun 19, 2008 BTFI PDR – 18-19 June 2008

VPH Modeling

Multiple-Layer ModelVs.

Kogelnik Model

KoMoPy

Jun 19, 2008 BTFI PDR – 18-19 June 2008

VPH Modeling

Multiple-Layer ModelVs.

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 θair: 35º

Incident angle within the grating θi: 22.45º

Bragg Wavelength λB: 550 nm

Spectral Resolution Rλ: 3000

0

-1

+1

+2

0

+1

-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

VPH Modeling

Simulated Modes

Jun 19, 2008 BTFI PDR – 18-19 June 2008

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

TX-HR Grating wl500 a35 R1200   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

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

TX-MR Grating wl500 a35 R340   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

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

TX-HR Grating wl450 a35 R1300    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

 

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

RX-HR Grating wl550 a35 R3300   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

 

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

RX-HR Grating wl550 a35 R1580   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

 

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

RX-HR Grating wl500 a35 R3450   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

 

VPH Modeling

Modeled Gratings – KoMoPy 2.4.0

TX-LR Grating wl550 a35 R10   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