# Presentation: 012319

## Optical vortex coronagraphwith subwavelength gratings

- AGPM & heirs
- D. Mawet1, P. Riaud1,2, A. Boccaletti2, P. Baudoz2, J. Baudrand2, O. Absil1,3, J.L. Beuzit3, P. Labeye4, J. Surdej1
- 1- IAGL, University of Liège
- 2- LESIA (Paris-Meudon Obs.)
- 3- LAOG (Grenoble)
- 4- CEA-LETI (Grenoble)

- Dimitri Mawet, Coronagraph workshop, Pasadena, September 2006

- © Technion - Israel Institute of Technology

## Subwavelength gratings

- m=0

- m=-1

- m=-2

- m=1

- m=2

- Λ

- λ

- Grating equation:

## Subwavelength gratings

- m=0

- m=-1

- m=1

- Λ

- Grating equation:

## Subwavelength gratings

- m=0

- Λ

- Grating equation:

## Subwavelength gratings

***m=0***

- Subwavelength grating are called
- zero-order gratings (ZOG) if they satisfy the
- ZOG condition:

## Subwavelength gratings

- m=0

- TE

- TM

- TE

- TM

- ∆Φ=2π/λ (nTM-nTE) h

- h

*1D subwavelength gratings are artificially birefringent.*
*By controlling the grating geometry, one can tune the *
*so-called dispersion of form birefringence **∆**n**form **(**λ**)=n**TM**-n**TE** *
*and  make the phase shift quasi-achromatic*

## RCWA

- To analyse the response of subwavelength gratings, the vectorial nature of light must be taken into account through a resolution of the Maxwell equation
*Rigorous Coupled-Wave Analysis (RCWA)*
*or Fourier Modal Method (FMM)*
*	**Fields and permittivities are decomposed in a Fourier basis and then matched at the grating layer boundaries to yield the diffraction order complex amplitudes..*

- x

- ε(x)

- TF

- x

## 4QZOG Mawet D. et al 2005, Appl. Opt.

- Anti-symmetrical implementation of 4 identical ZOG at 90°
- Unique monolithic substrate
- 	 phase distribution of FQPM
- 	for *s *and* p*
- 	 *OK in natural light*
- Final structure =
- 	integrated surface relief structure
- Optical function realized at the surface of the component (a few micron w/r to ~ mm)

## AGPMMawet et al. 2005, ApJ

- AGPM =
- 	Annular Groove Phase Mask Coronagraph.
- AGPM creates a second order *Optical Vortex* (OVC2) = phase singularity.
- Prevent the FQPM source attenuation on the quadrant transitions
- 	 very small IWA
- 	 discovery space complete
- Present a certain intrinsic achromaticity thanks to the ZOG technology

## IR preliminary numerical simulation

- IR preliminary numerical simulation

- Coronagraphic results in H, K and N bands:
**WFE of ****λ****/70 rms at 632.8 nm (e.g. state-of-the-art Virgo mirrors)**
- both polarizations
- 	(vectorial RCWA analysis)
- Residual chromatism
- Amplitude mismatches

| Filters | H 
(R=4.7) | K (R=5.5) | N (R=4.86) |
| --- | --- | --- | --- |
| Null Depth (global) | 3.5×10-5 | 1.7×10-5 | 4×10-5 |
| Contrast at 3λ/d | 2.9×10-7 | 1.4×10-7 | 3.3×10-7 |
| Grating period (C) | 525 nm | 740 nm | 3.3 μm |

- RCWA allows
- including technological
- limitations upstream

## CEA-LETI operation
Micro-electronic techniques
Silicon technology

- Micro-electronic techniques
- Silicon technology

- Manufacturing

- Silicon 8” wafer

- Stepper FOV

- ZOG geometry

## Current perspectives

- VLT-PF/SPHERE
- COAST

## COASTsim (beta version):

**  ****an example with the AGPM**

**Telescope input: **Diameter / overall transmission /  dust scattering
- 			        polarization and amplitude mismatch (Ag coating)

**Wavefront:  **one PSD before coronagraphic device  (f-1,5)  λ/100 rms (common)
- 	                 one PSD after coronagraph (f-1,5)  λ/100 rms @ 632 nm (common
- 										+ non-common TBD)

**Coronagraph:  **polarization mismatch with the AGPM coronagraph (RCWA input)
- 			   (amplitude and phase on the wavelength range  R~5)
-                                    Polychromatic Fourier simulation

**Gain:  ****	****       **gain after reference subtraction (currently ~ 10)
- 	     potential gain after ZIMPOL analysis (polarization)
- 	           	       after “SDI” analysis (spectral) 	   ~ 100

**S/N calculus: **stellar residue / zodiacal / exo-zodiacal /
- 			    stellar leakage / read-out / dark / TIS / Gain** **
-         (also stellar spectrum, planet spectrum, bandwidth )

**Stellar residue: ****@ ****λ****/d  for AGPM / CIA (simple radial function)**

- Pierre Riaud (IAGL/LESIA): riaud@astro.ulg.ac.be

## Warning: Check ...

**Telescope input: **Fresnel propagation on each mirror (increase size!)
-                                         Alignment (Zemax tolerancing)
- 			        Rotation of polarization

**Wavefront:  **Problem of high precision wavefront measurement during the
- 			telescope AIV for space mission ( T=100 K , L2 orbit )
- 			Mirror mounting (FUSE telescope WFE l/30 rms @ 632 nm !)
- 			Dust contamination

**Coronagraph:  **Check technical limitations for the ZOG technology
- 			    (the main ones are taken into account upstream via RCWA)
-                                    (Applicable whatever the coronagraphic device)
-                    		     limitation on the maximum input wavefront error (close loop)
- if we increase quality of the input wavefront, there is only a small
- gain on the speckle halo, but not on the residual stellar peak .

- Pierre Riaud (IAGL/LESIA): riaud@astro.ulg.ac.be

## Warning: Check diffraction  Σ Uc=1-ε

- Pierre Riaud (IAGL/LESIA): riaud@astro.ulg.ac.be

## Higher order masks 

- Increase the topological charge

- Geometry complexity

- E. Hasman group
- AsGa technology
- (10.6 microns)

**l****p****=4**

## Higher order masks 

- leakage growths as θm ;
- 	m being the topological
- 	charge of the mask

- Geometry complexity

- E. Hasman group
- AsGa technology
- (10.6 microns)

- AGPM
- & FQPM

- θ2

**l****p****=4**

## Higher order masks

**WFE****2**

**WFE****5**

## State-of-the-art in the visible

- R~5, eq. nulling of 1000-10000 but complexity !!!

- 200 nm

## Towards the 1010 !?

- With phase masks (FQPM, OVCm,...)
- control of the phase at the 10-4 radian level !!!
- ΔΦ=2π/λ Δn Δe  Δn Δe ~ 10-12
- 	- _case 1:_
- 	1 isotropic opt. mat.
- 	index step (OVC phase ramp)
- 	Δn ~ 1  Δe ~ 10-3 nm !!!
- 	- _case 2:_
- 	2 (or more) isotropic opt. mat.
- 	Δn <<  Δe relaxed, how much ?
- 	Find matched materials (dispersion)
- 	- _case 3:_
- 	1 anisotropic mat. (birefringent)
- 	Δn <<  Δe relaxed, how much ?
- 	Depends on microgeometry : ZOG tech.  filling factor F
- 	Δn # 1/F
- 	e # F

- relaxing Δe  photonic crystal of length e
- 	with the proper embedded
- 	geometry

- Foo et al. 2005

- Swartzlander 2006

- Chromatic

- (A)chromatic

- (A)chromatic

## Towards the 1010 !?

- Idea:
- Think vectorially and helically !!!
- Minimum efficiency of the polarization filter ?
- 1010 at 4 λ/D ?
- 	 ~ 108 total rej. / ZOG R~5 rej. ~ 100-1000 ER

- Residuals (ηTE≠ηTM ≠1; ΔΦ≠π)
- not affected by the vectorial vortex

- Left/right-handed circular
- « vortexified » light

- Left/right-handed circular
- polarization filter

- λ/4

- λ/4

- VOVC

- P

- P

## Conclusion

- OVC are attractive in terms of throughput, IWA, discovery space and simplicity of implementation (focal plane masks).
- Subwavelength gratings provide a powerful, flexible and integrated solution for manufacturing _*« achromatic » OVC*_* *_*of any order*_.
- Design necessitates upstream vectorial analysis (RCWA).
- Broadband 1010 extremely challenging (feasible?) for phase masks in general
- need some new ideas
- require R&D !!!
- Where are we ?
- 	_State-of-the-art_
- 	Hasman group: vect. vortex up to 4th order @ 10.6 micron (AsGa)
- 	Nanoopto: ZOG visible achromatic (R<5) phase shifters (equivalent rejection of 1000-10000)
- 	Our group (LESIA, ULg, LAOG, LETI):
- 		AGPM lab demonstration this year
- 		goal 5000 broadband (H/K) total nulling
- 		 10-5/10-6 at 3-4 λ/D