31 January 2023
Lieven Penninck, Bavo Robben and Peter Muys
SPIE Photonics West, San Fransico, USA
Lieven Penninck
Dispersion engineered hybrid
meta-surface design for highly
compact optical systems
Nano-scale design
Component design
System Integration
Planopsim’s mission
Planopsim supplies R&D tools to
engineers &scientists that allow to
unlock the maximum benefit of flat
optics in auser-friendly way.
PlanOpSim
❖Computer Aided Design software for Planar
Optics & metasurfaces
⮚All-in-one design workflow
❖Design service for metasurfaces and
photonics
⮚In-house and 3dparty tools
Why use meta-surfaces?
Miniaturization Simplification Functionalization
Invention
Why hybrid design
❖Strengths of meta-lenses
⮚Wavefront control
⮚Thin and flat
⮚Multi-functionality
❖Limitations of (current) meta-lenses
⮚Meta-surfaces size is still limited (40-80mm largest)
⮚Efficiency < refractive lens
⮚Chromatic focal length shift ~f*λ= cst
❖Mitigation strategies
⮚Hybrid design
⮚Dispersion engineering
⮚Combination of 2
40mm diameter metalens
Focal shift of single
wavelength metalens
Limits of dispersion engineering
❖Maximum dispersion in dielectric meta-
atom
❖Bandwidth, size and function are connected
*F. Presutti and F. Monticone, "Focusing on Bandwidth:
Achromatic Metalens Limits," Optica 7, (2020).)
Application parameters
⮚Bandwidth
⮚Diameter
⮚Spatial frequency, NA
Literature devices within bounds of theoretical formula*
Design parameters: ∆Φ
⮚Materials: index contrast
⮚Structure: Height + aspect ratio
⮚Complexity: multi-layers
1. Library building
•Structure library
•Extract
dispersion
3. Component Design
•Phase offset
•Target matching
•Mask generation
Step by step hybrid design
4. Analysis
•Chromatic focal
shift
•Efficiency & PSF
Workflow for hybrid design
2. System model
•Ray tracing
•Hybrid Design
❖Ideal target application
➢Narrow spectrum
➢Small diameters
➢High index contrast
➢Low NA / high F#
❖Which platforms have highest
potential for dispersion
engineered design?
➢IR: Si, Ge
➢Visible: TiO2, SiN, GaN
➢Height assumed = λ
Dispersion engineering size limit for different applications
Promising configurations
Maximum Radius (µm)
f#(-)
Example 1: fiber coupler
❖Example fiber to fiber coupling
➢Multimode fiber 50µm
➢NA : 0,4
➢Spectrum: 1530 –1625nm (C+L band)
❖Goal of example:
➢Design a metalens fiber coupler
➢Minimize coupling loss over spectrum using dispersion engineering
➢Minimize system volume
Data from (NA 0,2 , wl 850nm):
https://www.ieee802.org/3/OMEGA/public/12_may_2020/plinio_OMEGA_01_120
520_EBOandBCFeasibility.pdf
❖Ray tracing model set up:
➢Reference: aspheric lens coupler
➢Design candidates
➢All surfaces AR coated
❖Meta-surfaces:
➢Wavelength specific phase profiles
➢Phase dispersion limit enforced per metasurface
❖All systems separately optimized:
➢Wavelengths: 1530, 1555, 1625nm
Phase profile determination
Hybrid
Dual
Reference
BK7 asphere
spheric
Meta-surface
Meta-surface Meta-surface
Intensity at 2nd fiber
50µm
Dispersion extraction
❖Meta-atom simulation using PlanOpSim MetaCell
(RCWA)
❖Extensive parameter search
❖Critieria: avg. Transmission, phase coverage, phase
dispersion coverage
Structures in library
Si
Air
Phase vs. wavelength
Extracted dispersion
Example calculation for 1 structure
Parameter
Value
P
800nm
Height
1650nm
Spectrum
1530
-1625nm
Incidence
0
°
Polarization
TE
Substrate
SiO
2
Library 24-255°= ΔΦ= 0,641 * 2 π
Dispersion library
❖System optimization with restricted dispersion engineering: ΔΦ= 24-255°
Φ@ 1555nm(°)
ΔΦ in spectrum(°)
T(-)
ΔΦ in lens(2π)
x(µm)
25k structures
1 dot = 1 structure
❖The system has been reduced in
volume by factor 31
❖Potential coupling loss reduced
26%
Case
Avg
. Coupling
loss
Diameter
System
length
Volume
Asphere
-
0,57dB
1,2 mm
7,6 mm
34,4 mm
3
Spheric
+ metalens
-
0,45dB
1,8mm
8,9 mm
90 mm
3
2 metalens (single wavelength)
-
0,79dB
0,43mm
1,96mm
1,1 mm
3
2 metalens (
dispersion engineered)
-
0,42dB
0,43mm
1,96mm
1,1 mm
3
1530nm
1625nm
Single wavelength metalenses Dispersion engineered
Ray tracing outcome
87% coupling
73% coupling
91% coupling
91% coupling
❖Phase fronts from ray tracing
❖Meta-cell from library
❖Offset application
⮚Offset per wavelength
⮚Shifts required ΔΦ(x) into available
range for all positions
Metalens definition
Φ@ 1555nm(°)
ΔΦ in spectrum(°)
Free design
parameter
Target per wavelength
❖Phase error low (<20°) for all 3 design
wavelengths in both metalenses
❖Structure usage across available dispersion
range
❖Further improvements require:
⮚Denser population of library
⮚Increased transmission across spectrum
Metalens generated
Metalens 2 phase profile
Metalens 2 phase error
x(µm)
λ(µm)
(°)
Example 2: NIR imager
❖Use in sensing application: LIDAR, facial
recognition …
❖Dot pattern generation emitter + receiver
❖Imaging system
❖Specifications
Quantity
Specification
Field of view
HFOV 30
°
Imaging performance
MTF >70% @100lp/mm
Diffraction
limited
Telecentric
CRA <3
°
Back Focal Length
5mm
Design Wavelength
920
-960nm
Numerical aperture
0,276
F
-number
1,74
Image Size
6,4x4mm
Distortion
<10%
Dispersion extraction
❖Critieria: avg. Transmission, phase coverage,
phase dispersion coverage
❖Meta-atom simulation using PlanOpSim
MetaCell (RCWA)
Structures in library
Si
Air
Parameter
Value
P
450nm
Height
1300nm
Spectrum
920
-960nm
Incidence
0
°
Polarization
TE
Substrate
SiO
2
11k structures
1 dot = 1 structure
Φ@ 940nm(°)
ΔΦ in spectrum(°)
ΔΦ= 0,708 * 2 π
System design
❖Dispersion contrained optical system
Quantity
Specification
Hybrid
2 MOE + 2 Spherical
Field of view
HFOV 30
°
30
°
Imaging
performance
MTF >70% @100lp/mm
Diffraction
limited
0
°
5
°
10
°
15
°
72,6%
71,3%
71%
66,7%
Telecentric
CRA <3
°
0,8
°
Back Focal Length
5mm
5mm
Design Wavelength
920
-960nm
920
-960
Numerical aperture
0,276
0,276
F
-number
1,74
1,7474
Image Size
6,4x4mm
3,2 (
lateral colour)
Distortion
<10%
1,5%
Total volume
1311,6 mm³
MTF @940nm
MTF @920nm
MTF @960nm
Optical performance
MOE 1
MOE 2
Target error MOE1
❖Target well reproduced in active area
❖Corners exceed dispersion range -> poor target
reproduction
❖RMS Waverfront aberration <21°(= λ/17)
Phase error vs. wavelength
Target vs. Meta-surface phase
Target error MOE2
❖Corners exceed dispersion range -> poor
target reproduction
❖RMS Waverfront aberration <22°(= λ/16)
❖Transmission 49-78%
Phase error vs. wavelength
Target vs. Meta-surface phase
❖Wavefront phase for nominal and aberrated cases
❖Overall wavefront shape remains the same
❖Aberrated wavefront -> perturbation on ideal wavefront
⮚Focal distance remains the same
⮚Spot width remains the same
⮚Loss of efficiency to scattering and higher diffraction orders
What effects do errors have?
Phase error
(RMS)
Amplitude
error (RMS)
16,2
°
0,19
34,2
°
0,23
68,5
°
0,35
Intensity
❖Meta-surfaces alone limited by storng chromatic focal length shift
❖Hybrid meta-surface systems allow to combine advantage of classical and meta-
optics
➢Balance short comings of each system
➢Design incorporates time-bandwidth limits
❖Nano-to-Macro workflow for hybrid meta-optics
➢Fiber optics: small, lowloss broadband fiber coupler
➢NIR imaging: compact design for 920-960nm
Summary
