Building the Future of Optical Modeling and Design

Transcription

1 SIOM, Lecture Series Building the Future of Optical Modeling and Design Frank Wyrowski Friedrich-Schiller-University, Professor LightTrans GmbH, President Jena, Germany

2 Lecture 1: From Ray to Field Tracing

3 Optical Modeling Task Light distribution in source plane is given. Light distribution in target/detector plane is demanded. Light distribution is to be analyzed to allow evaluating the optical function of the system.

4 Basic Tasks in Optical Modeling Source modeling Propagation Detection

5 Basic Tasks in Optical Design Source modeling Propagation Detection Optimization of detector result

6 Basic Tasks in Optical Modeling Source modeling Propagation Detection

7 Basic Tasks in Optical Modeling? Source modeling Propagation Detection Modeling provides light field in source plane. Let s start with monochromatic/harmonic source. How do we need to describe this light field?

8 Electromagnetic Field Representation I

9 Electromagnetic Field Representation II

10 Electromagnetic Field Representation III

11 Polarization of Monochromatic Fields I

12 Polarization of Monochromatic Fields II

13 Field Tracing with VirtualLab : Experiment B.00 Gaussian Field Components (1, 20 ) Polarization dependency Donut mode Magnetic field, Data array => V

14 Field Propagation Operator Matrix I

15 Field Propagation Operator Matrix II

16 Field Propagation Operator Matrix III

17 Field Propagation Operator Matrix IV

18 Solution of Field Propagation Problem What do we know about the solution of this fundamental field propagation problem?

19 Topics in Typical Text Books I

20 Topics in Typical Text Books II

21 Topics in Typical Text Books III

22 Solutions of Field Propagation Problem Propagation Techniques FEM FDTD

23 Feasibility of Rigorous Solutions With today s PC technology: Rigorous modeling restricted to modeling volume of about V = (100 l) 3 = (100 µm) 3 A rigorous solution is very restricted in its practical feasibility!

24 Solutions of Field Propagation Problem Propagation Techniques FEM FDTD Solutions by restricting to special components/e(r)

25 Solutions of Field Propagation Problem Propagation Techniques FEM FDTD free space (SPW) plane interface (Fresnel) layers gratings (FMM) more Others? What is for example with propagation through lenses?

26 Propagation Through Lenses

27 Ray Optics = Ray Tracing Ray optics is the simplest theory of light. Light is described by rays that travel in different optical media in accordance with a set of geometrical rules. Ray optics is therefore also called geometrical optics. Is this the full truth?

28 Optical Modeling by Ray Tracing Source modeling Propagation Detection Ray Tracing Light representation: Rays Light propagation: Geometrical optics

29 Coherent Sources: Rays Limitations Rays are handled individually, that is coherence properties are not included. Wavefront must be smooth; scattered fields not included. Ray direction just depends on wavefront (phase); diffraction effects not included.

30 Rays: Example Gaussian Beams Gaussian beams have plane wavefront in its waist. All rays are parallel to z-axis. Divergence of Gaussian beam is not included.

31 Coherent Sources: Rays Source modeling of coherent sources extremely limited by ray representation of light.

32 Incoherent Sources: Rays Incoherent source modeling is reasonable by ray representation of light.

33 Source Modeling by Rays Yes: Incoherent sources No: Coherent sources No: Partially coherent sources

34 Optical Modeling by Ray Tracing Source modeling Propagation Detection What kind of detector functions can be defined on the basis of ray information?

35 Light Detection with Rays Limitations Each ray provides field information at one lateral location. Coherence properties of field are not included. Superposition (interference) of field information of different rays is not defined. Lateral interpolation of field information is restricted. Ray representation of light restricts definition of detector functions seriously!

36 Optical Modeling by Ray Tracing Source modeling Propagation Detection Propagation of light by tracing rays through the system.

37 Light Propagation by Ray Tracing: I The change of the direction of rays at any surface of the system must be well defined. That is only reasonable if surface is locally a Smooth interface => laws of reflection or refraction Grating => grating equation

38 Light Propagation by Ray Tracing: I The change of the direction of rays at any surface of the system must be well defined. That is only reasonable if surface is locally a Smooth interface => laws of reflection or refraction Grating => grating equation This limitation excludes reasonable modeling of Microstructured surfaces General diffractive optical elements (DOE) Scattering surfaces

39 Light Propagation by Ray Tracing: I The change of the direction of rays at any surface of the system must be well defined. That is only reasonable if surface is locally a Smooth interface => laws of reflection or refraction Grating => grating equation This limitation excludes reasonable modeling of Microstructured surfaces General diffractive optical elements (DOE) Scattering surfaces Ray tracing is very restricted in modeling of micro optics, diffractive optics and scattering!

40 Light Propagation by Ray Tracing: II Ray propagation through index modulated media requires rule to change ray direction locally. That is only possible for smoothly varying refractive index. This limitation excludes reasonable modeling of General index modulated media Volume gratings Volume scattering Ray tracing is very restricted in modeling of general index modulated media!

41 Light Propagation by Ray Tracing: III Systems become more miniaturized in practice. Rays are blocked at small apertures. Diffraction effects behind apertures are not included in ray tracing. Ray tracing restricted in modeling of miniaturized optical systems and micro optics.

42 Light Propagation by Ray Tracing: IV Ray propagation of convergent light into focal regions does not include diffraction and interference effects. Ray tracing does not allow propagation of light into focal regions.

43 Optical Modeling by Ray Tracing Source modeling Propagation Detection Ray tracing reveals some serious limitations for modern optical modeling and design.

44 Optical Modeling by Ray Tracing Source modeling Propagation Detection However, various of them are caused by the representation of light by rays and not by propagation with geometrical optics.

45 Advantages to Use Fields instead of Rays

46 Geometrical Optics Field Tracing Source modeling Propagation Detection Propagating a field by geometrical optics (GeOp) Light representation: Electromagnetic field Light propagation: Geometrical optics

47 Geometrical Optics Field Propagation (GeOp)

48 Geometrical Optics Field Propagation (GeOp)

49 Field Tracing with VirtualLab : Experiment.F.02b 3D view Ray tracing Field Tracing AM, IN PH E_x E_y and E_z

50 Solutions of Field Propagation Problem Propagation Techniques FEM FDTD free space (SPW) plane interface (Fresnel) layers gratings (FMM) more Others? What is for example with propagation through lenses?

51 Solutions of Field Propagation Problem Propagation Techniques FEM FDTD free space (SPW) plane interface (Fresnel) layers gratings (FMM) more lenses, etc. (GeOp)

52 Ray Optics = Ray Tracing Ray optics is the simplest theory of light. Light is described by rays that travel in different optical media in accordance with a set of geometrical rules. Ray optics is therefore also called geometrical optics. Is this the full truth? NO!

53 Solutions of Field Propagation Problem Propagation Techniques FEM FDTD free space (SPW) plane interface (Fresnel) layers gratings (FMM) more lenses, etc. (GeOp) more slight scatterer, DOE (TEA) weak variation: BPM free space: Fresnel, far field

54 Field Tracing Techniques Field Tracing Techniques FEM FDTD free space (SPW) plane interface (Fresnel) layers gratings (FMM) more lenses, etc. (GeOp) more slight scatterer, DOE (TEA) weak variation: BPM free space: Fresnel, far field

55 Principle of Field Tracing I

56 Principle of Field Tracing II

57 Principle of Field Tracing III

58 Field Tracing Diagram: Example lenses, etc. (GeOp) free space (SPW) free space: Fresnel, far field

59 Field Tracing Diagram: Example lenses, etc. (GeOp) Free space propagation is selected automatically: Single smart technique

60 Field Tracing Diagram: Example lenses, etc. (GeOp)

61 Field Tracing with VirtualLab The more field tracing techniques available the more probable you can model your systems! Requires interdisciplinay optical modeling environment: VirtualLab

62 Development of VirtualLab Field Tracing Techniques

63 Development of VirtualLab Field Tracing Techniques

64 Development of VirtualLab Field Tracing Techniques

65 Development of VirtualLab Field Tracing Techniques

66 Field Tracing in VirtualLab I

67 Field Tracing in VirtualLab II Light Path Diagram: The interdisciplinary optical modeling control panel

68 Add Missing Field Tracing Techniques Any technique can be used in the framework of field tracing. Thus VirtualLab cannot provide all. You can add missing techniques by: Option 1: You can program and integrate your own technique using C# or MATLAB. The resulting technique can be used together with all others in the VirtualLab modeling environment. Option 2: Field data interfaces to some specialized software which offers a missing technique, e.g. FDTD.

69 Add Missing Field Tracing Techniques Field Tracing Techniques Customized

70 Add Missing Field Tracing Techniques Use your MATLAB code (via dll ) Implement your technique in C# and use VirtualLab s powerful programming reference!

71 Add Missing Field Tracing Techniques Visit for more information!

72 Summary Field tracing is an interdisciplinary optical modeling approach for simulation of optical systems. It allows the combination of modeling techniques from any disciplines of optics in order to allow the propagation of elctromagnetic fields through any optical system. The representation of light by fields also overcomes the limitations in source modeling and light detection as it is known from ray optics.

73 Field Tracer VirtualLab VirtualLab is the first optics software which is based on field tracing. Thus it provides the first interdisciplinary optical modeling platform on the market.