Physical & Electromagnetic Optics: Diffraction Gratings

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$Diffraction Gratings Optical Engineering Prof.$ Elias N.

1 31/05/2018 Physical & Electromagnetic Optics: Diffraction Gratings Optical Engineering Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens

$Diffraction$

2 Multiple Slit Diffraction 2

3 Multiple Slit Diffraction (N=3) 3

4 Multiple Slit Diffraction (N=8) 4

5 Multiple Slit Diffraction 5

$com/books/holography-basic-principles-and-contemporary-applications/understanding-diffraction-in-volume-gratings-and-holograms Example of a reflecting surface-relief grating http://www.andor.$

6 Gratings Example of a reflecting and transmitting holographic (volume) gratings Example of a reflecting surface-relief grating 6

7 Grating Classification T. K. Gaylord, Notes on Gratings, Georgia Tech 7

8 Surface-Relief Grating Types T. K. Gaylord, Notes on Gratings, Georgia Tech 8

9 Grating Classification Transmission or Reflection Classification based on Regime T. K. Gaylord, Notes on Gratings, Georgia Tech 9

10 Diffraction by Gratings Acousto-Optics Diffractive Optics Integrated Optics Holography Optical Computing Optical Signal Processing Spectroscopy 10

11 Grating Applications Acoustic-Wave Generation Antireflection Surfaces Beam Coding, Coupling, Detection, etc. Grating Lenses Grating Scanners Head-Up Displays Holographic Optical Elements Interferometry Instrumentation Mode Conversion Multiplexing / Demultiplexing Modulation / Switching Optical Interconnections Photonic Crystal Devices Spectral Analysis 11

12 METHODS OF ANALYSIS OF GRATINGS Integral Methods Finite Elements Boundary Elements Differential Methods Exact Methods - Rigorous Coupled Wave Analysis (RCWA) - Modal Analysis Approximate Methods - Two-Wave Coupled-Wave Analysis (Kogelnik s) - Raman-Nath Analysis - Others 12

13 Differential Grating Diffraction Analysis Hierarchy Rigorous Coupled-Wave Analysis Exact Differential Formulations (no approximations to the model) Rigorous Modal Analysis i = 0,1 only Neglect Second Derivatives (neglect some boundary effects) i = 0,1 only Two-Wave Second-Order Coupled-Wave Analysis Multi-Wave Coupled-Wave Analysis Two-Wave Modal Analysis Neglect Second Derivatives (neglect some boundary effects) i = 0,1 only Small Modulation Λ >> λ Neglect Dephasing Kogelnik Two-Wave Coupled-Wave Analysis Optical Path Method Raman-Nath Analysis Incidence Along Fringes Amplitude Transmittance Analysis Small Modulation 13

14 HOLOGRAPHIC GRATING DIFFRACTION GEOMETRY Region 2 Region 1 -z Region 3 d k inc α θ y D ψ φ K x 0-th k inc Region 1 Region 2 Region 3 θ i-th x n 1 n 3 K φ θ 1i.... d Λ θ 3i 0-th z i-th 14

15 Electromagnetic Problem Formulation Maxwell Equations Constitutive Relations Medium Properties: Permittivity, Conductivity Tensors are Periodic Electromagnetic Boundary Conditions: Continuity of Tangential Electric and Magnetic Field Components 15

16 Input Region (Region I) Electromagnetic Field Expansions Rigorous Coupled Wave Analysis (RCWA) k inc Region 1 Region 2 Region 3 0-th θ i-th x n 1 n 3 K θ 1i φ.... d Λ θ 3i 0-th z i-th Output Region (Region III) 16

17 Electromagnetic Field Expansions Rigorous Coupled Wave Analysis (RCWA) Grating Region (Region II) Complex Permittivity Tensor Expansions (Region II) 17

18 Floquet Condition 18

19 Grating Equation T. K. Gaylord, Notes on Gratings, Georgia Tech 19

$Grating Equation Red laser beam split by a diffraction grating.$ $Light transmission through a diffraction grating occurs along discrete directions, called diffraction orders.$

20 Grating Equation Red laser beam split by a diffraction grating. Transmission diffraction gratings consist of many thin lines of either absorptive material or thin grooves on an otherwise transparent substrate. Light transmission through a diffraction grating occurs along discrete directions, called diffraction orders. Here a diode laser beam (635 nm) is split into three diffraction orders (+1, 0, -1). This grating's groove density is 500 lines/mm. 20

21 Rigorous Coupled Wave Analysis (RCWA) Numerical Implementation Truncation to Arbitrary Number of Diffraction Orders: M =2m+1 Grating Region Equations Standard Eigenvector/Eigenvalue Analysis Boundary Conditions: Input and Output Regions Boundaries 21

22 Rigorous Coupled Wave Analysis (RCWA) Numerical Implementation System of Linear Equations (10M x 10M) 22

23 Rigorous Coupled Wave Analysis (RCWA) Surface-Relief Grating T. K. Gaylord, Notes on Gratings, Georgia Tech 23

24 Rigorous Coupled Wave Analysis (RCWA) Surface-Relief Grating 24

$Incident Laser Beam Diffracted Laser Beam Direction of Rotation Motor Focusing Lens Disk Diffraction Grating$

25 Gratings Applications Examples DIFFRACTIVE PRINTER SCANNER Linear Scan Uniform Intensity Image Plane Motion Incident Laser Beam Diffracted Laser Beam Direction of Rotation Motor Focusing Lens Disk Diffraction Grating 25

26 Grating Applications in Integrated Optics From Optical Integrated Circuits, Nishihara, Haruna, and Suhara, McGraw-Hill

Diffraction Gratings as Anti Reflective Coatings Noah Gilbert. University of Arizona ngilbert .arizona.edu Phone: (520)

$Diffraction Gratings as Anti Reflective Coatings Noah Gilbert. University of Arizona ngilbert .arizona.edu Phone: (520)$ Diffraction Gratings as Anti Reflective Coatings Noah Gilbert University of Arizona Email: ngilbertemail.arizona.edu Phone: (520)304 4864 Abstract: Diffraction gratings with sub wavelength spatial frequencies