6. Tutorials

• Algorithms
  • 1. Fast Fourier Transform (FFT)
    • 1.1. X Scheme
    • 1.2. XY Scheme
  • 2. Rayleigh-Sommerfeld (RS)
    • 2.1. X scheme
      • 2.1.1. Bad quality parameter
      • 2.1.2. Amplification of the field
    • 2.2. XZ scheme
    • 2.3. XY scheme
    • 2.4. XYZ Scheme
  • 3. Beam Propagation Method (BPM)
    • 3.1. XZ scheme
  • 4. Wave propagation Method (WPM)
    • 4.1. XZ Scheme
    • 4.2. XYZ Scheme
  • 5. Chirped Z-transform (CZT)
    • 5.1. X Scheme
      • 5.1.1. to just one data
      • 5.1.2. to field_Z
      • 5.1.3. to field_X
      • 5.1.4. to field_XZ
      • 5.1.5. to data
      • 5.1.6. to field_X
      • 5.1.7. to field_XY
      • 5.1.8. to field_Z
      • 5.1.9. to field_XZ
      • 5.1.10. to field_XYZ
    • 5.2. CZT for reducing the output size
      • 5.2.1. X scheme
      • 5.2.2. XY scheme
  • 6. Vector Fast Fourier Transform (VFFT)
    • 6.1. XY scheme
  • 7. Vector Rayleigh-Sommerfeld method (VRS)
    • 7.1. Radial polarized Gaussian beam through a circular aperture
    • 7.2. Focusing with a lens a beam with a high \(E_z\) component
  • 8. Vector Chirped Z-transform (VCZT)
    • 8.1. to value
    • 8.2. to x_field
    • 8.3. to z_field
    • 8.4. to XZ_field
    • 8.5. to XY_field
    • 8.6. to XYZ_field
  • 9. Comparison between Rayleigh-Sommerfeld (RS) and WPM Propagation Method (WPM)
  • 10. Comparison between Wave propagation Method (WPM) and Beam Propagation Method (BPM)
    • 10.1. Diferences
  • 11. Comparison between Rayleigh-Sommerfeld (RS) and Chirped Z-transform (CZT)
    • 11.1. X Scheme
    • 11.2. XZ scheme
      • 11.2.1. XY scheme
    • 11.3. Vector scheme
• 6.1. Scalar_X
  • 6.1.1. Characteristics
    • 6.1.1.1. Basic operation: add two light sources
    • 6.1.1.2. Basic operations: multiplication of masks and fields
    • 6.1.1.3. Propagation
      • 6.1.1.3.1. Near field: Rayleigh-Sommerfeld approach
      • 6.1.1.3.2. Far field: Fast Fourier transform
      • 6.1.1.3.3. Inverse propagation: IFFT
      • 6.1.1.3.4. Amplification of the field
      • 6.1.1.3.5. Reduction of the field
    • 6.1.1.4. Other operations
      • 6.1.1.4.1. Saving and loading data from instance
    • 6.1.1.5. Inserting a mask in other instance
      • 6.1.1.5.1. Inserting an array of masks in an instance
    • 6.1.1.6. Multiprocessing
    • 6.1.1.7. Modulation transfer function (MTF)
  • 6.1.2. Example of light sources
    • 6.1.2.1. Creating an instance
    • 6.1.2.2. Plane wave
    • 6.1.2.3. Gauss beam
    • 6.1.2.4. Spherical wave
    • 6.1.2.5. Several plane waves with different inclination
    • 6.1.2.6. Several gauss beams with different position
    • 6.1.2.7. Several Gauss beam with different inclination
    • 6.1.2.8. Sum of two gauss beams with different inclination: interference
  • 6.1.3. Example of masks
    • 6.1.3.1. Creating an instance
    • 6.1.3.2. Procedures to generate masks
      • 6.1.3.2.1. mask_from_function
      • 6.1.3.2.2. mask_from_array
    • 6.1.3.3. slit
    • 6.1.3.4. double_slit
    • 6.1.3.5. two levels
    • 6.1.3.6. gray scale
    • 6.1.3.7. prism
    • 6.1.3.8. Fresnel biprism
    • 6.1.3.9. Fresnel biprism from material properties n and h
    • 6.1.3.10. standard lens
    • 6.1.3.11. Fresnel lens: amplitude and phase
    • 6.1.3.12. rough surface
    • 6.1.3.13. Dust particles with different sizas
    • 6.1.3.14. dust particles
    • 6.1.3.15. bit structure
    • 6.1.3.16. Gratings
      • 6.1.3.16.1. sine grating
      • 6.1.3.16.2. Ronchi grating
      • 6.1.3.16.3. binary grating: amplitude and phase
      • 6.1.3.16.4. blazed grating
      • 6.1.3.16.5. chirped grating: general
      • 6.1.3.16.6. chirped grating: linear p
      • 6.1.3.16.7. chirped grating: linear q
• Scalar_Z
  • 1. Scalar field Z
    • 1.1. Definition of variables
    • 1.2. CZT algorithm
    • 1.3. Scalar z
• Scalar_XZ
  • 1. Characteristics
  • 2. Propagation and other parameters
    • 2.1. Rayleigh-Sommerfeld propagation
    • 2.2. Wave Propagation Method (WPM)
    • 2.3. Beam Propagation Method (BPM)
  • 3. Save and load masks and fields
  • 4. Surface detection of masks
  • 5. Reduction of the field
  • 6. Incident field: location
  • 7. Recovering the final field
  • 8. Beam Propagation Method: Filtering
    • 8.1. Simulation properly sampled
    • 8.2. Simulation with bad sampling
    • 8.3. Simulation with filtering
  • 9. Rotating masks and fields
  • 10. Find focus tool
  • 11. Examples of multiprocessing
    • 11.1. Rayleigh-Sommerfeld: polychromatic light
    • 11.2. Rayleigh-Sommerfeld: polychromatic light without multiprocessing
    • 11.3. BPM: polychromatic light
  • 12. Example of masks
    • 12.1. Creating an instance
    • 12.2. mask from two functions
    • 12.3. mask from surfaces defined in file
    • 12.4. mask from several surfaces
    • 12.5. Refraction index from functions
    • 12.6. xz mask from a x mask
    • 12.7. xz mask from a xy mask
    • 12.8. Variable refraction index
      • 12.8.1. z direction
      • 12.8.2. x direction
      • 12.8.3. discretize_refractive_index
    • 12.9. add_masks
    • 12.10. mask from an image
  • 13. Definite masks
    • 13.1. semi plane
    • 13.2. layer
    • 13.3. rectangle
    • 13.4. slit
    • 13.5. sphere or ellipsoid
    • 13.6. semi sphere
    • 13.7. wedge
    • 13.8. prism
    • 13.9. biprism
    • 13.10. Ronchi grating
    • 13.11. grating with substrate
    • 13.12. sine grating
    • 13.13. probe
    • 13.14. convergent plane lens
    • 13.15. convergent lens
    • 13.16. divergent plane lens
    • 13.17. divergent lens
    • 13.18. rough surface
  • 14. Drawing XZ: focal area of an apheric lens
    • 14.1. Visualizing fields using interactive tools
• Scalar_XY
  • 1. Characteristics
    • 1.1. Basic operations: add to light sources.
    • 1.2. Basic operations: multiplication of masks and fields
  • 2. Propagation
    • 2.1. Near field: Rayleigh-Sommerfeld approach
    • 2.2. Amplification of the field
    • 2.3. Reduction of the field
    • 2.4. Focus position and profiles
  • 3. Example of light sources
    • 3.1. Creating an instance
      • 3.1.1. Creating an instance
    • 3.2. plane wave
    • 3.3. Gauss beam
    • 3.4. spherical wave
    • 3.5. vortex beam
    • 3.6. Vortex beams
    • 3.7. Laguerre beam
    • 3.8. Laguerre beams
    • 3.9. Hermite_Gauss
    • 3.10. Zernike beam
    • 3.11. Zernike beams
    • 3.12. Several plane waves inclined
    • 3.13. plane waves with parameters from dictionary
    • 3.14. several parallel Gauss beams
    • 3.15. several inclined Gauss beams
    • 3.16. Interference
  • 4. Examples of masks
    • 4.1. Standard masks
      • 4.1.1. Two_levels
      • 4.1.2. Edge Series
      • 4.1.3. slit
      • 4.1.4. sinusoidal slit
      • 4.1.5. slit_series
      • 4.1.6. double_slit
      • 4.1.7. triangle
      • 4.1.8. square
      • 4.1.9. polygon
      • 4.1.10. regular polygon
      • 4.1.11. star
      • 4.1.12. circle
      • 4.1.13. super_gauss
      • 4.1.14. square_circle
      • 4.1.15. angular_aperture
      • 4.1.16. ring
      • 4.1.17. rings
      • 4.1.18. cross
      • 4.1.19. image
      • 4.1.20. gray_scale
      • 4.1.21. hiperellipse
      • 4.1.22. superformula
      • 4.1.23. lens
      • 4.1.24. Cylindrical lens
      • 4.1.25. Fresnel lens
      • 4.1.26. biprism_fresnel
      • 4.1.27. axicon
      • 4.1.28. grating_forked
      • 4.1.29. roughness
      • 4.1.30. Sine grating
      • 4.1.31. Ronchi grating
      • 4.1.32. Binary grating (amplitude + phase)
      • 4.1.33. Blazed grating
      • 4.1.34. 2D grating
      • 4.1.35. Chess grating
      • 4.1.36. Angular grating
      • 4.1.37. random circle edge
      • 4.1.38. Random ring edge
  • 5. Other procedures to generate XY masks
    • 5.1. Adding masks
    • 5.2. Substracting masks
    • 5.3. Binarization of a previous mask
    • 5.4. Widen the shape of a previous mask
    • 5.5. Mask from surface functions
    • 5.6. Insert_array_masks
    • 5.7. repeat_structure
• 6.2. Scalar_XYZ
  • 6.2.1. Characteristics
    • 6.2.1.1. save_load
    • 6.2.1.2. clear_field
    • 6.2.1.3. show_index_refraccion
    • 6.2.1.4. RS propagation of a circular aperture
    • 6.2.1.5. Rayleigh-Sommerfeld propagation of a gauss beam passing through a Grating
    • 6.2.1.6. Video from a XYZ distribution
    • 6.2.1.7. benchmark_RS_multiprocessing
  • 6.2.2. Wave Propagation Method and BPM in 3D
    • 6.2.2.1. Propagation at vacuum
    • 6.2.2.2. WPM
    • 6.2.2.3. BPM
    • 6.2.2.4. Diffraction by an sphere
      • 6.2.2.4.1. WPM
      • 6.2.2.4.2. BPM
  • 6.2.3. WPM 3D with storing intermediate data
    • 6.2.3.1. Modules
    • 6.2.3.2. Comparison with 3D
    • 6.2.3.3. Differences between both algorithms
  • 6.2.4. Sphere
  • 6.2.5. Square
  • 6.2.6. Cylinder
• Vector_XY
  • 1. Characteristics
    • 1.1. Generation of light sources
    • 1.2. Creating an instance
    • 1.3. Generating a vectorial light source
  • 2. A vector light source passes through a linear polarizer
    • 2.1. Multiplying fields by mask
    • 2.2. Propagation
  • 3. Propagation of an spiral polarized beam
  • 4. Vector Rayleigh-Sommerfeld Approximation
  • 5. Vector Fast Fourier Transform
  • 6. Example of light sources
    • 6.1. Creating an instance
    • 6.2. Procedures to convert a scalar source into a vector source
      • 6.2.1. constant polarization wave
      • 6.2.2. Azimuthal wave
      • 6.2.3. Radial wave
      • 6.2.4. Azimuthal inverse wave
      • 6.2.5. Radial inverse wave
      • 6.2.6. local polarized vector wave
      • 6.2.7. local polarized vector radial beam
      • 6.2.8. local polarized vector hybrid beam
      • 6.2.9. spiral polarized beam
    • 6.3. Generation of a structured beam with polarization
    • 6.4. Vector wave from a scalar source
    • 6.5. Gauss Polarization
    • 6.6. interferences
      • 6.6.1. Partial polarization can also be possible.
  • 7. Example of masks
    • 7.1. Creating an instance
    • 7.2. Polarization from standard elements
      • 7.2.1. Using defined polarizers
      • 7.2.2. Using py_pol module
    • 7.3. Apply a mask to the polarizer
    • 7.4. circle
    • 7.5. Complementary mask
    • 7.6. Pass to py_pol
  • 8. Drawing for vector fields
• 6.3. Other cases
  • 6.3.1. Fresnel equations
    • 6.3.1.1. Fresnel with kx
    • 6.3.1.2. Fresnel with angles \(\theta\)
      • 6.3.1.2.1. \(n_2 > n_1\)
      • 6.3.1.2.2. \(n_2 < n_1\)
      • 6.3.1.2.3. \(n_2 > n_1\)
      • 6.3.1.2.4. \(n_2 = n + i \kappa\)
      • 6.3.1.2.5. \(n_1 = n + i \kappa\)
• 6.4. Some info about drawing and videos
  • 6.4.1. Drawing in logarithm scale
    • 6.4.1.1. Intensity at the focal distance from a lens
    • 6.4.1.2. Far field diffraction pattern of a small square aperture
  • 6.4.2. Development of video using Matplotlib
    • 6.4.2.1. Generates a XZ field and show plots for each z
    • 6.4.2.2. Generates a XYZ field and show plots XY for each z
  • 6.4.3. Interactive visualization of propagation of light in Jupyter notebook
  • 6.4.4. Interactive internal to diffractio
  • 6.4.5. Images external to jupyter: %matplotlib notebook
  • 6.4.6. image in an external window
    • 6.4.6.1. simulation of a video