9.4. Focusing light with a lens: vector approach

In this example, we will use the vectorial approach to calculate the electric field of a plane wave focused by a lens. We will use the XZ scheme, where the wave propagates in the X direction and the lens is in the XZ plane. The lens is a semi-cylinder with refractive index \(n\)=2.5 for a near focusing.

[1]:

from diffractio import np
from diffractio import degrees, um

[2]:

from diffractio.vector_fields_X import Vector_field_X
from diffractio.scalar_sources_X import Scalar_source_X
from diffractio.vector_fields_XZ import Vector_field_XZ
from diffractio.scalar_masks_XZ import Scalar_mask_XZ

[3]:

from py_pol.jones_vector import Jones_vector

9.4.1. Scalar definition in XZ scheme

[4]:

size=50* um

x0 = np.linspace(-size/2 , size/2, 2048)
z0 = np.linspace(0*um, 1.25*size, 2048)
wavelength = 2*um

u0 = Scalar_source_X(x=x0, wavelength=wavelength)
u0.plane_wave()

u_xz = Scalar_mask_XZ(x=x0, z=z0, wavelength=wavelength)

u_xz.incident_field(u0)

u_xz.semi_cylinder(r0=(0*um, size/2 + 5*um),
                radius = 22*um,
                angle = 180*degrees,
                refractive_index = 2.5)


u_xz.draw_refractive_index(scale='scaled', colorbar_kind='vertical')

../../_images/source_examples_vector_lens_5_0.png

9.4.1.1. Scalar calculation in XZ scheme

[5]:

u_xz.WPM(verbose=False, has_edges=30*um)

[6]:

u_xz.draw(logarithm=1, scale='scaled',  colorbar_kind='vertical',  draw_borders=True)
u_xz.draw('phase', scale='scaled',  colorbar_kind='vertical', draw_borders=True, percentage_intensity=0.001)

../../_images/source_examples_vector_lens_8_0.png

../../_images/source_examples_vector_lens_8_1.png

9.4.1.2. Vectorial calculation in XZ scheme

[7]:

# definition of polarization
j0 = Jones_vector().general_azimuth_ellipticity(azimuth=45*degrees, ellipticity=0*degrees)
print(j0)

E =
[+0.707]
[+0.707]

[8]:

# add vector incident field and refractive index to Vector_field_XZ

EH_xz = Vector_field_XZ(x0,z0, wavelength)
EH_xz.incident_field(u0=u0, j0=j0)
EH_xz.refractive_index_from_scalarXZ(u_xz)

[9]:

# Computation
EH_xz.FP_WPM(has_edges=30*um, verbose=False)

9.4.1.3. Drawings

[10]:

EH_xz.draw('intensity', logarithm=1, draw_borders=True, scale='scaled')

<Figure size 480x360 with 0 Axes>

../../_images/source_examples_vector_lens_14_1.png

[11]:

EH_xz.draw('intensities', logarithm=1, draw_borders=True, scale='scaled')

../../_images/source_examples_vector_lens_15_0.png

[12]:

EH_xz.draw('phases', percentage_intensity=0.001, draw_borders=True, scale='scaled')

../../_images/source_examples_vector_lens_16_0.png

[13]:

EH_xz.draw('EH', scale='scaled', color='k.', ms=0.05)

../../_images/source_examples_vector_lens_17_0.png

[14]:

EH_xz.draw('poynting_vector', logarithm=1e2, scale='scaled', color='k.', ms=0.05)

../../_images/source_examples_vector_lens_18_0.png

[15]:

EH_xz.draw('irradiance', logarithm=1e2, scale='scaled')

../../_images/source_examples_vector_lens_19_0.png

[16]:

EH_xz.draw('energy_density', logarithm=1e0, scale='scaled')

../../_images/source_examples_vector_lens_20_0.png

[17]:

EH_xz.draw('poynting_vector_averaged', logarithm=1e0, scale='scaled', color='k.')

../../_images/source_examples_vector_lens_21_0.png

9.4.2. Focusing light with a lens: inverted semi-cylinder

9.4.2.1. Scalar definition in XZ scheme

[18]:

size=50* um

x0 = np.linspace(-size/2 , size/2, 2048)
z0 = np.linspace(0*um, 1.25*size, 2048)
wavelength = 2*um

u0 = Scalar_source_X(x=x0, wavelength=wavelength)
u0.plane_wave()

u_xz = Scalar_mask_XZ(x=x0, z=z0, wavelength=wavelength)

u_xz.incident_field(u0)

u_xz.semi_cylinder(r0=(0*um, 10*um),
                radius=22*um,
                angle=0*degrees,
                refractive_index=2.5)


u_xz.draw_refractive_index(scale='scaled', colorbar_kind='vertical')

../../_images/source_examples_vector_lens_24_0.png

9.4.2.2. Scalar calculation in XZ scheme

[19]:

u_xz.WPM(verbose=False, has_edges=10*um)
u_xz.draw(logarithm=False, scale='scaled',  colorbar_kind='vertical',  draw_borders=True)
u_xz.draw('phase', scale='scaled',  colorbar_kind='vertical', draw_borders=True, percentage_intensity=0.001)

../../_images/source_examples_vector_lens_26_0.png

../../_images/source_examples_vector_lens_26_1.png

9.4.2.3. Vectorial calculation in XZ scheme

[20]:

# definition of polarization
j0 = Jones_vector().general_azimuth_ellipticity(azimuth=45*degrees, ellipticity=0*degrees)
print(j0)

E =
[+0.707]
[+0.707]

[21]:

# add vector incident field and refractive index to Vector_field_XZ
EH_xz = Vector_field_XZ(x0,z0, wavelength)
EH_xz.incident_field(u0=u0, j0=j0)
EH_xz.refractive_index_from_scalarXZ(u_xz)

[22]:

# Computation
EH_xz.FP_WPM(has_edges=10*um, verbose=False)

9.4.2.4. Drawings

[23]:

EH_xz.draw('EH', logarithm=1, draw_borders=True, color='k.', scale='scaled')

../../_images/source_examples_vector_lens_32_0.png

[24]:

EH_xz.draw('phases', percentage_intensity=0.001, draw_borders=True, scale='scaled')

../../_images/source_examples_vector_lens_33_0.png

[25]:

EH_xz.draw('E2H2', draw_borders=True, scale='scaled', color='w.', ms=0.05, logarithm=1e1)

../../_images/source_examples_vector_lens_34_0.png

[34]:

EH_xz.draw('irradiance', logarithm=1e1, scale='scaled')

../../_images/source_examples_vector_lens_35_0.png

[33]:

EH_xz.draw('energy_density', logarithm=1e1, scale='scaled')

../../_images/source_examples_vector_lens_36_0.png

[30]:

EH_xz.draw('poynting_vector_averaged', logarithm=1e1, scale='scaled', color='k.')

../../_images/source_examples_vector_lens_37_0.png