7.13. Objects with a variable refraction index

7.13.1. Sphere

[1]:

from diffractio import degrees, mm, plt, sp, um, np
from diffractio.scalar_masks_X import Scalar_mask_X
from diffractio.scalar_masks_XZ import Scalar_mask_XZ
from diffractio.scalar_sources_X import Scalar_source_X

[2]:

x0 = np.linspace(-120 * um, 120 * um, 1024 * 2)
z0 = np.linspace(0 * um, 250 * um, 1024 * 2)
wavelength = 1.5 * um

[3]:

w0 = 10 * um

u0 = Scalar_source_X(x=x0, wavelength=wavelength)
u0.gauss_beam(A=1, x0=35 * um, z0=-250 * um, w0=w0, theta=0. * degrees)
u1 = Scalar_source_X(x=x0, wavelength=wavelength)
u1.gauss_beam(A=1, x0=0 * um, z0=-250 * um, w0=w0, theta=0. * degrees)

u2 = Scalar_source_X(x=x0, wavelength=wavelength)
u2.gauss_beam(A=1, x0=-35 * um, z0=-250 * um, w0=w0, theta=0. * degrees)

uf = u0 + u1 + u2

[4]:

t0 = Scalar_mask_XZ(x=x0, z=z0, wavelength=wavelength, n_background=1.0)
t0.incident_field(uf)

pn = dict(n_out=1.5, n_center=4, cx=0, cz=125, radius=100)

# ref_index = "{p[n_out]}".format(p=pn)
center = (pn['cx'], pn['cz'])
radius = pn['radius']
# ref_index = '2*(((X-0)**2+(Z-300)**2)/75**2-0)'
ref_index = "{p[n_out]}+({p[n_center]}-{p[n_out]})*(1-((X-{p[cx]})**2+(Z-{p[cz]})**2)/{p[radius]}**2)".format(
    p=pn)
print("n={}".format(ref_index))

t0.sphere(r0=(0, 100),
          radius=(pn['radius'], pn['radius']),
          refractive_index=1.0,
          angle=0)
t0.sphere(r0=center,
          radius=(radius, radius),
          refractive_index=ref_index,
          angle=0)

n=1.5+(4-1.5)*(1-((X-0)**2+(Z-125)**2)/100**2)

[5]:

t0.draw_refractive_index(draw_borders=False, scale='scaled')

$../../_images/source_examples_variable_refraction_index_6_0.png$

[6]:

t0.BPM(verbose=False)

[7]:

t0.draw(kind='intensity',
        logarithm=True,
        draw_borders=True,
        min_incr=0.05,
        scale='scaled')

$../../_images/source_examples_variable_refraction_index_8_0.png$

[8]:

t0.draw(kind='phase',
        logarithm=True,
        draw_borders=True,
        min_incr=0.05,
        scale='scaled')
plt.ylim(-25, 25)
plt.xlim(200, 250)

$../../_images/source_examples_variable_refraction_index_9_0.png$

7.13.2. Grin Lens

[9]:

x0 = np.linspace(-1000 * um, 1000 * um, 1024 * 2)
z0 = np.linspace(0 * um, 14500 * um, 1024 * 2)
wavelength = .85 * um

[10]:

w0 = 500 * um
z0_beam = 200 * um

u0 = Scalar_source_X(x=x0, wavelength=wavelength)
u0.gauss_beam(A=1, x0=0 * um, z0=z0_beam, w0=w0, theta=0. * degrees)

[11]:

t0 = Scalar_mask_XZ(x=x0, z=z0, wavelength=wavelength, n_background=1.0)
t0.incident_field(u0)

pn = dict(n_out=1.5, n_center=1.8, width=1500 * um, x_fiber=0 * um)
ref_index = "{p[n_out]}+({p[n_center]}-{p[n_out]})*(np.exp(-abs(X-{p[x_fiber]})**2/{p[width]}**2))".format(
    p=pn)

print("n={}".format(ref_index))

t0.rectangle(r0=(0, 4600 * um),
             size=(1500 * um, 6075 * um),
             refractive_index=ref_index,
             angle=0 * degrees)

n=1.5+(1.8-1.5)*(np.exp(-abs(X-0.0)**2/1500.0**2))

[12]:

t0.draw_refractive_index(draw_borders=False, colorbar_kind='vertical')
plt.clim(1.5, 1.8)

$../../_images/source_examples_variable_refraction_index_14_0.png$

[13]:

t0.BPM(verbose=False)
t0.draw(kind='intensity', logarithm=True, draw_borders=True, min_incr=0.05)

$../../_images/source_examples_variable_refraction_index_15_0.png$

Now, let us see the phase of the final field, which is quite plane at the center.

[14]:

u1 = t0.final_field()

[15]:

phase = np.unwrap(np.angle(u1.u))
phase = phase - phase.min()

7.13.3. Optical Fiber

In this example, we see how a optical fiber can be modelled using diffractio.scalar_mask_xy. First, we define a rectangle as a shape, and after, we provide a refraction index with a cuadratic shape.

[17]:

x0 = np.linspace(-15 * um, 15 * um, 1024)
z0 = np.linspace(0 * um, 700 * um, 4096)
wavelength = 0.5 * um

7.13.3.1. Aligned beam input

Beam definition

[18]:

w0 = 2 * um
z0_beam = 25 * um
aligment = 0 * um

[19]:

u0 = Scalar_source_X(x=x0, wavelength=wavelength)
u0.gauss_beam(A=1, x0=aligment, z0=50 * um, w0=2 * um, theta=0. * degrees)

Fiber definition

[20]:

t0 = Scalar_mask_XZ(x=x0, z=z0, wavelength=wavelength, n_background=1.0)
t0.incident_field(u0)

pn = dict(n_out=1.48, n_center=1.5, width=2 * um, x_fiber=0 * um)
# ref_index = 'nexp(-(x-x0)**2/w0**2)'
ref_index = "{p[n_out]}+({p[n_center]}-{p[n_out]})*(np.exp(-(X-{p[x_fiber]})**2/{p[width]}**2))".format(
    p=pn)

print("n={}".format(ref_index))

t0.rectangle(r0=(0, 300 * um),
             size=(20 * um, 500 * um),
             refractive_index=ref_index)

t0.draw_refractive_index(draw_borders=False, scale='')

n=1.48+(1.5-1.48)*(np.exp(-(X-0.0)**2/2.0**2))

$../../_images/source_examples_variable_refraction_index_26_1.png$

Propagation and representation

[21]:

t0.BPM(verbose=False)

[22]:

t0.draw(kind='intensity', logarithm=False, draw_borders=True, min_incr=0.05)

$../../_images/source_examples_variable_refraction_index_29_0.png$