8.17. Objects with a variable refractive index

8.17.1. Sphere

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

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

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

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.cylinder(
    r0=(0, 100), radius=(pn["radius"], pn["radius"]), refractive_index=1.0, angle=0
)
t0.cylinder(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)

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

t0.BPM(verbose=False)

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

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

8.17.2. Grin Lens

x0 = np.linspace(-1000 * um, 1000 * um, 1024 * 2)
z0 = np.linspace(0 * um, 14500 * um, 1024 * 2)
wavelength = 0.85 * um

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)

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.square(
    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))

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

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

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

u1 = t0.final_field()

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

8.17.3. Optical Fiber

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

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

8.17.3.1. Aligned beam input

Beam definition

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

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

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.square(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))

Propagation and representation

t0.BPM(verbose=False)

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