Effective Index¶

Effective Index of the Fundamental Mode¶

Effective index of the fundamental mode of a waveguide can be accessed by using neff function of effective_index module. Note that for the default parameters below, this mode happens to be a TE mode. The function takes the following arguments:

• wavelength: Wavelength of the light in the waveguide, in micrometers. A list of wavelengths can also be passed. Wavelength range is from 1.2 μm to 1.7 μm; it will return 0 for wavelengths out of range.
• width: Width of the waveguide, in micrometers. A list of widths can also be passed. Width range is from 0.240 μm to 0.700 μm; it will return 0 for widths out of range.

In [1]:

from sipkit.effective_index import neff
import jax.numpy as jnp

neff(width=0.5, wavelength=1.55)

from sipkit.effective_index import neff import jax.numpy as jnp neff(width=0.5, wavelength=1.55)

WARNING:jax._src.lib.xla_bridge:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)

Out[1]:

DeviceArray(2.44523381, dtype=float64)

Use Cases¶

• Scalar width, scalar wavelength

In [2]:

neff(width=0.5, wavelength=1.55)

neff(width=0.5, wavelength=1.55)

Out[2]:

DeviceArray(2.44523381, dtype=float64)

• Scalar width, 1D Array wavelength

In [3]:

neff(width=0.5, wavelength=jnp.linspace(1.4, 1.5, 5))

neff(width=0.5, wavelength=jnp.linspace(1.4, 1.5, 5))

Out[3]:

DeviceArray([2.6138077 , 2.58583721, 2.55782222, 2.52975709, 2.50163816],            dtype=float64)

• 1D Array width, scalar wavelength

In [4]:

neff(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55)

neff(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55)

Out[4]:

DeviceArray([2.22706193, 2.29512748, 2.35308258, 2.40263554, 2.44523381],            dtype=float64)

• 1D Array width, 1D Array wavelength

In [5]:

neff(width=jnp.linspace(0.4, 0.5, 5), wavelength=jnp.linspace(1.4, 1.5, 5))

neff(width=jnp.linspace(0.4, 0.5, 5), wavelength=jnp.linspace(1.4, 1.5, 5))

Out[5]:

DeviceArray([2.43643383, 2.45969938, 2.47767491, 2.49138915, 2.50163816],            dtype=float64)

• Scalar width, 2D Array wavelength

In [6]:

neff(width=0.45, wavelength=jnp.array([[1.4, 1.5], [1.6, 1.7]]))

neff(width=0.45, wavelength=jnp.array([[1.4, 1.5], [1.6, 1.7]]))

Out[6]:

DeviceArray([[2.53952222, 2.41551475],
             [2.2904706 , 2.16536619]], dtype=float64)

• 2D Array width, scalar wavelength

In [7]:

neff(width=jnp.array([[0.4, 0.45], [0.5, 0.55]]), wavelength=1.55)

neff(width=jnp.array([[0.4, 0.45], [0.5, 0.55]]), wavelength=1.55)

Out[7]:

DeviceArray([[2.22706193, 2.35308258],
             [2.44523381, 2.51410111]], dtype=float64)

• 2D Array width, 2D Array wavelength

In [8]:

waveguide_width = jnp.array([0.5, 0.6])
wavelength = jnp.array([1.5, 1.6, 1.7])
waveguide_width, wavelength = jnp.meshgrid(waveguide_width, wavelength)
neff(waveguide_width, wavelength)

waveguide_width = jnp.array([0.5, 0.6]) wavelength = jnp.array([1.5, 1.6, 1.7]) waveguide_width, wavelength = jnp.meshgrid(waveguide_width, wavelength) neff(waveguide_width, wavelength)

Out[8]:

DeviceArray([[2.50163816, 2.61481455],
             [2.38861872, 2.5186588 ],
             [2.27496007, 2.42226799]], dtype=float64)

Effective Index of Higher Order Modes¶

Effective Index of first 5 modes in a waveguide can be accessed by using the following functions of effective_index module:

• neff_te0: Effective index of TE0 mode. (Note that currently this is the same as neff, due to the waveguide width boundaries used.)
• neff_tm0: Effective index of TM0 mode.
• neff_te1: Effective index of TE1 mode.
• neff_tm1: Effective index of TM0 mode.
• neff_te2: Effective index of TE3 mode.

In [9]:

from sipkit.effective_index import neff_te0, neff_tm0


neff_te0_list = neff_te0(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55)
print(neff_te0_list)

neff_tm0_list = neff_tm0(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55)
print(neff_tm0_list)

from sipkit.effective_index import neff_te0, neff_tm0 neff_te0_list = neff_te0(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55) print(neff_te0_list) neff_tm0_list = neff_tm0(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55) print(neff_tm0_list)

[2.22706193 2.29512748 2.35308258 2.40263554 2.44523381]
[1.69157614 1.71344278 1.73396505 1.75313724 1.77099004]

For the cases where the effective index of a mode does not exist, the function will return index of oxide layer as the effective index at that wavelength.

In [10]:

from sipkit.effective_index import neff_te2


neff_te2_list = neff_te2(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55)
print(neff_te2_list)

from sipkit.effective_index import neff_te2 neff_te2_list = neff_te2(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55) print(neff_te2_list)

[1.4440023 1.4440023 1.4440023 1.4440023 1.4440023]

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Last update: 2022-12-29
Created: 2022-10-19