Effective Index¶

First Order Effective Index¶

Effective index of the fundamental mode of a waveguide can be accessed by using neff function of effective_index module. The function takes the following arguments:

• wavelength: Wavelength of the light in the waveguide, in microns. A list of wavelengths can also be passed. Wavelength range is from 1.2 to 1.7 microns, it will return 0 for wavelengths out of range.
• width: Width of the waveguide, in microns. A list of widths can also be passed. Width range is from 0.24 to 0.7 microns, it will return 0 for widths out of range.

In [ ]:

from siphotonics.effective_index import neff

neff(width=0.5, wavelength=1.55)

from siphotonics.effective_index import neff neff(width=0.5, wavelength=1.55)

Effective Index of a Waveguide at multiple wavelengths and widths can be calculated by passing a list of wavelengths or widths. Type of the list should be a DeviceArray from Jax. There are three ways to make neff function work with multiple wavelengths or widths:

• Pass a DeviceArray of wavelengths and a width value as arguments to the function to get effective index with respect to wavelengths for a fixed width value.

In [ ]:

import jax.numpy as jnp

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

import jax.numpy as jnp neff_list = neff(width=jnp.linspace(0.4, 0.5, 5), wavelength=1.55) print(neff_list)

• Pass a DeviceArray of widths and a wavelength value as arguments to the function to get effective index with respect to widths for a fixed wavelength value.

In [ ]:

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

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

• Pass a DeviceArray of widths and wavelengths as arguments to the function to get effective index for pairs of widths and wavelengths. The function will return a 1D array of effective indices for each pair of width and wavelength. Note that the length of wavelengths and widths should be same since the function will return a 1D array of effective indices by pairing the elements of the two lists.

In [ ]:

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

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

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.
• 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 [ ]:

from siphotonics.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 siphotonics.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)

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 [ ]:

from siphotonics.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 siphotonics.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)

---

Last update: 2022-12-16
Created: 2022-10-19