Tidy3D mode solver

Tidy3D mode solver#

Tidy3D includes an open-source FDFD mode solver for simulating waveguide modes.

Waveguides#

Guided electromagnetic modes are those with an effective index larger than that of the waveguide cladding.

In the example below, we have a silicon waveguide (n = 3.4) surrounded by a SiO₂ cladding (n = 1.44). For a waveguide with dimensions of 220 nm in height and 450 nm in width, the effective index is calculated to be 2.466.

import gdsfactory as gf
import gplugins.tidy3d as gt
import matplotlib.pyplot as plt
import numpy as np
from gdsfactory.generic_tech import get_generic_pdk

gf.config.rich_output()
PDK = get_generic_pdk()
PDK.activate()

nm = 1e-3

strip = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=0.5,
    core_thickness=0.22,
    slab_thickness=0.0,
    core_material="si",
    clad_material="sio2",
)
strip.plot_index()



<matplotlib.collections.QuadMesh object at 0x7effefaa7b90>







../_images/3ecca40ccc2ffd4b6370b3027f95c673b58598c6b6989bafa65137ed6f392b70.png









strip.plot_grid()











../_images/45bed9b85622ab57ff22b7d6318e4d2deaeca9c8409026a1579a0ac6426f4b55.png









strip.plot_field(field_name="Ex", mode_index=0)  # TE











<matplotlib.collections.QuadMesh object at 0x7effed7d9e50>







../_images/ad46e3ea51c9bff85aa12a31209a652eaa7c3ddb447b5c7f20b70d6181b57630.png









strip.plot_field(field_name="Ex", mode_index=0, value="dB")  # TE











<matplotlib.collections.QuadMesh object at 0x7effed689990>







../_images/f74137dac1f39503fdd176e90e0e312f0d4a4f6f5951cf2330ab6eacee32d747.png









strip.plot_field(field_name="Ey", mode_index=1)  # TM











<matplotlib.collections.QuadMesh object at 0x7effed549f50>







../_images/7ab6dd8a992e5702cacec6ab822d825a42265ce5775734e0d126f579c855146d.png









strip.n_eff











array([2.51134734+4.42777628e-05j, 1.86463643+2.09422901e-04j])













rib = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=0.5,
    core_thickness=0.22,
    slab_thickness=0.15,
    core_material="si",
    clad_material="sio2",
)
rib.plot_index()
rib.n_eff











array([2.67427418+3.10179974e-05j, 2.50854926+4.47861069e-05j])







../_images/1a1f2057e6cfae6e9bc6ebb2338cba4d68ec920c24f56f90b2273ee612abbe6c.png









rib.plot_field(field_name="Ex", mode_index=0)  # TE











<matplotlib.collections.QuadMesh object at 0x7effed4d1f10>







../_images/4a2e16b79f36c665ca60d3e6aceaff88f4a69756962778586bb4a00e34fba10f.png









nitride = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=1.0,
    core_thickness=400 * nm,
    slab_thickness=0.0,
    core_material="sin",
    clad_material="sio2",
)
nitride.plot_index()
nitride.n_eff











array([1.64461788+8.05914279e-05j, 1.57796343+1.42713228e-04j])







../_images/cc244328d9c5c0fca517db939161ee0f9f58cb1c69551c9776c4022321fa4ebc.png









nitride.plot_field(field_name="Ex", mode_index=0)  # TE











<matplotlib.collections.QuadMesh object at 0x7effed3fe4d0>







../_images/c4b847dd3b9da375d4d0cf7232f0fa309719ea2d7171dad58b0c5fa510e2440c.png









Sweep width#


You can sweep the waveguide width and compute the modes.


By increasing the waveguide width, the waveguide supports many more TE and TM modes. Where TE modes have a dominant Ex field and TM modes have larger Ey fields.


Notice that waveguides wider than 0.450 um support more than one TE mode. Therefore the maximum width for single mode operation is 0.450 um.






strip = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=1.0,
    slab_thickness=0.0,
    core_material="si",
    clad_material="sio2",
    core_thickness=220 * nm,
    num_modes=4,
)
w = np.linspace(400 * nm, 1000 * nm, 7)
n_eff = gt.modes.sweep_n_eff(strip, core_width=w)
fraction_te = gt.modes.sweep_fraction_te(strip, core_width=w)

for i in range(4):
    plt.plot(w, n_eff.sel(mode_index=i).real, c="k")
    plt.scatter(
        w, n_eff.sel(mode_index=i).real, c=fraction_te.sel(mode_index=i), vmin=0, vmax=1
    )
plt.axhline(y=1.44, color="k", ls="--")
plt.colorbar().set_label("TE fraction")
plt.xlabel("Width of waveguide µm")
plt.ylabel("Effective refractive index")
plt.title("Effective index sweep")











Text(0.5, 1.0, 'Effective index sweep')







../_images/18ea2c314a595e4b474ad2cb2a6d972481c0330389c9aced0e229916204e9436.png





Exercises


    

  • What is the maximum width to support a single TE mode at 1310 nm?
    • 

  • For a Silicon Nitride (n=2) 400nm thick waveguide surrounded by SiO2 (n=1.44), what is the maximum width to support a single TE mode at 1550 nm?
    • 

  • For two 500x220nm Silicon waveguides surrounded by SiO2, what is the coupling length (100% coupling) for 200 nm gap?
    • 







Group index#


You can also compute the group index for a waveguide.






nm = 1e-3

strip = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=500 * nm,
    slab_thickness=0.0,
    core_material="si",
    clad_material="sio2",
    core_thickness=220 * nm,
    num_modes=4,
    group_index_step=10 * nm,
)
print(strip.n_group)









[4.17803969 4.08299706 2.71577378 1.50332985]













Bend modes#


You can compute bend modes specifying the bend radius.






strip_bend = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=500 * nm,
    core_thickness=220 * nm,
    slab_thickness=0.0,
    bend_radius=4,
    core_material="si",
    clad_material="sio2",
)
strip_bend.plot_field(field_name="Ex", mode_index=0)  # TE











<matplotlib.collections.QuadMesh object at 0x7effed1693d0>







../_images/e24925126a60943ed2673a5953f6f3781862e7c58ea467f16b934c351860df52.png









Bend loss#


You can also compute the losses coming from the mode mismatch from the bend into a straight waveguide.
To compute the bend loss due to mode mismatch you can calculate the mode overlap of the straight mode and the bent mode.
Because there are two mode mismatch interfaces the total loss due to mode mismatch will be squared (from bend to straight and from straight to bend).




from paper






radii = np.arange(4, 7)
bend = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=500 * nm,
    core_thickness=220 * nm,
    core_material="si",
    clad_material="sio2",
    num_modes=1,
    bend_radius=radii.min(),
)
mismatch = gt.modes.sweep_bend_mismatch(bend, radii)

plt.plot(radii, 10 * np.log10(mismatch))
plt.title("Strip waveguide bend")
plt.xlabel("Radius (μm)")
plt.ylabel("Mismatch (dB)")











Text(0, 0.5, 'Mismatch (dB)')







../_images/32bdf5e2f250f17fbdec4ff7b515fc244538c39894ccf99c131a1b37a0dfaedf.png









dB_cm = 2  # dB/cm
length = 2 * np.pi * radii * 1e-6
propagation_loss = dB_cm * length * 1e2
print(propagation_loss)

plt.title("Bend90 loss for TE polarization")
plt.plot(radii, -10 * np.log10(mismatch), ".", label="mode loss")
plt.plot(radii, propagation_loss, ".", label="propagation loss")
plt.xlabel("bend radius (um)")
plt.ylabel("Loss (dB)")
plt.legend()









[0.00502655 0.00628319 0.00753982]







<matplotlib.legend.Legend object at 0x7effed22f5d0>







../_images/d7d7b333ac71543cac5ab0e41eebb19587ecfc67e6c504bf84cdfa3461ee62d0.png









rib = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=1000 * nm,
    core_thickness=220 * nm,
    slab_thickness=110 * nm,
    bend_radius=15,
    core_material="si",
    clad_material="sio2",
)
rib.plot_field(field_name="Ex", mode_index=0)  # TE











<matplotlib.collections.QuadMesh object at 0x7effebd81050>







../_images/66b23f95d8aead630b293fc081e84bb73649943e2b20eb3f4e57cbec30f45ba9.png









nitride_bend = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=1000 * nm,
    core_thickness=400 * nm,
    slab_thickness=0.0,
    bend_radius=30,
    core_material="sin",
    clad_material="sio2",
)
nitride_bend.plot_field(field_name="Ex", mode_index=0, value="abs")  # TE











<matplotlib.collections.QuadMesh object at 0x7effebc75a10>







../_images/1ce94a598c2cd49b1aefa16149df3d479a83fbb0112629b0743ce8e4c5b0f924.png









radii = np.array([30, 35, 40])
bend = gt.modes.Waveguide(
    wavelength=1.55,
    core_width=1000 * nm,
    core_thickness=400 * nm,
    core_material="sin",
    clad_material="sio2",
    num_modes=1,
    bend_radius=radii.min(),
)
mismatch = gt.modes.sweep_bend_mismatch(bend, radii)

















dB_cm = 2  # dB/cm
length = 2 * np.pi * radii * 1e-6
propagation_loss = dB_cm * length * 1e2
print(propagation_loss)

plt.title("Bend90 loss for TE polarization")
plt.plot(radii, -10 * np.log10(mismatch), ".", label="mode loss")
plt.plot(radii, propagation_loss, ".", label="propagation loss")
plt.xlabel("bend radius (um)")
plt.ylabel("Loss (dB)")
plt.legend()









[0.03769911 0.0439823  0.05026548]







<matplotlib.legend.Legend object at 0x7effebce5310>







../_images/1771c6818973f0882c5a8364623ddca3d6d87b8c7dd54658251c4d13a609cb8f.png





Exercises


    

  • For a 500nm wide 220nm thick Silicon waveguide surrounded by SiO2, what is the minimum bend radius to have less than 0.04dB loss for TE polarization at 1550nm?
    • 

  • For a 500nm wide 220nm thick Silicon waveguide surrounded by SiO2, what is the minimum bend radius to have 99% power transmission for TM polarization at 1550nm?
    • 







Waveguide coupler#


You can also compute the modes of a waveguide coupler.


       ore_width[0]  core_width[1]
        <------->     <------->
         _______       _______   _
        |       |     |       | |
        |       |     |       |
        |       |_____|       | | core_thickness
        |slab_thickness       |
        |_____________________| |_
                <----->
                  gap











c = gt.modes.WaveguideCoupler(
    wavelength=1.55,
    core_width=(500 * nm, 500 * nm),
    gap=200 * nm,
    core_thickness=220 * nm,
    slab_thickness=100 * nm,
    core_material="si",
    clad_material="sio2",
)
c.plot_index()











<matplotlib.collections.QuadMesh object at 0x7effebfa1410>







../_images/129849ee6ebd61ca6748542adb5fff0f2aa87b314458d73c03b79764a5efdcc3.png









c.plot_field(field_name="Ex", mode_index=0)  # TE











<matplotlib.collections.QuadMesh object at 0x7effed3c1050>







../_images/f7e785736c6bfffbb906ed5d0062483405b4b1e274d91f787b80c6d17a66fa28.png









c.plot_field(field_name="Ex", mode_index=1)  # TE











<matplotlib.collections.QuadMesh object at 0x7effebcda890>







../_images/da8d983867fe1a56947dad723052e2932a12dc585fe66c338febc6b6499f5819.png









coupler = gt.modes.WaveguideCoupler(
    wavelength=1.55,
    core_width=(450 * nm, 450 * nm),
    core_thickness=220 * nm,
    core_material="si",
    clad_material="sio2",
    num_modes=4,
    gap=0.1,
)

print("\nCoupler:", coupler)
print("Effective indices:", coupler.n_eff)
print("Mode areas:", coupler.mode_area)
print("Coupling length:", coupler.coupling_length())

gaps = np.linspace(0.05, 0.15, 11)
lengths = gt.modes.sweep_coupling_length(coupler, gaps)

_, ax = plt.subplots(1, 1)
ax.plot(gaps, lengths)
ax.set(xlabel="Gap (μm)", ylabel="Coupling length (μm)")
ax.legend(["TE", "TM"])
ax.grid()









Coupler: WaveguideCoupler(wavelength=array(1.55), core_width=['0.45', '0.45'], core_thickness='0.22', core_material='si', clad_material='sio2', box_material=None, slab_thickness='0.0', clad_thickness=None, box_thickness=None, side_margin=None, sidewall_angle='0.0', sidewall_thickness='0.0', sidewall_k='0.0', surface_thickness='0.0', surface_k='0.0', bend_radius=None, num_modes='4', group_index_step='False', precision='double', grid_resolution='20', max_grid_scaling='1.2', cache_path='/home/runner/.gdsfactory/modes', overwrite='False', gap='0.1')





Effective indices: [2.4637647 +6.57552457e-05j 2.39007229+5.06214923e-05j
 1.9225165 +1.99036730e-04j 1.71420814+2.37015946e-04j]
Mode areas: [0.31003254 0.33258301 0.57286555 0.59002858]
Coupling length: [10.5166863   3.72044606]







../_images/6e5b17741bd2211f6602df1739112d11b90a14153f1c2e3a1309cb5f14561c19.png