Micro-ring resonator

import os
import numpy as np
import matplotlib.pyplot as plt

import gdsfactory as gf
from gdsfactory.technology import LogicalLayer, LayerLevel, LayerStack
import luminescent as lumi

# simulation folder
path = os.path.join("runs", "ring")

# length units are arbitrary so long as they are consistent, in this case [um]. everything gets normalized around origin wavelength and period at backend.
wavelength = 1.55  # characteristic wavelength [um]
bandwidth = 0.1  # wavelength bandwidth [um]
wavelengths = np.linspace(wavelength - bandwidth / 2, wavelength + bandwidth / 2, 201)

# horizontal dims
r = 3.1  # radius of ring
w_wg = 0.4  # width of waveguide
gap = 0.1  # gap between waveguide and ring

# vertical dims
h_wg = 0.18  # height of waveguide

def setup(path,r,gap,w_wg,h_wg):
    # simulation parameters
    nres = 6  # number of grid points per wavelength in material (not vacuum)
    stop_decay = 0.003
    courant = 0.95  # Courant factor for time step size, relative to max allowed by grid
    subpixel_smoothing = 1
    PML_decay = [.001,.1,.1]
    tmax = 1000  # max time [periods]
    shot_every = 10  # save and plot field every _ periods, involves slow disk write
    views = [lumi.view("Hz", x=0, z=0)]

    boundaries = ['PML', ('PEC', 'PML'), ('PMC', 'PML')]  # z midplane PMC symmetry
    
    # margins
    source_offset = 2
    xmargin = 1.5 
    ymargin = lateral_port_margin = 1 

    # vertical midplane symmetry as PMC boundary on z-
    zmargin = height_port_margin = 1 
    zmin = 0
    zmax = h_wg / 2 + zmargin

    # materials
    core = 'Si'
    clad = 'SiO2'
    background = clad
    nSi = 3.5
    nSiO2 = 1.5
    materials = {
        'Si': lumi.material(nSi),
        'SiO2': lumi.material(nSiO2),
    }

    # layer stack
    WG = (1, 0)  # waveguide layer
    BBOX = (10, 0)  # bounding box layer
    layer_stack = LayerStack(
        layers={
            'core': LayerLevel(
                layer=LogicalLayer(layer=WG),
                thickness=h_wg / 2,
                zmin=0.0,
                material=core,
                mesh_order=1,
            )    })

    ## Geometry
    """
    2 symmetries:
    - mid waveguide height z PMC boundary
    - ring frame y PEC boundary (implies fictious mirror source at port o2 on other side of ring. original S21 turns into S11 in our mirror setup assuming no back coupling)
    """

    # make component in gdsfactory. alternatively, you can import .gds layout into gdsfactory or .stl bodies directly into ours
    c = gf.Component()

    b = c << gf.components.bend_circular180(radius=r, width=w_wg, layer=WG, allow_min_radius_violation=True)
    b.rotate(90)
    b.movex(r)

    l = 2 * r + 2 * xmargin + w_wg
    s = c << gf.components.straight(length=l - source_offset, width=w_wg)
    s.move((-l / 2 + source_offset, w_wg + gap + r))

    s1 = c << gf.components.straight(length=source_offset, width=w_wg)
    s1.connect('o2', s.ports['o1'])

    c.add_port('o1', port=s.ports['o1'])
    c.add_port('o3', port=s.ports['o2'])
    c << gf.components.bbox(component=c, layer=BBOX, top=ymargin)
    c.plot()

    bbox = c.bbox_np().tolist()
    bbox[0].append(zmin)
    bbox[1].append(zmax)

    # source and modes setup
    w_port = w_wg + 2 * lateral_port_margin

    frames = [
        lumi.plane_frame('mode', wls_mode_solver=[wavelength], start=[-w_port / 2, zmin], stop=[w_port / 2, zmax], boundaries=['PML', ['PMC', 'PML']], nmodes=1),  # local xy basis
        lumi.points_frame('trace', points=[[0,0]], time_domain=True),
    ]

    sources = [lumi.gf_source('o1', c, layer_stack, source_offset, frame='mode', wl=wavelength, bandwidth=max(max(wavelengths) - min(wavelengths), wavelength / 4))]

    monitors = [
        lumi.gf_monitor('o1', c, layer_stack, frame='mode'),
        lumi.gf_monitor('o3', c, layer_stack, frame='mode', mirrored=True),
        lumi.gf_monitor('o1', c, layer_stack, frame='trace', name='u1')
    ]

    lumi.mesh(path, c, layer_stack, materials, zmin, zmax)
    lumi.setup(
        path=path,
        wl=wavelength,
        wls=wavelengths,
        materials=materials,
        background=background,
        boundaries=boundaries,
        bbox=bbox,
        # 
        frames=frames,
        sources=sources,
        monitors=monitors,
        # 
        nres=nres,
        courant=courant,
        subpixel_smoothing=subpixel_smoothing,
        tmax=tmax,
        PML_decay=PML_decay,
        # 
        views=views,
        shot_every=shot_every,
        stop_decay=stop_decay,
        device='gpu',
    )

setup(path,r,gap,w_wg,h_wg)

lumi.solve(path)

lumi.movie(path)

sol = lumi.load(path)
o1=sol['monitors']['o1']
o3=sol['monitors']['o3']

S21 = o1['modes'][0]['+'] / o1['modes'][0]['-'] # drop port power, S21 aliased as S11 with mirrored source
S31 = o3['modes'][0]['+'] / o1['modes'][0]['-'] # through port power

plt.plot(wavelengths, np.abs(S21)**2, label="S21")
# plt.plot(wavelengths, S31, label="S31")

plt.xlabel("wavelength [um]")
plt.ylabel("power")
plt.legend()
plt.show()

from scipy.signal import find_peaks

dw=bandwidth/len(wavelengths)
I, props = find_peaks(np.abs(S21), height=0.4, distance=.01//dw)

peaks = wavelengths[I]
print(f'Peaks: {", ".join(f"{1000*x:.2f}nm" for x in peaks)}')

FSR = np.mean(np.diff(peaks))
print(f'FSR: {1000*FSR:.2f}nm')

i=len(I)//2
mid = I[i]
y=np.abs(S21)**2   # power: FWHM is the half-power (-3 dB) width
half = y[mid]/2

l = mid
while y[l] > half: l -= 1
wl_lo = np.interp(half, [y[l], y[l+1]], [wavelengths[l], wavelengths[l+1]])

r = mid
while y[r] > half: r += 1
wl_hi = np.interp(half, [y[r], y[r-1]], [wavelengths[r], wavelengths[r-1]])  # np.interp needs increasing y

FWHM = wl_hi - wl_lo
wl=wavelengths[mid]
Q=wl/FWHM
print(f'FWHM: {1000*FWHM:.2f}nm\nQ factor (FWHM method): {Q:.0f}')

t = np.array(sol['t'])
y = np.array(sol['monitors']['u1']['fields']['Ex'][0,:])
t = t[:len(y)]

# zero transients before t0, leaving only ring decay:
# the source pulse peaks at the monitor, then takes ~its duration (~4 periods here) to pass
t0 = t[np.argmax(np.abs(y))] + 4
i = np.searchsorted(t, t0)
y[:i] = 0

plt.plot(t, y)
plt.xlabel("t [period]")
plt.ylabel("u1 Ex (monitor basis of reference)")
plt.show()

import subprocess

# harmonic inversion of the ringdown (needs harminv: sudo apt install harminv)
# time is in periods of `wavelength`, so frequency f = wavelength / λ
fmin, fmax = wavelength / wavelengths[-1], wavelength / wavelengths[0]
dt = t[1] - t[0]
out = subprocess.run(["harminv", "-t", str(dt), f"{fmin}-{fmax}"],
                     input="\n".join(map(str, y[i:])), capture_output=True, text=True).stdout

# columns: frequency, decay constant, Q, |amplitude|, phase, error
for line in out.splitlines()[1:]:
    f, decay, Q, amp, phase, err = map(float, line.split(","))
    if fmin <= f <= fmax:
        print(f"{1000 * wavelength / f:.2f}nm   Q = {Q:.0f}   |amp| = {amp:.2g}   error = {err:.1e}")