"""Si3N4 inverse-taper spot-size converter to UHNA3 fiber at 1550 nm. Platform -------- 3 um thermal SiO2 (BOX) | Si3N4 core 1.5 um (W) x 0.3 um (H) | 5 um SiO2 top n_Si3N4 = 1.99628 (Luke 2015 Sellmeier), n_SiO2 = 1.44402 (Malitson) @ 1550 nm Fiber: Nufern UHNA3, NA 0.35, MFD 4.1 um @ 1550 nm. Mechanism --------- The bright, tightly-confined 1.5 um Si3N4 mode is a poor match to the 4.1 um fiber (~5 dB butt loss). An INVERSE taper narrows the Si3N4 width toward a sub-wavelength tip; as the width shrinks the effective index drops toward the SiO2 cladding and the mode delocalises, expanding to ~fiber size. The coupling loss is the mode-overlap integral between the tip mode and the UHNA3 field. Why a finite-difference eigensolver ----------------------------------- For a high-contrast Si3N4 wire near cutoff, an imaginary-distance paraxial BPM mode solve is unstable (it collapses onto a spurious tightly-bound mode). We solve the true 2-D scalar Helmholtz eigenproblem with a sparse shift-invert eigensolve, which is robust and grid-convergent. Result (fine grid): best tip w = 0.23 um -> mode D4sigma 4.6 x 4.5 um, overlap 90.8% with UHNA3 -> 0.42 dB (vs 5.0 dB for the bare 1.5 um guide). """ import os, math, argparse import numpy as np import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt from fdmode import (build_index, solve_fd, d4sigma, gauss2d, overlap, N_SIN, N_OX, LAM) W_CHIP = 1.50 # um, Si3N4 chip width H_CORE = 0.30 # um, Si3N4 thickness MFD = 4.1 # um, UHNA3 mode-field diameter @1550nm def loss_of(mode, uh, x, y): eta = overlap(mode, uh, x, y) return eta, -10.0 * math.log10(max(eta, 1e-12)) def main(): ap = argparse.ArgumentParser() ap.add_argument("--out", default=".") ap.add_argument("--dx", type=float, default=0.022) ap.add_argument("--dy", type=float, default=0.016) a = ap.parse_args() os.makedirs(a.out, exist_ok=True) k0 = 2 * math.pi / LAM w0 = MFD / 2 x = np.arange(-9, 9 + 1e-9, a.dx) y = np.arange(-7, 7 + 1e-9, a.dy) uh = gauss2d(x, y, w0) print(f"n_Si3N4={N_SIN:.5f} n_SiO2={N_OX:.5f} grid {len(x)}x{len(y)}") # tip-width sweep -> coupling curve tips = [0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.28, 0.30] curve = [] best = None for w in tips: n = build_index(x, y, w) ne, md = solve_fd(x, y, n, k0, 1) m = md[0] eta, L = loss_of(m, uh, x, y) d4 = (d4sigma(m, x, 0), d4sigma(m, y, 1)) curve.append((w, ne[0], d4[0], d4[1], eta, L)) if best is None or L < best[-1]: best = (w, ne[0], d4[0], d4[1], eta, L) print(f" w={w:.2f} neff={ne[0]:.5f} D4={d4[0]:.2f}x{d4[1]:.2f} " f"eta={eta*100:.2f}% loss={L:.4f}") w_opt = best[0] print(f"\nBEST tip w={w_opt:.2f}um loss={best[-1]:.4f} dB (eta={best[4]*100:.2f}%)") # solve the optimal tip mode and the bare chip mode (high res) n_tip = build_index(x, y, w_opt); _, md = solve_fd(x, y, n_tip, k0, 1); tipmode = md[0] n_chip = build_index(x, y, W_CHIP); _, mc = solve_fd(x, y, n_chip, k0, 1); chipmode = mc[0] eta_tip, loss_tip = loss_of(tipmode, uh, x, y) eta_chip, loss_chip = loss_of(chipmode, uh, x, y) d4_tip = (d4sigma(tipmode, x, 0), d4sigma(tipmode, y, 1)) d4_chip = (d4sigma(chipmode, x, 0), d4sigma(chipmode, y, 1)) # ---- GDS: linear inverse taper on the Si3N4 layer ---- import gdstk L_lead_chip, L_taper, L_tip = 20.0, 200.0, 10.0 # um lib = gdstk.Library(); cell = lib.new_cell("SIN_SSC") zc = [-L_lead_chip, 0.0, L_taper, L_taper + L_tip] hw = [W_CHIP/2, W_CHIP/2, w_opt/2, w_opt/2] top = list(zip(zc, hw)); bot = list(zip(zc[::-1], [-h for h in hw[::-1]])) cell.add(gdstk.Polygon(top + bot, layer=1, datatype=0)) lib.write_gds(os.path.join(a.out, "ssc_optimized.gds")) # reference: straight 1.5um Si3N4 (no taper) lib2 = gdstk.Library(); c2 = lib2.new_cell("SIN_STRAIGHT") c2.add(gdstk.rectangle((-20, -W_CHIP/2), (120, W_CHIP/2), layer=1, datatype=0)) lib2.write_gds(os.path.join(a.out, "ssc_reference.gds")) # ---- summary figure ---- fig = plt.figure(figsize=(11, 7)) gs = fig.add_gridspec(2, 3) ext = [x[0], x[-1], y[0], y[-1]] # (a) taper geometry ax = fig.add_subplot(gs[0, 0]) ax.fill(np.array(zc + zc[::-1]), np.array(hw + [-h for h in hw[::-1]]), color="#3b5bdb", alpha=0.7) ax.set_xlabel("z [um]"); ax.set_ylabel("Si3N4 width [um]") ax.set_title(f"Inverse taper {W_CHIP}→{w_opt:.2f} µm") ax.set_ylim(-1.0, 1.0); ax.grid(alpha=0.3) # (b) chip mode ax = fig.add_subplot(gs[0, 1]) ax.imshow((np.abs(chipmode)**2).T, origin="lower", extent=ext, cmap="magma", aspect="equal") ax.set_xlim(-4, 4); ax.set_ylim(-4, 4) ax.set_title(f"chip mode {W_CHIP}µm\nD4σ={d4_chip[0]:.2f}×{d4_chip[1]:.2f}µm ({loss_chip:.2f} dB)") ax.set_xlabel("x [um]"); ax.set_ylabel("y [um]") # (c) tip mode + UHNA3 circle ax = fig.add_subplot(gs[0, 2]) ax.imshow((np.abs(tipmode)**2).T, origin="lower", extent=ext, cmap="viridis", aspect="equal") th = np.linspace(0, 2*np.pi, 200) ax.plot((MFD/2)*np.cos(th), (MFD/2)*np.sin(th), "w--", lw=1.2) ax.set_xlim(-6, 6); ax.set_ylim(-6, 6) ax.set_title(f"tip mode {w_opt:.2f}µm\nD4σ={d4_tip[0]:.1f}×{d4_tip[1]:.1f}µm ({loss_tip:.3f} dB)") ax.set_xlabel("x [um]"); ax.set_ylabel("y [um]") # (d) coupling loss vs tip width ax = fig.add_subplot(gs[1, :2]) ws = [c[0] for c in curve]; Ls = [c[5] for c in curve] ax.plot(ws, Ls, "o-", color="#3b5bdb") ax.axvline(w_opt, ls=":", color="#2f9e44") ax.annotate(f"{best[-1]:.3f} dB @ {w_opt:.2f}µm", (w_opt, best[-1]), textcoords="offset points", xytext=(8, 8), color="#2f9e44") ax.set_xlabel("Si3N4 tip width [um]"); ax.set_ylabel("UHNA3 coupling loss [dB]") ax.set_title("Coupling loss vs inverse-taper tip width"); ax.grid(alpha=0.3) # (e) 1-D mode cut ax = fig.add_subplot(gs[1, 2]) iy = np.argmin(np.abs(y)); nrm = lambda f: f/np.max(np.abs(f)) ax.plot(x, nrm(np.abs(uh[:, iy])), "k--", lw=2, label="UHNA3 (4.1µm)") ax.plot(x, nrm(np.abs(tipmode[:, iy])), color="#2f9e44", lw=2, label="tip mode") ax.plot(x, nrm(np.abs(chipmode[:, iy])), color="#e8590c", lw=1.5, label="chip mode") ax.set_xlim(-8, 8); ax.set_xlabel("x [um]"); ax.set_ylabel("|E| (norm.)") ax.legend(fontsize=8); ax.set_title("Mode-field cut (y=0)"); ax.grid(alpha=0.3) fig.suptitle(f"Si3N4 (1.5×0.3µm) → UHNA3 inverse-taper SSC @ {int(LAM*1000)} nm — " f"modal-overlap coupling", fontsize=12) fig.tight_layout() fig.savefig(os.path.join(a.out, "ssc_result_summary.png"), dpi=130) plt.close(fig) # ---- compare figure ---- fig, ax = plt.subplots(1, 2, figsize=(11, 4.6)) for k, (tag, m, d4, L, cmap) in enumerate([ (f"Bare {W_CHIP}µm chip", chipmode, d4_chip, loss_chip, "magma"), (f"Inverse-taper tip {w_opt:.2f}µm", tipmode, d4_tip, loss_tip, "viridis")]): ax[k].imshow((np.abs(m)**2).T, origin="lower", extent=ext, cmap=cmap, aspect="equal") ax[k].plot((MFD/2)*np.cos(th), (MFD/2)*np.sin(th), "w--", lw=1.2) ax[k].set_xlim(-6, 6); ax[k].set_ylim(-6, 6) ax[k].set_xlabel("x [um]"); ax[k].set_ylabel("y [um]") ax[k].set_title(f"{tag}\nD4σ={d4[0]:.2f}×{d4[1]:.2f}µm · {L:.3f} dB") fig.suptitle("Mode matching to UHNA3 (white dashed = 4.1µm MFD) @ 1550 nm", fontsize=12) fig.tight_layout() fig.savefig(os.path.join(a.out, "ssc_compare.png"), dpi=130) plt.close(fig) with open(os.path.join(a.out, "result_1550.txt"), "w") as f: f.write("method=fd_mode_overlap\n") f.write(f"loss_dB={loss_tip:.4f}\n") f.write(f"eff={eta_tip:.5f}\n") f.write(f"tip_w_um={w_opt:.3f}\n") f.write(f"tip_neff={best[1]:.5f}\n") f.write(f"tip_d4x={d4_tip[0]:.3f}\n") f.write(f"tip_d4y={d4_tip[1]:.3f}\n") f.write(f"bare_loss_dB={loss_chip:.4f}\n") f.write(f"bare_eff={eta_chip:.5f}\n") f.write(f"bare_d4x={d4_chip[0]:.3f}\n") f.write(f"bare_d4y={d4_chip[1]:.3f}\n") f.write(f"n_sin={N_SIN:.5f}\n") f.write(f"n_sio2={N_OX:.5f}\n") f.write(f"mfd_um={MFD}\n") f.write(f"taper_length_um={L_taper}\n") print("\nWrote GDS + figures + result to", os.path.abspath(a.out)) if __name__ == "__main__": main()