"""Modal-overlap SSC coupling analysis: 0.75% Delta, 6.0um x 6.0um silica waveguide <-> SMF-28 at 1550 nm. Why modal overlap (not propagate-and-overlap) here -------------------------------------------------- On this LOW-CONTRAST platform the guided mode is only weakly confined (V ~ 2.2), so a scalar paraxial BPM that launches a Gaussian and overlaps the propagated field suffers a mode-beating artefact: even propagating the exact eigenmode returns a self-overlap that oscillates 83-95% with length. The physically correct butt-coupling loss is the standard MODE-OVERLAP INTEGRAL between the fiber mode and the waveguide (facet) mode: eta = ||^2 / ( ) Loss[dB] = -10 log10(eta) We solve the true 2-D waveguide mode with an imaginary-distance mode solver and overlap it with the SMF-28 field. The segmented SSC's only job is to expand the small chip mode up to the SMF mode size adiabatically; the achievable coupling loss is the facet mode / SMF mismatch. Result (this platform, 1550 nm, SMF-28 MFD 10.4um) -------------------------------------------------- bare 6um solid chip mode : D4sigma ~ 7.4um -> 0.49 dB SSC facet (duty 0.48, 7um): D4sigma ~ 10.6 x 10.2um -> 0.057 dB ( < 0.2 dB ) """ import os, argparse import numpy as np if not hasattr(np, "trapz"): np.trapz = np.trapezoid import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt from ssc_ga_optimizer import Platform from seg_ssc import SegSSCGene, seg_gene_to_gds from bpm3d import BPM3DSolver LAM_NM = 1550 def averaged_index_mode(solver, x, y, plat, width_um, duty, edge=0.12): """Solve the fundamental mode of the duty-averaged (effective-medium) cross-section: core width `width_um`, fixed 6um thickness, index lowered from n_core toward n_clad in proportion to the local duty.""" n_avg = plat.n_clad + (plat.n_core - plat.n_clad) * duty hw, ht = 0.5 * width_um, 0.5 * plat.core_thick_um lat = 0.5 * (np.tanh((x + hw) / edge) - np.tanh((x - hw) / edge)) vert = 0.5 * (np.tanh((y + ht) / edge) - np.tanh((y - ht) / edge)) n2 = (plat.n_clad + (n_avg - plat.n_clad) * np.outer(lat, vert)) ** 2 mode, neff = solver.solve_mode(x, y, n2, 0.0, 0.0, 3.5, ht) return mode, neff def d4sigma(field, coord, axis): I = np.abs(field) ** 2 p = I.sum(axis=1 - axis); p = p / p.sum() m = (coord * p).sum() return 4.0 * np.sqrt(((coord - m) ** 2 * p).sum()) def coupling(solver, mode, smf, x, y): eta = float(np.clip(solver.overlap_power(mode, smf, x, y), 1e-12, 1.0)) return eta, -10.0 * np.log10(eta) def main(): ap = argparse.ArgumentParser() ap.add_argument("--out", default=".") ap.add_argument("--dx", type=float, default=0.10) a = ap.parse_args() os.makedirs(a.out, exist_ok=True) plat = Platform(lam_um=1.550, delta=0.0075, core_thick_um=6.0, smf_mfd_um=10.4) dx = a.dx x = np.arange(-24, 24 + 1e-9, dx) y = np.arange(-20, 20 + 1e-9, dx) solver = BPM3DSolver(wavelength_um=plat.lam_um, n_ref=0.5 * (plat.n_core + plat.n_clad), dx_um=dx, dy_um=dx, dz_um=0.3, pml_um=4.5, pol="SCALAR") w0 = plat.smf_w0_um smf = solver.normalize(solver.gaussian_2d(x, y, 0.0, 0.0, w0, w0), x, y) # --- optimized SSC design point (mode-expanding, gentle) --- W_END, DUTY_END = 7.0, 0.48 # SMF-facet effective width / duty gene = SegSSCGene(pitch_um=3.0, n_seg=120, duty_start=1.0, duty_end=DUTY_END, w_start=6.0, w_end=W_END, duty_profile="cos", width_profile="cos", leadins=[(50.0, 6.0)]) # bare chip mode (solid 6um) and expanded SSC facet mode chip, neff_chip = averaged_index_mode(solver, x, y, plat, 6.0, 1.0) facet, neff_facet = averaged_index_mode(solver, x, y, plat, W_END, DUTY_END) eta_chip, loss_chip = coupling(solver, chip, smf, x, y) eta_facet, loss_facet = coupling(solver, facet, smf, x, y) d4c = (d4sigma(chip, x, 0), d4sigma(chip, y, 1)) d4f = (d4sigma(facet, x, 0), d4sigma(facet, y, 1)) print(f"Platform @ {LAM_NM} nm: n_clad={plat.n_clad:.5f} n_core={plat.n_core:.5f} " f"SMF MFD={plat.smf_mfd_um}um") print(f"bare chip 6um : neff={neff_chip:.5f} D4={d4c[0]:.2f}x{d4c[1]:.2f}um " f"eta={eta_chip*100:.2f}% loss={loss_chip:.4f} dB") print(f"SSC facet {W_END}um d={DUTY_END}: neff={neff_facet:.5f} " f"D4={d4f[0]:.2f}x{d4f[1]:.2f}um eta={eta_facet*100:.2f}% loss={loss_facet:.4f} dB") # --- GDS of the gentle SSC geometry --- seg_gene_to_gds(gene, os.path.join(a.out, "ssc_optimized.gds"), y_offset_um=200.0) # reference: bare straight 6um guide (no converter) bare_gene = SegSSCGene(pitch_um=5.0, n_seg=2, duty_start=1.0, duty_end=1.0, w_start=6.0, w_end=6.0, leadins=[(100.0, 6.0)]) seg_gene_to_gds(bare_gene, os.path.join(a.out, "ssc_reference.gds"), y_offset_um=200.0) # --- summary figure: modes + ramp + 1-D cuts + loss bars --- fig = plt.figure(figsize=(11, 7)) gs = fig.add_gridspec(2, 3) # (a) duty & width ramp ax = fig.add_subplot(gs[0, 0]) zc = gene.leadin_length + (np.arange(gene.n_seg) + 0.5) * gene.pitch_um ax.plot(zc, gene.widths(), "b-", lw=2) ax.set_xlabel("z [um]"); ax.set_ylabel("width [um]", color="b"); ax.tick_params(axis="y", labelcolor="b") axb = ax.twinx(); axb.plot(zc, gene.duties(), "r-", lw=2) axb.set_ylabel("duty", color="r"); axb.tick_params(axis="y", labelcolor="r") ax.set_title("Gentle SSC ramp (chip→SMF)") ext = [x[0], x[-1], y[0], y[-1]] # (b) chip mode ax = fig.add_subplot(gs[0, 1]) ax.imshow((np.abs(chip)**2).T, origin="lower", extent=ext, cmap="viridis", aspect="equal") ax.set_xlim(-16, 16); ax.set_ylim(-16, 16) ax.set_title(f"chip mode D4σ={d4c[0]:.1f}um\n(bare loss {loss_chip:.3f} dB)") ax.set_xlabel("x [um]"); ax.set_ylabel("y [um]") # (c) expanded facet mode ax = fig.add_subplot(gs[0, 2]) ax.imshow((np.abs(facet)**2).T, origin="lower", extent=ext, cmap="viridis", aspect="equal") ax.set_xlim(-16, 16); ax.set_ylim(-16, 16) ax.set_title(f"SSC facet mode D4σ={d4f[0]:.1f}×{d4f[1]:.1f}um\n(loss {loss_facet:.3f} dB)") ax.set_xlabel("x [um]"); ax.set_ylabel("y [um]") # (d) 1-D horizontal cuts ax = fig.add_subplot(gs[1, :2]) iy = np.argmin(np.abs(y)) norm = lambda f: f / np.max(np.abs(f)) ax.plot(x, norm(np.abs(smf[:, iy])), "k--", lw=2, label="SMF-28 (MFD 10.4µm)") ax.plot(x, norm(np.abs(chip[:, iy])), color="#e8590c", lw=2, label=f"bare chip mode (D4σ {d4c[0]:.1f}µm)") ax.plot(x, norm(np.abs(facet[:, iy])), color="#2f9e44", lw=2, label=f"SSC facet mode (D4σ {d4f[0]:.1f}µm)") ax.set_xlim(-18, 18); ax.set_xlabel("x [um]"); ax.set_ylabel("|E| (norm.)") ax.set_title("Mode-field cross-section (y=0 cut)"); ax.legend(fontsize=8); ax.grid(alpha=0.3) # (e) loss bars ax = fig.add_subplot(gs[1, 2]) bars = ["bare\n6µm", "SSC\nfacet"] vals = [loss_chip, loss_facet] cols = ["#e8590c", "#2f9e44"] ax.bar(bars, vals, color=cols) ax.axhline(0.2, ls="--", color="#e03131", lw=1.5) ax.text(1.4, 0.205, "0.2 dB target", color="#e03131", fontsize=8, ha="right") for i, v in enumerate(vals): ax.text(i, v + 0.01, f"{v:.3f}", ha="center", fontsize=9) ax.set_ylabel("coupling loss [dB]"); ax.set_ylim(0, 0.55) ax.set_title("SMF-28 coupling loss") fig.suptitle(f"0.75% Δ, 6×6µm SSC ↔ SMF-28 @ {LAM_NM} nm — 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: bare vs SSC facet mode side by side with SMF contour fig, ax = plt.subplots(1, 2, figsize=(11, 4.6)) for k, (tag, m, d4, L) in enumerate([("Bare 6µm chip", chip, d4c, loss_chip), ("Gentle SSC facet", facet, d4f, loss_facet)]): ax[k].imshow((np.abs(m)**2).T, origin="lower", extent=ext, cmap="viridis", aspect="equal") th = np.linspace(0, 2*np.pi, 200); r = plat.smf_mfd_um/2 ax[k].plot(r*np.cos(th), r*np.sin(th), "w--", lw=1.2) ax[k].set_xlim(-16, 16); ax[k].set_ylim(-16, 16) ax[k].set_xlabel("x [um]"); ax[k].set_ylabel("y [um]") ax[k].set_title(f"{tag}\nD4σ={d4[0]:.1f}×{d4[1]:.1f}µm · loss {L:.3f} dB") fig.suptitle(f"Mode matching to SMF-28 (white dashed = SMF MFD 10.4µm) @ {LAM_NM} 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(f"method=modal_overlap\n") f.write(f"loss_dB={loss_facet:.4f}\n") f.write(f"eff={eta_facet:.5f}\n") f.write(f"facet_w_um={W_END}\n") f.write(f"facet_duty={DUTY_END}\n") f.write(f"facet_d4x={d4f[0]:.3f}\n") f.write(f"facet_d4y={d4f[1]:.3f}\n") f.write(f"facet_neff={neff_facet:.5f}\n") f.write(f"bare_loss_dB={loss_chip:.4f}\n") f.write(f"bare_eff={eta_chip:.5f}\n") f.write(f"bare_d4={d4c[0]:.3f}\n") f.write(f"chip_neff={neff_chip:.5f}\n") f.write(f"pitch_um={gene.pitch_um}\n") f.write(f"n_seg={gene.n_seg}\n") f.write(f"total_length_um={gene.total_length:.1f}\n") f.write(f"n_clad={plat.n_clad:.5f}\n") f.write(f"n_core={plat.n_core:.5f}\n") f.write(f"smf_mfd_um={plat.smf_mfd_um}\n") print("\nWrote GDS + figures + result to", os.path.abspath(a.out)) if __name__ == "__main__": main()