Physics inspired ML dataset for Cylindrical Photonic Waveguides or Interconnects in Glass Substrate

Dataset Overview This synthetic dataset is designed for training physics‐inspired neural networks in the domain of optical waveguide characterization. The dataset consists of 50,000 samples. Each sample comprises 15 input features that capture the physical, material, and geometrical attributes of a waveguide and 14 output targets that describe its optical performance (losses, mode characteristics, effective index, and polarization components). The dataset is especially useful for developing data‐driven models that can predict waveguide performance from basic design parameters, enabling applications in integrated photonics for both glass and silicon-based devices. Input Parameter List (15 Features) core_index Description: Complex refractive index of the waveguide core. Range: Real part between 1.48 and 1.52 (for single-mode) or 1.50–1.52 (for multimode) with a very small negative imaginary part (loss) between –1×10⁻⁸ and –1×10⁻⁷. Format: Stored as a string in the form “x+yj” (e.g., “1.488000-3.200000e-08j”) without any extra brackets. clad_index Description: Complex refractive index of the cladding. Range: Real part between ~1.44 and just below the core index (close for single-mode, larger difference for multimode) with a similar small negative imaginary part. Format: Same string format as the core index. core_radius_m Description: Core radius (a) in meters. Range: For single-mode: 0.5–2 µm (diameter 1–4 µm); for multimode: 2–10 µm (diameter 4–20 µm). clad_radius_m Description: Cladding radius (b) in meters. Range: 20 µm to 50 µm. length_m Description: Waveguide length (L) in meters. Range: 1 mm to 50 cm (0.001 to 0.5 m). wavelength_m Description: Operating wavelength (λ) in meters. Range: 500 nm to 1600 nm (500×10⁻⁹ to 1.6×10⁻⁶ m). polarization Description: Input polarization as a unitless number, where 0 represents pure TE and 1 represents pure TM. Range: 0 to 1. alpha_core Description: Intrinsic loss coefficient for the core (α₁) in inverse meters (m⁻¹). Range: 1×10⁻⁴ to 1×10⁻³ m⁻¹. alpha_clad Description: Intrinsic loss coefficient for the cladding (α₂) in m⁻¹. Range: 1×10⁻⁴ to 1×10⁻³ m⁻¹. photoelastic_coeff Description: Photoelastic coefficient (p) of the core material. Range: 0.20 to 0.25. delta_rho_over_rho Description: Density variation ratio (Δρ/ρ) representing the fractional density fluctuation. Range: 1×10⁻¹² to 1×10⁻¹¹. sigma_rms_m Description: RMS surface roughness (σ) at the core–cladding interface (in meters). Range: 1 to 10 nm (1×10⁻⁹ to 1×10⁻⁸ m). roughness_corr_length_m Description: Correlation length (L_corr) of the interface roughness (in meters). Range: 100 nm to 1 µm (1×10⁻⁷ to 1×10⁻⁶ m). w_in_m Description: Input beam waist (w_in) in meters. Range: 1 µm to 5 µm (1×10⁻⁶ to 5×10⁻⁶ m). input_power Description: Input optical power (P_in) in Watts. Range: 1 mW to 10 mW (1×10⁻³ to 1×10⁻² W). Output Parameter List (14 Targets) propagation_loss_dB Description: Propagation loss (in dB) computed based on the exponential decay of optical power along the waveguide. Equation: Pout=Pinexp⁡(−αtotalL),Propagation Loss (dB)=10log⁡10(PinPout).P_{\text{out}} = P_{\text{in}} \exp(-\alpha_{\text{total}} L), \quad \text{Propagation Loss (dB)} = 10\log_{10}\left(\frac{P_{\text{in}}}{P_{\text{out}}}\right).Pout=Pinexp(−αtotalL),Propagation Loss (dB)=10log10(PoutPin). insertion_loss_dB Description: Insertion (or coupling) loss (in dB) computed from the mode mismatch between the input beam and the guided mode. coupling_loss_dB Description: Coupling loss (in dB). In our model, this is identical to the insertion loss. mode_field_diameter_m Description: Mode field diameter (MFD) computed via an empirical (Marcuse) formula. Equation: w=a(0.65+1.619V1.5+2.879V6),MFD=2w.w = a\left(0.65 + \frac{1.619}{V^{1.5}} + \frac{2.879}{V^6}\right), \quad \text{MFD} = 2w.w=a(0.65+V1.51.619+V62.879),MFD=2w. mode_confinement_factor Description: Fraction of the optical power confined in the core. Equation: Γ=u2V2,u={0.9 V,V<2.405,V−0.5,V≥2.405.\Gamma = \frac{u^2}{V^2},\quad u = \begin{cases} 0.9\,V, & V < 2.405,\\[1mm] V-0.5, & V \ge 2.405. \end{cases}Γ=V2u2,u={0.9V,V−0.5,V<2.405,V≥2.405. single_mode Description: A flag indicating whether the waveguide is single-mode (“Y”) (i.e., V<2.405V < 2.405V<2.405). multi_mode Description: A flag indicating multimode operation (“Y”) (i.e., V≥2.405V \ge 2.405V≥2.405); complementary to the single_mode flag. scattering_loss_dB Description: Scattering loss (in dB) computed from the scattering loss coefficient. Equation: scattering_loss_dB=4.343 αscatt,total L,\text{scattering\_loss\_dB} = 4.343\,\alpha_{\text{scatt,total}}\,L,scattering_loss_dB=4.343αscatt,totalL, where αscatt,total=αscatt,bulk+αscatt,surface,\alpha_{\text{scatt,total}} = \alpha_{\text{scatt,bulk}} + \alpha_{\text{scatt,surface}},αscatt,total=αscatt,bulk+αscatt,surface, with αscatt,bulk=8π33λ4(p2)(Δρρ)2Γ,αscatt,surface=4π3λ2σrms2Lcorr.\alpha_{\text{scatt,bulk}} = \frac{8\pi^3}{3\lambda^4}(p^2)\left(\frac{\Delta\rho}{\rho}\right)^2 \Gamma,\quad \alpha_{\text{scatt,surface}} = \frac{4\pi^3}{\lambda^2}\sigma_{rms}^2 L_{corr}.αscatt,bulk=3λ48π3(p2)(ρΔρ)2Γ,αscatt,surface=λ24π3σrms2Lcorr. effective_index Description: Effective refractive index (neffn_{\text{eff}}neff) of the guided mode, computed from an approximate eigenvalue solution. Equation: neff=n2,real2+(u2V2)(n1,real2−n2,real2).n_{\text{eff}} = \sqrt{n_{2,\text{real}}^2 + \left(\frac{u^2}{V^2}\right)(n_{1,\text{real}}^2 - n_{2,\text{real}}^2)}.neff=n2,real2+(V2u2)(n1,real2−n2,real2). cross_coupling Description: An approximate measure of mode cross coupling. Equation: Cross Coupling={0,V<2.405,0.5 (V−2.405)V,V≥2.405.\text{Cross Coupling} = \begin{cases} 0, & V < 2.405,\\[1mm] 0.5\,\frac{(V-2.405)}{V}, & V \ge 2.405. \end{cases}Cross Coupling={0,0.5V(V−2.405),V<2.405,V≥2.405. TE_percent Description: Percentage of the transverse electric (TE) component in the mode field. For single-mode, it is computed as (1−polarization)×100(1-\text{polarization}) \times 100(1−polarization)×100, while for multimode it is adjusted by cross coupling. TM_percent Description: Percentage of the transverse magnetic (TM) component (complementary to TE_percent). V_parameter Description: The normalized frequency of the waveguide, computed as V=2π aλn12−n22.V = \frac{2\pi\,a}{\lambda}\sqrt{n_1^2-n_2^2}.V=λ2πan12−n22. output_power Description: The optical power at the output of the waveguide computed from the exponential decay of the input power, Pout=Pinexp⁡(−αtotalL).P_{out} = P_{in}\exp\Bigl(-\alpha_{\text{total}}L\Bigr).Pout=Pinexp(−αtotalL). Equations and Methodology Key Equations: Normalized Frequency (V): V=2π aλn1,real2−n2,real2V = \frac{2\pi\, a}{\lambda} \sqrt{n_{1,\text{real}}^2 - n_{2,\text{real}}^2}V=λ2πan1,real2−n2,real2 Mode Field Diameter (MFD): w=a(0.65+1.619V1.5+2.879V6),MFD=2w.w = a\left(0.65 + \frac{1.619}{V^{1.5}} + \frac{2.879}{V^6}\right), \quad \text{MFD} = 2w.w=a(0.65+V1.51.619+V62.879),MFD=2w. Mode Confinement Factor: Γ=u2V2,u={0.9 V,V<2.405,V−0.5,V≥2.405.\Gamma = \frac{u^2}{V^2},\quad u = \begin{cases} 0.9\,V, & V < 2.405,\\[1mm] V - 0.5, & V \ge 2.405. \end{cases}Γ=V2u2,u={0.9V,V−0.5,V<2.405,V≥2.405. Effective Attenuation: αeff=αcore Γ+αclad (1−Γ).\alpha_{\text{eff}} = \alpha_{\text{core}}\,\Gamma + \alpha_{\text{clad}}\,(1-\Gamma).αeff=αcoreΓ+αclad(1−Γ). Scattering Loss Coefficient: αscatt,bulk=8π33λ4 (p2)(Δρρ)2Γ,αscatt,surface=4π3λ2 σrms2 Lcorr,\alpha_{\text{scatt,bulk}} = \frac{8\pi^3}{3\lambda^4}\,(p^2)\left(\frac{\Delta\rho}{\rho}\right)^2 \Gamma,\quad \alpha_{\text{scatt,surface}} = \frac{4\pi^3}{\lambda^2}\,\sigma_{rms}^2\,L_{corr},αscatt,bulk=3λ48π3(p2)(ρΔρ)2Γ,αscatt,surface=λ24π3σrms2Lcorr, αscatt,total=αscatt,bulk+αscatt,surface.\alpha_{\text{scatt,total}} = \alpha_{\text{scatt,bulk}} + \alpha_{\text{scatt,surface}}.αscatt,total=αscatt,bulk+αscatt,surface. Total Attenuation: αtotal=αeff+αscatt,total.\alpha_{\text{total}} = \alpha_{\text{eff}} + \alpha_{\text{scatt,total}}.αtotal=αeff+αscatt,total. Output Power and Propagation Loss: Pout=Pinexp⁡(−αtotal L),Propagation Loss (dB)=10log⁡10 ⁣(PinPout).P_{out} = P_{in} \exp(-\alpha_{\text{total}}\,L),\quad \text{Propagation Loss (dB)} = 10 \log_{10}\!\left(\frac{P_{in}}{P_{out}}\right).Pout=Pinexp(−αtotalL),Propagation Loss (dB)=10log10(PoutPin). Insertion Loss (Coupling Loss) via Gaussian Overlap: Tnom=2 win wwin2+w2 exp⁡ ⁣(−Δx2win2+w2),IL (dB)=−20log⁡10(Tnom).T_{nom} = \frac{2\,w_{in}\,w}{w_{in}^2+w^2}\,\exp\!\left(-\frac{\Delta x^2}{w_{in}^2+w^2}\right),\quad \text{IL (dB)} = -20 \log_{10}(T_{nom}).Tnom=win2+w22winwexp(−win2+w2Δx2),IL (dB)=−20log10(Tnom). Methodology: Random Sampling:Each input parameter is sampled uniformly from a range grounded in literature values for glass/Si-photonic waveguides. Mode Balancing:Approximately half of the samples are forced into a single-mode regime (using lower core diameter and very small index contrast) and the other half into a multimode regime (using larger core diameters and higher contrast). Physics-Based Computation:Using the sampled inputs, the equations above compute the optical performance, including losses (propagation, scattering, insertion), mode field properties, effective index, and mode coupling characteristics. Complex Refractive Indices:The refractive indices are generated as complex numbers with small imaginary parts to emulate realistic material losses. They are stored in string format without extra brackets to aid later preprocessing.