Four-Fold Truncated Double-Nested Fiber (4T-DNANF)

• 4T-DNANF is a photonic waveguide featuring a four-fold truncated, double-nested anti-resonant cladding that achieves ultralow LP₀₁ loss (<0.1 dB/km) and high higher-order mode suppression.
• It leverages precision laser-cut truncations and nested silica capillaries to optimize anti-resonant guidance and phase-matching, yielding HOM extinction ratios up to 50,000.
• Compatible with standard stack-and-draw fabrication, its design balances structural precision with manufacturability for use in high-speed coherent communications and fiber optic gyroscopes.

The four-fold truncated double-nested anti-resonant hollow-core fiber (4T-DNANF) is a photonic waveguide structure engineered to simultaneously achieve ultralow fundamental mode (FM, LP₀₁) loss and ultrahigh higher-order mode (HOM, e.g., LP₁₁) suppression for demanding optical fiber applications such as high-speed coherent communications and precision fiber optic gyroscopes. Characterized by a circular air core surrounded by a precisely engineered cladding comprising four partially truncated silica capillaries, each double-nested with a concentric inner capillary, the 4T-DNANF leverages anti-resonant guidance and symmetry-breaking truncations to optimize phase-matched loss pathways for unwanted modes while preserving single-mode performance. This architecture enables FM losses near 0.1 dB/km and record HOM extinction ratios (HOMER) up to 50,000, surpassing prior anti-resonant hollow-core fiber (AR-HCF) designs while remaining compatible with standard stack-and-draw fiber fabrication techniques (Gao et al., 2024).

1. Structural Topology and Geometric Features

The 4T-DNANF is topologically defined by a central air core of radius $R_\mathrm{core} \approx 15\,\mu\mathrm{m}$, enclosed by four symmetrically arranged "large" silica capillaries. Each capillary undergoes a "four-fold truncation" wherein 120° of its circumference is removed via precision laser cutting, resulting in crescent-shaped cross-sections rather than full rings. These truncated capillaries are nested with smaller, concentric silica capillaries, yielding a double anti-resonant cladding structure. Each nesting produces two distinct air layers, termed the first and second air crescents, with thicknesses $Z_1$ and $Z_2$ respectively.

The double-nested configuration introduces two anti-resonant silica membranes per sector, each with nominal thickness $$t \approx 1.1\,\mu\mathrm{m}\,(\pm0.05\,\mu\mathrm{m})$$, separated by air crescents. The physical arrangement is maintained using silica struts (thickness $\sim1.0\,\mu\mathrm{m}$) to minimize glass content in the cladding. The inter-tube gap at the truncation edges is constrained within $5.3$–$7.7\,\mu\mathrm{m}$ (design target $\sim7\,\mu\mathrm{m}$), ensuring robust field confinement and manufacturability. Fabrication tolerances are $\pm0.1\,\mu\mathrm{m}$ for membrane thickness, $\pm0.5\,\mu\mathrm{m}$ for inter-tube gap, and $\pm0.02$ (unitless) for $Z_1/R_\mathrm{core}$ and $Z_2/R_\mathrm{core}$.

2. Anti-Resonant Guidance Mechanism

Guidance within the 4T-DNANF relies primarily on the anti-resonant effect at each silica membrane, by which light is confined via multiple anti-resonant reflections. The condition for anti-resonance is determined by destructive interference, such that the $m^\mathrm{th}$ resonance wavelength is given by

$$\lambda_m \approx \frac{2 n_\mathrm{silica} t}{m\pi}$$

where $n_\mathrm{silica}$ is the refractive index of silica, and $t$ is the membrane thickness. Minimum leakage (i.e., maximal confinement) occurs for wavelengths $\lambda$ slightly longer than $\lambda_m$, corresponding to the anti-resonant regime. The confinement loss then approximately follows

$\mathrm{CL} \propto \exp(-2\kappa t)$

where $\kappa$ is the imaginary component of the transverse wavevector in the glass.

With $t \approx 1.1\,\mu\mathrm{m}$, the second anti-resonant band is centered around $1.55\,\mu\mathrm{m}$, aligning with the optical C-band and minimizing LP₀₁ leakage loss.

3. Mode Filtering via Phase-Matching and Symmetry Engineering

The double-nested cladding architecture generates two families of cladding air-cavity modes, each localized within one of the air crescents. By adjusting the ratios $Z_1/R_\mathrm{core}$ and $Z_2/R_\mathrm{core}$, the phase-matching condition between the core LP₁₁ mode and the cladding air-cavity modes can be precisely tuned, resulting in pronounced anti-crossings at which the LP₁₁ mode couples to a highly lossy cladding mode and is thus rapidly attenuated.

The four-fold truncation of the outer capillaries, compared to traditional five-fold symmetric double-nested AR-HCFs (5-DNANF), eliminates the "void" regions behind inter-tube gaps present in 5-capillary configurations. In 5-DNANF, such regions can admit LP₀₁-phase-matched air modes leading to increased FM loss. In the 4T-DNANF, the intentional symmetry breaking renders these regions smaller and asymmetric, which sustains strong LP₀₁ confinement even as the LP₁₁ is efficiently filtered by anti-crossing with the first-crescent mode.

4. Fabrication Protocols and Tolerance Management

4T-DNANF fabrication proceeds via a multi-step stack-and-draw process:

• Preform assembly involves pre-cutting the four large silica capillaries at 120° intervals and inserting four smaller nested capillaries concentrically within each. The eight capillaries are then radial-stacked around a central support rod. Spacers are used to precisely set $Z_1$ and $Z_2$.
• Intermediate draw reduces the preform to a $\sim5\,\mathrm{mm}$ “cane,” with tension carefully regulated to maintain inter-tube gap near the $7\,\mu$m target.
• Sleeving and final draw produce a fiber of $\sim300\,\mu\mathrm{m}$ outer diameter, with monitored temperature control to preserve $t = 1.1\,\mu\mathrm{m} \pm 0.05\,\mu\mathrm{m}$.

Fabrication challenges include: preventing collapse of the truncated edges due to surface tension; strictly maintaining gap uniformity (tension control within $\pm3\,\mathrm{g}$); and avoiding hollow-core contamination (notably gas absorption lines).

5. Experimental Performance and Mode Suppression Metrics

Empirical characterization of the 4T-DNANF includes two representative fibers subjected to cutback loss, optical spectrum analyzer (OSA), distributed feedback (DFB) laser, and S² imaging measurements:

Fiber #	$Z_1/R_\mathrm{core}$	$Z_2/R_\mathrm{core}$	FM loss (dB/km, 1550 nm)	HOM loss (dB/km)	HOMER
#1	0.65	1.14	0.09–0.10	430	4,300
#5	0.88	1.06	0.13	6,500	50,000

The fundamental mode loss (LP₀₁) in Fiber #1, optimized for lowest attenuation, is consistently measured as $0.09\pm0.01$ dB/km (OSA), $0.10\pm0.01$ dB/km (DFB laser), and $0.108$ dB/km (OTDR). Higher-order mode loss (LP₁₁) is $0.43$ dB/m, corresponding to $430$ dB/km, yielding a HOMER of $4,300$. In Fiber #5, optimized for maximum mode purity, FM loss is $0.13\pm0.01$ dB/km and HOM loss is $6.5\pm0.5$ dB/m ($6,500$ dB/km), resulting in a record HOMER of $50,000$. The transmission window spans $1,514$–$1,600$ nm with baseline losses <$0.1$ dB/km. High-resolution spectra reveal the presence of gas absorption lines (notably CO₂).

6. Comparison with Prior AR-HCF and DNANF Designs

The 4T-DNANF demonstrates several key improvements over canonical five-capillary double-nested anti-resonant hollow-core fibers (5-DNANFs). In 5-DNANF, lowest LP₀₁ loss ($\lesssim0.1$ dB/km) and a HOMER of $\sim3,500$ can be achieved for $Z_2/R_\mathrm{core}\approx1.05$, but at larger $Z_1$, while stronger mode filtering increases FM loss substantially (to $\sim0.5$ dB/km). In contrast, simulations and experiments on 4T-DNANF show that $Z_1/R_\mathrm{core}\approx1.0$ allows for simultaneous achievement of LP₀₁ confinement loss $<0.01$ dB/km and HOMER $>1.8\times10^5$, attributed to optimal placement of the first air crescent and the truncation-induced suppression of unwanted FM coupling. Minimum attainable CL for 4T-DNANF is $\sim0.002$ dB/km (at $Z_1/R_\mathrm{core}=0.8$, HOMER $\sim4,000$), outperforming 5-DNANF (minimum CL $\sim0.009$ dB/km, HOMER $\sim25$).

7. Schematic Representations and Field Distributions

Cross-sectional schematics (Fig. 1(b) in (Gao et al., 2024)) depict the four-fold truncation geometry, indicating truncated outer capillaries, nested inner capillaries, core radius $R_{\mathrm{core}}$, inner air crescent $Z_1$, outer air crescent $Z_2$, and the inter-tube gap. At the phase-matching anti-crossing between LP₁₁ and the first air-crescent mode, field intensity spreads between the core and adjacent air crescent, highlighting strong loss pathways for HOMs while LP₀₁ intensity remains localized. SEMs (Fig. 2(a–e)) reveal the uniformity of truncations, membrane thickness, and a clean, round hollow core. S² imaging reconstructs distinct LP₁₁ field patterns, confirming efficacy of mode filtering.

---

The 4T-DNANF integrates nested anti-resonant membranes, two tunable air crescents for phase-matching-controlled HOM suppression, and a four-fold truncated cladding that disrupts FM–cladding coupling via symmetry breaking. This topology enables record low LP₀₁ loss and record HOMER, with practical fabrication tolerances and compatibility with standard fiber-drawing techniques (Gao et al., 2024). For optimal performance reproduction or further architectural enhancements, critical parameters include precise control of $Z_1/R_{\mathrm{core}}$ (recommended range $0.65$–$0.9$), maintenance of $t=1.1\,\mu$m, high uniformity in truncations, and preform cleaning to mitigate gas absorption.