Cutoff wavelength

The cutoff wavelength $\lambda_c$ of a fiber or optical waveguide is the wavelength below which the structure supports more than one guided mode. Above $\lambda_c$, the fiber is single-mode (only LP01 propagates); below $\lambda_c$, the LP11 mode (and higher) is also guided.

Cutoff wavelength is the fundamental design parameter for single-mode fibers, distinguishing them from multimode fibers. For SMF-28 (the standard telecom single-mode fiber), $\lambda_c \approx 1260$ nm, ensuring single-mode operation across the C-band (1530 – 1565 nm) and L-band (1565 – 1625 nm).

Mathematical condition. For a step-index fiber, the cutoff condition for the LP11 mode is:

$$V \;=\; \frac{2\pi a}{\lambda} \sqrt{n_1^2 - n_2^2} \;=\; 2.405,$$

where $a$ is core radius, $n_1$ is core index, and $n_2$ is cladding index. Solving for the cutoff wavelength:

$$\lambda_c \;=\; \frac{2\pi a \sqrt{n_1^2 - n_2^2}}{2.405} \;\approx\; \frac{2\pi a \cdot \text{NA}}{2.405},$$

where NA is the numerical aperture. The 2.405 is the first root of the Bessel function $J_0$, mathematically setting the LP11 mode cutoff.

Standard fiber specifications.

Fiber type	Core diameter	NA	$\lambda_c$	Single-mode wavelengths
SMF-28 (telecom std)	8.2 μm	0.14	1260 nm	1310, 1490, 1550 nm
HI 1060 (1060 nm SMF)	6.0 μm	0.14	980 nm	1060 – 1500 nm
HI 780 (780 nm SMF)	4.4 μm	0.13	730 nm	780, 800, 850 nm
HI 633 (632.8 nm SMF)	3.5 μm	0.13	600 nm	633 nm only (HeNe)
Visible SM fiber (400 nm)	2.5 μm	0.12	350 – 400 nm	400 – 500 nm
LMA / LMA-PM	10 – 25 μm	0.06 – 0.08	varies	1030, 1064, 1550 nm
Polarization-maintaining (PM)	4 – 9 μm	0.12 – 0.16	various	application-dependent

Effective vs cable cutoff wavelength. Two measurement conventions:

• Theoretical cutoff ($\lambda_c$): from fiber's geometry and indices; the wavelength at which LP11 becomes guided. Sharply defined in theory.
• Cable cutoff ($\lambda_{cc}$ or $\lambda_{ccc}$): measured cutoff in a coiled/installed fiber; typically 60 – 80 nm shorter than theoretical because real fibers leak the LP11 mode in tight bends, effectively making the fiber single-mode at wavelengths slightly below the theoretical cutoff.

ITU-T G.652 (standard SMF) specifies cable cutoff $\leq 1260$ nm.

Why $\lambda_c$ is set below operating wavelength.

The fiber is single-mode for $\lambda > \lambda_c$, but operation directly at or near cutoff suffers from:

1. High bend loss for LP01: near cutoff, the mode is weakly confined and large fraction of its energy is in the cladding; tight bends radiate the mode away
2. Modal noise from LP11 partial guidance: just below cutoff, LP11 is "weakly leaky" and contributes interfering noise
3. Increased PMD: large mode-field diameter at cutoff increases PMD sensitivity

Standard practice is to operate $\geq 200$ nm above cutoff. SMF-28 at 1310 nm operates 50 nm above $\lambda_c$ — sometimes acceptable, sometimes shows residual bend sensitivity; at 1550 nm operates 290 nm above $\lambda_c$ — comfortably single-mode and bend-tolerant.

Cutoff in chip waveguides. Silicon photonic waveguides have a similar cutoff condition based on the waveguide's geometric parameters. For a 220 nm × 500 nm silicon waveguide on SiO₂ at 1550 nm:

• TE₀ guided
• TE₁ cutoff at $\sim 700$ nm width
• TE₂ cutoff at $\sim 1100$ nm width
• TM₀ guided
• TM₁ cutoff at $\sim 250$ nm height

For applications requiring strict single-mode operation, waveguide width $\leq 500$ nm is typical. For applications requiring multi-mode operation (e.g., MMI couplers), widths of 2 – 10 μm are used.

Cutoff measurement. Standard techniques:

1. Bend reference technique: measure the fiber transmission with and without a tight bend. The bend-induced loss vs wavelength shows a sharp increase at $\lambda_c$ (because LP01 loss rises). This is the IEC 60793-1-44 method.

2. Multimode reference technique: measure transmission relative to a known multimode fiber. The ratio drops at $\lambda_c$ where the LP11 mode begins to contribute.

3. Cut-back method: cut fiber to shorter length; the loss change indicates which modes are still guided.

Cutoff design tradeoffs.

Lower $\lambda_c$ (smaller core, lower NA)	Higher $\lambda_c$ (larger core, higher NA)
Single-mode over wider range	More flexible coupling to lasers
Better bend tolerance at long $\lambda$	Higher coupling to fiber-pigtailed lasers
Smaller mode-field diameter	More efficient nonlinear processes
Less bending-induced macro-loss	Easier mechanical splicing

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 9 for fiber modal analysis; Snyder & Love, Optical Waveguide Theory (Chapman & Hall, 1983) for the rigorous mathematical treatment; ITU-T G.652 for standard SMF specifications.