Cladding modes

Cladding modes are the modes of light guided by the cladding of an optical fiber as a whole, with the coating, a low-index polymer or air as the outer boundary, rather than by the core. In standard single-mode fiber the core and cladding are 8.2 µm and 125 µm across; the core supports one guided mode, while a bare 125 µm silica cylinder in air has a numerical aperture of about 1.04 (capped at 1 in practice) and a V-number near 250 at 1550 nm, which corresponds to roughly 32,000 modes. Light reaches these modes when it is launched outside the core, scattered out of it at a splice or connector, or coupled out of it by a grating. They are distinct from the evanescent tail of the core mode, which carries about 19% of the power in the cladding at 1310 nm and 27% at 1550 nm without being a cladding mode.

Loss through the coating

Standard acrylate coatings have a higher refractive index than silica, so the cladding-coating boundary is not totally reflecting and cladding modes leak into the coating. Most cladding light is gone within a few meters of coated fiber, faster for high-order modes than for low-order ones. Low-order cladding modes travel at shallow angles and can survive tens of centimeters to meters, which is long enough to reach a detector at the end of a short fiber.

In a double-clad fiber the outer coating has a lower index than silica, and the cladding becomes a deliberate waveguide for multimode pump light. With an outer index of 1.375 against silica at 1.451 (976 nm), the pump NA is about 0.46. Here the cladding modes are the pump, and whatever pump or signal light remains in them at the end of the fiber has to be removed.

Observation and removal

Cladding light shows up in the lab as a coupled power that falls during the first meter or so of fiber, as a bright ring around the core in a near-field image of the end face, and as a far field wider than the core mode's. A short-fiber measurement of coupling efficiency or insertion loss can read too high because cladding light still reaches the power meter.

A cladding mode stripper removes it. In the laboratory form, a few centimeters of fiber are stripped of coating and laid in index-matching gel or a high-index polymer, which makes the cladding boundary transparent. A tight loop of coated fiber serves a similar purpose for low-order modes. In high-power fiber lasers the stripper must dissipate watts to hundreds of watts of unabsorbed pump and is spread along a length of fiber and heat-sunk. Launch conditioning in a mode scrambler includes a stripper for the same reason.

Coupling by gratings

A fiber grating couples the core mode to a cladding mode when its period matches the difference of their propagation constants. For a fiber Bragg grating, which couples to backward-traveling modes, the resonance is

$$\lambda_m = \left(n_\text{co} + n_{\text{cl},m}\right)\Lambda,$$

where $n_\text{co}$ is the effective index of the core mode and $n_{\text{cl},m}$ that of cladding mode $m$. The Bragg reflection itself is at $2n_\text{co}\Lambda$, so each cladding-mode resonance falls short of it by $(n_\text{co} - n_{\text{cl},m})\Lambda$. For a 1550 nm grating with $n_\text{co} = 1.447$, $\Lambda = 535.6$ nm, and an index difference of 0.002 to 0.01 places the dips 1.1 to 5.4 nm below the Bragg wavelength. These dips appear as a comb of loss on the short-wavelength side of the transmission spectrum, which matters when gratings are cascaded.

A long-period grating couples the core mode to forward-traveling cladding modes. Its resonance is

$$\lambda_m = \left(n_\text{co} - n_{\text{cl},m}\right)\Lambda,$$

and with an index difference near 0.003 a period of about 500 µm gives a resonance near 1.5 µm. The transmission shows a dip several nanometers to tens of nanometers wide. Because $n_{\text{cl},m}$ depends on the medium surrounding the cladding, long-period gratings are used as refractive-index, bend and temperature sensors and as gain-flattening filters for erbium amplifiers.

Microbending couples the core mode to cladding modes in the same way, with the bend spectrum of the deformation taking the place of a grating, which is why microbend loss grows at longer wavelengths where the propagation constants of core and cladding modes approach each other.

Pitfalls

Short-length cutback measurements and mode mismatch measurements can both include cladding light, which inflates the apparent coupling; enough fiber or a stripper before the detector removes it. Recoating a splice in double-clad fiber with a higher-index material releases pump light at that spot and can burn the recoat.

Common questions

Do cladding modes exist in single-mode fiber?

Yes. A single-mode fiber has one core mode, but its cladding is a large multimode waveguide. In coated telecom fiber the cladding modes are lossy and usually vanish within a few meters.

Why do fiber Bragg gratings show loss at wavelengths below the Bragg peak?

The grating also couples the forward core mode to backward cladding modes, at wavelengths shorter than the Bragg wavelength by $(n_\text{co} - n_{\text{cl},m})\Lambda$. The light coupled into those modes is lost in the coating.

How long must a fiber be to strip cladding modes?

With a standard high-index coating, a meter or two is usually sufficient for measurements at the 0.1 dB level; a stripper with index-matching gel works within centimeters.

References: A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983); T. Erdogan, "Fiber grating spectra," Journal of Lightwave Technology 15, 1277 (1997); A. M. Vengsarkar et al., "Long-period fiber gratings as band-rejection filters," Journal of Lightwave Technology 14, 58 (1996); K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, 2006).