Long-period grid

Coupling of the core mode (red) into a cladding mode (blue)

Long Period Fiber Grids (LPGs) are optical notch filters inscribed in glass fibers . A periodic index modification of the core with a grating period of approx. 0.1–1 mm leads to a resonant coupling of the mode guided in the core (red in the picture) into a cladding mode of the glass fiber (blue in the picture). Due to the resonance , this coupling is dependent on the wavelength. In the range of the resonance wavelength λ _D , the light of the core mode can be almost completely coupled into the cladding mode, which is noticeable as a corresponding notch in the transmission spectrum of the core of the fiber. The bandwidth, shape and depth of the spectral notch can be influenced by varying the number of periods and the index modification. In the case of LPGs, the parties involved above have Modes have the same direction of propagation, while in fiber Bragg gratings (FBGs) the core mode is resonantly coupled into the opposing core mode. The mathematical description of both LPGs and FBGs is very similar as both are based on the coupled mode theory.

Manufacturing

The modification of the refractive index in the core is mainly done using two methods:

Irradiation of a glass fiber with a photosensitive core with UV light. The core of the fiber is irradiated with a UV laser through an amplitude mask. A rastered amplitude mask leads to periodically alternating zones with and without irradiation, the refractive index is increased accordingly or not.
Using a carbon dioxide laser , the fiber is heated locally and temporarily above the melting temperature from the side . After each melting process, the carbon dioxide laser moves on by the grating period along the fiber. A change in the stress-induced birefringence in the core of the fiber caused by melting causes a modification of the refractive index there.

function

The effect of the LPG in the core of the fiber can be described like an optical grating . The LPG diffracts the light that propagates in the core mode into the cladding mode. In other words, the LPG effects a phase adjustment between the core and cladding modes, and the power is transferred from core to cladding.

The modes are eigenvectors (solutions) of the Helmholtz equation . In the case of cylindrical index distributions like a glass fiber , the solutions are Bessel functions . The effective refractive indices can be understood as eigenvalues of the Helmholtz equation . Ready-made software solutions exist today for determining the Bessel functions and the associated effective refraction indices.

The resonance wavelength of the LPG λ _D results from the grating period Λ, as well as from the effective refractive indices of the core mode and cladding mode:

{\ displaystyle \ lambda _ {D} = \ Lambda \ cdot (n _ {\ mathrm {eff, K}} -n _ {\ mathrm {eff, M}})}

The strength of the coupling between core and cladding mode is expressed by the coupling factor κ [1 / m]. It results from the overlap integral of the core and cladding mode as well as the strength of the actual index modification. The coupling from the core to the cladding mode is optimal if:

{\ displaystyle \ kappa \ cdot L = {\ frac {\ pi} {2}}; \ quad L = N \ Lambda}

This corresponds to the length of the LPG and the number of grid periods. ${\ displaystyle L}$ ${\ displaystyle N}$

Applications

As notch filters, long-period gratings are complementary to the fiber Bragg gratings , which have the properties of a spectral bandpass filter . In this way, an optical spectrum can be specifically influenced by attenuating certain wavelengths using the LPGs.
Changes in the effective refractive indices of the core or cladding mode in the range of 10 ⁻⁵ are noticeable through an easily measurable shift in the resonance wavelength. LPGs are therefore often used in sensor technology.

credentials

↑ T. Erdogan: Cladding-mode resonances in short- and long-period fiber grating filters . In: Journal of the Optical Society of America A . 14, 1997, pp. 1760-1773.
^ "Suppression of stimulated Raman scattering employing long period gratings in double-clad fiber amplifiers", D. Nodop et al., Optics Letters 35, 2982-2984, (2010)

[1] T. Erdogan: Cladding-mode resonances in short- and long-period fiber grating filters . In: Journal of the Optical Society of America A . 14, 1997, pp. 1760-1773.

[2] "Suppression of stimulated Raman scattering employing long period gratings in double-clad fiber amplifiers", D. Nodop et al., Optics Letters 35, 2982-2984, (2010)