Fiber Bragg gratings (FBGs) are one of the key elements in various optical systems [1], [2]. An FBG can be formed by periodic refractive-index perturbations along the fiber axis, its fundamental spectral response features one or multiple narrowband reflections depending on the number of modes that can interact with the periodic index perturbations [3]. To better suit the specific applications, however, it is often desirable to tailor the grating’s spectral characteristics such as the spectral location and spacing of the reflection peaks. For example, in fiber lasers where FBGs are widely used as the end mirror and/or spectral filter [4], [5], [6], it is beneficial to enable multiwavelength lasing that can bring advantages in optical communication, optical instrument testing, and other fields [7], [8], [9], [10]. It therefore requires the utilization of multiwavelength FBGs with desired peak wavelengths and spectral spacing. Other applications, such as wavelength-division multiplexing systems where FBGs are attractive in-line spectral filters, would also benefit from the multiwavelength FBGs with flexible and adjustable spectral spacing [11], [12], [13].

To achieve these goals of creating FBGs with desired spectral location and spacing of the reflection peaks, numerous novel designs in single-mode fibers have been proposed, including sampled FBGs [14], [15], superimposed FBGs [16], [17], and cascaded FBGs [18], [19], to name just a few. In general, the aforementioned designs consist of multiple “small” FBGs, through tuning their individual pitches, relative spatial locations, and the number of these small FBGs, one can tailor the resulting overall peak wavelengths and their spectral spacing. Alternatively, Bragg gratings in few-mode (FM) and multimode (MM) fibers naturally exhibit multiple reflection peak wavelengths [3], which can realize multiwavelength operation in a single FBG and show promises for smaller footprint, simpler fabrication, and higher degree of multiplexing [20], [21], [22]. For a given FM- or MM-FBG (FBG in the FM or MM fiber), the spectral location of the reflection peaks can be tuned through varying the grating pitch (Λ) as determined by the phase-matching condition: λk=2neff,kΛ/m, where λk represents the Bragg wavelength of the kth mode (here we only consider the self-coupling cases), m signifies the order of the grating. The spectral spacing between different λk, however, would also be fixed once the grating pitch is determined for this given FBG. It is therefore desirable to add another dimension, as a complement of the grating pitch, in tailoring the spectral spacing of a single FM- or MM-FBG.

On this basis, here we propose and experimentally show that the extra degree of freedom in tuning the spectral spacing of the reflection peaks of a single FBG can be added by the higher-order modes (HOMs) via modulating the envelope of the index perturbations, as inspired by the quasi-Fourier transformation between the index perturbations and the spectral responses of FBGs [23]. Fabrication of FBGs with modulated perturbation envelopes has been demonstrated using both phase masks [24], [25] and direct inscription techniques [26], [27], [28], [29], the latter can provide higher inscription flexibility without using pre-made masks, and therefore is of our better interest. In particular, direct grating inscription can be implemented with plane-by-plane, line-by-line, and point-by-point (PbP) techniques [30]; the plane-by-plane and line-by-line inscriptions often result in large laser-modified regions [28], [29], which may add complexities and difficulties in precisely controlling the perturbation envelopes. In contrast, PbP inscription can tune the depth of index modulation at each pitch through a complete position control of the focused laser beam [31], owing to the use of objectives with high NAs and the multi-photon interaction. We therefore employ the PbP inscription provided by tightly focused infrared femtosecond (fs) pulses for FBG fabrication in this work. As a proof-of-concept, we inscribed multiple cross-axis Bragg gratings in a step-index two-mode fiber (TMF) by writing straight lines of damage points crossing the fiber axis at different tilting angles. The envelope of the index perturbations is modulated by the spatial overlapping between the damage points and the optical fields of the HOMs. We experimentally show that the cross-axis structure can introduce multiple main reflection bands associated with the HOMs, with the spectral spacing proportional to the tilting angle. We also developed a numerical model for PbP-inscribed gratings based on pulse-wave approximation and the standard coupled-mode theory, which was then validated with the experimental results. This model has the potential to offer a useful tool for the design of PbP FBGs with more complex index perturbations in optical fibers.