The higher-order modes (HOMs) of an optical fiber has been demonstrated as a new dimension to transmitting signals with the development of mode-division multiplexing (MDM) technique. This dissertation aims to explore the HOMs as an extra degree of freedom for device innovation. In particular, with femtosecond (FS) laser point-by-point (PbP) inscription technique which opens up a unique possibility to explore the HOMs for device innovation, we design, fabricate, and characterize novel-structured fiber Bragg gratings (FBGs) written in the step-index two-mode fibers. We also develop a numerical model for the PbP gratings which has the potential for inverse design problem.

Chapter 2 begins with a general framework of MDM with adaptive wavefront shaping in few-mode fibers (FMFs) and multimode fibers (MMFs), followed by two examples in slightly more detail. The fabrication setup and an short overview of the FS laser system will also be covered.

In Chapter 3, we show the design, fabrication, and characterization of off-axis Bragg gratings in a step-index two-mode fiber (TMF). Through measuring the transmission and reflection spectra along with the associated reflected mode intensity profiles under different input polarization, we experimentally investigate the off-axis TM-FBGs (FBGs in a TMF) with multiple characteristics reported for the first time to our best knowledge. To highlight, we report the laser-induced birefringence exhibits strong offset dependence, the reflectivity heavily depends on the offset and polarization, and particularly the mode pattern can be controlled solely through polarization.

The design and characterization of cross-axis TM-FBGs are presented in Chapter 4. Specifically, these gratings show six primary reflection peaks, which are identified through mode-decomposition based on the intensity profiles through nonlinear optimization problem. We also show in this chapter the development of a numerical model for the general PbP gratings, implementation of this model into standard coupled-wave analysis shows reasonable agreement to the experimental findings.

In Chapter 5, discussions and suggestions for future studies are given.