Contents I. Introduction
Rare-Earth-Doped cladding-pumped double-clad fiber (DCF) lasers have been extensively studied in recent years because of their advantages, which include the relative ease of realizing high power with a high efficiency, simple thermal management because of their geometric configurations, high reliability, high beam quality, compactness, etc. [1]–[5]. DCFs permit a good match to be made with multimode diode pump sources because of their large inner cladding. These multimode diodes emit much higher output power than that of single-mode ones. In cladding-pumped fiber lasers, signal waves are generated in the small doped core while pump waves are coupled to the large inner cladding. Thus, a high-brightness output is possible even when low-brightness multimode diode lasers are used as pump sources. However, the pump absorption rate in a cladding-pumping scheme is much smaller than that in core-pumping because of the small overlap between the pump waves and the doped core of a DCF. The low pump absorption rate results in excessively long cavity lengths of the fiber lasers, resulting in excessive background loss, which leads to degradation of the output power of a fiber laser. Therefore, achieving good pump absorption in a reasonable fiber length is essential to cladding-pumped fiber lasers, particularly for fiber lasers in which the fiber length is tightly constrained because a large amount of ground-state absorption must be overcome, e.g., in 980-nm ytterbium (Yb)-doped fiber lasers and three-level lasers [6] [7] [8]. A variety of attempts have been made to improve the low pump absorption rate of DCFs, e.g., the use of noncircular fibers (D-shaped, rectangular-shaped, etc.) and mode mixing by bending the fibers (kidney-shaped, etc.) [9]. The double passing pump scheme can also increase pump absorption rate via an external pump-feedback mirror. The use of an external mirror is simple and efficient, but, the setup becomes relatively bulky. Furthermore, it is far from cost-effective. A pump-reflecting inner-cladding fiber Bragg grating has also been reported for overcoming these drawbacks [10]. Increasing the pump absorption rate for a low numerical aperture (NA) DCF or caustic modes of DCF is still a challenging problem in a circularly symmetric DCF because the interaction of the pump with the core is rarely increased, even when a doubly passing pump wave structure is adopted. The effective coupling of cladding modes into a core mode represents a possible solution for enhancing the pump absorption rate in the cladding-pumping scheme, especially for enhancing the absorption rate of low NA and/or caustic modes, because the coupling can realize an increase in the interaction between core and cladding modes, resulting in a partial core-pumping effect. Long-period fiber gratings (LPFGs) have good potential for effectively coupling pump waves that are propagated through the inner cladding into the doped core of the active fibers. LPFGs are widely used as band-rejection filters, which are based on codirectional coupling between the core mode and the leaky cladding modes [11], [12]. In cladding-pumped fiber lasers, if the pump wave is launched into active fibers that have LPFGs, some of the pump wave that satisfies the phase-matching condition of the LPFGs is effectively coupled to the doped core and the pump wave coupled into the core is effectively absorbed by the dopant, compared to the pump wave propagating through the cladding of the fibers. Transmission spectrum of the LPFG inscribed in the SMF. The inset shows the magnified spectrum of the LPFG (solid line) around the pump wavelength region and the spectrum of the pump source (dotted line).
