I. Introduction
Femtosecond micromachining [1] has been used to fabricate a variety of photonic devices using transparent materials. Waveguide fabrication is an attractive application of this technique in relation to fabricating photonic devices [2]. Femtosecond pulses can directly increase the refractive index inside a transparent dielectric material as a result of multiphoton absorption [1], [3], [4]. This phenomenon allows us to fabricate waveguides directly in the material and realize passive and active optical devices. For example, Y-junction splitters [5], [6], X-couplers [7], periodic gratings [8]–[10], waveguide amplifiers [11], [12], couplers [22], and photonic interconnections [23] have been fabricated by using 2-D or 3-D waveguides. Writing a waveguide with a femtosecond laser is a very flexible and attractive way to make simple optical circuits, but it takes time to fabricate large-scale optical circuits.