## 1 Introduction  
For a passive optical network (PON), such as ethernet passive optical network (EPON), gigabit-capable passive optical network (GPON), broadband passive optical network (BPON), and fiber to the x (FTTX), a fiber optic splitter is one of the essential components in the optical fiber link [1]; the 3-dB splitter is one of the most common. However, for network monitoring and flexibility in the PON architecture, a free choice of power splitting ratios is desirable, such as asymmetric Mach-Zehnder interferometers [2]. Moreover, the optic splitters with a broadband characteristic are often required in the wavelength division multiplexing (WDM) applications. Several power splitting technologies have been developed, such as adiabatic Y branches [3], directional couplers [4], and multimode interference (MMI) couplers [5]. Some special MMI couplers based on special design are proposed to realize the function of arbitrary power splitting ratio, such as surface relief holograms [6], angled structure [7], special butterfly geometrical structure [8], cascaded step-size structure [9], quick response (QR) code-like structure [10], and asymmetric interference structure [11]. Some of those techniques are wavelength sensitive and some are wavelength insensitive. Some of those MMI components are sensitive to wavelength [6; 7; 8] while some are wavelength insensitive [9; 10; 11]. Arbitrary-ratio power splitters with wavelength insensitivity are appealing for power splitter applications. In this study, 1 \(\times\) 2 MMI power splitters with 1:1, 1:2, 1:3 split ratios by using QR code-like structure are demonstrated [10]. The measured transmission efficiencies of those splitters are near 80% within the range from 1530 to 1560 nm. A 1 \(\times\) 2 MMI splitter with arbitrary splitting ratio is numerically and experimentally investigated [11]. The splitting ratio from 100:0 to 50:50 can be obtained by an asymmetric multimode interference (MMI) region, one of which corners is slightly removed. However, the above broadband MMI power splitters still have weak wavelength dependence. Adiabatic directional couplers (ADCs) with excellent performance for wavelength independence are presented [12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. ADCs have other advantages, such as polarization insensitivity [18; 19; 21] and relaxed fabrication tolerance [18; 19; 20; 21]. Two types of ADC were investigated: one with weighted propagation and coupling coefficients [15; 16; 17; 18; 19; 20; 21] and the other with constant propagation coefficients and weighted coupling coefficients [12; 13; 14]. The coupler with weighted propagation and coupling coefficients results in the structure of coupling-weighted and velocity-tapered waveguides (CVW). CVW couplers have recently made use of an optical switch [15; 16; 17; 18; 19] and splitter [20; 21]. The gradual change of the CVW structure causes normal mode evolution, which is involved to the changeable propagation and coupling coefficients [15; 16; 17; 18; 19; 20; 21]. The properties of switching [15; 16; 17; 18; 19] and splitting [20; 21] can be obtained as the de-phasing variations and coupling coefficients are appropriately selected. In order to design the slow change of the guide structure, a weighting function should be used [17; 18; 19; 20; 21]. A 3-dB CVW splitter weighted by the Blackman weighting function is investigated [21]. It is shown that such 3-dB splitter has some advantages such as low excess loss, low crosstalk, high power uniformity, polarization insensitivity, broadband, and wavelength insensitivity. We aim at designing planar-lightwave-circuit (PLC) splitters with variable splitting-ratio based on the ADCs which are insensitive to wavelength and polarization.