I. Introduction
Recently, microfiber resonators have been utilized as basic components in photonics systems [1]. Due to their characteristics such as supporting single-mode operation [2], low cost alternative waveguide and easy shaping [3]; a wide range of microfiber resonators have been proposed and fabricated [4]. One simple structure with twisting a -microfiber to shape a 1mm diameter loop with quality factor of 630000 has been demonstrated [4]. Theoretically QF value of up to 1010 is predicated [5] and a value of 470000 has been realized by the formation of microfiber coil [6]. Among the proposed structures, microfiber knot has been widely used in applications such as modulators and convertors [7], [8], tunable lasers [9], [10] and sensors [11] due to stable light coupling [12], its firm structure and easy manipulation compare with the others. Also this structure has been considered as all pass filter and as an add-drop filter (including an extra microfiber beside the knot) with QF of 13000 [13]. For the output spectrum of a filter, the flatness and the width of both transmission and rejection regions on the spectrum are important characteristics especially for wavelength division multiplexing applications and notch filters [14], [15]. Sharper roll off, adjustable pass band and less in-band ripple spectrum provide a desired filter [15], [16]. The dimensions and coupling length of the ring are the main design parameters. Though, controlling those two parameters only has limited filter response. To enhance the characteristic of the filter, multi-ring resonators have been proposed as a solution to obtain the desired pass-band spectrum [17], [18].