## 1 Introduction  
Modal purity or indistinguishability is an essential factor in achieving high visibility of quantum interference for quantum photonic applications such as quantum teleportation [1] and linear optical quantum computing [2]. High visibility yields high operation fidelity and a high probability of success in quantum information processing using non-classical states of single photons. Among many approaches to obtain non-classical states of photons, spontaneous four-wave mixing (SFWM) has been intensively investigated for the frequency correlated photon-pair generation and heralded single-photon states [3]. However, frequency-correlated photon pairs by the spontaneous parametric process have complicated two-photon states and have a multi-mode nature [4; 5]. The multi-mode nature makes photons distinguishable, degrading the quantum interference's visibility. Therefore, spectrally uncorrelated photon pairs with a factorable joint spectral amplitude (JSA) can induce high visibility of quantum interference [4; 6] with high indistinguishability and high spectral purity. The simplest way to obtain spectrally uncorrelated photon-pair is the spectral filtering method with narrow-band filters, but this method can degrade the brightness and photon-number purity due to the optical loss by the filters [7]. The other ways for spectrally uncorrelated photons comes from engineering the dispersion of a parametric medium [8; 9]. In spontaneous parametric down-conversion, near unity spectral purity can be achieved with a periodically poled structure [10; 11; 12], and SFWM has been tested as well with similar techniques [8; 13; 14; 15; 16; 17]. While most of the methods are successful to some extent, many sources are expensive to make, not easy to implement, or limited to a specific wavelength range of operation due to strict requirements for dispersion and phase matching [18]. Recently, a new method of engineering the quantum states with nonlinear interference (NLI) is proposed and demonstrated [18; 19; 20]. The NLI system consists of two identical nonlinear media and one linear dispersive medium, which is placed in between them. Due to the phase shift induced by the linear dispersive medium, the joint spectral intensity (JSI) function of bi-photons shows oscillating interference patterns. By adjusting the NLI properties, the authors demonstrated the improved quantum properties of single-photon, spectral correlation, and Hong-Ou-Mandel interference using commercially available optical fibers [19; 20]. The author used programmable and tunable filters as the signal and idler filters to reduce noise photons other than the generated photon pair and to have high spectral purity. Optical fiber systems can guarantee the interoperability between systems and improve their price competitiveness through the standardization of optical communications technology. The standardization of optical frequency channels is necessary for wavelength division multiplexing and is defined by the International Telecommunication Union-Telecommunication standardization sector (ITU-T). Note that the use of customized filters or optical devices raises the entire system's price and makes system development difficult. Using photons on the ITU-T grids makes quantum technologies simple, as most optical devices in current telecommunication systems have frequency channels specified on the ITU-T grids and are commercially available with a reasonable price, high transmittance, narrow bandwidth, well-defined wavelength, etc. The center wavelength of the constructive interference is mainly determined by the length of the linear medium of an NLI system [18; 19; 20]. A carefully selected linear medium can make one of the constructive interference modes in a transmission window of DWDM filters without degrading brightness and collection efficiency to obtain high spectral purity.