## 1 Introduction
For the case of using single-mode fiber (SMF) as a dispersive medium, only one constructive island can be matched on the ITU grid as \(\Delta k_{SMF}\) of SMF is quadratically dependent on the detuning of pairs from the pump frequency (\(\Delta\omega_{s(i)}=\ |\omega_{p}-\omega_{s(i)}|\)) [18; 21]. In order to match all islands on the ITU grids, \(\Delta k_{SMF}\) should be linearly proportional to the detuning, and this requires the replacement of SMF with a device having linear \(\Delta k_{SMF}\) on the detuning [18]. Having pairs over the several ITU-T grids would be helpful for complex multi-photon interference experiments or multi-wavelength channel QKD. A simple NLI system consists of two dispersion-shifted fiber (DSF) segments as a nonlinear pair generation medium and a section of standard SMF (Corning SMF-28), which is placed between two DSF segments as a linear dispersive medium. The NLI system can be extended by repeatedly adding additional sections of SMF and DSF, and the number of stage (\(N\)) is the number of DSF sections in the NLI system. For the case of pumping in the C-band (1530-1560 nm) and using a sufficiently long fiber, C-band photon-pair generation in SMF is negligible for a signal and idler detuning of 400 GHz (\(\sim\)3.2 nm) [21]. Ignoring the propagation loss of fibers and pump chirping, the bi-photon state amplitude through an \(N\)-stage NLI system can be calculated by [18],  
\[F_{\text{NLI}}(\omega_{s},\ \omega_{i})=F_{\text{DSF}}(\omega_{s},\omega_{i}) \times\Bigg{[}\sum_{n=1}^{N}\exp\{i(n-1)(\Delta k_{\text{DSF}}L_{\text{DSF}}+ \Delta k_{\text{SMF}}L_{\text{SMF}})\}\Bigg{]} \tag{1}\]  
where \(F_{\text{DSF}}(\omega_{s},\omega_{i})\) is the JSA at the signal (\(\omega_{s}\)) and idler (\(\omega_{i}\)) frequency generated by SFWM in a single DSF section, \(\Delta k_{\text{DSF}}\) (\(\Delta k_{\text{SMF}}\)) is the phase mismatch between signal, idler, and two pump fields in DSF (SMF), \(L_{\text{DSF}}\) (\(L_{\text{SMF}}\)) is the length of DSF (SMF), respectively. Each \(n\)-th segment of DSF generates an identical bi-photon state to each other, and the phase shift of \(\Delta k_{\text{DSF}}L_{\text{DSF}}+\Delta k_{\text{SMF}}L_{\text{SMF}}\) induces the quantum interference in the bi-photon state [18]. From Equation (1), the center wavelength of a constructive interference pattern is tunable by changing \(\Delta k_{\text{DSF}}\), \(\Delta k_{\text{SMF}}\), \(L_{\text{DSF}}\), \(L_{\text{SMF}}\), and \(N\). The physical parameters such as \(L_{\text{DSF}}\), \(L_{\text{SMF}}\), and \(N\) are variable by changing the length of DSF and SMF and the number of DSF and SMF sections in the NLI system. The optical parameters of \(\Delta k_{\text{DSF}}\) and \(\Delta k_{\text{SMF}}\) are controllable with the pump wavelength, types of fiber, and temperature. Here, we investigate the coarse and fine tunability of the nonlinear interference method for creating bi-photon states with high spectral purity. The stimulated-emission-based JSI, which is the absolute square of JSA, measurement technique [22] is used for fast measurements of the JSI spectra, and the measured results are compared to the theoretical prediction, which is calculated using Equation (1). We change the pump wavelength, length of DSF and SMF sections, number of stages, and temperature. The coarse and fine tunability of the NLI method is experimentally demonstrated to control a bright JSI pattern to enter into one of the 100-GHz DWDM filters with the ITU-T channel grid. These results prove that the study in this paper enriches the usefulness and practicality of the NLI method for the efficient photon-pair generation with high spectral purity.