With the continuous development of fiber optic communication technology， the demand for communication capacity is endless^［1］. The Mode-Division Multiplexing （MDM）system^［2］ in near-infrared wavelength， as an effective method to expand communication capacity^［3］， has received extensive research in areas such as orbital angular momentum^［4］， p1hotonic integration^［5］ and few-mode lasers^［6］. Besides， MDM is preferred in near-infrared application areas such as laser processing^［7］， optical sensing^［8］， and optical imaging^［9］. Adopting MDM systems can improve laser beam quality， enhance sensor sensitivity， and reduce the complexity of optical imaging devices. In the process of multimode transmission， it is particularly important to detect modes.

In order to monitor the types and distribution of transmitted modes， the modes of near-infrared wavelength to be monitored need to be separated first from the optical signal. Traditional methods for near-infrared mode monitoring include imaging and numerical analysis. Imaging methods mainly include spatially and spectrally resolved imaging （S²）^［10］ and cross-correlated imaging （C²）. In 2008， Rydberg et al. proposed the S² method^［11］to quantify the number and types of modes transmitted in large mode-field optical fibers. In 2014， Demas et al. determined the distribution and the weights of modes in the fiber based on the C² method at the wavelength of 1 046 nm ^［12］. In 2015， Liang Jin Huang et al. proposed a method for separating the modes of a fiber laser beam at the wavelength of 1 073 nm ^［13］. By measuring the near-field and far-field intensity distributions of the fiber output beam and using numerical analysis， various combinations of mode coefficients are calculated.

In recent years， with the rapid development of burgeoning subjects such as optical field modulation， the realization of mode-specific optical field output based on fiber laser within near-infrared wavelength has received extensive attention. Among them， near-infrared all-fiber mode converters have become a research hotspot because of their small size and ease of integration^［14］. In 2018， Wang et al. proposed a near-infrared fiber laser with transverse mode switching output based on mode-selective photonic lanterns. The mode-selective photonic lantern was used to excite the LP₀₁， LP_11a， LP_11b， LP_21a， LP_21b， and LP₀₂ modes， respectively， achieving the transverse mode-switched output of the fiber laser^［15］.In 2019， Zhang et al. proposed a mode-selective coupler based on elliptical-core FMF， which realized a seven-mode multiplexer based on the mode selection coupler in the C-band ^［16］. For various near-infrared all-fiber mode converters， detecting the modes involved is necessary ^［17-18］. However， the traditional imaging methods are not compatible with optical devices and lack an all-fiber structure. Numerical analysis methods face the challenges of the complexity of optical systems. Additionally， the aforementioned techniques for modes converting devices were only suitable for cases involving a few number of high-order modes. Currently， there is no relevant research available for analysis of large number of higher-order modes within near-infrared wavelength， especially for monitoring of them. Lately， Zhuang et al. utilized SMFs to prepare the MZI structure with miniaturized two paths for curvature sensing measurement， offering an effective approach to achieving high sensitivity with two-path MZI sensors near the wavelength of 1 550 nm ^［8］. However， its single-sensing experiment limits the application of the structure.

In this paper， we present a novel near-infrared all-fiber mode monitor based on a Mini-Two-Path Mach-Zehnder Interferometer （MTP-MZI）. By observing the distribution of the transmission and spatial frequency spectra of the MTP-MZI， we can analyze the characteristics of the modes involved in the interference and thus achieve the all-fiber modes monitoring. In addition， by introducing additional higher-order modes into the input light by HCF and then allowing their leakage through the bending， the feasibility of the mode monitoring using MTP-MZI is demonstrated. The MTP-MZI based near-infrared mode monitor offers a compact solution for all-fiber mode monitoring. Moreover， integrating advanced technologies like deep learning with MTP-MZI can enhance qualitative mode analysis， potentially transforming multimode laser communications， where dynamic mode monitoring is essential.

The principal structure of the near-infrared all-fiber mode monitor is shown in Fig. 1（a）. The MTP-MZI consists of two couplers and two transmission paths. The incident light enters the Coupler 1 region through the SMF and divides into two parts. One part of the light transmits as a fundamental mode in the SMF， and the other transmits as the multimode in the NCF. Due to the different optical path distance， the various modes produce a transmission phase shift in the two interference paths. The light interference occurs when the two-path light signal reaches Coupler 2. Therefore， we can obtain the interfering mode characteristics by analyzing the transmission and spatial frequency spectra of the MTP-MZI. When curvature occurs in the MTP-MZI， as shown in Fig. 1（b）， the fundamental mode in the SMF remains unchanged due to minimal bending， while the higher-order modes in the NCF are more sensitive to the bending. The curvature-induced leakage will cause interference fringe change. After analyzing the transmission spectrum of the output light and its spatial frequency spectrum， we can monitor the mode characteristics in the transmission path.

We use the beam propagation method to numerically simulate the optical field distribution of the NCF. Figure 2 shows the optical field distribution of the NCF before and after bending. Comparatively， bending causes significant changes in NCF modes， with high-order mode leakage.

The proposed MTP-MZI can be fabricated only with a commercial fiber optic fusion splicer. The schematic diagram of the fabrication setup is shown in Fig. 3（a）. The SMF features core and cladding diameters of 8.2 μm and 125 μm， respectively， and the NCF has a diameter of 125 μm. At first， the SMF and NCF are fixed side-by-side in the fixture of the fiber fusion splicer after stripping off their coating layer. To achieve a good coupling effect， it is necessary to pull the two optical fibers tightly and present both fibers on the same plane with the discharge electrode， as shown in Fig. 3（b）. Then， the SMF and NCF are fused by the fiber fusion splicer in manual mode， whose discharge intensity is 250 bit and the discharge time is 2 500 ms. By conducting arc discharge on the two fibers， the coupling point of the two different optical fibers is shown in Fig. 3 （c）. We can see that the length of the coupling region is 500 μm， which is smaller than the conventional tapered coupling length of about 10 centimeters. Finally， by repeating the same operation， the MZI is obtained while the second coupling point is achieved. Since most of the operation of our structure is done automatically by the optical fiber splicer during the fabrication process， we can ensure that there is no gap between SMF and NCF during multiple experiments. And in the production process， we always maintain the same welding parameters， and the final coupling area is almost the same. Therefore， with the above process， we successfully fabricate the MZI with a mini-two-path of about 4.5 cm and two coupling regions of 500 μm. Compared with traditional linear MZI with a meter scale， our MTP-MZI is more compact and affordable. In addition， the MTA-MZI structure also has the advantage of the coupler-based two-path light splitting principle， providing constant optical energy distribution and precise and stable mode control.

Fig. 4 shows the experimental setup of the MTP-MZI for the fiber mode monitoring. We fixed the proposed mode monitor onto a flexible thin steel ruler and secured it to a precision translation stage using fixtures. The position of the displacement stage was slowly controlled by a micrometer screw to act precisely at the center of the steel ruler， inducing slight deformations in the ruler to achieve precise control over the curvature of the MTP-MZI. The input port of the MTP-MZI is linked to a Broadband light Source （BBS）， while its output port is linked to an Optical Spectrum Analyzer （OSA）boasting a resolution of 0.02 nm. The curvature of the whole MTP-MZI can be calculated as：

where x is the displacement of the precision displacement stage， L is the distance between fixtures， R is the radius of curvature and C is the curvature.

Figure 5 illustrates the experimental and validation flow of the MTP-MZI all-fiber mode monitor. Figure 5（a）shows the initial state of the MTP-MZI. In Fig. 5（b）， the MZI is in a bent state. The high-order modes in NCF leak due to bending， resulting in changes in the transmission spectrum and thus the phenomenon of mode hopping. To validate the MTP-MZI can monitor higher-order modes， the HCF is inserted in the input of MTP-MZI to excite higher-order modes， as shown in Fig. 5（c）. In Fig. 5（d）， after bending， the modes in MTP-MZI returns to its original state. Experiment shows that higher-order modes can accurately be filtered， and the MTP-MZI can monitor input modes effectively.

In the experiment of this paper， we choose the near-infrared band range from 1 525 nm to 1 610 nm. Fig. 6 presents transmission and spatial frequency spectra of the mode monitor with curvature increasing from 0 m ^-1 to 0.078 37 m ^-1. In Fig. 6（a）， the intensity of each wavelength dip changes as the curvature gradually increases. For example， the intensity of Dip 1 changes from -35 dB to -30 dB， but the wavelength position and the number of the dips of the whole spectra do not change. In Fig. 6（b）， many peaks exist in the spatial frequency， where the highest peak （0 Hz）corresponds to the fundamental mode of LP₀₁， the second highest peaks （smaller frequency）correspond to the dominant transmission modes and the remaining peaks correspond to the weak transmission modes. The spatial frequency spectra of the MTP-MZI show one primary high-order mode and two secondary high-order modes. As the curvature increases， the peaks corresponding to the primary higher-order modes decrease， which indicates that the higher-order modes are leaking. By comparing the transmission and spatial frequency spectra of the MTP-MZI in Fig. 6， it is clear that the MTP-MZI is highly sensitive to curvature. Even a slight change in curvature can be detected through the intensity change of each mode. Therefore， it can be employed as a mode monitor in multimode systems.

Figure 7 shows the transmission and corresponding spatial frequency spectra of the different curvatures of the MTP-MZI. In Fig. 7（a）， the mode hopping phenomenon occurs as the curvature changes from 0.626 47 m^-1 to 1.042 72 m^-1， with the Dip2 transitioning into a peak （the green dashed rectangle）. This means that the modes in MTP-MZI have changed， as shown in Fig. 7（b）， the energy of the dominant higher-order modes is gradually coupled into the lower-order modes as the curvature increases. As curvature changes from 1.842 56 m^-1 to 2.326 41 m^-1， the mode hopping phenomena also occurs in Fig. 7（c）. In Fig. 7（d）， most minor modes are leaked. Experiments show that the functions of mode conversion and higher-order mode filtering is realized by bending the MTP-MZI structure.

On this basis， we expect to test whether newly added higher-order modes can be leaked by bending the MTP-MZI structure. If the transmission spectrum is reduced to the initial transmission spectrum where the input is fundamental mode light， then it can be determined that the externally introduced higher-order modes are entirely encompassed within the leaked higher-order modes. By the qualitative analysis of the modes， monitoring of the input light modes can be achieved. So， we carried out validation experiments.

A section of HCF is fused in front of the MTP-MZI structures to excite high-order modes. Other types of fibers can be used in place of HCF， but new interference cannot be generated during the mode excitation process， otherwise the newly generated interference spectrum will overlap with the transmission spectrum of the MTP-MZI. In Fig. 8（a）， we compare the transmission spectra before and after adding HCF in MTP-MZI. The black waveform is the initial transmission spectrum， which is represented by INIT， and the red waveform is the transmission spectrum for MTP-MZI with HCF. We can see that the increase in higher-order modes in the input light causes the dense wavelets to be superimposed on the original interference spectrum. Figure 8（b）shows the corresponding spatial frequency spectrum comparison. Compared to the initial spatial frequency spectrum， the spatial frequency spectrum changes from one dominant higher-order mode to two dominant modes after adding higher-order modes by HCF.

In Fig. 9（a）and （b）， as curvature changes from 0.574 33 m^-1 to 1.868 17m^-1， higher-order modes leakage occurs， and the wavelets in the transmission spectra gradually decrease even basically disappear. In Fig. 9（c）， when the curvature is 2.225 04 m^-1， the transmission spectrum of MTP-MZI with HCF is basically the same as the initial spectrum without HCF. In Fig. 9（d）， the curve distributions of the two structures are basically the same， and the spatial spectra are only slightly shifted in terms of the wavelengths， which indicates that the modes involved in the interference are the same in the two structures. It is worth noting that the difference between the initial black waveform and the red waveform in Fig. 9 （c）and （d）is unavoidable. Due to the introduction of high-order modes by splicing HCF， there is an inevitable core diameter and mode mismatch between HCF and SMF， leading to transmission loss. After bending， the effective length of the interference path is increased， resulting in a smaller FSR.

By comparing Fig. 8 with Fig. 9， we illustrate the mechanism of the MTP-MZI in the mode monitor. Fusing an HCF in front of MTP-MZI， dense wavelets is superimposed on the original transmission spectrum， and new high-order modes appear in spatial frequency spectrum. When the curvature changes slightly， the transmission spectrum only shows intensity changes or slight wavelength shifts. As the curvature increases， the mode hopping happens. Higher-order modes in the corresponding spatial frequency spectrum couple with lower-order modes. When the MTP-MZI is bent to a certain extent， the higher-order mode leakage occurs， and the dense wavelets on the transmission spectrum gradually disappear. The transmission and spatial frequency spectra essentially revert to the initial spectra before the fusion of the HCF. Therefore， the modes introduced externally are included in the modes corresponding to the curvature from the coupling of the higher-order subpeaks to the disappearance of the higher-order subpeaks. In the other words， the higher-order modes filtered out in this process are the newly added modes introduced externally by HCF. If we can statistically analyze all the modes of the MTP-MZI， we can quantitatively analyze the main modes involved in the interferometer from the transmission and spatial frequency spectra of the proposed structure， and monitor the unknown modes that mixed into the input signal.

At last， we conducted repeatability experiments to measure the reproducibility and stability of the structure. In the manuscript， we obtained two additional mode monitors using the same manufacturing process. The obtained transmission spectrum and corresponding spatial frequency are shown in Fig. 10（a）and （b）， respectively. We can see that the transmission and corresponding spatial frequency spectrum show a high degree of similarity， indicating that the design is robust enough to handle such changes. Figure 10（c）， （d）， （e）， and （f）show that after the same curvature adjustment， the MTP-MZI of Repeat 1 and 2 experiments can be approximately restored to the original spectrum after undergoing the same curvature adjustment and being connected to HCF， which indicates that these experiments exhibit the expected monitoring performance， showcasing excellent robustness and repeatability of our structure.

In this paper， we proposed a centimeter-scale near-infrared all-fiber mode monitor based on MTP-MZI. By changing the curvature of the MTP-MZI， the curvature-induced leakage of the high-order mode in the NCF changed， causing variations in the transmission spectrum and corresponding spatial frequency spectrum. In the validation experiments， the higher-order modes are introduced by fusion splicing the HCF， and the higher-order modes are leaked after bending the MTP-MZI structure. The transmission and spatial frequency spectra were finally recovered to the spectra without connecting the HCF， which realized the monitoring of externally introduced modes. The proposed near-infrared mode monitor offers a new approach to the feasibility investigation of mode monitors with an all-fiber format. It also has several advantages， such as small size， high robustness， easy preparation， and low cost， making it ideal for various near-infrared wavelength field applications such as optical communication， laser processing， optical sensing， and imaging.