For an MMF, as the guided mode propagates, the self-imaging effect occurs when the phase relationship between the modes returns to the input-field state. However, because the number of excited modes in SI-MMFs is large and the propagation constants of each mode do not change uniformly, the aforementioned self-imaging cannot be realized in a short SI-MMF length. The GI-MMF has more evenly propagating constants and fewer guided modes; therefore, it produces self-imaging that is similar to the incident field.
The transmission light fields of the two types of fibers were simulated using the beam propagation method (BPM: from Rsoft). In the simulation process, the numerical aperture (NA = 0.2) and transmission distance (Z = 2400 µm) of the fibers were set equal, and the refractive index distribution is shown in Fig. 1. The MMF models were subsequently analyzed for normalized field strength, and the results are shown in Fig. 2. The self-imaging of the GI-MMF was clearly observed, and the extreme value of light intensity appeared every 600 µm.
When an MMF is spliced using an SMF, it forms a traditional SMS structure. For the SGIMS structure, the length of the GI-MMF significantly influences the transmission spectrum. When the GI-MMF length was set to 600 µm, owing to the existence of a self-imaging point, the spectrum exhibited low loss, and no observable dips existed. The intensity of the transmitted light field was monitored using simulation software, and the SGIMS with different lengths was additionally parametrically scanned (parameter: wavelength, 1100–1700 nm). As shown in Fig. 3, when the splicing point of the GI-MMF was set between two adjacent self-imaging points, the initial loss of the spectrum was higher, and the amplitude showed significant wavelength dependence. In addition, the light field intensity of the self-imaging point decreased with an increase in the transmission distance. Therefore, when designing the length of the experimental structure, priority should be given to samples with shorter lengths.
The core sections at three positions in Fig. 2 were monitored to investigate the field strength distribution in the core. As shown in Fig. 4, all the core modes of the GI-MMF at different positions existed in the fundamental mode (LP01), which differs from the superposition of multiple modes in the SI-MMF. In addition, because the field strength of the GI-MMF was completely concentrated at the core midpoint, re-modulation would be more difficult. When re-modulation was applied, especially in the preparation process with the cladding as the initial modulation area (such as mechanical polishing and the hydrofluoric acid etching method), the GI-MMF required a large re-modulation depth to affect the core and produce visible interference peaks.
In recent years, owing to the low cost and high efficiency of CO2 laser preparation, researchers have used CO2 lasers to prepare various optical fiber-based sensing structures. CO2 laser irradiation simultaneously produces transmission and reflection on the fiber surface. Because SiO2 strongly absorbs CO2 laser energy at a wavelength of 10.6 µm, the energy of the transmitted laser is gradually weakened along the irradiation direction of the laser. Therefore, the RI distribution of the fiber cross-section can be changed. Compared to the mechanical polishing method, the CO2 laser modulates the geometric structure and RI distribution simultaneously. The polished depth is significantly reduced; thus, the mechanical strength and modulation efficiency are improved.
When D-shaped modulation is applied to the SGIMS structure, the self-imaging of the GI-MMF is destroyed. Therefore, energy leaks from the core to the cladding, exciting the cladding modes. For the entire structure, a composite interference fringe of the MMI and Mach–Zehnder interferometer (MZI) is formed [21].
The increase in the mode order strengthens the evanescent field; therefore, higher-order modes have a larger optical power distribution in the evanescent area. In the D-shaped area, the number of modes is defined as [24]
$${V_D}=\frac{{2\pi {r_{eff}}(d)}}{\lambda }\sqrt {{n_{co}} - {n_{ext}}}$$
,
where \({r_{eff}}\) denotes the effective radius of the D-shaped area, \({n_{co}}\) denotes the equivalent RI of the D-shaped area, and \({n_{ext}}\) denotes the external RI. Therefore, when the external RI changes, the number of modes and the output spectrum change.
Owing to the limitations of the cladding, the traditional SMS cannot effectively generate an evanescent field, which results in a lower RI response. To compare the characteristic changes after modulation, the transmission light field and transmission spectrum of D-shaped modulated SGIMS (DM-SGIMS) structure were simulated. As shown in Fig. 5(a), when light was transmitted from the SMF to the modulated GI-MMF, a portion of the energy was coupled to the cladding, resulting in a strong evanescent field. In addition, owing to the one-sided modulation, the cross-section of the light field in the GI-MMF was asymmetric.