1 Introduction

Microwave photonics entails the generation, distribution, processing, and measurement of radio frequency (RF) signals in optoelectronics components [1] and has attracted great research interest due to its various advantages that range from fast response times [2], broad operating bandwidths [3], high tunability [4], low loss [5] and high immunity to electromagnetic interference [6]. In particular, microwave photonics technologies find increasing applications in high-performance analog microwave photonic links as in antenna remotes for radar systems [7, 8], microwave photonic fiber links for cellular, wireless, satellite and radio astronomy applications [9,10,11] as well as in cable television systems [12, 13], optical signal processing [14, 15] and high-speed packet-switched networks [14, 16]. In this regard, multi-wavelength fiber lasers are deemed as highly stable optical sources for microwave photonic fiber links in cellular applications. These sources are used primarily for the generation of high-frequency RF signals to cater for future 5G technology as well as RF filters for signal processing in the cellular network. For these applications, a highly stable yet tunable multi-wavelength laser source is necessary.

To achieve the desired RF output, researchers initially utilized the dual-wavelength heterodyne technique as it had simple optimization characteristics [17] as well as being cost-effective [18] and easy to obtain [19] unlike other microwave photonics techniques such as optical injection locking, optical phase-lock loops and external modulation technique. On the other hand, the application of a stable multi-wavelength optical source for realizing RF filtering through the incoherent optical summing scheme can avoid the possibility of optical interference as compared to coherent optical summing methods utilizing only a single-wavelength laser [20].

The multi-wavelength optical source is highly desired, and the proposed multi-wavelength laser in this work is designed with careful consideration of the output properties such as free spectral range (FSR), tunabilty and stability to ensure its optimal performance in both microwave signal generation and RF signal filtering. Therefore, in this work, six single–multi–single (SMS) mode fiber-based Mach–Zehnder Interferometers (MZI) with different spooling radii are designed and demonstrated as spatial mode filtering elements for multi-wavelength laser generation. The length of the two-mode step index fiber (TMSIF) section in each SMS based MZI is determined such that the FSR is maintained at around 100 GHz to cater to its potential application in 5G networks. In addition to this, the ability to tune the FSR is also incorporated into the design for flexibility in RF filter implementation. The multi-wavelength lasers exhibit FSRs from 0.89 to 0.99 nm which makes them suitable as optical sources for microwave signal generation at around 100 GHz as well as for RF filter implementation.

2 Fabrication and characterization of SMS structure-based MZI

The MZI used in this proposed work is designed using a simple SMS fiber structure which comprises of two conventional 0.5 m long pigtailed single-mode fibers (SMF-28s) and a 2.5 m long TMSIF purchased from OFS, Denmark. The SMS structure is fabricated by fusion-splicing both ends of the TMSIF with the SMF-28 pigtails using a FITEL 178A fusion splicer. Figure 1 provides the critical parameters of both the SMF-28 and TMSIF.

Fig. 1
figure 1

a Fiber structure of the SMS-based MZI, b dimension comparison of the SMF and TMSIF, c fiber parameters of SMF and TMSIF, and d propagation path of injected light in the SMS-based MZI

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The operation of the MZI begins by initially allowing only the fundamental LP01 mode to propagate effectively through the cavity. As it propagates through the SMS structure, the fundamental LP01 mode experiences refraction at the SMF–TMSIF interface as it travels from the single to the multi-mode structure. As the multi-mode fiber supports more than one mode, an LP11 mode is also formed on top of the LP01 mode. Thus, the difference in the effective refractive index of the two propagating modes in the TMSIF results in a significant phase difference. An interference pattern is produced when the two propagating modes with a phase difference recombine at the end-point after the second SMF–TMSIF interface.

The interference fringes that are produced serve as comb-filters in the laser resonator to generate the multi-wavelength output. In general, the phase difference between the fundamental LP01 and higher LP11 mode can be represented by Eq. (1) where ∆ϕ is the phase difference, neff is the effective refractive index difference, L is the physical length of the interferometer and λ is the injected light wavelength. Equation (1) can be further simplified to Eq. (2) to better show the effect of the path difference between the LP01 and LP11 modes has on the phase difference. L1 and L2 in Eq. (2) represent the propagation length of the LP01 and LP11 modes, respectively [21], and only when the phase difference is an even integer of π will a peak transmission occur in the propagating light. On the other hand, a minimum transmission would occur when the phase difference multiple is an odd integer of π. The combined effect of the MZI peak transmission together with the gain spectrum and cavity modes of the laser resonator defines the mode filtering characteristics of the comb filter.

$$\Delta \emptyset = \frac{{2\pi \Delta {n_{\text{eff}}}L}}{\lambda }$$
(1)
$$\Delta \emptyset = \frac{{2\pi ({L_1} - {L_2})}}{\lambda }$$
(2)

A simple FSR tuning mechanism has also been added into the proposed design to further extend the potential applications of the multi-wavelength laser. The ability to tune the FSR is achieved by simply changing the spooling radius of the TMSIF section in the SMS-based MZI. The macro-bending imposed onto the TMSIF through spooling induces geometric and material stress in the fiber. These in turn changes the refractive index and propagation path in the TMSIF and thus the phase difference. The relationship between the changes of phase difference with bending radius is given in Eq. (3) where δϕ represents the changes in phase difference, ko represents the vacuum wavenumber, n represents the refractive index of the core in straight fiber, l is the physical length of TMSIF section, δn1 and δn2 represents the changes in refractive index of the fundamental and higher-order mode, respectively, Ʌ represents the distance between two propagating path and R represents the fiber bending radius [22].

$$\delta \phi \approx 2{k_o}nl\left[ {\frac{{(\delta {n_1} - \delta {n_2})}}{n} + \frac{\varLambda }{R}} \right]$$
(3)

Owing to the changes in bending radius, the phase difference between the fundamental LP01 and higher LP11 mode is varied. These changes in turn vary the resulting interference fringes and transmission characteristics of the MZI. The variation of the transmission characteristic manifests itself as changes in the FSR when incorporated into a laser resonator. A total of six mandrels with different radii ranging from 30 to 100 mm have been utilized for analysis. The result from the analysis successfully verifies the changes of the phase difference with macro-bending of fiber (Fig. 2).

Fig. 2
figure 2

Macro-bending of TMSIF on mandrel of different radius a R: 100 mm, b R: 90 mm, c R: 80 mm, d R: 70 mm, e R: 60 mm, f R: 50 mm, g R: 40 mm, and h R: 30 mm

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Transmission analysis is performed on the 6 different MZI setups using a broadband amplified spontaneous emission (ASE) source operating at 1440–1560 nm from a thulium–fluoride fiber (TFF) gain medium using the setup as shown in Fig. 3.

Fig. 3
figure 3

Experimental setup for characterization of MZI design using ASE source from TFF gain medium

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Figure 4a–f illustrates the changes in transmission characteristics of the SMS-based MZI when at different magnitudes of macro-bending. The spooling radius of the TMSIF section presented in this work is limited to a range of 30–80 mm. The spooling radius is defined so that the macro-bending shows significant effect on the transmission characteristics but does not exceed the threshold to excite the propagating modes into radiation modes. The macro-bending effect induced by spooling the TMSIF using mandrels of different sizes can be seen to significantly affect the interference fringes of the MZI. As seen in Fig. 4, the FSR of the transmitted signal through the MZI generally increases as the spooling radius of the TMSIF decreases and augurs well with the result predicted by Eq. (3). On the other hand, the extinction ratio (ER) of the transmitted signal decreases as the spooling radius reduces, which is due to the decreasing strength of propagating signals in which a large portion will be travelling in the cladding. This is also the limiting factor which defines the smallest spooling radius of the TMSIF in the MZI design.

Fig. 4
figure 4

Transmission characteristics of six different MZI setups, each with different TMSIF spooling radius of a R: 80 mm, b R: 70 mm, c R: 60 mm, d R: 50 mm, e R: 40 mm and f R: 30 mm

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The detailed transmission characteristics of the different MZIs are given in Fig. 5. Figure 5a shows the comparison of the transmission spectra of the 6 different MZI setups at wavelength ranges of 1502–1508 nm. In this figure, obvious differences can be observed both in terms of phase and amplitude of the transmitted signals. The random phases of the transmitted light originate from the various phase-difference magnitudes induced on the propagating light by the TMSIF sections in the different MZI setups. On the contrary, the differences in amplitude originate from the macro-bending loss in the TMSIF sections due to the small spooling radii. These two observations validate that the transmission characteristics of proposed MZI structures can be varied by simply changing the spooling diameter of the TMSIF in the SMS fiber structure.

Fig. 5
figure 5

a The transmission spectrum of the different MZI setup with different spooling radius, b changes in FSR and ER of optical signal transmitted through the six different MZI setups

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The detailed evolution of the FSR and ER of the signal transmitted through the 6 different MZI setups is given in Fig. 5b. By decreasing the spooling radius from 80 to 30 mm, the ER of the transmitted signal reduce from ~ 7.0 to 3.0 dB. Beyond the spooling radius of 30 mm, no interference pattern can be observed in the transmitted signal. The reduction of the ER with the decreasing spooling radius as well as the absence of light interference in the MZI setup with spooling radii of less than 30 mm verify that the macro-bending imposed on the TMSIF causes the redistribution of the mode field to the modes away from the center of curvature [23, 24]. On the other hand, the observed FSR increases from 0.89 to 0.99 nm as the spooling radius decreases from 80 to 30 mm. The evolution trend in both the ER and FSR of the six MZI setups agrees well with fiber-bending theory [25].

3 Experimental demonstration of SMS-based MZI for multi-wavelength laser generation

Figure 6 illustrates the experimental setup of the proposed multi-wavelength laser cavity. In this work, a TFF laser cavity is chosen as the resonator system for multi-wavelength laser generation. The cavity is constructed using a 1400 nm laser diode (LD) as the pump source together with two polarization-insensitive (PI) isolators to protect the LD and ensure unidirectional propagation in the cavity. A wavelength division multiplexer (WDM) is used as coupling device for the pump and signal laser while a 11.6 m TFF serves as the laser gain medium. A polarization controller and a 90/10 tapped coupler act as a signal extractor in the laser cavity. The 11.6 m-long TFF gain medium used in this proposed work is obtained from FiberLabs Inc with a dopant concentration of 3200 ppm mol, numerical aperture of 0.26, mode field diameter of 4.5 μm at 1500 nm and ground-state absorption of 0.15 dB/m at 1400 nm. Signal analysis of the sample signal extracted through the 10% port of the optical coupler is carried out using a Yokogawa AQ6370C optical spectrum analyzer with resolution of 0.02 nm and a Thorlabs optical power meter.

Fig. 6
figure 6

Experimental setup of the proposed laser resonator incorporating SMS-based MZI as comb filter for multi-wavelength laser generation

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Figure 7 illustrates the mode filtering performance of the different MZI setups when incorporated into the laser resonator. In general, the multi-wavelength laser generated using the MZI with a decreasing spooling radius exhibits an increasing FSR. This observation is the same with that observed from the transmission spectra of the different MZI setup. The number of lasing lines within the 10 dB range of the spectral peak intensity shows a decreasing trend with decreasing spooling radius as a result of the increasing loss of the laser resonator from the increasing bending of TMSIF. On the other hand, all the generated multi-wavelength lasers exhibit high optical signal-to-noise ratios (OSNRs) of > 47 dB. The high OSNR implies the strength of the multi-wavelength laser.

Fig. 7
figure 7

The optical spectra of multi-wavelength laser generated using MZI with different spooling radii a 80 mm, b 70 mm, c 60 mm, d 50 mm, e 40 mm, and f 30 mm

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In addition, the stability of the generated multi-wavelength laser is observed and analyzed over a period of 100 min. The measurement is taken at time intervals of 5 min and shows the high stability of the multi-wavelength laser. As seen in Fig. 8, all the multi-wavelength spectra generated using different MZI setups show stable performance with clear lasing lines throughout the 100 min period and no significant power fluctuation and wavelength drift observable.

Fig. 8
figure 8

Spectral domain stability of the multi-wavelength laser generated using MZI of different spooling radii a 80 mm, b 70 mm, c 60 mm, d 50 mm, e 40 mm and f 30 mm

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Figure 9 shows the detailed stability performance of the multi-wavelength laser generated using different MZI setup. As shown in Fig. 9a, all the MZI setups generate multi-wavelength outputs with highly consistent FSR throughout the period of 100 min. The maximum fluctuation that has been observed in the FSR measurement is ~ 0.02 nm. It is possibly caused by excess twisting of TMSIF in the MZI setup. The excess fiber twisting resulted in inconsistency of the propagation path length difference in the TMSIF fiber and hence causes FSR fluctuation [26]. Moreover, the measured OSNR differs for MZI setups with different spooling diameters. This is caused by the variation of power distribution during multi-wavelength laser stabilization process which resulted in shifting of the cavity gain as well as different magnitude of ASE suppression in the different setup [27]. The measured ONSR is taken from the peak lasing wavelength to that of the peak ASE spectrum. In addition, a slightly higher fluctuation of approximately 4 dB has been observed in the OSNR of the multi-wavelength laser generated using MZI setup with bend radius of 30 mm and 80 mm. The reduced OSNR performance is attributable to unavoidable environmental perturbations that will affect the laser system [28].

Fig. 9
figure 9

Stability performance of the generated multi-wavelength laser using MZI setup with different spooling radii ranging from 80 to 30 mm over 100 min period in terms of a FSR, b OSNR, c centre wavelength, and d peak intensity

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On the other hand, high stability has been observed in the center wavelength and peak intensity performance of the multi-wavelength lasers. Minimal fluctuations of < 0.1 nm and < 0.5 dB are observed at the center wavelength and peak intensity of the multi-wavelength laser generated over the 100 min’ period. The minimal fluctuation in the observed center wavelength and peak intensity further verifies the stability of the generated multi-wavelength laser. The SMS-based MZI shows significant promise for the generation of multi-wavelength lasing at the S-band region, and also shows significant promise for applications in other laser cavities that utilize broad emission bandwidth gain media such as ytterbium- [29] and erbium-doped fiber lasers [30].

4 Potential applications of proposed multi-wavelength fiber laser in microwave photonics

The proposed multi-wavelength fiber laser is a promising optical source for the generation of microwave signal using optical heterodyne technique. The FSR range of 0.89 –0.99 nm can successfully generate microwave signal at frequency ranging from ~ 118 GHz to 131 GHz. The relationship between FSR of the multi-wavelength laser and the frequency of microwave signal to be generated is illustrated in Eq. (4). The term FRF in Eq. (4) represents the frequency of generated microwave signal, c represents the speed of light in vacuum, λ represents the centre wavelength, and ∆λ represents the FSR of the multi-wavelength laser [31].

$${F_{{\text{RF}}}} = \frac{c}{\lambda^2}(\Delta \lambda )$$
(4)

Owing to the high stability and high wavelength spacing, the proposed multi-wavelength laser can have application in RF carrier generation for future 5G technology of cellular network. In particular, the microwave signal that can be generated from the proposed multi-wavelength laser has high compliance to the frequency range of target 5G technologies around 100 GHz [32, 33]. Furthermore, the operating wavelength of the optical resonator in the shorter S-band region can better ensure the stability of generated RF carrier due to its better immunity to fiber bending. The relationship between the critical bend radius of a fiber and its operating wavelength is presented by Eq. 5 where n1 represents the core refractive index, λ represents the operating wavelength and NA represents the numerical aperture [34]. The critical bend radius is the minimum bend radius that can be sustained by the fiber without additional losses. As proven by Eq. (5), the proposed multi-wavelength laser can sustain lower bend radius and thus less susceptibility to bending loss due to its shorter operating wavelength as compared to commonly proposed multi-wavelength laser operating in longer C-band region. This ensures the stability of the multi-wavelength laser and thus the stability of the generated RF carrier.

$${R_{\text{c}}} = \frac{{3{n_1}^2(\lambda )}}{{4\pi {{(NA)}^{\frac{3}{2}}}}}$$
(5)

As the proposed laser can also provide FSR tuning, many microwave photonics filter applications using incoherent optical summing scheme can be realized. Owing to the FSR tunability of the proposed multi-wavelength laser, MPF implemented using it as optical source can have FSR with flexible tuning range. The relationship between the FSR of RF filter and that of the multi-wavelength laser is presented in Eq. (6) where D and L represent the dispersion parameter and length of the dispersive medium, respectively, and ∆λ represents the FSR of the multi-wavelength laser source [35].

$${\text{FS}}{{\text{R}}_{\text{RF}}} = \frac{1}{D(\Delta \lambda )L}$$
(6)

Besides, the large FSR of the multi-wavelength laser can result in a broad Nyquist zone in the implemented RF filter. A broad Nyquist region is an important parameter that can significantly affect the performance of a designed RF system by avoiding sideband mixing between adjacent comb lines, which is highly desirable for real-world applications. The relationship between the frequency limit of the Nyquist zone and the FSR of the multi-wavelength laser is presented in Eq. (7) [36].

$${F_{\text{Nq}}} = \frac{1}{2}\left( {\frac{c}{\lambda^2}} \right)\Delta \lambda$$
(7)

On the other hand, the considerably large spectral range of the multi-wavelength laser as compared to dual-wavelength laser source can help to reduce the demand of dispersion to generate a RF filter with some targeted bandwidth. Owing to the inverse proportional relationship between RF bandwidth with comb spectral range and dispersion, the considerably wide spectral range of the proposed multi-wavelength lasers as compared to dual-wavelength laser source can result in reduce need of dispersion which is in other words the length of dispersive medium and hence the filter latency. The relationship between RF bandwidth and the required dispersion is presented in Eq. (8) where BWRF represents the RF bandwidth and BWoptical represents the spectral range of optical source [37] (Table 1).

$${\text{B}}{{\text{W}}_{\text{RF}}} = \frac{1}{{{\text{B}}{{\text{W}}_{\text{optical}}}(D)}}$$
(8)
Table 1 Summary of the characteristics of the proposed multi-wavelength laser source and their advantages for application of (i) microwave signal source generation and (ii) microwave photonics filter implementation
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It must be noted, however, that the above is merely a discussion on the possible applications from this work, and any real-world system would require further enhancement and optimization beforehand.

5 Conclusion

Six different SMS-based MZI setups are designed and incorporated into a laser resonator operating in the S-band region for multi-wavelength laser generation. The different macro-bending magnitudes in each of the MZI setups enable the generation of multi-wavelength laser with FSR tuning capabilities. Changing the spooling radii from 80 to 30 nm results in the FSR changing over a range of 0.89–0.99 nm. The generated multi-wavelength output shows high stability both in terms of wavelength and amplitude, making them highly suitable for various applications in the field of microwave photonics.