The ever-growing demand for data transmission capacities has inspired research in dense wavelength-division multiplexing (DWDM) technology with several wavelengths as optical carriers^[1,2]. Compared to continuous-wave (CW) laser sources, ultrafast lasers with high repetition rates and wide mode spacing are capable of the highest baud rate of the data signal, which is more desirable in the DWDM transmission systems^[3]. It has been demonstrated that an optical transmission system using a GHz-repetition-rate ultrafast fiber laser enabled a baud rate up to 661Tbits−1^[3], which is equivalent to the effect of hundreds of parallel CW lasers, showing great advantage in power consumption^[4]. Thus, it can be expected that a GHz-repetition-rate ultrafast fiber laser with multi-wavelength operation might be one of the ideal optical sources for the next generation DWDM transmission systems.

Despite substantial progress in the generation of GHz-repetition-rate ultrafast fiber lasers^[5–7], the GHz laser with multi-wavelength operation remains a challenge since the existing structure of the cavity cannot support its operation. The laser design is essential for the properties of GHz lasers. On the one hand, to generate multi-wavelength operation in mode-locked fiber lasers, the spectral filters or certain configurations that exert filtering effects were expected to be inserted into the resonant cavity of the lasers. However, for ultrafast lasers that can yield pulse trains with fundamental repetition rates of >1GHz, the length of the optical cavities is generally smaller than 10 cm, which makes it difficult to insert real filter devices again. In the past, an all-fiber spectral filter could be realized using the single-mode fiber/multi-mode fiber/single-mode fiber (SMF-MMF-SMF) structure based on the multimode interference effect^[8]. Subsequently, the mode-locked fiber lasers with more than 5-m-long ring cavities were constructed using SMF-MMF-SMF structures as all-fiber filters to provide tunable and multi-wavelength performance^[9–11]. On the other hand, the performance of the laser is intrinsically susceptible to the cavity parameters^[12]. For example, by inducing a low filtering effect through Fabry-Pérot cavities with finesse of <2, the laser output in the spectral domain is modulated in intensity, and the repetition rate reaching 36.4 GHz was realized^[13]. Two types of pulsations were previously observed in the laser resulting from a heterogeneous gain geometry and a soliton dynamic^[14]. In addition to the instability, additional linear losses might even lead to the disappearance of the mode locking. So even if we introduce the SMF-MMF-SMF structure in the short cavity, it would not be easy to attain the mode locking operation. Until now, the multi-wavelength performance has not yet been observed in the GHz-repetition-rate fiber lasers with the SMF-MMF-SMF cavity structure.

To solve this conflict, herein, we proposed a novel centimeter-scale hybrid laser cavity structure for the GHz-repetition-rate fiber laser with multi-wavelength operation. The proposed cavity is constructed with the hybrid SMF-MMF- SMF configuration by directly splicing a piece of MMF in both single-mode (SM) highly Yb3+-doped fiber segments. To reduce the transmission loss between the SMF and MMF of the hybrid cavity, the length of the MMF segment was identical to the reimaging distance of the input field^[16], which led to the low CW laser threshold being only 22 mW in the experiment. Taking advantage of the centimeter length and spectral filtering effect from the SMF-MMF-SMF configuration, the hybrid cavity makes it possible to achieve a mode-locked ultrafast fiber laser with 1.1 GHz and four wavelength peaks. Furthermore, by manipulating the launched cavity parameters, the shapes of the mode-locked spectra can also be tuned. The availability of such multi-wavelength mode-locked pulses is extremely significant progress among all the GHz ultrafast fiber lasers with the SMF-MMF-SMF cavity structure, which might provide a new opportunity for the next generation of large-capacity and high-speed optical communication systems.

The schematic diagram of the GHz mode-locked fiber laser with multi-wavelength operation is shown in Fig. 1(a). Indicated by a black arrow, the centimeter-scale hybrid laser cavity consists of a SM Yb3+-doped fiber (YDF, SCF-YB550-4/125, Coractive) and a passive graded index MMF (GIMF, G651A1a-50/125) with a symmetric SMF-MMF-SMF configuration. The lengths of YDF and GIMF are 2.8 and 3.4 cm, respectively. One end of the hybrid structure is connected to a fiber-type dielectric film (DF), which has a reflectance of 89.28% for the wavelength range of 1000–1100 nm. The other end of the structure is coupled to a semiconductor saturable absorber mirror (SESAM), which has a reflectance of more than 88% for 1020–1100 nm and a modulation depth of 5% at 1040 nm (Batop GmbH). A 976 nm SM laser diode is used as the pump source and is spliced to a fiber-type isolator, which is injected into the cavity by a 980/1030 nm wavelength division multiplexer (WDM). The generated laser is extracted through the signal port of the WDM and then passes through the other fiber-type isolator at a wavelength of signal lights.

It can be supposed that there would be additional transmission loss between the SMF and MMF. To reduce the loss, the length of the MMF needs to be carefully selected. A simulation is adopted to find the optimum length of the MMF. The calculated electric field intensity of the transverse modes in the structure of the SMF-MMF-SMF configuration is then depicted in Fig. 1(b). For centimeter-scale fiber lasers, the realization of CW mode locking would not be successful if the transmission loss of the laser resonator is too large. Intuitively, the transmission loss from MMF to SMF would be considerably large, so the mode locking operation in the laser is hard to achieve. Therefore, we analyze the mode coupling condition from MMF to SMF using mathematical theories. However, the coupling efficiency can be significantly increased if the following condition is required^[8]: η=∑j=0M−1∑h=0M−1a˜j2ah*2exp[i(βj−βh)z],(1)where βj and βh are the propagation constants of the jth and hth modes, respectively. M is the number of excited modes inside the MMF, and z=0 is the splicing point of the first SMF and MMF. a˜j is the modified expansion coefficient, defined as a˜j=ajPj/Ps,aj=∫θ=02π∫r=0∞ESMF(r,θ)×ψj(r,θ)*rdrdθPj,(2)where ψj(r,θ) is the mode electric field amplitude, Ps is the power of the input field, Pj is the power of the jth mode and is related with ψj(r,θ), and ESMF is the field distribution in the SMF. In the experiment, the MMF and SMF are concentrically aligned. Using the linearly polarized mode approximation, the input field distribution in SMF can be written as^[16]ESMF(r,θ,z=0)=∑j=0Ma˜jψj(r,θ).(3)

When the argument of the exponential term in Eq. (1) becomes an integer multiple of 2π, the coupling efficiency is maximized. The MMF segment is selected so that the field distribution at the end of the MMF is an image of the input field. This phenomenon is called a self-imaging effect, and the length of MMF is referred to as the self-imaging distance. To investigate the self-imaging effect based on multimode interference, the field distribution along the MMF is expressed as^[8,17]EMMF(r,θ,z)=∑j=0Ma˜jψj(r,θ)exp(iβjz).(4)

Equation (4) implies that the electric field within MMF can be decomposed into excitation eigenmodes. Self-imaging occurs at specific positions within the MMF when the subsequent condition is satisfied for all propagating modes^[15]: (βj−β0)zself-imaging=Δβjzself-imaging=mj2π,(5)where mj is an integer, and zself-imaging is the self-imaging distance. The light within the MMF converges to the self-imaging point on the axis of propagation direction when the phase difference of any modes in the MMF is equal to the integer multiple of 2π, as shown in Eq. (5). At this point, the coupling efficiency is the highest and the field distribution in the MMF is equal to the original input field distribution in the SMF.

Therefore, if the length of MMF is the same as an integer multiple of zself-imaging, most of the transmitted light will return to the SMF, instead of extinction. In our experiment, the length of MMF is 3.4 cm. The coupling efficiency from GIMF to SM YDF is approximately 77%, illustrating efficient light coupling between the two fiber segments.

Based on the results of the simulation, the hybrid cavity was constructed by a segment of 3.4 cm MMF in the middle and two segments of 2.8 cm SM gain fiber at the two ends of the MMF, limiting the total length of the cavity to under 10 cm to guarantee its GHz laser output ability. In order to obtain the transmission spectrum, a broadband light source in the 1 µm wavelength band passes through the SMF-MMF-SMF structure. The hybrid structure yielded the transmission spectra shown in Fig. 1(c) with a measurement resolution of 0.05 nm. The fundamental mode beam is coupled from the SMF into MMF, exciting many higher-order modes within MMF. As the light further propagates from the MMF into SMF, the higher-order modes are effectively filtered out and only the fundamental mode is allowed to pass through. As a result, the hybrid structure functions as a spatial filter. The spectra can be obtained by measuring a broadband light source after passing through the structure. It is apparent that the optical spectra are modulated in intensity with a period of approximately 1.4 nm in the wavelength range of 1015–1040 nm. The transmission spectrum through the fiber cavity structure exhibits a periodic distribution, and the period can also be modulated by altering the parameters of the MMF^[15] and light wavelength. This unique feature of the laser output in the spectral domain is responsible for multi-wavelength output in the GHz ultrafast fiber laser.

After constructing the hybrid cavity, its lasing performance is investigated experimentally. The multi-wavelength lasing operation ability is first investigated. At the pump power P of 430 mW, the laser operated in CW mode locking with multi-wavelength operation. The mode-locked spectra for the GHz laser with the hybrid SMF-MMF-SMF structure are presented in Fig. 2. A panoramic view of the laser spectrum [Fig. 2(a)] shows wavelength peaks extending from below 1024 nm to beyond 1032 nm. The main peaks at 1025.6, 1026.8,1028.3, and 1029.6 nm exhibit a spectral periodicity of approximately 1.4 nm. The spectral period is consistent with that of the measured transmission spectrum for the cavity structure shown in Fig. 1(c). Further, in order to verify the stability of the multi-wavelength operation, several representative spectra recorded for the present oscillator are shown in Fig. 2(b) for 1 h. With few exceptions, however, the laser spectrum is stable, without wavelength shift or any significant change in the intensity. In the experiment, the spectral shape of CW mode locking operation with multi-wavelength operation could be modulated [relative to the one in Fig. 2(a)] by changing pump power or birefringence by twisting the fiber’s polarization state in the hybrid structure, and the corresponding results are shown in Figs. 2(c) and 2(d). By twisting the polarization state of the hybrid structure, the mode coupling and interference at the fusion splice between the SMF and MMF will change, ultimately affecting the optical field transmission characteristics in the hybrid cavity. For all the spectra data in Fig. 2, the laser was held in CW mode locking operation.

The temporal, frequency, and energy characteristics for the GHz laser with multi-wavelength operation are summarized in Fig. 3. Measurements of the pulse train temporal behavior with an oscilloscope and a photodiode having bandwidths of 6 and 25 GHz, respectively, show [cf. Fig. 3(a)] output pulses separated by 896 ps, which corresponds to the fundamental repetition rate of 1.11 GHz. Figure 3(b) is representative of the radio frequency (RF) spectrum recorded between 1.11238 and 1.11738 GHz. A single peak at 1.1149 GHz is observed, and it must be emphasized that, as indicated, the background noise is suppressed by 90 dB, despite the multi-wavelength output from the centimeter-scale laser resonant cavity reported here. Figure 3(c) is a measured autocorrelation trace, and its temporal width [full width at half-maximum (FWHM)] is observed to be 2.3 ps, assuming the intensity profile to be Gaussian. In addition, the dependence of the output average power of the GHz laser with multi-wavelength operation on launched pump power P is illustrated in Fig. 3(d). The pump threshold for multi-wavelength mode locking operation is 430 mW, and the maximum average power can be obtained to be 1.76 mW at the launched pump power of 479 mW. Note, too, that the CW laser threshold lies at a low value of approximately 22 mW, confirming low transmission loss for the hybrid resonant cavity configuration.

In order to understand the function of the spectral modulation and gain of the hybrid structure in the pulse shaping process, the features of the spectral evolution of the GHz laser with P are summarized in Fig. 4. For the pump power P from the CW laser threshold of 22 to 322 mW, there was single peak in the spectral domain, as shown in Fig. 4(a). For the pump power in the 322≤P≤358mW range, the laser operated in a Q-switched mode-locked regime. New spectral components (peaks) were gradually generated according to the spectrally modulated period [Fig. 4(b)], owing to the broadened gain spectrum. Then, in the 375≤P≤393mW range, the whole linewidth of the spectra became narrow; meanwhile, the spectral “gap” between adjacent peaks was increasingly flatter. As P further increased to 456 mW, as shown in Fig. 4(f), the state reached the CW mode locking operation from Q-switched mode locking. In the evolution, the hybrid effects, such as gain, spectral modulation from the resonant structure, nonlinear effect, and amplitude modulation produced by the saturable absorber^[18], together played a significant role in pulse shaping and driving the system towards a steady state, which also demonstrated the tenability in spectra by the constructed hybrid cavity.

In summary, we have proposed a hybrid centimeter-scale SMF-MMF-SMF structure in the laser cavity for GHz mode-locked fiber laser with multi-wavelength operation. To reduce the transmission loss between the SMF and MMF, the length of MMF was elaborately set at 3.4 cm, near the self-imaging point. By adopting the constructed hybrid cavity, 1.1 GHz mode-locked ultrafast fiber laser operation with four wavelength peaks was demonstrated. A 90 dB SNR for the RF signal for the four-wavelength GHz laser can be reached. Furthermore, the tenability of the spectra was also proved. To the best of our knowledge, this is the first realization of multi-wavelength operation among the GHz lasers. The high-repetition-rate laser with multi-wavelength operation described here is readily incorporated into existing laser communication systems and devices for large-capacity and high-speed optical communications.