In this paper, we reported a multi-wavelength third-harmonic generation (THG) induced by supercontinuum (SC) in an in-house fabricated suspended-core microstructured optical fiber (MOF). The adjustment of pump wavelength and pump power exerted an influence on SC which simultaneously emitted third harmonic (TH) waves in the visible light range. At the pump wavelength of 1220 nm and the average pump power of 450 mW, a multi-wavelength TH spectrum (373∼589 nm) with over twenty distinct peaks was observed under the phase matching (PM) condition between the fundamental mode and the higher-order modes. To the best of our knowledge, this is the first report on THG in optical fibers with so great a number of wavelengths. The maximal THG conversion efficiency ∼6.791 × 10−4 was obtained at 1480 nm, 350 mW, which is highly competitive compared with the values reported previously. Furthermore, theoretical simulation has been carried out, which corresponded well with the experimental observation. This multi-wavelength THG in the suspended-core MOF may provide a unique pathway towards tailored multi-wavelength ultrafast light sources for applications in sensing and imaging technologies.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Third-harmonic generation (THG) is one of the most basic nonlinear processes, which can be achieved by either frequency-doubling followed by sum-frequency generation χ(2)(ω +ω = 2ω): χ(2)(ω +2ω = 3ω) in nonlinear crystals, or by direct frequency tripling of a fundamental beam χ(3)(ω +ω+ω = 3ω) in isotropic materials (bulk glass and waveguides) [1–3]. For the former, the polarization within a birefringent material should be controlled to compensate the material dispersion . For the latter, the intermodal phase matching (PM) condition of the fundamental wave (ω0) to the higher-order waves (3ω0) needs to be satisfied [5,6]. While isotropic materials used for THG purpose suffer from technical limitations in size and length, optical fibers are considered better candidates. THG was first observed in optical fibers by Gabriagues in 1983 , and currently has been widely applied to three-dimensional optical data storage , nonlinear microscopy [9,10] and spectroscopy , etc. Certain factors are necessary for highly efficient THG in optical fibers, namely, a high third-order nonlinear susceptibility χ(3), the satisfaction of PM condition and the modal overlap between the fundamental mode and the third-harmonic (TH) mode [12–14]. Up to now, various means have been proposed to improve THG in optical fibers. For example, highly nonlinear optical fibers including tellurite microstructured optical fibers (MOFs), chalcogenide optical fibers and chalcogenide-tellurite hybrid optical fibers were designed and fabricated [15–18]. Proposition of a large core-cladding index difference or large air holes in the cladding has been put forward to help satisfy the required PM condition [19–22] and exploration has been carried out in hollow fibers , hybrid photonic-crystal fibers (PCFs) , hollow-core PCFs , exposed-core MOFs  and high-air filling MOFs , etc.
Suspended-core MOFs have both small cores and large air holes in the cladding, which are conducive to improving the fiber nonlinearity and meeting the PM condition for THG. Due to the high index contrast, a sufficient number of higher-order modes can be supported. When the fundamental mode achieves the PM with more than one higher-order modes, multi-wavelength THG can be obtained. Omenetto et al. reported a two-wavelength THG (517 and 571 nm) in PCFs induced by the fundamental wave and self-frequency-shift wave , and Warren-Smith et al. have investigated the tunable multi-wavelength THG in the exposed-core MOFs . Researchers agree that multi-wavelength THG is highly promising for the development of multi-wavelength ultrafast visible light sources. However, for the realization of practical application, following issues need to be addressed: the wavelength range is to be broadened, the wavelength number is to be increased and the conversion efficiency is to be further enhanced.
Supercontinuum (SC) is another important nonlinear process, which refers to the narrow-band incident pulses undergo nonlinear spectral broadening to yield a broadband spectrum [30,31]. SC generation in MOFs is of great interest because of the long interaction length as well as the flexibility of the fiber design [32,33]. Recently, broadband and high-powered SC generation in optical fibers has been obtained [34–37], which has attracted considerable attention for its potential application in frequency metrology, pulse compression, optical coherence tomography and long-distance remote sensing [38–41]. Within the SC range, THG would be emitted under the intermodal PM condition between the fundamental mode to the higher-order mode, and multiple PM could lead to the generation of multiple-wavelength TH waves.
In this paper, a suspended-core MOF was designed and fabricated for THG. Using a femtosecond laser as the pump source, multi-wavelength THG induced by SC was observed. By modulating SC range through controlling pump wavelength and pump power, the wavelength range and peak number of the generated TH wave were adjusted. At the pump wavelength of 1220 nm and the average pump power of 450 mW, over twenty distinct TH peaks was observed, ranging from 373to 589 nm.
2. Experiments and results
In this work, the suspended-core MOF was designed by the commercial software MODE Solutions (Lumerical Solutions, Inc.) using the full vectorial finite difference method. It was fabricated using the ultrasonic drilled method , and the cross-section scanned by an optical microscope is shown in the inset of Fig. 1(a). The core diameter was ∼2.6 µm, which was defined as the diameter of the circle inscribed in the three air holes. The fundamental mode calculated by MODE Solutions, as shown in Fig. 1(b). The nonlinear coefficient γ of the fundamental mode from 400∼2000 nm was calculated based on the effective mode area and the nonlinear refractive index of the silica glass (∼2.69×10 −20 m2/W), as shown in Fig. 1(c). The chromatic dispersion is plotted in Fig. 1(d). The fiber has a zero-dispersion wavelength (ZDW) at ∼830 nm.
The experimental setup for investigating THG in a 30 cm suspended-core MOF is shown in Fig. 2. An OPO (Coherent Inc.) with a pulse width of ∼200 fs and a repetition rate of ∼80 MHz was used as the pump source, the pumping of which was performed by a Ti: sapphire laser with a wavelength of 800 nm. The signal wavelength could be tuned from 1000 to 1550 nm, and the idler wavelength could be tuned from 1700 to 3000 nm. A neutral density (ND) filter was used to control the average pump power. During the experimental process, the signal was coupled into the fiber core by an aspheric lens (AL1) with a focal length of 6.24 mm and a numerical aperture (NA) of 0.40 (NEWPORT, F-LA11, 510∼1550 nm), while the idler was coupled into the fiber core by an AL2 with a focal length of 5.95 mm and a NA of 0.56 (THORLABS C028TME-D, 1.8∼3 µm). The output signal from the suspended-core MOF was butt-coupled into a 0.3 m large-mode-area (LMA) optical fiber with a core diameter of 105 µm and a coupling efficiency of over 95%. Finally, the LMA optical fiber was connected to optical spectrum analyzers (OSAs) with a measurement range of 350∼1200 nm or 1200∼2400 nm (Yokogawa, AQ6373B, AQ6375B) to measure the output spectrum. During the experimental process, the suspended-core MOF was fixed straight onto a stage to prevent bending or twisting.
Figure 3 shows the dependence of output spectrum on the average pump power at the pump wavelength of 1480 nm. The red line represents TH spectrum and the black line SC spectrum. The average pump power, average output power, peak input power, THG average power and THG conversion efficiency are respectively shown in Table 1. The average pump power was measured by a power meter after the ND filter. The average output power was measured by OSA from the output end of the large-mode-area (LMA) optical fiber. For such a 30 cm-long suspended-core MOF, the fiber loss (0.3 m×0.001dB/m) could be neglected, thus the average output power was treated approximately the same as the average input power. Based on it, the peak power launched into the MOF was calculated. The THG average power was also measured by OSA from the output end of the LMA optical fiber. In the experimental setup, the coupling efficiency was low due to several possible reasons: the beam quality of OPO was very poor (as shown in Fig. 1); the spot after the lens was larger than the core; the numerical aperture (NA) of the fiber and the lens did not match well, and the surface of the tellurite HBMOF was not smooth.
At the average pump power of 80 mW, SC spectrum dominated by optical solitons was obtained from 1420∼1800 nm. Within the SC range, once the fundamental mode (ω0) achieves PM (having the same effective index) with a higher-order mode (3ω0), TH wave will be emitted. From Fig. 3(a), we can see that two distinct peaks were generated at 503 nm and 518 nm. The corresponding wavelengths of the fundamental mode were 1509 nm and 1554 nm, exhibiting a cubic relationship with the peaks. When the average pump power increased to 100 and 140 mW, optical solitons carried more power away from the pump, and SC became increasingly stronger, leading to a growing TH output and more distinct peaks, namely, at 503 nm, 518 nm and 549 nm. With the further increase of the average pump power, soliton self-frequency shift (SSFS) on the red edge (long wavelength region) continually induced the SC spectrum to broaden, which eventually supported more higher-order modes to match with the fundamental mode. Consequently, more and more TH peaks were observed. At 350 mW, a broadband SC (1400∼2150 nm) induced a comb-like THG with nine wavelengths, respectively at 503 nm, 518 nm, 549 nm, 564 nm, 578 nm, 587 nm, 650 nm, 656 nm and 674 nm. The spectral span of this multi-wavelength THG amounted to 144 nm (503∼674 nm).
The THG conversion efficiency was obtained based on the experimentally measured THG average power P3ω0 and average input power (≈average output power Pω0) using η=P3ω0/Pω0, as presented in Table 1, which exhibited a growing tendency with the increment of the average pump power. However, limited by the OPO output power, the maximal conversion efficiency was halted at ∼6.791 × 10−4 (4.72 µW generated from 6.95 mW coupled power), which was highly competitive compared with those reported previously [3,13,24,26]. Theoretically, the conversion efficiency can also be obtained by the equation: η=(n(2)k1J3LPω0)2 , where n(2) is the nonlinear refractive index coefficient, k1 is the wave vector of the pump, J3 is the nonlinear overlap integral between the fundamental and the TH modes, L is the length of the fiber. From it we can see clearly that the conversion efficiency is directly proportional to Pω0, which matches well with the experimental result. Moreover, based on Table 1, the dependence of the THG average output power on the average input power was analyzed and the result is shown in Fig. 4, where the linear behavior of the curve is with a slope of 3.4, deviating slightly from the theoretical cubic relationship (a slope of 3). There were mainly two reasons accounting for this disparity: the butt-couple method led to a difference between the real power of the pump transmitting in the fiber core and the measured THG average power; the neglect of fiber loss led to a substitution of the average output power for the average input power. However, the experimentally measured power of the TH wave can be largely regarded as posing a cubic relationship with the average input power, adding evidence that the peaks resulted from THG.
To investigate the influence of pump wavelength on the output spectrum, the OPO was tuned to 1220 nm, 1375 nm, 1730 nm, 1760 nm, 1950 nm, and 2030 nm. However, due to the limitation of the OPO, pump wavelengths ranging from 1550 to 1700 nm were not available. Table 2 respectively shows the corresponding average pump power, average output power, peak input power, THG average power and THG conversion efficiency. Figure 5 shows the output SC and TH spectra, where the black line indicates the former and the red line indicates the latter. At 1220 nm, a flat SC spectrum from 1060 to 1800 nm was obtained, which was caused by the collaborative effect of self-phase modulation (SPM), the formation of higher-order soliton, and SSFS. Meanwhile, it emitted a multi-wavelength TH spectrum (373∼589 nm) with over twenty distinct peaks, which implied that more than twenty PM conditions have been achieved. To the best of our knowledge, this is the first report on THG in optical fibers with so great a number of wavelengths, surpassing far the multi-wavelength THG reported in Ref.26 and 29. In the short wavelength edge, the SC spectrum activated more higher-order modes, so the generated TH peaks were much denser than near the long wavelength edge. When the pump wavelength shifted to 1375 nm, the multi-wavelength THG reduced its peak number to sixteen and its range to λSC/3 (407∼700 nm). When the OPO wavelength was tuned to 1730 nm, only two TH peaks were obtained, namely, at 580 nm and 590 nm. However, the SC power at 1740 nm (3 × 580 nm) was too weak to induce THG, thus the peak at 580 nm disappeared when the pump wavelength shifted to 1760 nm. With the further increase of the pump wavelengths, the pump wavelength moved away from ZDW and only SPM effect remained, thus the SC spectrum range started to shrink. At 1950 nm, the TH peaks were located at 653 nm and 658 nm, and at 677 nm, a single peak was obtained at 2030 nm. Due the variation both in pump wavelength and average input power Pω0, the THG conversion efficiency obtained based on η=P3ω0/Pω0 fluctuated irregularly, as presented in Table 2. The intensified TH wave emission in this work was primarily due to the following factors: the sharp core-cladding index difference of the suspended-core MOF which supported a large number of higher-order modes; the broadband SC generation in the suspended-core MOF which promised a larger scope of PM wavelength for THG; the same of the effective index of the fundamental mode to that of the multiple higher-order modes.
The above experimental observation showed that a variation in pump wavelength or pump power directly influences the SC generation, which in turn exerts an impact on the multi-wavelength THG. The wavelength range and peak number of the generated TH wave were closely related to the broadness of the SC spectrum range. To further clarify this point, the output TH spectra at the pump wavelength of 1220 nm and 1375 nm as well as the broadest TH wave at 1480 nm (350 mW) were selected for comparison, as shown in Fig. 6. With the increase of the pump wavelength, SC gradually extended towards the long wavelength region and the spectrum width at these three wavelengths varied. Simultaneously, the emitted TH spectrum showed a same extending trend and the corresponding TH wavelength range was 353∼600 nm for 1220 nm, 407∼700 nm for 1375 nm and 467∼717 nm for 1480 nm. Within the overlapping SC range, the locations of the generated TH peaks were largely identical, that is to say, from 480 to 640 nm the output TH waves were almost the same. It indicates that within a SC range, the TH peak location is relatively determined. This is because for a certain optical fiber, the TH spectrum it can possibly generate is fixed, for the effective indices of the fundamental mode and the higher-order modes are settled upon the determination of the fiber structure, which defines the intermodal PM condition for THG. In this work, the adjustment of pump wavelength and pump power exerted an influence on the SC generation which simultaneously emitted TH waves in the suspended-core MOF. A broader SC spectrum range allows more PM conditions for THG, and at the same SC range the possible PM wavelengths for THG are invariant in spite of the pump wavelength and the pump power.
Figure 7 shows in sequence the different visible light of TH wave generated from the suspended-core MOF at 1220 nm (450 mW), 1480 nm (100 mW), 1480 nm (200 mW), 1730 nm (400 mW) and 1760 nm (327 mW). We can see that the visible light was different at different average pump powers and different pump wavelengths. At 1220 nm (450 mW), the short wavelength edge of SC extended to 1060 nm, the emitted TH wave extended to 373 nm and blue light was observed. At 1480 nm, green light was observed at 100 mW and yellow light at 200 mW. At 1730 nm (400 mW) and 1760 nm (327 mW), orange and red light was respectively observed. The frequency change of the visible light showed the wavelength of the generated THG could be tuned by modulating SC range through adjusting the pump wavelength and the pump power.
3. Numerical modeling and discussion
To verify the generation mechanism of the multi-wavelength THG in the suspended-core MOF, the intermodal PM condition between the fundamental mode and the higher-order mode was simulated. For simplicity, sixteen higher-order modes were selected, which were simulated using the full vectorial finite difference method (MODE Solutions). No modes exist between the fundamental mode (LP01) and Higher-order Mode 1. Figure 8(a) shows the intensity distributions of the sixteen higher-order modes, and Fig. 8(b) shows the calculated effective indices of the fundamental mode and the sixteen higher-order modes, where the red straight line denotes the former (LP01) from 1200 to 2100 nm and the dotted lines the latter from 400 to 700 nm. We can see that the higher-order modes have all phase matched with the fundamental mode, which corresponds to the sixteen TH waves observed in the experiment (Fig. 5(b)). Figure 8(c) presents the enlarged PM condition at the range of 550 ∼ 600 nm, which shows three PM wavelengths are achieved at 563 nm, 578 nm and 589 nm, corresponding well to the three TH waves observed in the experiment in Fig. 6. From 600 to 640 nm, no PM wavelengths were obtained, matching the fact that no TH waves were experimentally obtained in this wavelength range, as shown is Fig. 6. The theoretical calculation is basically consistent with the experimental observation. However, due to the group-velocity mismatch (GVM) between the pump pulse and the TH wave, the experimental TH wavelengths exhibited a slight deviation from the calculated PM wavelengths. Apart from it, the nonlinear contribution of SPM and cross-phase modulation (XPM) in the experiment also resulted in a disparity between the calculation and the experiment.
In Fig. 8(b), Higher-order Mode 1 has the highest effective index while that of the other fifteen declines gradually. It phase matches with the fundamental mode at 671 nm, implying that over 671 nm no TH wave can be obtained even if the SC spectrum exceeds 2013 nm (3 × 671 nm). In the experiment, the maximal TH wavelength was obtained around ∼671 nm despite the SC spectrum had extended to 2150 nm, as shown in Fig. 4(f) and Fig. 5(f). To further verify it, OPO was tuned to 2130 nm as the pump source. The average pump power and average output power were 292 mW and 2.19 mW, respectively. Figure 9 shows the SPM effect-dominated SC spectrum which ranges from 1980 to 2220 nm. We can see that no TH wave was emitted in the range of 660∼740 nm even though the SC spectrum has already extended to 2220 nm. It again proves the correspondence between the simulation analysis and the experimental observation.
In summary, both experimental observation and theoretical simulation have been carried out concerning the multi-wavelength THG induced by SC in an in-house fabricated suspended-core MOF. The SC generation is under direct influence of the variation in pump wavelength or pump power, and it in turn exerts an impact on the multi-wavelength THG. The wavelength range and peak number of the generated TH wave are closely related to the broadness of the SC spectrum range. At the pump wavelength of 1220 nm and the average pump power of 450 mW, a multi-wavelength TH spectrum (373∼589 nm) with over twenty distinct peaks was observed. The maximal THG conversion efficiency ∼6.791 × 10−4 was obtained at 1480 nm, 350 mW, which is highly competitive compared with the values reported previously. This multi-wavelength THG observed in the suspended-core MOF may provide a chance for tailored multi-wavelength ultrafast light sources for applications in sensing and imaging technologies.
National Key Research and Development Program of China (2017YFA0701201); National Natural Science Foundation of China (11604042, 61775032); Fundamental Research Funds for the Central Universities (N180406002, N180408018, N2004021); Japan Society for the Promotion of Science KAKENHI (17K18891, 18H01504); CERN under the JSPS-CERN joint research program and 111 Project (B16009).
The authors thank the Liao Ning Revitalization Talents Program.
The authors declare no conflicts of interest.
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