Supercontinuum (SC) generation in all-normal dispersion (ANDi) photonic crystal fibers (PCF) has recently been investigated due to its ability to generate a low-noise broadband coherent spectrum [1–6], with a noise level much lower than typical SC sources using anomalous dispersion. The main issues with typical soliton-based SC generation is the poor flatness and the coherence degradation for a soliton number higher than 16, associated with large pulse-to-pulse fluctuations due to noise amplification by modulation instability (MI), soliton fission, and rogue wave generation [7]. On the contrary, ANDi SC generation, which is essentially based on nonlinear coherent effects such as self-phase modulation (SPM) and subsequently optical wave breaking (OWB), has a high degree of coherence and pulse-to-pulse stability [8,9]. ANDi SC generation is thus a topic being extensively investigated for several applications such as optical coherent tomography (OCT) [10], coherent amplification [11], nonlinear microscopy [12], hyperspectral stimulated Raman scattering (SRS) microscopy [13], and coherent anti-Stokes Raman scattering (CARS) spectroscopy [14]. Several recent studies have, however, shown some limitations on the input pulse duration due to SRS and polarization MI (PMI) [5,6,9,15,16]. Specifically, it has been shown that for input pulse duration longer than ${\sim}500\;{\rm{fs}}$, SRS-induced noise amplification impacts the SC pulse coherence and spectral flatness [9]. Furthermore, for input pulse duration longer than ${\sim}120\;{\rm{fs}}$, PMI can take place between the two orthogonal eigenmodes of the fiber, thus degrading the relative intensity noise (RIN) and the output polarization for non-polarization-maintaining (PM) fibers [5].

In this work, we overcome these limitations by using a silica-based PM ANDi PCF pumped with a low-noise, short pulse duration (180 fs) compact ytterbium mode-locked laser at 1049 nm. Using this system, symmetrically flat and ripple-free SC generation is generated from 670 to 1390 nm with a maximum output power of 720 mW. It is shown in particular that pumping on the fast axis of the fiber provides the flattest and most stable SC while removing the cross-phase MI (XPMI) that has recently been evidenced in PM ANDi fibers [17]. A polarization extinction ratio (PER) of 17 dB and an average RIN of 0.54% from 700 to 1100 nm are further measured. We finally compare the spectrally resolved RIN of our ANDi-fiber-based SC source with those recently published in the literature and show excellent noise and polarization characteristics.

The experimental setup used to observe and analyze coherent SC generation in the PM-ANDi PCF is shown in Fig. 1. As a pump laser, we used a femtosecond ytterbium solid-state mode-locked laser (Origami 10 HP, NKT Photonics) centered at 1049 nm, delivering a 180 fs pulse train at an 80 MHz repetition rate with a maximum average power of 4 W, low RIN of 0.5%, and PER of 31 dB. The laser output power was controlled using a variable neutral density (ND) filter. A half-wave plate was used to rotate the field polarization state at the fiber input. An aspheric lens with a focal length of 6 mm was used to couple the light into the fiber core. The fiber is the NL-1050-NEG-PM from NKT Photonics. This fiber has a core diameter of 2.4 µm, relative hole diameter of ${\rm{d}}/\Lambda = 0.45$, small hole-to-hole pitch of $\Lambda = 1.44\;\unicode{x00B5}{\rm m}$, and nonlinear coefficient of $\gamma = 26.8\;{{\rm{W}}^{- 1}}{\rm{k}}{{\rm{m}}^{- 1}}$ at 1040 nm. The fiber’s dispersion and loss profiles are shown as an inset in Fig. 1 [17]. The dispersion has an all-normal parabolic profile with a peak at ${-}{{13}}\;{\rm{ps/nm/km}}$ at 1040 nm. The PM property of the PCF is mainly stress-rod induced, and it has a slightly elliptic core, which together gives it a high birefringence of $4.7\;{{1}}{{{0}}^{- 4}}$ at the pump wavelength. The output spectrum is recorded using an optical spectrum analyzer (OSA) and analyzed as a function of input polarization and pump power, while the RIN is measured in another path using a monochromator as a filter passband, two different fast photodetectors to cover the whole SC bandwidth, and an oscilloscope.

 

Fig. 1. Schematic of the setup, including ytterbium femtosecond mode-locked laser (ORIGAMI 10 HP), variable neutral density filter (ND), half-wave plate (HWP), aspheric lenses (AL), 3D translation stages (S), 2 m of PM-ANDi PCF, flip-mirror (FM), integrating sphere (IS), 2 m of multimode pick-up fiber (MM), optical spectrum analyzer (OSA), monochromator (MONO), photodiode (PD), and oscilloscope (OSCI).

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Fig. 2. Experimental SC spectra at the output of the PM-ANDi PCF for output average power of 720 mW with an input pulse duration of 180 fs while pumping along the slow axis (red curve), fast axis (blue curve), and at 45° from the axes (pink curve). The blue and red curves are offset by 15 dB and 30 dB from the pink curve, respectively.

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Figure 2 shows the spectral intensity profile for three selected polarizations and an average output power from the fiber of 720 mW (estimated input peak power of 48 kW). We obtain the broadest bandwidth while pumping along the slow axis (red curve), with a spectrum going from 685 to 1395 nm at ${-}{{3}}\;{\rm{dB}}$ if we disregard the oscillations in the central part of the spectrum. We find the spectrum becomes more noticeably modulated as we move closer to the center of the spectrum. Furthermore, the modulations appear together with the observation of an XPMI peak [17] when pumping along the slow axis. This clarifies the importance of avoiding XPMI, since the modulation can be detrimental to interference-based imaging. The spectrum is the narrowest when pumping at 45° from the principal axes (pink curve) spanning from 700 to 1370 nm at ${-}{{3}}\;{\rm{dB}}$, which is expected because only half of the power is available on each axis. We observe that the spectrum for 45° is highly modulated from 870 to 1120 nm. The XPMI sideband is again present and slightly stronger than the one obtained on the red curve, as expected from the theory [17–19]. Then, we obtain an extremely flat spectrum when pumping on the fast axis (blue curve) with a spectrum spanning from 670 to 1390 nm at ${-}{{3}}\;{\rm{dB}}$ without any trace of an XPMI sideband around 1400 nm.

We now investigate the case with pumping along the fast axis, for which we observed the best spectrum with the least ripples. Thus, Fig. 3 shows the evolution of the SC generation for a fiber output average power increasing from 1 to 720 mW (peak power going from 8 W to 48 kW). We observe two SPM fringes on the pink curve (for a power of 6 mW). Then, by increasing further the power up to 30 mW (brown spectrum), we can clearly see the appearance of OWB on the edges. Furthermore, the SC bandwidth goes from 9 nm (in the linear regime) to 720 nm (going from 670 to 1390 nm) at ${-}{{3}}\;{\rm{dB}}$, which is more than one octave with a power spectral density (PSD) higher than 0.4 mW/nm. Next, as expected from coherent ANDi SC generation, the spectrum broadens symmetrically and is extremely flat (the maximum amplitude of the ripples in the SPM area is 1.65 dB). Finally, we do not observe any SRS components in the final spectra at high power (red and black spectra) across the whole bandwidth [5,9]. Thus, we can expect this SC generation to be extremely low-noise and highly stable.

 

Fig. 3. Experimental SC spectra at the output of the PM-ANDi PCF for output average power of 1 to 720 mW with an input pulse duration of 180 fs and an input beam polarized along the fast axis.

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Using a polarizer at the output of the ANDi-PCF, we measured the PER of the generated SC using the OSA. Figure 4 depicts the SC spectra when the input beam is polarized along the fast axis and the output polarizer is aligned on either the fast axis (red curve) or the slow axis (blue curve). Specifically, the polarizer is rotated to measure the minimum power including the whole spectrum, and then the spectrum is measured at this angle and at a 90° rotation. This way, we can measure an average PER of 17 dB over the full SC bandwidth, which means that the SC output is nearly linearly polarized. We noticed, however, a PER degradation of 14 dB compared to the input pump laser (PER of 31 dB). This degradation of 14 dB is also measured at low power (no spectral broadening) and may be explained by the collapse of the air holes at the entrance of the fiber required to remove back-reflection in the laser cavity.

 

Fig. 4. Experimental SC spectra when pumping on the fiber’s fast axis and using a polarizer aligned either on the fast axis (red) or on the slow axis (blue). The difference between the flat parts of the spectra gives a PER of about 17 dB.

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Let us now turn our attention to the noise properties of the pump and the generated SC. For the pump noise measurement, we coupled the output beam onto a silicon photodiode connected to a fast oscilloscope (DSA91204A from Agilent). After recording 10,000 pulses, we obtained the histogram depicted in Fig. 5. Using a Gaussian fit of this distribution, we extract a mean value of 2.5 and a standard deviation of 0.011. Thus, calculating the ratio of the standard deviation to the mean, we obtain a RIN value of 0.44% using this method, in rather good agreement with the laser manufacturer data (0.5%).

 

Fig. 5. Histogram of the variation of the energy of 10,000 pulses measured with the oscilloscope. The red curve represents a Gaussian fit of the distribution.

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After measuring the pump laser noise, we further investigated the RIN over the whole SC bandwidth. To this end, we used a monochromator (from Princeton Instruments) as a tunable spectral filter, and the spectrally sliced SC was sent to the photodetector and oscilloscope. We specifically used two photodetectors to cover the SC bandwidth: a silicon photodetector from 650 to 1100 nm and an InGaAs photodetector for longer wavelengths. The SC RIN was still measured using the Gaussian fit method by saving 10,000 pulses onto an oscilloscope (PicoScope) every 10 nm, with a 3 nm bandwidth for the silicon photodetector and a 1 nm bandwidth for the InGaAs one. Figure 6 depicts the two spectrally resolved RIN measurements as red dots (silicon) and as green dots (InGaAs), while the blue curve shows the related SC spectrum while pumping the fiber at 45° off the axes. We find an average RIN from 700 to 1100 nm down to 0.54%, when we omit the high edge RIN values. The results also show that the RIN increases drastically on the SC edges due to both the reduction in SC power and the strong effect of laser peak power fluctuations on the SC bandwidth [6]. Furthermore, the pink curve in Fig. 6 depicts the estimated minimum RIN values measured by our system as a function of wavelength. Indeed, our scope has an estimated dark noise standard deviation of 1 mV. Thus, if we divide this number by the mean of our Gaussian distribution, for each spectrally resolved bin, we obtain a minimum estimated spectrally resolved RIN value of 0.14%. Finally, we observe that our measured spectrally resolved RIN values are all slighty above the estimated minimum.

 

Fig. 6. Measured spectrally resolved RIN using the oscilloscope method with silicon (red dots) and InGaAs (green dots) photodetector and corresponding average normalized SC spectrum (solid blue), pumping at 45° from the principal axes plus simulated SC (black dots) and RIN spectra (dashed brown). The pink curve shows the estimated minimum RIN values from our measurement system.

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These experimental measurements have been further compared to numerical simulations of the two-coupled generalized nonlinear Schrödinger equations (CGNLSEs), as those described in [20] for highly birefringent PM fibers. We performed SC and RIN simulations solving the CGNLSEs using the split-step method and the initial conditions as described in [6] with an input pulse duration of 180 fs (full width half maximum), input peak power of 48 kW, input amplitude noise value of 0.22% (amplitude noise $\approx \;{\rm{RIN/2}}$), and associated anti-correlated pulse duration fluctuations to keep the energy of the mode-locked laser constant. To plot the simulated RIN, we used the following equation with an ensemble size of 50 independent pulses, which is sufficient to minimize modeling error:

The simulation results are shown in Fig. 6 (black dots for the spectrum and dashed brown for the RIN). As can be seen, the agreement is excellent with the experimental spectrum, for both the shape and bandwidth, with a highly modulated spectrum and generation of an XPMI sideband near 1400 nm. This agreement is also rather good between the measured and simulated RIN.

Table 1 compares the noise performances of our SC source to those in the literature [5,11,21,22]. The second column indicates the SC bandwidth. The third one explains the method used to measure the RIN of the SC system, based on either an oscilloscope in the time domain or an electric spectrum analyzer (ESA) in the frequency domain. The fourth and fifth ones stipulate the measurement and filter bandwidth to obtain the average RIN specified in the last column. Few methods have indeed been implemented to measure the coherence or the RIN of ANDi SC generation [5,21,23]. For the coherence, in [23], the authors use a dispersive Fourier transform technique to highlight the stability of ANDi SC generation. Then, using a fiber-based unequal-path Michelson interferometer, they demonstrate a high fringe visibility meaning a high degree of coherence for ANDi SC generation. Also, in [5,21], the authors use a setup composed of bandpass filters (10/12 nm), a fast photodiode, and an oscilloscope to measure the spectrally resolved RIN of the SC spectrum. In [5], the authors report an average RIN of 33%. This value can be considered high, but in this study, the coherence of ANDi SC generation is degraded by the PMI effect. In [21], the authors report a very low average RIN of 1.2%, due to the low input peak power used to obtain their ANDI SC and the large bandwidth of their filters.

Table 1. Average RIN Values in ANDi SC Generation from the Current Literature and Our System

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In Table 1, we see that we obtain the lowest average RIN value using the oscilloscope measurement method. In Refs. [11,22] the authors used an ESA for their noise measurements. Unfortunately, it is not possible to compare directly our RIN value to the 0.07% announced in [11] because they do not use any passband filters and thus measure a single RIN value for the whole SC spectrum. Furthermore, they limit their ESA measurement bandwidth from 10 Hz to 20 MHz, while the repetition rate of their laser is up to 80 MHz. Therefore, it reduces the overall RIN value. Finally, we underline the setup composed by the Origami 10 HP laser and the PM-ANDi silica PCF is the system with the lowest average RIN to our knowledge and the highest PER (measured PER of 10 dB in [11]), and thus it can also be considered as one of the state-of-the-art systems.

In conclusion, using a compact ytterbium mode-locked laser producing 180 fs pulses and a highly nonlinear PM ANDi PCF, we were able to generate an ultra-flat octave-spanning SC spectrum with a bandwidth up to 720 nm (from 670 to 1390 nm) and associated PSD higher than 0.4 mW/nm. We have shown that the SC is linearly polarized with a PER of 17 dB across the whole spectrum bandwidth and with a spectrally resolved RIN below 0.54% from 700 to 1100 nm, which is, to the best of our knowledge, the lowest average SC ANDi RIN value ever reported with this measurement method. This system could find many applications in OCT, metrology, or as a wavelength-tunable femtosecond laser source due to its octave-spanning bandwidth, flatness, low noise, high coherence, polarization, and near-linear chirp properties.