1. Introduction

Raman coherent optical combs [1,2] are emerging as a very promising alternative to high harmonic generation for the generation of multi-octaves optical comb-like spectra and their subsequent attosecond pulse synthesis [3,4]. These combs are excited by either molecular modulation (MM) or transient stimulated Raman scattering (TSRS). In both techniques, the resulted spectra consist of a set of discrete sidebands lying on the blue and the red spectral-side of the pumping field frequencies. MM, pioneered by Steve Harris and his associates, has proven to be an excellent means to synthesize waveforms within nanosecond optical pulses [5]. The principle of the MM is the excitation of a Raman medium by two high power pulsed lasers whose frequency difference is slightly detuned from the Raman resonance so to adiabatically drive the medium to a maximum coherence [5]. With this dual strong excitation, a Raman comb with quantum conversion efficiency approaching 100% has been generated [5]. This configuration, however, involves two powerful nanosecond pulsed lasers with tight frequency control. It is thus desirable to explore alternative avenues which have less complicate laser pumping schemes.

Recently, a series of experimental results, using hydrogen filled hollow-core photonic crystal fibers (HC-PCF) have shown that TSRS is a potential path to synthesize optical waveform within nanosecond optical pulses [6–8]. Unlike the MM, and similarly to conventional stimulated Raman scattering (SRS) generation, the used pumping scheme in TSRS relies on one single 12 ns pulse laser. Consequently, the Raman coherence is no longer driven classically by external fields but grows from the quantum noise. In that work, TSRS, which corresponds to SRS generation with the pump pulse-duration τ_p being shorter than the GT₂ [9], was achieved with such a large pump pulse-duration thanks to the tight transverse confinement and the long interaction length of the pump laser coupled to a HC-PCF. Indeed, the Raman steady-state net gain G = g.I_p.l_eff can be enhanced with very moderate pump power levels by increasing the pump laser intensity I_p via a strong modal area reduction, and/or increasing the fiber effective length l_eff. Here, T₂ is the dephasing time of the Raman molecules, and g is the steady-state Raman coefficient [10]. Remarkably, the results we reported in [2,8] showed that under the high gain transient regime, the resulted initial Stokes (S) and anti-Stokes (AS) fields could be transform-limited pulses with deterministic phases and single spatial-modes [9], [11,12]. In turn, higher-orders S and AS are subsequently generated through cascade and parametric process to form an intra-pulse coherent Raman comb. This quantum-seeded coherent comb is explained using the coherent mode model introduced by Raymer and associates [13,14]. Within this model, the spontaneously emitted field or equivalently the collective molecular excitation is considered as a sum of statistically uncorrelated coherent spatio-temporal modes (STM). Under TSRS regime, the high gain and the short pulse duration conspire to amplify to the macroscopic level only a few of these STM. The pulse duration narrowness acts as a temporal filter feeding back the filtered modes to the amplification process. The larger the ratio GT₂/τ_p, the stronger the temporal modes filtering process; and thus the fewer vacuum temporal modes are amplified [9]. Furthermore, if the propagation takes place with an unity Fresnel-number propagation [14] or in a photonic structure that allows only a few spatial modes like in the case of references [2,8], a similar filtering and amplification process occur for the spatial modes. Consequently, and based on this modal picture, the level of the mutual coherence of the spectral components (i.e. phase locking) of the TSRS initiated comb one could achieved is determined by the relative strength of the dominant STM over the rest of the amplified coherent modes [2,8,9]. Consequently, in order to generate intra-pulse coherent comb with a minimum phase noise, one needs to combine the two opposing conditions of a high transient net gain G_t=√(G.τ_p/T₂) [8], and short pump-pulse duration. In the work reported in [2,8] intra-pulse phase-locking between the spectral components of ~3-octaves Raman comb was demonstrated using pump duration of 12 ns, ratio GT₂/τ_p of around 10, and net gain of G ~150. However, the measured cross-phase histograms show a non-negligible phase noise which was attributed to the contribution of the amplification of more than one temporal coherent mode [2]. Thus, reducing further τ_p/T₂ whilst keeping the net gain sufficiently high for the comb generation is a necessary condition to achieve intra-pulse phase-locked comb with much reduced phase noise as reported in [2].

2. Experimental set-up

Here, we report on the generation of TSRS initiated Raman comb in hydrogen filled HC-PCF exhibiting over five octaves wide bandwidth and pumped with picosecond pulsed laser. The fiber is inhibited coupling (IC) guiding hypocycloid-core Kagome HC-PCF [8] and contrasts with the one used in [2,8] with a much lower propagation loss. The present excitation configuration presents a maximum net gain G of ~8530 for the rotational resonance and ~28400 for the vibrational resonance, whilst the pump pulse duration of 27 ps is almost 3 orders of magnitude narrower than in [2,8].

The experimental set-up consists of a high power picosecond fiber laser whose beam, after passing through a set of half wave plate (HWP), a beamsplitter and a quarter wave plate (QWP) for power and polarization control, is coupled to a HC-PCF with 40 mm focal length anti-reflection coating lens. The laser operates at 1030 nm with pulse duration of 27 ps and a repetition rate of 1 MHz. The maximum average power is 22.7 W, corresponding to 840 kW of peak power, to intensity of 94 GW/cm² and to 22.7 µJ of energy per pulse. The fiber is a homemade IC guiding Kagome-lattice HC-PCF with 7-cell core-defect and based on a hypocycloid-core-contour (i.e. negative curvature) design [15,16]. Figure 1 shows the transmission of 3 m long section of the fiber. The transmission spectrum spans over the whole detectable spectral range of 400-2200 nm of the used optical spectrum analyzers (OSA). Within this range, the spectrum shows two transmission windows separated by high-loss band in the range of 700-850 nm corresponding to the resonance with the glass strut thickness. The long wavelength band corresponds to the fundamental transmission band and exhibits measured loss figures in the range of 200-400 dB/km. At the pump wavelength, the transmission loss was found to be 300 dB/km. In addition, the first higher-order transmission band spans from 400 to 700 nm and has a loss figure in the order of 1 dB/m. The inset of Fig. 1 shows the scanning electron micrograph (SEM) of the fiber. It exhibits a hypocycloid-like core contour with an outer-diameter of 58 µm, and inner-diameter of 48 μm, corresponding to a mode-field diameter of ~34 μm. The silica-struts thickness of the core contour was measured to be 360 nm, which is consistent with the center- wavelength of the high-loss band of ~790 nm shown in the transmission spectrum. The core-contour inward arc negative curvature parameter was measured to b = 0.41 (see reference [17] for the definition of b). The two ends of the 3 m long fiber are mounted in two commercial mechanical gas cells for gas loading into the HC-PCF and in a hermetic fashion to form a hydrogen photonic microcell (PMC).

 

Fig. 1 Transmission curve through 3 m of the IC HC-PCF over 400-2200 nm – Inset: the fiber SEM in the vicinity of its core.

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The input end of the PMC is formed with a SiO₂ window with anti-reflection coating for optimum transmission at the pump wavelength. The window of the PMC output-end is a CaF₂ window with a transmission spectrum spanning from 0.2 to 8 µm. Figure 2 shows the evolution with the input pump power of the gas-unloaded PMC output power and transmission coefficient. The power transmission coefficient reaches a maximum of over 83% for input power of less than 5 W, and then slowly decreases at 70% at the maximum input power of 22.7 W. We attribute this decrease to a mode field mismatch with the fiber fundamental guided mode due to the laser beam-size change with emitted power and to self-focusing.

 

Fig. 2 Output power versus the input power (black line). Transmission coefficient versus the input power after a 3 m air-filled fiber (blue line).

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3. Results

For the Raman comb generation, the PMC was filled with hydrogen at a constant gas pressure of 24 bar. Raman combs spanning from ~321 nm in the UV to 12.5 µm in the long-wavelength infrared have been successfully generated with input-laser polarization-controlled spectral content, constituting a new record for such configuration.

The spectral content of these combs is detailed later. This ultra-wide spectrum is partly illustrated in the bright white light that is scattered off fiber as shown in the inset of Fig. 3. Figure 3 also shows the evolution with the input-power of the measured total output power (solid curves) and the transmission coefficient (dashed curves) for circular (red curves) and linear (black curves) input laser polarization. The power was measured by a thermal sensor based powermeter. Despite the over 5 octaves wide bandwidth, the output power increases with input power with no saturation effects over the whole available input power range. Furthermore, the maximum total output comb power was measured to be 10.1 W (i.e. total transmission coefficient of 44.5%) for circular pump polarization, and 8.6 W (i.e. total transmission coefficient of 37.8%) for linear pump polarization. Figure 4 shows the spectra for both input polarizations. Both combs consist of spectral lines with frequency $\nu (m,n)={\nu }_p+m{\nu }_{vib}+n{\nu }_{rot}$. Here, ν_p is the pump laser frequency, ν_vib and ν_rot are the frequencies of H₂ Raman vibrational resonance (124.8 THz), and rotational resonance (17.6 THz) respectively. $m,n=\pm 1,\pm 2,\dots$ correspond respectively to the vibrational and rotational higher order S (negative integers) and AS (positive integers). Using different detection schemes, the spectra were measured with a detectable spectral range spanning from 200 nm to 4.8 µm. Three different optical spectral analyzers (OSA) were used to record the generated comb at the spectral ranges of 200-1000 nm, 350-1750 nm and 1200-2400 nm respectively.

 

Fig. 3 Evolution of the total measured output power for the two Raman combs with the input power of the pump laser: pumped by a circular polarization (red line) and by a linear polarization (black line). Inset: photography of the hydrogen PMC when excited by a circular polarization.

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Fig. 4 (a) Optical spectrum (b) and its associated diffracted output beam picture generated with pump linear polarization. (c-d) same as (a-b) for pump circular polarization. The pump laser line is identified with red color, the vibrational stokes and antistokes in blue and the rotational shifts in black. The three arbitrarily estimated laser lines are in dot line.

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For wavelengths longer than 2400 nm, the spectrum is measured using a homemade spectrometer with a spectral response range of 2.5-4.8 µm. The spectrometer operates by sending part of the output laser beam through linearly variable spectral filter (LVSF) and then to a PbSe photodetector. The LVSF whose transmitted spectrum is continuously tunable by sweeping the 15 mm long filter over the impinging laser beam, covers a band of 2.5-5 µm. The PbSe detector has a spectral response of 1.5-4.8 µm. These recorded spectra are then merged within a single spectrum by calibrating the relative line power strengths using common lines to two detection spectral ranges for the ranges of 200-1000 nm, 350-1750 nm and 1200-2400 nm. For the 2.5-4.8 µm range, the calibration was undertaken by directly measuring the power of one of the comb lines (see below).

As expected, with linearly polarized input pump, the spectrum is dominated by the vibrational (i.e. ν_(m,0)) Stokes and anti-Stokes (see Fig. 4(a)). Figure 4(b) shows the associated diffracted beam projected on a screen. Conversely, with pump circular polarization, the spectrum exhibits more and stronger rotational Raman lines (Fig. 4(c) and Fig. 4(d)). This is explained by the rotational Raman gain coefficient being weaker for linear pump-polarization than when it is circular [18]. For linear pump polarization, the spectrum comprises 7 vibrational lines (blue-colored lines), with a pump line (red-colored line) being strongly depleted, thus indicating a strong quantum conversion. Furthermore, each vibrational line is accompanied with relatively weaker rotational sidebands, giving a total measured lines number of 30. The power strength of these Raman lines is altered from what one would expect in free-space because of the fiber transmission spectral structure. For example, the particularly low power of the first-order AS (i.e. m = + 2, and wavelength of 722 nm) is due to its wavelength being in high loss region (Fig. 1). With circular polarization, the spectrum contrasts with the above-mentioned spectrum with a much denser comb with a total line number of over 70 lines. For both spectra, the highest Raman orders achieved are (m,n) = ( + 5, + 1), corresponding to the wavelength of ~321 nm, and (m,n) = (−2,-1), corresponding to the wavelength of 12.5 µm. The lines of the latter and that of those of order (−2,0) and (−2, + 1) (shown in dotted lines in Fig. 4(a) and 4(d)) weren’t directly measured, as their wavelength lies outside out detection spectral range, but deduced from the measured line at 3.9 µm. Recalling that the present generated Raman combs result from a cascade process whereby the vibrational Stokes and anti-Stokes lines act as pump to generate rotational Raman sidebands [8], then each rotational line is associated either with the input pump or with a vibrational Raman line. Consequently, the 3.9 µm line, which corresponds to the Raman order of (−2, + 2), i.e. to the second-order rotational anti-Stokes of the second vibrational Stokes, necessarily implies the emission of the 2nd order Stokes of the vibrational Raman resonance (−2,0) at 7.3 µm. Furthermore, in this cascade scenario, the rotational Stokes and anti-Stokes sidebands of the vibrational line (−2,0) are related parametrically to the other rotational Raman sidebands of the (−2,0) line through the energy conservation equality $2 \nu \left(-2,n\right)= \nu \left(-2,n+1\right)+\nu \left(-2,n-1\right)$. Thus, the measured (−2, + 2) requires at least (−2, + 1) and (−2,0) lines. In turn, the first-order rotational anti-Stokes line (−2, + 1) implies the generation of the 1st order rotational Stokes (−2,-1).

The strength of the spectral lines within the 2.5-4.8 µm range was calibrated by measuring the power of the 3.9 µm line. This was carried out using bandpass filter centered at 4 µm, with a FWHM of 500 nm and extinction ratio of 64 dB. We further ensured that no light outside the wavelength range of 4 ± 0.250 µm is transmitted through the filter by monitoring the transmitted beam with both OSA. Figure 5(a) shows the line power evolution with the input power for both input polarization. A maximum of 5.2 mW was achieved with a linear input polarization, corresponding to ~0.06% of the total output power, and 0.11% to power of ν_(−1,0) line. The maximum power achieved at 3.9 µm with circular input polarization was almost twice lower than with linear polarization. It is important to note here the absence of laser lines within the range of 3.1-3.2 µm due to the strong absorption peak of the water [19]. Moreover, the amplitudes of the laser lines detected by the homemade system are fully calibrated with the responses of the PbSe detector and the 1.0 optical density placed before. Finally, it is noteworthy that the generation of such a wide comb is also indicative that our IC guiding HC-PCF guides over from the UV to LWIR.

 

Fig. 5 (a) Evolution of 3.9 µm (ν_(−2,2) = 76 THz) line output power with input power for both input polarizations. (b) Example of measured trace of the oscilloscope for linear polarization.

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4. Conclusion

In conclusion, over 5 octaves combs were generated via TSRS in hydrogen filled IC guiding hypocycloid-core Kagome HC-PCF, with line emission from the UV to LWIR. The combination of a pump pulse-duration as narrow as 27 ps and the extremely high net gain of over 8530 indicates that the generated combs exhibit intra-pulse phase-locking with much lower noise than previously reported. In addition, these unprecedentedly broad laser combs present an excellent fiber based laser to address the need of many applications such as military, stand-off explosive detection, wide array sensing, new medical diagnostics or protein folding dynamics studies. To the best of our knowledge, these laser lines beyond 3.9 µm are the first high power fiber laser emissions in picosecond regime in this mid infrared spectral range. Finally, the IR range of the comb could be used in the detection of atmospheric gases such as greenhouse gases and their high absorption peaks like CO₂ (2 and 2.6 µm), CH₄ (3.3 and 7.6 µm) or H₂O (2.7-3.2 and 6.1 µm).