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A nearly two-octave wide coherent mid-infrared supercontinuum is demonstrated in a dispersion-engineered step-index indium fluoride fiber pumped near 2 µm. The pump source is an all-fiber femtosecond laser with 100 fs pulse width, 570 mW average power and 50 MHz repetition rate. The supercontinuum spectrum spans from 1.25 µm to 4.6 µm. Numerical modelling of the supercontinuum spectra show good agreement with the measurements. The coherence of the supercontinuum is calculated using a numerical model and shows a high degree of coherence across the generated bandwidth allowing it to be used for frequency comb applications.
© 2015 Optical Society of America
1. Introduction
Broadband mid-infrared (MIR) supercontinuum (SC) sources are sought for a number of applications including - among many others - spectroscopy, environmental sensing, standoff detection, and imaging [1]. The SC sources are especially important for spectroscopy applications in the MIR due to the abundance of unique molecular signatures in this part of the optical spectrum. Additionally, SC sources can be used to realize broadband frequency combs, which are vital tools for frequency metrology and high-resolution spectroscopy [2]. The key characteristic that enables the generation of stabilized frequency combs is the shot-to-shot coherence of the SC. The coherence properties of the SC have been studied in detail by other groups and depend on a number of factors such as the pump pulse width and the properties of the nonlinear waveguide used for the spectral broadening [3]. It is widely understood that in order to generate a SC with high coherence, the pump source needs to operate in the femtosecond regime [3,4]. While MIR-SC generation is possible by employing high-energy nanosecond and picosecond pulsed sources [1, 5–9], these SC systems inherently lack the shot-to-shot coherence. A number of systems have been demonstrated for SC generation in the MIR using femtosecond pump lasers [10–14], which could in principle provide the shot-to-shot coherence. However, most of the existing demonstrations rely on solid-state femtosecond pump sources that are relatively large and expensive and usually suffer from low (kHz level) repetition rates [10,12,14]. In particular, the low repetition rate makes these sources unsuitable for frequency comb spectroscopy in the molecular fingerprint region, as the comb spacing is given by the pump repetition rate. Therefore, there is a need for developing MIR-SC sources that are pumped using high (tens of MHz) repetition rate femtosecond fiber lasers, which in addition lowers the size, complexity, and cost of such a system, allowing it to be field-deployable for environmental sensing applications. Additionally, such high-repetition-rate SC sources have the advantage of being compatible with fast-scanning FTIR spectrometers.
A number of material systems have been proposed for MIR-SC generation. Some primary examples include optical fibers based on fluoride [1,5,7–10,15], tellurite [6,11], and chalcogenide [12–14] glass, as well as micro-fabricated waveguides based on silicon [16] and chalcogenide [17]. The majority of the experimental MIR-SC demonstrations using fluoride-based fibers have been focused on nanosecond and picosecond pumping at high energies [1,5,8,9], which result in a broadband but incoherent SC. In these systems, fibers with weak waveguide dispersion can be used without the need for dispersion engineering. This stems from the fact that the material zero-dispersion wavelength for fluoride-based fibers is between 1600 nm and 1700 nm, which allows the generation of a MIR-SC using high-energy pulses around 2 µm by utilizing Raman scattering processes in the anomalous dispersion regime. On the contrary, the generation of a femtosecond-pumped MIR-SC would require significantly more careful dispersion engineering using the waveguide dispersion of the fiber. In this case, a near-zero dispersion at the pump wavelength and a small dispersion in the MIR region are required to optimize the bandwidth of the SC in the MIR. Zirconium fluoride (ZrF4) and Indium fluoride (InF3) glasses are two commonly used fluoride-based materials that are used in the optical fiber fabrication. Optical fibers made of indium fluoride (InF3) glass are known to have robust fabrication process, environmental stability, and broad transmission window from the visible wavelengths to 5.5 µm [18]. This transmission window in the MIR is superior compared with ZrF4 fibers, which only transmit up to 4.5 µm. While ZrF4 fibers have been the subject of most MIR-SC demonstrations using fluoride-based fibers, the advantages of InF3 fibers have motivated recent demonstrations of SC generation using these fibers [8–10]. In addition to the transmission it turns out that the easy-to-manufacture step-index fibers made from InF3 exhibit favorable dispersion properties for SC generation when pumped within the Thulium gain window, which opens up a way for reliable and high power fiber based pump sources. In this work we demonstrate, for the first time, the ability to engineer the dispersion of fluoride-based step-index fibers for SC generation using a femtosecond pump at 2 µm. We show that by controlling the geometric parameters of the step-index fiber, a broadband and smooth MIR-SC can be generated using a femtosecond Thulium-based fiber laser. To our knowledge, this work is the first experimental demonstration of dispersion engineering in step-index fluoride-based optical fibers for MIR-SC generation in the femtosecond regime. The reported results are also the first demonstration of MIR-SC generation in InF3 fibers pumped by a femtosecond fiber laser. We believe this is a significant step in realizing a MIR-SC source that is coherent, high-repetition-rate, and compact. In addition to experimental data, we present numerical modelling results that show good agreement with the measured spectra. The numerical model is used to estimate the SC coherence for a pump pulse with the same pulse energy and pulse width, but with added quantum-limited noise. The calculated coherence shows a highly coherent SC across most of the generated spectrum.
2. Pump Laser Design
A newly developed femtosecond fiber laser (Thorlabs FS-1900) has been employed for this work. The design of the pump laser is shown in Fig. 1(a). A femtosecond mode-locked fiber laser (MLFL) at 1560 nm with a 50 MHz repetition rate is amplified in an Er-doped fiber amplifier (EDFA). The amplified pulses are sent into a highly nonlinear fiber, which shifts more than half of the pulse energy to 1960 nm through Raman soliton self-frequency shifting process. The shifted soliton pulse train has a bandwidth of 20 nm and an average power of 30 mW. The output of the nonlinear fiber is spliced to a tap-coupler for wavelength monitoring and a 2 µm fiber isolator before entering the amplification stage. A cladding-pumped Thulium-doped fiber amplifier (TDFA) pumped in the forward direction using a 793 nm multi-mode pump diode is used for boosting the signal power in the 2 µm region to > 500 mW. The unconverted part of the 1550 nm pump pulse that exits the nonlinear fiber is absorbed in the TDFA and does not generate any significant output power. The output of the Thulium doped fiber is spliced to a 50-cm-long passive fiber terminated with an FC/APC connector for output delivery and the unabsorbed 793 nm pump is stripped from the cladding. The dispersion in the TDFA and the delivery fiber is anomalous and is compensated using a dispersion compensating fiber (DCF) pre-chirp. The DCF has an estimated mode-field diameter of 6 µm and an estimated group velocity dispersion (GVD) of + 0.08 ps2/m at 1960 nm. The spectra for the input pulses entering the TDFA and the output at 570 mW average power are shown in Fig. 1(b). The output spectrum shows that more than 90% of the pulse energy is red-shifted to around 2125 nm center wavelength as a result of the soliton self-frequency shifting in the TDFA and the delivery fiber. Figure 1(c) shows the intensity auto-correlation trace of the output pulse at 570 mW average power. The auto-correlation FWHM is 150 fs, and the pulse FWHM is calculated to be 97.5 fs assuming a sech2 intensity profile for the output pulse.
Fig. 1 (a) Pump laser diagram. MMPC: Multi-mode pump combiner. TDF: Thulium-doped fiber. (b) Optical spectra for the input pulses entering the TDFA and the output pulses. (c) Intensity auto-correlation.
3. Fiber Design
Optical Fibers made from InF3 are known to have high transmission out to about 5.5 µm [18]. The material dispersion for InF3 crosses zero at approximately 1.7 µm and monotonically increases with wavelength. By controlling the core size and the numerical aperture of an easy-to-manufacture – compared to e.g., photonic crystal and tapered fibers – step-index fiber, the waveguide dispersion can shift the zero-dispersion wavelength into the gain spectrum of Thulium, which makes step-index InF3 fibers the ideal candidate for SC work in the Mid-IR. Further it is possible to keep the dispersion value in the MIR portion of the spectrum low. The InF3 glass used in this experiment is developed and produced by Thorlabs. After the glass has been turned into preforms, the fibers are drawn on an in-house dedicated soft-glass tower in a process that allows accurate control of the numerical aperture and the core size. The wavelength-dependent refractive indices of the core glass and the cladding glass of an InF3 fiber were measured by M3 Measurement Solutions Inc. over the wavelength range from 0.3 µm to 5.5 µm. The refractive indices and the calculated numerical aperture (NA) are plotted over the wavelength range from 0.5 to 5.5 µm in Fig. 2.
Fig. 2 Measured core and cladding refractive indices and numerical aperture of InF3 fiber from 0.5 to 5.5 µm.
Figure 3(a) shows the dispersion of InF3 fibers with a numerical aperture (NA) of 0.256 at 2 µm and varied core diameters between 5 and 9 µm. The dispersion plots are calculated from the propagation constant of the fundamental mode, which is derived numerically using commercial Finite Element Method (FEM) software (COMSOL). For a core diameter of 7 µm, the InF3 fiber has a zero dispersion wavelength at 1.9 µm with a small anomalous dispersion at 2.1 µm. Also outside of the pump band the fiber shows small dispersion (<7 ps/nm.km) over the MIR region out to 4.5µm. These characteristics make the 7 µm core fiber most suitable for MIR-SC generation pumped at 2.1µm. The cut-off wavelength of the fiber with 7 µm core diameter and 0.256 NA at 2 µm is calculated to be at 2.34 µm. All dispersion calculations and SC modelling results are based on the assumption that the most of the pulse energy is coupled into the fundamental mode of the fiber. This assumption agrees with the experimental results presented in section 4 and is consistent with similar experimental results in fiber and rectangular waveguides.
Fig. 3 (a) Calculated dispersion for step-index InF3 fiber with NA = 0.256 and varied core sizes from 5 µm to 9 µm. (b) Propagation loss of the fabricated step-index fiber with 7 µm core size measured over 1.3 µm to 5 µm wavelength range. Dashed line shows extrapolated curve used for modelling the SC generation.
The fiber with the optimal core diameter of 7 µm for 0.256 NA was drawn for SC generation experiments. The propagation loss of the fiber was measured using a Fourier-Transform Infrared Spectroscopy (FTIR) system by cut-back method. The loss was measured between 1.3 µm and 5 µm and is plotted in Fig. 3(b). In the simulations, an extrapolated curve between 1 µm and 1.3 µm was used based on polynomial fit to the measured data (dashed curve in Fig. 3(b)). It is worth noting that the fiber was drawn using a new variation of the multi-draw technique that leads to more efficient processing but is still in development. We believe that the use of this technique – as opposed to the more conventional multi-draw technique – resulted in higher-than-usual propagation loss in the fiber. However, our simulations discussed in the next paragraph show that this high loss does not significantly impact the SC bandwidth over short propagation distances (< 0.5 m) considered in our work.
We have performed numerical modelling of the SC generation process in the fiber. Figure 4(a) shows the evolution of the SC spectrum in the fiber versus the fiber length for the optimal fiber parameters (7 µm core size, 0.256 NA). More details about the modelling method and assumptions are provided in section 5. The simulations show that the output SC spectrum reaches beyond 4 µm wavelength at around 10 cm length and that the bandwidth saturates around 50 cm length. Extending the fiber length beyond 50 cm does not impact the bandwidth of the SC, while it contributes to additional modulations in the spectrum. Based on the modelling results we select two lengths of 30 cm and 55 cm for experimental evaluation of the SC generation. In order to demonstrate the impact of the core size on the SC bandwidth, we also simulate the SC evolution in the fiber with 8 µm core size, which has the second most favorable dispersion for SC generation amongst the dispersion profiles shown in Fig. 3(a). This evolution plot, given in Fig. 4(b), shows that the SC bandwidth in the MIR part of the spectrum is limited and is primarily dominated by soliton self-frequency shifting. This outcome is a result of the larger anomalous dispersion in the MIR part of the spectrum in the 8 µm core fiber.
Fig. 4 Numerically simulated evolution of the SC spectrum over a propagation length of 200 cm for step-index fibers with 7 µm core size (a) and the 8 µm core size (b). The pump pulse is assumed as sech2-shaped with a central wavelength of 2.1 µm, a pulse duration of 100 fs and a peak power of 66 kW.
4. Experimental Setup and Results
The experimental setup used for characterizing the SC is shown in Fig. 5(a). A number of patch cords with different lengths and standard FC connectors are built using the InF3 fiber with the optimal core diameter of 7 µm. The output from the pump source is collimated using an aspheric lens (FiberPort) collimator (Part# PAF-2-X-D) and is focused onto the InF3 fiber using another FiberPort collimator. The coupling efficiency at the pump wavelength was estimated by recording the output power for different fiber lengths and factoring in the propagation loss based on the fiber transmission data. The average coupling efficiency is estimated to be 75%. The InF3 fiber output is collimated using a reflective collimator and is passed through a MIR neutral density filter. The attenuated SC light is sent into a MIR (1 µm to 5.6 µm) Fourier-transform optical spectrum analyzer (Thorlabs OSA205).
Fig. 5 (a) The experimental setup of the SC generation experiment. (b) Output SC spectra for 30 cm and 55 cm length fibers.
The output power spectral densities (in dBm/nm) for two different lengths of the InF3 fiber are shown in Fig. 5(b). The output SC power levels for the two lengths of 30 cm and 55 cm are 258 mW and 247 mW, receptively. The 20-dB bandwidths are calculated as 2250 nm for the 30 cm fiber and 2980 nm for the 55 cm fiber.
The ratio of the SC power that is outside of the pump spectral region (1850 nm to 2200 nm) to the total SC power provides an estimate for the conversion efficiency of the SC generation process. This ratio, which is calculated by integrating the power spectral density, is estimated to be 70%. Approximately half of the output SC power is in the spectral region that is longer than the pump wavelength (the MIR band), while the other half is in the short-wavelength region (the NIR band). It should be noted that the conversion efficiency does not include the free-space coupling loss, which can be improved by developing a low-loss splice between the fluoride fiber and the pump laser.
5. Numerical Modelling and Coherence Calculations
The SC generation was simulated by solving the generalized nonlinear Schrödinger equation for the fundamental mode of the fiber using a fourth-order Runge–Kutta method [7,19,20]. The pump pulse is assumed as sech2–shaped with a central wavelength of 2.1 µm, a pulse duration of 100 fs and a peak power of 66 kW. The effective mode area, the effective refractive index, and the propagation constant of the step-index InF3 fiber with an NA of 0.256 and a core diameter of 7 µm were calculated numerically from COMSOL. In the absence of measured Raman gain coefficients for InF3 fiber, the coefficients of zirconium fluoride (ZrF4) fiber are adopted in the simulations. ZrF4 is optically similar and the closest in composition to InF3 among fluoride-based glasses for which data is available. We model the Raman response function as a simple damped oscillation [21,22], which is defined by the fractional Raman contribution, , and two temporal parameters, (inverse of the phonon frequency) and (damping time constant). Various sets of Raman response coefficients have been reported for ZrF4 fibers [20,23,24]. The values reported in [23], fs, fs, and, are used in simulations which match the SC generation experimental results from InF3 fibers better than the other values reported. Similarly, the nonlinear refractive index of ZrF4 fiber is adopted in simulations with a value of m2/W [23].
Figure 6 shows the simulation results for the SC generation in 30 cm and 55 cm long fibers along with the experimental results presented in section 4. At fiber length of 30 cm, the simulation overlaps well with the measurement but with additional spectral modulations. Also, the simulation expands more into near-infrared than the experimental data and overestimates the SC at wavelengths > 3.5 µm. At fiber length of 55 cm, both the simulation and the measurement exhibit a finer structure in comparison with the 30 cm length. The measured spectrum for the 55 cm length extends further into the mid-IR than the simulated spectrum. These differences might indicate a smaller n2 and a stronger Raman gain in InF3 fiber than in ZrF4 fibers. The accurate values of n2 and Raman gain parameters from measurements are necessary for more precise simulation.
Fig. 6 Comparison between simulations and measurements of SC generation in InF3 fibers with lengths of 30cm (upper) and 55cm (lower).
We have also incorporated modelling of the coherence properties of the SC into our numerical simulations. The spectral coherence degree of the SC over an ensemble of simulations with random noise can be modeled as [3,25,26]
where is the spectral electric field envelope of each simulation and the angular bracket denotes average over the ensemble. Quantum-limited noise is added to the pump pulse using the one-photon-per-mode model [4,27] in order to calculate the spectral coherence degree of the SC. The degree of coherence for 100 simulations is plotted in Fig. 7. At 30 cm length, the coherence is very good with g ≈1 over most of the generated spectrum > 2 µm. A degradation of the coherence can be seen at wavelengths which coincide with very low power spectral density in the SC spectrum as shown in Fig. 6. At 55 cm length, the coherence degrades as compared to the 30 cm length. There have been a number of studies on the dependence of the coherence on the length of the nonlinear waveguide, which indicate a degradation of the coherence as the waveguide length is increased [3,4]. It should be noted that the plots shown in Fig. 7 do not model the propagation of the noise through the Raman soliton self-frequency shifting and the amplification process inside the fiber laser. A simplifying assumption has been made, which models the noise as an added quantum noise to the ideal pump pulses with the same energy and pulse width as our fiber laser. While a similar approach has been used by other groups to estimate the coherence, we realize that a more rigorous analysis of this noise will be needed in our future work. This includes the incorporation of the actual laser noise as well as the modelling of the noise generated by the Raman soliton self-frequency shifting in order to provide a more accurate estimate of the coherence. Therefore, the plots shown in Fig. 7 should only be treated as an upper limit for the coherence. A number of experimental methods have been introduced for characterizing the coherence of the SC [28,29], which can be pursued in future work. Additionally, the ability to generate a stabilized frequency comb from the SC can be validated using the well-known f-2f beat-note measurement.Fig. 7 Spectral coherence degree for 100 simulations with random noise for InF3 fibers with lengths of 30cm (upper) and 55cm (lower).
5. Conclusion
Mid-infrared super-continuum generation spanning nearly two octaves of bandwidth and extending up to 4.6 µm was demonstrated using a dispersion-engineered indium step-index fluoride fiber. The fiber was pumped near its zero-dispersion wavelength using a femtosecond fiber laser at 2.1 µm. Numerical modelling results suggest that the SC is coherent over most of the generated bandwidth when quantum-limited noise is added to the pump pulse. The results are promising for the realization of coherent and high-repetition-rate (tens of MHz) SC sources, two conditions that are critical for spectroscopy applications using FTIR spectrometers. Additionally, the entire SC system is built using optical fibers with similar core diameters, which enables integration into a compact platform.
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