We present the first detailed demonstrations of octave-spanning SC generation in all-normal dispersion photonic crystal fibers (ANDi PCF) in the visible and near-infrared spectral regions. The resulting spectral profiles are extremely flat without significant fine structure and with excellent stability and coherence properties. The key benefit of SC generation in ANDi PCF is the conservation of a single ultrashort pulse in the time domain with smooth and recompressible phase distribution. For the first time we confirm the exceptional temporal properties of the generated SC pulses experimentally and demonstrate their applicability in ultrafast transient absorption spectroscopy. The experimental results are in excellent agreement with numerical simulations, which are used to illustrate the SC generation dynamics by self-phase modulation and optical wave breaking. To our knowledge, we present the broadest spectra generated in the normal dispersion regime of an optical fiber.
©2011 Optical Society of America
Photonic crystal fibers (PCF) are the medium of choice for supercontinuum (SC) generation in optical fibers due to the design flexibilities in their dispersive and nonlinear properties . When femtosecond pulses are used as a pump source, the broadest more than octave-spanning SC spectra have so far been generated by pumping in the anomalous dispersion regime close to the zero dispersion wavelength (ZDW) . The broadening mechanism is in this case dominated by soliton dynamics, in particular the breakup of the injected pulse due to soliton fission, which is sensitive to input pulse fluctuations and pump laser shot noise [2–4]. Consequently, these ultra-broad SCs are characterized by a complex temporal profile, pulse-to-pulse variations in intensity and phase as well as considerable fine structures over their bandwidth [5,6].
One approach to achieve coherent and recompressible SC spectra has been the suppression of soliton fission in PCF with two closely spaced ZDWs centered near the pump. The resulting stable and coherent SC spectrum features two distinct spectral peaks on the normal dispersion side of each ZDW , and has found successful application in coherent anti-Stokes Raman scattering microscopy . In a further development, this type of PCF has also been numerically investigated in a taper configuration having all-normal dispersion after a certain distance, which was shown to result in improved stability .
Soliton dynamics and the associated problems can also be avoided when pumping occurs entirely in the normal dispersion regime, but this is usually associated with significantly reduced spectral bandwidths . In a numerical study and preliminary experiments it was recently shown that highly coherent, flat-top and octave-spanning SC generation is possible in optimized designs of all-normal dispersion photonic crystal fibers (ANDi PCFs), which exhibit convex dispersion profiles flattened near the pump wavelength [10–12]. The SC generation dynamics in ANDi PCF allow the conservation of a single ultrashort pulse in the time domain with smooth phase distribution, which permits external recompression approaching the single cycle limit. These properties would allow the use of broadband fiber-generated SCs in their entirety for applications in which the temporal profile of the SC pulse is of importance, e.g. time-resolved measurements, amplification of SC pulses in parametric processes or for few- or single-cycle pulse generation.
In this manuscript we experimentally verify these numerical predictions and present the first detailed demonstrations of octave-spanning SC generation in two realizations of ANDi PCF optimized for the visible and near-infrared spectral regions. A nanostructured ANDi PCF with extremely small air hole diameters in the order of 400 nm allows us to generate flat and temporally recompressible visible SC spectra down to 420 nm wavelength. For the first time we experimentally confirm the conservation of a single temporal pulse with smooth and stable phase distribution during the SC generation process. We demonstrate the applicability of these SC pulses in ultrafast transient absorption spectroscopy where they enable probing in the direct vicinity of the pump wavelength, which is not possible with bulk generated SC pulses usually employed in this technique. Numerical simulations in excellent agreement with the experimental results are used to illustrate the SC generation dynamics, which are dominated by self-phase modulation (SPM) and optical wave breaking (OWB).
2. Fiber properties
In the following experiments we used two PCFs (A and B) with hexagonal lattice geometry and convex all-normal dispersion profiles, shown in Fig. 1 . Fiber A was manufactured by NKT Photonics (Denmark) with a core diameter of 2.3 μm, pitch Λ = 1.44 μm and relative air hole diameter d/Λ = 0.39, resulting in a peak dispersion parameter of D = −11 ps/(nm km) at a wavelength of 1020 nm . These parameters are within the optimized range for broadband near-infrared SC generation considered in the numerical study in . Figure 1a) shows the measured dispersion profile of PCF A, supplied by the manufacturer, as well as the calculated mode field diameter (MFD) obtained from a fully vectorial finite element mode solver. Fiber B was drawn in-house at the IPHT and has a core diameter of 1.05 μm and design parameter Λ = 0.67 μm and d/Λ = 0.6. Due to input coupling difficulties into the small core, a measurement of the fiber’s dispersion properties was not possible and Fig. 1b) shows the calculated profile. The dispersion curve assumes its maximum at 650 nm with D = −127 ps/(nm km). Due to its smaller core diameter, fiber B exhibits a smaller MFD and therefore a larger nonlinearity than fiber A.
3. Numerical model
In order to interpret the experimental results, we employ a numerical model based on the Runge-Kutta in the interaction picture (RK4IP) integration method to solve the generalized nonlinear Schrödinger equation (GNLSE) . The entire GNLSE is evaluated in the frequency domain, because inaccuracies due to numerical derivatives are avoided and the calculation in the frequency domain is faster and more efficient than the time domain approach . In order to improve computational speed and ensure sufficient accuracy, the conservation quantity error (CQE) adaptive step size algorithm is employed, which is based on the photon number conservation of the GNLSE .
The details of the implementation are identical to , with the exception that all simulations presented in this paper were calculated neglecting the wavelength dependence of the nonlinear parameter γ. We will discuss this point in section 4.5.
For the initial condition for the simulations, a complex temporal Gaussian input pulse envelope was assumed, where t is the time, α the chirp factor and t0 is connected with the full width at half maximum (FWHM) pulse duration . The peak power is calculated as , where Ep is the pulse energy. tFWHM is determined from the time-bandwidth product of the chirped Gaussian pulse , where with Δf and Δλ the FWHM spectral widths measured in frequency and wavelength, respectively. λ0 is the central wavelength of the pulse and c the vacuum speed of light. α introduces a linear frequency chirp across the pulse and accounts for the propagation through beam guiding optics and variable attenuation prior to the injection into the fiber. Typical values are in the range α = 0.5 – 1. This definition of the pump pulse makes it possible to use Δλ, Ep and λ0 as the primary input parameters for the simulation, which are directly accessible from spectrum and power measurements.
When comparing simulations to experiments for anomalous dispersion pumping, ensemble averages have to be calculated in order to achieve good agreement due to the above-mentioned noise-sensitive pulse-to-pulse fluctuations, which can be significant . Since the generated spectra in ANDi PCF are highly coherent, the ensemble average and a single shot simulation are virtually identical and cannot be separated on the given scales. Therefore, single shot simulations are depicted in all subsequent figures.
4. Experiments and discussion
It was determined in  that the broadest spectra can be expected when pumping occurs close to the maximum of the fiber dispersion curve. Therefore, fiber A is employed for near-infrared SC generation pumped at 1050 nm, while fiber B is more suitable for visible SC generation pumped at 650 nm. In addition, we investigate the performance of both fibers at 790 nm, the typical operating wavelength of Ti:Sapphire femtosecond laser systems.
4.1 Near-infrared supercontinuum generation with PCF A
A Coherent OPerA optical parametric amplifier system (OPA) was used to generate ultrashort pulses of ca. 50 fs duration at central wavelengths of 1050 nm and 790 nm with 1 kHz repetition rate. After variable attenuation, the pulses were coupled into a ca. 0.5 m long piece of PCF A and the spectrum after the fiber was recorded with an optical spectrum analyzer. Using an 8 mm focal length aspherical lens, input-coupling efficiencies as high as 40% could be achieved.
Figure 2 shows the experimentally recorded spectra for various pump pulse energies on a logarithmic scale. For the 1050 nm pump, the broadening occurs almost symmetrically around the pump wavelength. With the highest applied pump pulse energy of 7.8 nJ, a spectral bandwidth of 905 nm (−20 dB) is achieved, which corresponds to almost 1.5 octaves. To our knowledge, this is the broadest spectrum created in the normal dispersion regime of an optical fiber to date. While for lower and medium pump energies the spectra exhibit a flat-top structure with only marginal intensity variations over the entire bandwidth (< ±1.5 dB), at higher energies a “dip” is forming around the pump wavelength whose depth increases with pump energy and reaches ca. −10 dB for 7.8 nJ. This effect was predicted and analyzed in detail in  and can be attributed to the increasing steepening of the temporal trailing pulse edge in combination with optical wave braking induced four wave mixing processes.
When pumping the fiber at 790 nm, i.e. far away from the maximum of the dispersion curve, the broadening occurs asymmetrically. A broad shoulder is formed towards the maximum of the dispersion curve on the long wavelength side. At comparable pump energies the spectrum is narrower than in the case of pumping close to the dispersion maximum, at 8 nJ a −20 dB spectral bandwidth of 670 nm is achieved. When the pump energy is increased to 12.5 nJ, the bandwidth expands to 880 nm and the spectrum spans from 540 nm to 1420 nm.
In order to interpret the experimental results, numerical simulations were performed with the experimentally determined Δλ = 42 nm for 1050 nm pumping and Δλ = 15 nm for 790 nm pumping. The remaining parameters matched the stated experimental conditions and loss in the fiber was neglected. In Fig. 3a ) the comparison between experimental and numerical results is presented, which shows remarkable agreement both in bandwidth and shape of the spectrum. The modulation around the 1050 nm pump is most likely caused by higher order phase modulations and imperfections of the input pulse generated by the OPA and cannot be reproduced by the simulation. Figure 3b) shows the simulated spectral evolution for the example of the 8 nJ pump pulse at 790 nm over a propagation distance of 25 cm. The full spectral bandwidth is generated within the first 3 cm of propagation and after ca. 10 cm a steady state is reached, i.e. the spectrum does not change significantly with further propagation.
A deeper understanding of the SC generation dynamics in this type of ANDi PCF can be obtained by following the evolution of the pulse in a spectrogram representation, shown in Fig. 4 for the example of 8 nJ, 790 nm pump pulses. During the initial few millimeters of propagation in the fiber, the spectral broadening is dominated by SPM. The spectrogram in Fig. 4a) exhibits the SPM-characteristic “S”-shaped feature with a red-shift on the leading and a blue-shift on the trailing pulse edge. The spectrum also displays the typical oscillatory structure associated with SPM, which is created by spectral interference of identical spectral components being present at different temporal positions within the pulse. Since the fiber exhibits normal dispersions at all wavelengths, the faster tail eventually overtakes the slower blue-shifted intermediate section and therefore optical wave breaking (OWB) sets on . The temporal overlap of two pulse components with different instantaneous frequencies leads to (i) interference beats in the temporal pulse profile and (ii) the nonlinear generation of new frequency components at18,19], where ω is the angular frequency. Both temporal beats and nonlinear frequency generation are evident in Fig. 4 b). The SPM generated components around 700 nm act as pump and the pulse tail at 790 nm acts as seed and create a new frequency band around 650 nm. After further propagation, OWB also occurs on the leading pulse edge (Fig. 4c)) and generates new wavelengths up to a maximum of 1300 nm. During further propagation, energy is further redistributed from the central frequency to the spectral wings until smooth, continuous and flat temporal and spectral profiles are generated with a well-defined phase distribution, Fig. 4d). No interference structures are present in neither temporal nor spectral profile as the OWB process assigns each wavelength to a unique temporal position within the pulse.
It is important to note that the OWB induced FWM processes are not phase-matched. The FWM energy transfer occurs only in the instant of temporal overlap of pump and seed, which propagate with different phase velocities. Therefore there is no restriction on the achievable bandwidth of the spectrum – it solely depends on the amount of SPM-induced broadening before WB occurs. The wider the separation between SPM generated components and the original center wavelength of the pulse at the point of OWB, the broader the spectrum will be, according to (1). Flat dispersion slopes, higher pump power or higher nonlinearity therefore enhance spectral broadening.
Also note that a single pulse with smooth phase is maintained in the time domain. If full higher order phase compensation is applied, the temporal duration of the recompressed pulse approaches the single optical cycle limit, which will be pursued in future research.
4.2 Visible supercontinuum generation with PCF B
PCF B was used for visible and near-infrared supercontinuum generation in an identical setup as described in section 4.1. The OPA was set to generate 50 fs pulses at the fiber dispersion maximum of 650 nm as well as at 790 nm. Due to its small core diameter, the input coupling efficiency was only 15 – 20%.
Figure 5a ) shows the experimentally recorded and simulated spectra in a 18 cm long piece of PCF B. Interestingly, the generated spectra seem to be almost independent of the pump wavelength. Both spectra, generated with either 650 nm or 790 nm central pump wavelength, span from ca. 425 nm to 900 nm (−20 dB) over more than one octave. The intriguing similarity is caused by the exponentially increasing fiber loss above 700 nm, which dampens wavelength components generated in this region. The unusual loss profile can be explained by the fact that the confinement loss in PCF structures increases with wavelength and becomes significant already at 700 nm in this case due to the extremely small structures of the fiber. In addition, the large dispersion slope prevents significant broadening for shorter wavelengths. The agreement between simulation and experiment is again excellent. In this case, the full loss profile is included into the simulations and slight deviations between experiment and simulation are caused by uncertainties in the fiber loss measurement for the high loss region.
The high fiber losses above 700 nm wavelength can lead to the unusual phenomenon that the SC spectrum at the end of the fiber does not contain any components of the pump wavelength, which is depicted in Fig. 5b). Here the fiber was also pumped at 790 nm, but a longer 0.5 m fiber piece was used in the experiment. Note that the coupled pump pulse energy was less than in Fig. 5a) which explains the slightly narrower spectrum on the short wavelength side.
The fact that a broad SC spectrum is generated even when pumping occurs in the high loss region indicates that the SC generation dynamics must be extremely fast. The numerical simulation of the spectral evolution, shown in Fig. 6a ), confirms this: the spectrum is generated within the first few millimeters of propagation. It remains constant on the short wavelength side but its extent decreases on the long wavelength side due to the high losses. If the fiber length is kept to a few centimeters, a spectrum spanning from ca. 400 – 1100 nm can be obtained. The SC generation dynamics are identical to those discussed in section 4.1, but they are accelerated due to the large nonlinearity of PCF B. The spectrogram of the generated SC pulse is shown in Fig. 6b). Due to the uncomplicated phase distribution, temporal recompression should be realizable.
4.3 Temporal characterization through ultrafast transient absorption spectroscopy
Up to this point we inferred the temporal characteristics of the generated SC pulse from numerical simulations. Since the agreement between experiment and simulation is excellent in the spectral domain, it is fair to assume that the same is valid in the temporal domain. However, the experimental validation of the numerical predictions is critical for many applications, especially the conservation of a single temporal pulse and the generation of a smooth and stable phase distribution need to be confirmed.
We decided to temporally characterize the SC pulses and at the same time demonstrate their application using a pump-probe ultrafast transient absorption spectroscopy (UTAS) measurement . A photo-induced process is investigated by exciting sample molecules with a short laser pulse. The dynamics of the excited sample molecule are then probed by a second light pulse that monitors the photo-induced transmission changes in dependence of the time delay between pump and probe pulse. If a SC pulse is used as probe and the full spectrum is recorded at each delay step, the chirp of the pulse is directly accessible from the measurement .
The key benefit of using SCs generated in ANDi PCF for UTAS is the possibility of probing in the direct vicinity of the wavelength used for pumping the SC generation process. This is not possible with bulk-generated SC pulses usually employed in this technique, because the low conversion efficiency in bulk requires filtering of the fundamental, which creates a spectral gap not accessible for probing molecular dynamics .
Figure 7a ) illustrates the experimental setup. As the central light source we use a Ti:Sapphire regenerative amplifier system (Clark MXR 2101) emitting 150 fs pulses at 775 nm with a repetition rate of 1 kHz. A fraction of the available output power drives a noncollinearly phase-matched optical parametric amplifier (NOPA) capable of generating pulses of ca. 25 fs duration at 600 nm wavelength, which will excite the sample molecules in the subsequent UTAS measurement and define its temporal resolution. About 5 nJ of the CPA output at 775 nm is coupled into a 20 cm piece of PCF A to generate the SC used as probe pulse. The fiber length was determined by experimental constraints, in principle it would be possible to use much shorter fibers. The generated SC spectrum is narrower than discussed in section 4.1 and spans from 620 – 1100 nm due to the longer input pulse duration. After passing through the sample, the probe is analyzed in a spectrometer with a fast line-scan CCD camera capable of single shot measurements. The time delay Δt between NOPA pump and SC probe pulse can be controlled with a retro reflector mounted on a linear stage.
In order to generate a large signal-to-noise ratio, we used a sample mixture of two laser dyes (1:1 ratio of Rhodamine 700 and Styryl 9 dissolved in methanol) with strong absorption and fluorescence characteristics. Since both dyes can be excited at 600 nm, the NOPA was set to generate pump pulses at this wavelength. Rhodamine 700 has a broad fluorescence band around 720 nm, while Styryl 9 emits from 780 – 850 nm. Since the upper range limit of the used spectrometer was 900 nm, the mixture was sufficient to generate a transient absorption signal over the accessible bandwidth of the generated SC spectrum.
A chopper wheel in the pump beam blocks every second excitation pulse so that the normalized transmission TN of the sample can be calculated as
Figure 7b) shows the experimentally recorded normalized transmission in dependence of wavelength and time delay between NOPA pump and SC probe pulse. Such a plot is usually used to extract molecular dynamics, but this is beyond the scope of this paper. We concentrate on the onset of an increased TN between −4 ps and +1 ps delay. TN can only increase if the NOPA pump pulse arrives first at the sample, excites the fluorescent molecules and causes either ground state bleach or stimulated emission is generated by a specific wavelength component of the SC probe pulse. Due to its chirp, the different wavelength components of the SC pulse arrive at different times at the sample. Therefore also the delay for the onset of increased TN signal is wavelength dependent. This specific delay is also called “time zero”, as it corresponds to the exact temporal overlap between the short pump pulse and the specific probe pulse component, if the excitation of the sample molecules is assumed to be instantaneous. In our case this is a valid assumption, because the NOPA pump pulses are extremely short compared to the SC probe pulse and the excitation time of Rhodamine 700 is in the order of a few femtoseconds . By extracting the wavelength dependent time zero from Fig. 7b), the temporal position of each wavelength component within the probe pulse, i.e. the chirp of the SC pulse, can be determined. This is a well-understood procedure for the temporal characterization of bulk-generated SC pulses in UTAS measurements .
In Fig. 7c), the experimentally determined chirp is compared to the chirp extracted from a numerically simulated spectrogram similar to Fig. 4d) after adaption to the experimental conditions. The comparison shows again the excellent agreement between simulation and experiment, both in spectral and temporal domain. This measurement therefore confirms the numerical prediction of the conservation of a single ultrashort pulse in the time domain with deterministic phase distribution.
The SC pulse is stretched to nearly 6 ps after propagation through the 20 cm of PCF A. Note that the choice of fiber length was purely due to experimental constraints. As discussed in section 4.1, the SC generation dynamics are quite fast and a much shorter piece of fiber could be used to generate the same bandwidth, reducing chirp and pulse duration accordingly.
4.4 Coherence and stability
The SC generation dynamics in ANDi PCF are dominated by SPM and OWB, which create new frequency components with a deterministic phase relation to the injected pulse. Consequently, the resulting spectrum is expected to be highly coherent. This argumentation is verified by including input pulse shot noise and spontaneous Raman noise into the numerical simulation and computing the complex degree of first order coherence according to the procedure explained in . Figure 8a ) shows the simulation for the SC used for the UTAS measurement in section 4.3 pumped with 150 fs, 5 nJ pulses at 775 nm. As expected, over the entire bandwidth, which corresponds to perfect coherence. Simulations for all the other spectra shown in this manuscript show identical results. Note that the coherence of the generated spectrum does not degrade with increasing pump pulse duration, besides a possible change in the spectral width, as was already shown in . This is distinctly different to SCs generated with soliton fission dynamics, which exhibit poor coherence properties for pump pulse durations above ca. 100 fs .
Important information about the coherence properties can be extracted from the UTAS measurement in Fig. 7b). Firstly, the SC pulses need to be extremely stable in pulse duration and phase in order to produce the sharp chirp line visible in the experiment. Since the measurement takes about 10 minutes to complete, this already implies high stability and temporal coherence of the generated SC pulses. Secondly, the pulse-to-pulse intensity fluctuations can be extracted from early time delays for which the probe pulse arrives before the pump pulse at the sample. Then two subsequent SC pulses passing through the unpumped sample are referenced to each other according to (2). Figure 8b) shows the wavelength dependent fluctuations for 50 individual traces over the bandwidth of the measurable spectrum as well as the average and standard deviation of the ensemble. While fluctuation spikes are present up to ±2%, the standard deviation is well below 1%. This is consistent with amplitude stability measurements of the CPA pump system used in the experiment. Therefore we can conclude that the observed fluctuations of the SC spectrum are induced by the noise of the pump system and no obvious additional noise has been added during the SC generation process. Significantly better fluctuation stability can be expected if the fiber is pumped directly from a modelocked oscillator instead of a CPA system, because the amplitude fluctuations of the input pulse arising from the amplification stage and subsequent attenuation can be avoided.
It is interesting to note that the measured fluctuations decrease towards the edges of the spectrum. While this can be attributed to the reduced sensitivity of the spectrometer close to its range limit at 900 nm, the increased stability below 680 nm was clearly visible and is also evident in the measurement of Fig. 7b). Simulations including pump pulse amplitude fluctuations could not reproduce this effect, and we will investigate it further in the future.
4.5. Numerical observations
On a final note, we mentioned in section 3 that all numerical simulations in this paper were performed assuming a constant nonlinear parameter for all wavelengths, where is the central frequency of the pump. Since the frequency dependence of γ originates mainly from the variation of the effective mode-field area , this assumption mainly neglects the varying MFD shown in Fig. 1. If this variation is included into the simulation using a modified GNLSE explained in detail in  with a rigorous treatment of the frequency dependent MFD, the comparison with the experimental results reveals a significant underestimation of the spectral bandwidth for long wavelengths in the order of 80 - 100 nm, as exemplary shown in Fig. 9 for 790 nm pumping of PCF A. In contrast, the calculation assuming constant γ agrees perfectly with the measurement. In this case the short wavelength edge is also well reproduced with variable γ due to the small variation of the MFD in the range 600 – 800 nm. In the case of the symmetric broadening with 1050 nm pumping, a variable γ also produces an overestimation of the bandwidth on the short wavelength side.
SPM and OWB generate new wavelength components where the pump intensity is highest, i.e. in the center of the mode field area of the pump. Our hypothesis is that these new wavelength components do not assume their equilibrium MFD instantaneously, but initially propagate in the mode-field area of the pump that creates them. In combination with the very fast SC generation dynamics observed here, this hypothesis can explain why the generated spectra are better produced with a constant MFD. We will test this initial premise in future research.
We have shown ultra-broadband SC generation in the visible and near-infrared spectral regimes in two different ANDi PCF realizations. The experimental results are in excellent agreement with previous numerical predictions and highlight the exceptional temporal properties of the generated SC pulses. The SC generation process is dominated by SPM and OWB which create new wavelength components with a deterministic phase relation to the injected pulse, resulting in a highly coherent and phase-stable spectrum only limited by the input pulse stability. We temporally characterize the generated SC pulses with an UTAS measurement and demonstrate the applicability of the generated SC pulses for the study of molecular dynamics. Due to the resulting smooth temporal phase distribution and good coherence properties, ANDi PCFs are suitable even for applications in which fiber-based white light sources are currently hardly used, e.g. in optical parametric amplification, high quality single cycle pulse generation or time-resolved spectroscopy applications.
Although we used complex OPA and CPA laser systems as pump sources due to convenience and availability, we would like to stress that the necessary pump pulse energies could have also been achieved with standard femtosecond oscillators, either Ti:Sapphire based for 790 nm or Ytterbium fiber laser based for 1050 nm pumping. Employing these oscillators and ANDi PCF, it is possible to construct simple, compact and stable broadband coherent SC light sources.
The presented concept of broadband coherent SC generation is not restricted to PCF, but can also be achieved in other fibers with flattened all-normal dispersion profiles. Using photonic nanowires or tapered suspended-core PCF, the concept has the potential to extend the bandwidth of fiber-generated SCs into the deep-ultraviolet region down to 300 nm wavelength and below .
Funding by the Thuringian Ministry of Education, Science and Culture is gratefully acknowledged. A. Heidt acknowledges partial funding by the German Academic Exchange Service (DAAD). The authors wish to thank A. Dellith for the SEM images.
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