By means of a delayed pulsed method, we carry out an experimental study of the mutual spectral coherence of supercontinuum trains generated through a tapered fiber. We observe a strong dependence of the spectral coherence on the input wavelength. Analysis of the interferograms shows that this is related to the robustness of different order soliton fission processes. A broadband continuum with 20dB wavelength from 500nm~1300nm with high coherence (mean visibility g12~0.7) is obtained.
©2004 Optical Society of America
Supercontinuum (SC) has been successfully generated at high repetition rates using laser oscillators inside photonic crystal fibers (PCF) and tapered fibers [1,2]. The octave-spanning spectrum provides an interesting source for optical coherence tomography (OCT) and optical frequency metrology, however experiments and numerical simulations have shown that the SC generation process is very sensitive to both the fundamental (quantum noise) [3,4] and technical noises [5–7] (input shot-to-shot intensity fluctuations) associated with the input pulses. High quality SC light with small excess noise is essential for applications such as optical frequency metrology  and OCT. It is thus important to investigate the factors impacting the SC coherence and noise properties and to find the conditions under which high coherence can be maintained over the whole SC spectrum without sacrificing spectral width.
Recently, Young’s interference  between the SC generated from two separate PCFs was used to investigate the SC’s spectral coherence . It is known that SC generation, as a high nonlinear process, depends strongly on the fiber properties such as the input coupling efficiency, dispersion and nonlinear parameters, fiber length, etc. As a result, SC generated from different PCFs might not be identical to each other, which considerably affects the coherence characterization and introduces additional uncertainties. In this paper, we circumvent this problem by using the delayed pulse method to characterize the mutual spectral coherence between adjacent SC pulses generated through only one tapered fiber. For the first time to the best of our knowledge, a dramatic degradation and significant recovery of mutual coherence are clearly observed with respect to the input wavelength. Moreover, a SC with 20dB-bandwidth from 500nm to 1300nm with high coherence (mean visibility~0.7) over the whole spectrum is obtained by appropriately tuning the input wavelength.
2. Experiment setup
Using a CO2 laser heating technique [11,12] we fabricated a uniform tapered single-mode fiber that consists of a 6-cm taper waist with 2.7µm diameter. The inset on top of Fig. 1(a) shows three photos of different sections of the tapered fiber. 80MHz 100fs pulses from a Ti-sapphire laser (Spectra-Physics Mai-Tai) are coupled into the tapered fiber to generate continuum trains which are sent to a Michelson interferometer with 3.8-m optical path difference (one pulse delay), as shown in Fig. 1(a). The adjacent continuum pulses interfere with each other at the output port and the associated spectral interferograms are analyzed with an optical spectral analyzer (OSA).
The measurement range of the Ando OSA from 350nm to 1700nm covers the whole generated SC spectrum. The interference fringes are recorded for the whole SC spectrum by tuning the center wavelength and the span range of the OSA. Fig. 1(b) shows a typical fringe pattern of SC spectral interference generated by pulses at 820nm. The OSA integration time is 0.5 second, corresponding to an average over an ensemble of 4×106 spectral interference patterns. Therefore, the visibility measured from such fringe pattern is exactly the mutual spectral coherence g12 between adjacent continuum pulses defined as :
where t1-t2, equals to the period of input femtosecond pulses.
Clearly, what we characterize is strictly the coherence property of the SC trains generated through a single tapered fiber. The fringe visibilities directly reflect the realistic shot-to-shot stability of the SC generation process in the presence of the input intensity fluctuations and phase noise from a single femtosecond source. It is apparent that the delayed pulse method precludes effectively the uncertainty factors induced by using two separate PCFs. Furthermore, the equipment required for the coherence analysis is only an OSA, which provides a wide bandwidth range and a high resolution for the coherence characterization.
3. Experiment results and analysis
The group velocity dispersion (GVD) of the tapered fiber is characterized with two methods. First, the tapered waist is measured under a microscope (2.7 microns +/-0.2 microns) and the GVD is calculated assuming a step-index model. Since the core diameter of the single mode fiber is tapered from 8~9um down to less than 200nm (assuming no core diffusion), and in addition the index difference between core and cladding is so small that the tapered waist can be closely modeled as an isotropic glass rod with 2.7 microns diameter. This is verified by an experimental measurement of the GVD using white-light interferometry, and both methods indicate that the zero dispersion wavelength is around 820nm.
Then we characterize the laser source by attenuating the input pulse intensity to a low level (average power <1mw). The fringe visibility is nearly unity for any input wavelength, which indicates that the laser source is highly stable and that the phase slip between consecutive pulses does not affect the coherence measurement. We also confirm that the intensity fluctuations for all the input wavelengths are nearly constant (rms~0.8%) so that the input noise conditions maintain the same during characterizing coherence at different input wavelengths.
The spectral output of the tapered fiber changes dramatically with input pulse intensity. SC is generated when the input power is increased to larger than 30mW. Its spectral bandwidth and coherence property are characterized as a function of input wavelength from 780nm to 920 with 20nm step size while the input intensity is maintained at a constant level. Figure 2 shows SC spectra at four typical input wavelengths where the GVD is normal (780nm), zero (820nm), slightly anomalous (860nm), and considerably anomalous (920nm), respectively.
Because of different spectral broadening mechanisms, the 20dB bandwidth of SC increases significantly from 200nm to 800nm when the input wavelength is tuned from the normal dispersion regime to the anomalous dispersion regime. Self-phase modulation (SPM) dominates and results in a relatively small spectral broadening when the input wavelength is located in the normal dispersion regime , while the soliton fission process  produces much larger SC bandwidth through complicated interaction among SPM, four wave mixing (FWM), Cherenkov radiation and stimulated Raman scattering (SRS) when the input wavelength shifts to the anomalous dispersion region. As a result, the SC bandwidth remains almost the same when the input wavelength changes from 860nm to 920nm.
Although the SC bandwidth increases monotonically with increased input wavelength, we find that the spectral coherence behaves in a considerably different way. The left column of Fig. 3 shows the detailed fringe patterns in different spectral windows when the input is located at 860nm. It can be seen clearly that low visibility is the common feature of all the four spectral windows. The coherence degrades dramatically for such SC although its spectrum spans over more than an octave from 500nm to 1300nm. Slightly different visibilities in different spectral windows stem from the different spectral broadening mechanisms. The long wavelength spectral region ((a) and (b) of Fig. 3) corresponds to the soliton spectra generated by the soliton fission process. The short wavelength region ((d) of Fig. 3) is related to phase-matching processes such as the FWM and Cherenkov radiation [14,15] associated with these solitons. These two spectral regions are sensitive to noise perturbations and the coherence is rather low, resulting in low visibilities close to zero in (a), (b), and especially (d) of Fig. 3. In the spectral region close to the input wavelength ((c) of Fig. 3), robust SPM contributes more than other processes and conserves the spectral coherence to some extent.
Figure 4 shows the complete measured mutual spectral coherence over the whole 20dB bandwidth of the SC spectrum at typical input wavelengths. The coherence maintains a rather high level over the whole spectrum when the input is located at 780nm (green curve). It not only decreases on average, but also becomes non-uniform over the spectrum when input wavelength increases to 820nm (red curve). Spectral coherence degrades dramatically, over the whole spectrum (mean visibility g12~0.15), when the input wavelength is tuned to the anomalous dispersion side to 860nm (black curve), although the spectral width expands considerably. These experimental observations verify the previous numerical simulations  and can be understood as follows. In the normal dispersion region (such as 780nm input) where modulation instability (MI) is forbidden , SC generation is dominated by self phase modulation, leading to a high coherence but a small 200nm bandwidth. The coherence decreases slightly with increased SC bandwidth when the input wavelength is located around the zero-dispersion wavelength at 820nm. Since different nonlinear processes such as SPM, FWM, SRS and MI start to act simultaneously and contribute differently to different spectral portions, the coherence becomes non-uniform over the spectrum. The coherence is degraded even more severely when the input is tuned to the anomalous dispersion side at 860nm, because the dominant high-order soliton fission process (SFP) is accompanied with broadband modulational instability (MI) and becomes vulnerable to both the input intensity fluctuations and quantum noise [4,16].
Surprisingly, the coherence does not degrade further when the input wavelength is tuned deeper into the anomalous dispersion region at 920 nm. On the contrary, not only is the broad SC bandwidth maintained, but also a high coherence (mean visibility g12~0.7) is observed over the whole spectrum (blue curve in Fig. 4). The right column of Fig. 3 shows the detailed interference fringes in the same spectral windows as those for 860nm input. In contrast to those in the left column, good visibility at a similar high level is clearly observed over all the spectral windows.
Such significant coherence recovery has not been predicted in previous theoretical simulations, and it can be heuristically understood as follows. One of the main sources of coherence degradation is the MI process, and the other source comes from the sensitivity of the high order soliton towards the intensity fluctuations of the input source . Qualitatively, both the soliton order N and MI bandwidth Ωc depends inversely on the amount of group velocity dispersion as 
where γ, P 0 and T 0 are the nonlinear parameter, input peak power, and input pulse width, respectively. As the magnitude of GVD increases at 920 nm compared with that at 860 nm, the MI bandwidth decreases considerably at 920 nm, and thus does the soliton order. As a result, the soliton fission process becomes more insensitive to noise perturbations. The solitons generated from SFP are more deterministic with less amplitude fluctuations and time jitter (corresponding to the fringe patterns in (e) and (f) of Fig. 3), which in turn sheds more stable dispersive waves in the blue-shifted spectral region (corresponding to the fringe pattern in (h) of Fig. 3). Therefore, high coherence is maintained for the whole octave-spanning SC spectrum. Furthermore, we find that conditions of high spectral coherence correspond to relatively low RF noise. These results will be reported elsewhere.
In summary, by applying the delayed pulse method, we have observed, for the first time, a significant degradation and recovery of the mutual spectral coherence, depending strongly on the input wavelength, over the whole spectrum of the supercontinuum trains generated inside a tapered fiber. We have obtained a broadband continuum with a 20dB bandwidth from 500nm to 1300nm and a high spectral coherence of overall visibility around 0.7 by properly locating the input wavelength in the relatively deep anomalous dispersion region at 920nm. Apart from the coherence improvement method by using shorter pulses (<50fs) , we show that there exists another region where the broadband continuum with high coherence can be obtained by using only ~100fs pulse input.
This research was supported by a faculty development grant from NYSTAR.
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