We present measurements of cross-coherence between independent supercontinua, generated at 1550 nm. An all-fiber supercontinuum source, consisting of a femtosecond fiber laser, fiber amplifier, and highly-nonlinear dispersion shifted fiber is characterized. Supercontinua generated from both 2 picosecond and 188 femtosecond pump pulses are considered. The continua generated with picosecond pulses show a degradation in coherence as the pump power is increased, whereas a high degree of cross-coherence over a broad wavelength range can be maintained when femtosecond pulses are used.
©2004 Optical Society of America
Supercontinuum spectra generated in nonlinear optical fibers with ultrashort optical pulses are a unique source of broadband light for use in a variety of different applications. Ti:Sapphire pulses launched into microstructured optical fibers or tapered optical fiber can generate a supercontinuum that spans the visible and the near infrared [1, 2]. More recently, supercontinuum covering the range from 1 to 2.5 µm has been generated by launching femtosecond pulses from a modelocked erbium-doped fiber laser into a highly-nonlinear, dispersion shifted fiber [3–5]. Spectra that span an octave have been used for measuring and stabilizing the pulse to pulse carrier-envelope phase, and as high precision optical frequency combs [6–8]. Other applications for supercontinuum from fibers include optical coherence tomography , spectrally sliced sources for WDM communication systems [10–13], and as high power, low noise sources for device characterization [14, 15].
Bellini and Hänsch recently performed cross-coherence measurements of independently generated supercontinua by splitting a single pump pulse in two and generating a supercontinuum in bulk optic media with each of the pump pulse replicas and then interfering the two resulting supercontinuum . The ability to interfere independently generated supercontinua is important for applications such as frequency metrology that depend on a well defined phase relation between pulses in a pulse train, and consequently require that the excess noise introduced in the continuum generating process be kept to a minimum.
The first order cross-coherence at a given wavelength λ between two independent electric fields E 1(λ, t 1) and E 2(λ, t 2) at times t 1 and t 2 is given by the function (λ, τ), where τ=t 1-t 2 is the relative delay between the electric fields. Experimentally, the cross-coherence can be measured by interfering the two independent electric fields in a Young’s double slit type configuration, for example. The visibility, V, of the fringes measured by the detector is
I(λ, τ) is the signal measured by the detector at the output of the interferometer as a function of wavelength and interferometer delay. Imax (λ, τ) and Imin (λ, τ) are the maximum and minimum values of I at delay τ due to the interference fringes. If the intensity of the two fields, I 1 and I 2, is equal, V(λ, τ)=(λ, τ). The maximum value of V=1 corresponds to full coherence. A value less than one means that the fields have less than perfect cross-coherence. The experiments in this work were performed at zero delay between pulses, i.e. (λ, τ=0).
Anomalous dispersion fiber is capable of generating the broadest continuum because it maintains soliton pulses, and hence high peak power, during the generation process. However, the coherence of a supercontinuum generated with ps pulses in dispersion shifted fiber with anomalous dispersion is not maintained [16, 17]. Since coherence degradation corresponds to increased timing jitter and amplitude fluctuations, it is critical that coherence be maintained in order to use a supercontinuum as a spectral slicing source.
Recent simulations have modelled the loss of coherence in continuum generation in short, (several cm lengths) small core microstructure fibers pumped by 800 nm, Ti:sapphire pulses . These numerical simulations, based on a modified nonlinear Schrödinger equation , show that coherence is better maintained as the launched pulse becomes shorter. For pulses shorter than 100 fs, no loss of coherence was observed over the entire length of the continuum, while for launched pulses longer then 150 fs coherence was severely degraded. Measurements of cross-coherence of supercontinua generated with femtosecond pulses in a microstructured fiber and highly nonlinear dispersion shifted fiber were recently performed, showing that a high degree of coherence was maintained with femtosecond pump pulses [20, 21]. In this work, we present cross-coherence measurements of supercontinua from femtosecond and picosecond pulses derived from the same laser source at 1550 nm in highly-nonlinear, dispersion-shifted fiber (HNLF). These experiments show the degradation in coherence in supercontinuum generated in the HNLF when going from femtosecond to picosecond pulses.
2. Continuum generation in Highly-Nonlinear, Dispersion-Shifted Fiber
Passively-modelocked erbium-doped fiber lasers are robust sources of sub-100 femtosecond pulses centered at 1550 nm [22–24]. Using amplified pulses from erbium-doped fiber lasers, octave spanning spectra have been demonstrated in HNLF [4, 5]. The HNLF, a Ge and F doped silica fiber, is fusion spliced directly to the amplifier output, mitigating difficulties caused by focusing into small core nonlinear fibers with bulk optics.
The HNLF dispersion slope was 0.024 ps/nm2-km at 1550 nm. The effective area of the HNLF, Aeff ≈13.9 µm2 at 1550 nm, and the nonlinear coefficient, γ≈8.5 W-1km-1, were calculated from the measured index profile. Measured splice losses from the HNLF to SMF were typically less than 0.2 dB and varied by less than 0.02 dB from 1500 nm to 1600 nm. Measured attenuation was 1.1 dB/km at 1550 nm for the HNLF in these experiments.
The all-fiber supercontinuum sources characterized with cross-coherence measurements are illustrated in Fig. 1. Continua generated directly from the laser oscillator [Fig. 1(a)] as well as continua generated by pulses amplified in an erbium-doped fiber amplifier [Fig. 1(b)] were characterized. In both cases, the pulses were compressed by tailoring the length of the single-mode fiber (SMF) output lead to generate the shortest possible pulses. The HNLF was then fusion spliced to the SMF output lead.
In order to perform the cross-coherence measurements, a Michelson interferometer was constructed from all-fiber components. One way to interfere independently generated continua is split a single pump pulse in two and then use separate lengths of HNLF to generate two separate continua. This setup is illustrated in Fig. 2(a) and is conceptually similar to the experiments described by Bellini and Hänsch in bulk optics . The difficulty is that we wish to generate the broadest possible continuum, but the experimental setup in Fig. 2(a) decreases the pump power launched into the HNLF by a factor of 2.
Therefore, an alternate setup was used, based on an unbalanced interferometer, illustrated in Fig. 2(b). The continuum was generated in a single length of HNLF and launched into the interferometer. One arm of the interferometer was longer than the other by exactly one half the round trip time of the laser cavity. Consequently, continua generated by consecutive pulses in the pulse train were overlapped in the output arm of the interferometer.
One arm of the interferometer was fixed in length, with a gold coated fiber tip used as a reflector. The other arm was angle cleaved, collimated, and then retro-reflected with a mirror mounted on a translation stage, for fine control of the temporal overlap at the interferometer output. A polarizer was used before the detector to ensure polarization overlap. Spectral fringes generated from interference were measured using an OSA. While using fiber components in the interferometer ensured optimal mode overlap at the output on the detector, one drawback was the transmission of the 50/50 beam-splitter dropped rapidly above 1800 nm, limiting the range of measurement that could be made.
2.1. Cross-coherence measurements of supercontinua generated from picosecond pulses
Numerical models of the coherence properties of the supercontinua generated at 800 nm in microstructured fiber show a strong pump pulse width dependance . We therefore performed measurements of supercontinuum coherence on spectra generated by both picosecond and femtosecond pulses. To generate picosecond pulses, the femtosecond pulses from a passively modelocked fiber laser were reflected from a fiber Bragg grating that had a reflectance full width at half maximum (FWHM) of approximately 1.3 nm, as illustrated in Fig. 3(a). The fiber laser repetition rate was approximately 50 MHz. The pulses were then amplified and launched into a 1 km length of HNLF. At the point of launch into the HNLF, the pulses were approximately bandwidth limited, with a FWHM of 2 ps. A variable optical attenuator (VOA) after the amplifier controlled the launch power into the HNLF. At the maximum launch power of 4.5 dBm, a continuum from 1520 nm to 1620 nm was generated as shown in Fig. 3(b). Also shown in Fig. 3(b) is the initial launched spectrum of the picosecond pulses.
The initial picosecond pulse spectrum is shown on a finer scale in Fig. 4. The delay between the two arms of the interferometer was set to the round-trip of the fiber laser, plus a small offset. The spectral fringes caused by interference between consecutive pulses, measured after the amplifier, are plotted in Fig. 4 as a blue line. The consecutive pulses in the pulse train clearly show strong fringes and a high degree of cross-coherence. Therefore, any decrease in the fringe visibility of the continuum generated after the HNLF will be caused by a degradation in the cross-coherence due to noise during the continuum generation.
The interference spectra as a function of launch power into the HNLF is shown in Fig. 5. At a launch power of -17 dBm [Fig. 5(a)], little spectral broadening, and strong interference fringes with the same contrast as the launch pulses were observed. At a launch power of 0 dBm [Fig. 5(b)], the spectrum broadened to almost 20 nm, and spectral fringes were still observed, however the visibility of the fringes dropped to almost 50% over most of the spectrum. At the full launch power of 4.5 dBm [Fig. 5(c)] very little interference between the consecutive pulses was observed.
An expanded view of the interference spectrum at full launch power is shown in Fig. 5(d), showing that small regions of the spectrum still show some weak spectral fringes near the wavelength of the original pulses. For the most part, however, by the time the picosecond pulses are broadened to 100 nm in bandwidth, very little of the original cross-coherence of the generating pulse train is maintained, especially in regions far away from the wavelength of the original pulses.
These measurements are in agreement with Nakazawa et al. , where coherence of picosecond pulse trains was measured in supercontinuum from several types of nonlinear fibers. In contrast with the measurements presented here, a harmonically modelocked laser operating at 10 GHz was used as a pulse source. The high repetition rate of the laser allowed the coherence to be measured by looking at the quality of the longitudinal mode pattern in a high-resolution Fabry-Perot interferometer; whereas in the measurements presented here, the cross-coherence function was directly obtained in an unbalanced Michelson interferometer. In Ref.  coherence was only partially maintained in the wavelength region near the launched pulse when picosecond pulses were launched into kilometer lengths of dispersion shifted fiber with anomalous dispersion. In addition in Ref.  it was shown that an N=1 soliton actually maintained it’s coherence in a kilometer length dispersion decreasing fiber. While that situation was not examined in the current work, femtosecond pulses were not considered by Nakazawa et al. Coherence measurements using femtosecond pump pulses are considered in the following section.
2.2. Cross-coherence measurements of supercontinua generated from femtosecond pulses
The cross-coherence measurements were then repeated using the femtosecond pulses from the oscillator only, as well as continua generated from amplified femtosecond pulses. The pulses from the oscillator were approximately 188 fs with 2 mW of average power at 50 MHz. The pulses could be amplified to average powers as high as 50 mW.
The spectrum of the pulses from the oscillator is shown in Fig. 6(a). Also shown is the measured interference spectrum between consecutive pulses. Again, we observed strong interference, and consequently high cross-coherence, between consecutive pulses in the pulse train.
The HNLF was drawn to a variety of different dispersion values by changing the diameter of the fiber slightly during the draw process. By fusing splicing short lengths of different dispersion HNLF together, we were able to create a nonlinear fiber with a dispersion that varied along it’s length. The continuum from this dispersion managed hybrid fiber was broader and flatter than the continuum generated from the constant dispersion fibers, even though the length used was shorter [4, 5].
A hybrid fiber consisting of four, 1.5m long sections of HNLF was constructed. The dispersion decreased along the hybrid fiber; the dispersion of the HNLF sections at 1550 nm was, in order, 3.8, 2.2, -0.5 and -2 ps/nm-km. The continuum generated in this 6 m long hybrid fiber compared to the continuum generated in a 10 m section of constant dispersion HNLF is shown in Fig. 6(b). The spectra have been offset vertically for clarity. The average power of the launched pulses was 1 mW.
The interference between consecutive continuum pulses is shown in Fig. 7. Figure 7(a) shows the interference spectrum from the hybrid HNLF, and Fig. 7(b) shows the interference spectrum from the constant dispersion HNLF. Both spectra show strong fringes along the entire length of the continua. The interference fringes do not appear to go to zero in Figs. 7(a) and (b), because of insufficient resolution in the OSA to fully resolve the fringe minima. Figures 7(c) and 7(d) show expanded views of the interference spectrum from the hybrid HNLF in Fig. 7(a) at two different wavelength regions. It can be seen that the fringes show a visibility of one (i.e., the minimum value is zero). In fact the fringe visibility was one along the entire length of the continuum for both the hybrid fiber and the constant dispersion fibers. In other words, the original cross-coherence of the pulse train was maintained during the continuum generation process.
The continuum generated with the full amplified power of 50mWin the hybrid fiber is shown in Fig. 8(a). The continuum spectrum showed a large amount of structure; however this structure was stable with time. The fringe visibility was measured as a function of wavelength for zero delay in the interferometer (i.e., the round trip delay exactly equal to the pulse spacing) and is plotted in Fig. 8(b) for continua generated from the 6 m long hybrid HNLF, as well as 10 m long lengths of constant dispersion HNLF. Over the available measurement range, the continua generated the hybrid fiber as well as the constant dispersion fibers all showed very high degrees of cross coherence - approximately one for most of the measurement range. The hybrid HNLF showed a slight decrease in coherence in the region of the zero dispersion wavelengths, and the D=3.8ps/nm-km fiber showed a drop in coherence at long wavelengths. However, overall, the continua from the HNLF showed the same degree of cross-coherence as the generating pulse train. This result is in agreement with the simulations of Dudley et al.  which show that the coherence of the continuum generated in microstructured fibers is strongly dependant on the pump pulse width, and is better maintained for shorter pulses. For this reason, we measure a coherence degradation for the broadest continuum using picosecond pulses, but measure high levels of coherence in the broadest continuum with the use of femtosecond pulses.
It is worth pointing out that a broad continuum does not guarantee a high degree of coherence. The fiber laser could be driven into an unstable state by rotating the polarizers, such that the output pulse train showed temporal fluctuations on a microsecond time scale. In such a case, the output continuum showed a smooth intensity profile, and almost zero measured cross coherence. In this situation however, the continuum generating processes was starting from a laser showing strong fluctuations and poor measured coherence. Of more interest, in the context of frequency metrology for example, is the situation in which the laser starts from a high degree of coherence, but the continuum generation process degrades the coherence, as shown for picosecond pulses in section 2.1. In contrast with the picosecond pulses of section 2.1, we find that when the laser is operating with a high degree of coherence, femtosecond pump pulses maintain the coherence during the generation process.
In conclusion, we have presented cross-coherence measurements of supercontinua generated with picosecond and femtosecond pulses from an erbium-doped fiber laser. Our results are in agreement with simulations of coherence in continuum generation in microstructured fibers, which show that the coherence of the continuum depends strongly on the width of the incident pump pulse. We found that with picosecond pulses the broadest continua showed almost no coherence between independently generated spectra, although the initial pulses showed a high level of cross-coherence. In contrast, with femtosecond pulses a high level of cross-coherence could be maintained across the entire measurement range. Such a system is capable of producing octave spanning spectra and is ideal as a compact all-fiber source for frequency metrology.
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