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We investigate the interaction of visible supercontinuum light with fiber Bragg gratings that are UV-written in a birefringent air-silica microstructure fiber. Spectral enhancements near the grating resonance are observed, and their variations are studied by adjusting the power level and polarization of input pulses. With weak input pulses (<0.5nJ), individual Raman solitons are observed in the spectrum, and the grating generates a picosecond dispersive wave centered near its bandgap when a Raman soliton has both spatial and spectral overlap with the grating resonance. Using the nonlinear Schrödinger equation (NLSE) with a simplified model of the grating dispersion, our numerical modeling reproduces the salient features of this enhancement, and shows the important role played by grating dispersion outside the bandgap.
©2005 Optical Society of America
1. Introduction
Supercontinuum (SC) generation in microstructure fibers, as first demonstrated by Ranka et al [1] in 2000, has attracted great attention since then. Due to their unique dispersion profile and an extremely confined mode area, these fibers are able to produce octave-spanning spectra ranging from near UV to near IR wavelengths, and they have already found important applications in precision optical frequency metrology [2] and optical coherence tomography (OCT) [3], among others [4–6]. The effect of waveguide structure and pump pulse profile on the generation of SC has been studied extensively [7–13], and many new schemes for efficient SC generation have also been reported [14–20]. Periodic structures, such as fiber Bragg gratings, are capable of modifying the phase matching process [21], which is critical for the nonlinear pulse evolution of SC. Recently, the effect of fiber gratings [22] has been studied in germanosilicate highly nonlinear fibers (HNLF) exhibiting IR supercontinua. These studies showed that amplification of SC can occur near a Bragg resonance, and that this amplification can be accounted for qualitatively in simulations by including the grating dispersion in the NLSE.
In this paper, we examine the interaction of visible SC light with Bragg gratings, which are holographically written into the Ge-doped core region of a UV photosensitive microstructure fiber [23,24]. We observed similar spectral enhancements as in the HNLF experiment [22], and we recorded the variations of grating’s response as the power of SC light coupled into the grating was changed. For lower-energy launch pulses, where the SC reduces to individual Raman solitons [25], we found that the spectral enhancement could be attributed to the interplay between the grating and a single Raman soliton. Even though the grating bandgap is much smaller than the soliton bandwidth, it still disturbs the soliton and couples a narrow band of light into a dispersive wave, corresponding to a spectral peak near the grating bandgap. After passing through the grating section, the Raman solitons continue their self-frequency shift [26] to longer wavelength as they propagate down the fiber. With enough fiber, the dispersive wave, which remains centered near the Bragg wavelength, can be completely separated from the Raman soliton that generated it. As in the case of germanosilcate fiber gratings [22], the grating-SC interaction results largely from the grating-induced dispersion for transmitted light [27], rather than the Bragg reflection inside the bandgap. Our simulations based on the nonlinear Schrödinger equation (NLSE), which was modified to include grating dispersion in transmission, have qualitatively reproduced the observed local spectral enhancements, and they show that the spectral peaks correspond to picosecond dispersive waves in the time domain. The ability of fiber gratings to greatly alter the dispersion profile for pulse propagation, combined with the flexibility of fiber grating fabrication techniques, allows additional tailoring of SC light. For applications where higher signal to noise ratio is desired, such as the carrier-envelope phase-locking of a frequency comb [2], gratings provide a potential means of selective frequency amplification within a SC spectral comb.
2. Experiments
Fig. 1. Experimental setup for grating interaction with supercontinuum, where fiber Bragg gratings are UV-inscribed into the Ge-doped core of a microstructure fiber. ISO: Isolator, MO: Microscope Objective, MSF: Microstructure Fiber, SMF: Single-Mode Fiber, OSA: Optical Spectrum Analyzer. Direct coupling means either butt-coupling or fusion splicing.
The main experimental setup is illustrated in Fig. 1. A Spectra-Physics Ti:sapphire laser provides femtosecond pulses with 150fs FWHM for supercontinuum generation. The center wavelength is set at 800nm, and the pulse repetition rate is 82MHz. Polarizing components (i.e. wave plates and polarizers) are used to adjust the polarization state of the pulses, and to attenuate the power before they are focused into the microstructure fiber. For coupling into the optical spectrum analyzer (OSA) after the SC light passes through the fiber grating, the exit end of the microstructure fiber is either butt-coupled or fusion spliced to a single mode fiber. Unless otherwise mentioned, the excess fiber at both sides of the fiber grating is about 25cm in length.
Fig. 2. Microstructure fiber for supercontinuum generation and grating writing. (a) Overview of the fiber end surface; (b) Detail view of fiber core. The Ge-doped, photosensitive area is indicated using broken white lines.
The fiber used for SC generation and grating writing is a high-delta microstructure fiber fabricated at OFS Laboratories [24]. As shown in the scanning electron microscopy (SEM) pictures (Fig. 2), it has an outer diameter of 126µm; the Ge-doped core, about 0.7µm in size, is surrounded by 5 large air holes (~4µm in size) and one small air hole (~0.5µm in size). The photosensitivity of the fiber is further enhanced by D2-loading prior to grating writing.
Fig. 3. (a) Measured transmission of a grating along two principal axes (X: slow, Y: fast), and (b) Dispersion and birefringence (inset) of the microstructure fiber as computed from the full-vector, finite difference simulation [30].
The fiber gratings are 3cm long, formed by scanning a 242nm pulsed UV laser beam (Gaussian profile, 10mm FWHM) across a phase mask at uniform velocity. The phase mask has a pitch of Λ=0.672µm and the corresponding Bragg resonances are around 950nm. Linear transmission measurement of one grating is shown in Fig. 3(a). The coupling constant κ of the grating, estimated from the bandwidth of the resonance, is approximately 0.6/mm. Here κ=π·δn·η/λB, λB is the Bragg wavelength of the grating, δn is the grating index modulation, and η is the modal overlap coefficient as defined in Ref. [24]. The measured depth of grating resonances, 12~13dB as shown in Fig. 3(a), is limited by the extinction ratio of the supercontinuum light source used in our experiment. The 1.24nm shift between the two polarizations in Fig. 3(a) is a result of the large form birefringence of this fiber. Using a full-vector finite-difference simulation [30], we have calculated the dispersion profile of the fiber as well as the birefringence (see Fig. 3(b) and inset), which agrees well with experimental measurements.
Fig. 4. Grating response at high pulse energy. (a) Overall SC spectrum for fiber with or without grating inscribed, showing little difference except around the bandgap. Inset: A typical zoom-in view, with sharp peaks accompanied by spectral dips. (b) The spectral peaks could show up alone without visible dip features depending on pulse energy and input alignment.
Figure 4 to 6 shows measured SC spectra and their interaction with the grating. The overall SC shape is not significantly modified from the case with no grating, as demonstrated in Fig. 4(a). However, unlike the linear grating response that causes dips in transmission at the Bragg resonances, we observe distinct peaks near each Bragg resonance in the SC spectrum around their bandgap. With high input pulse energy (>2nJ per pulse before focusing), the SC spectrum is flat around 950nm. In this case, gratings produce sharp spectral peaks 2~5dB above the baseline. Such peaks are often accompanied by spectral dips at their shorter wavelength side (see inset in Fig. 4(a)), but spectral dips can also be absent depending on the incident power and alignment, as demonstrated in Fig. 4(b). For the plots here, the input pulse is not aligned to either principal axis of the fiber, so both polarizations are present, causing double peaks (and dips) to show up. The OSA resolution used for the broad scan in Fig. 4(a) is 2nm; the measured spectrum was combined with a high-resolution scan (0.1nm) around the grating bandgap for comparison to the broader features of the entire continuum.
Fig. 5. SC spectra at lower pulse energy, with insets showing grating response around the 950nm grating bandgap. (a) Minimal grating interaction when the bandgap is around a soliton peak in the final spectrum. (b) Grating peak appears against low power background when the bandgap sits between two soliton peaks.
With the input pulse energy lowered to 0.5~1.5nJ, there is still continuum generation around 950nm, but no longer flat, suggesting the continuum consist of individual Raman solitons [25] with small spectral overlaps (Fig. 5). In this case, if a grating is around the center of a soliton in the final spectrum (Fig. 5(a)), there will be no visible grating peaks at all (shown as inset in Fig. 5(a)). If, on the contrary, the grating sits between two neighboring solitons in the final spectrum (Fig. 5(b)), then a grating peak will show up against the lower power spectrum between the peaks. This peak can be 15~20dB higher than the nearby spectrum (see inset in Fig. 5(b)).
To understand this grating behavior, we use a longer piece of microstructure fiber (~1.5m on either end of the grating) and further reduce the input pulse energy so that the continuum breaks down into isolated solitons for wavelengths around the 950nm bandgap. The longest wavelength soliton is then tuned through the 950nm region by fine adjustment of the input pulse energy, allowing us to observe the interplay between the grating and this single Raman soliton. Figure 6 shows 6 measured spectra with increasing pulse energy; we can see narrow-band dispersive waves arise as the soliton spectrum shifts through the grating. The dispersive wave reaches a maximum as the soliton shifts to wavelengths beyond the bandgap, as indicated in spectrum No. (4) and No. (5) in Fig. 6.
Fig. 6. Measured transmission spectra, showing dispersive waves arise as the Raman soliton of longest wavelength is tuned through the grating bandgap at 950nm. Vertical offsets added for clarity.
This result can be understood by considering the additional Raman self-frequency shift that the soliton undergoes in the fiber section after the grating [26], as illustrated in Fig. 7. If a Raman soliton has spectral overlap with the grating bandgap when it is traveling inside the grating section of the fiber (Fig. 7(b)), the spectral component of the soliton around the grating bandgap will be dispersed and becomes separated from the soliton. The dispersive waves will propagate down the fiber without frequency shifts, while the remaining soliton will continue its Raman shift to longer wavelength. As a result, the dispersive waves and the soliton will end up at different spectral locations in the final spectrum, which corresponds to the spectrum No. (3)~(5) in Fig. 6. On the other hand, if the soliton only shifts to the grating wavelength region after it has passed the grating section (Fig. 7(a)), or if the soliton has already moved out of this region before it reaches the grating (Fig. 7(c)), then the grating will not have any significant impact on the soliton, as in the case of spectrum No. (1), (2) and (6) in Fig. 6. Once we take this nonlinear propagation distance into account, we schematically shift (Fig. 7) the soliton spectrum back to where it was centered when it was propagating through the grating, and we find that the intensities of the successive dispersive waves in Fig. 6 track the spectral intensity of the soliton. This strongly indicates that the grating is able to disturb the Raman soliton and convert the spectral component around its bandgap into dispersive waves. In addition, the final soliton still possesses a smooth spectral profile, showing that it has survived the grating perturbation and regenerated itself.
Fig. 7. Illustration of 3 different scenarios as the soliton propagates through the grating. RS: Raman soliton, DW: dispersive wave. (a) The soliton is at shorter wavelength side of the grating bandgap at the grating section, no dispersive wave is generated; (b) The soliton spectrum overlaps with the grating bandgap at the grating section, dispersive wave is generated and then spectrally separated from the soliton; (c) The soliton is at longer wavelength side of the grating bandgap at the grating section, no dispersive wave is generated.
Interactions at higher input pulse energy (Fig. 4 and Fig. 5) can be similarly explained, if we treat the nonlinear grating interaction with SC as a superposition of grating interaction with individual Raman solitons. The dispersive wave generated from a soliton will stay around the grating bandgap, while that soliton itself will shift to longer wavelength. Therefore, the dispersive wave will appear pronounced if no other solitons have moved into the spectral region at the end of the microstructure fiber (Fig. 5(b)). However, if none of the solitons is around the bandgap while they travel through the grating section, which is possible for input pulses of moderate energy, then the grating will not produce any spectral peak in transmission (Fig. 5(a)). At high pulse energies, simultaneous spatial and spectral overlap can always be found since there are many solitons covering the entire spectral region (Fig. 4). Therefore, small grating-induced dispersive waves can always be seen with our gratings. Even though continuum generation is not always the result of spectrally overlapping solitons, gratings in principle should be able to disrupt other nonlinear waves as well.
In a second set of experiments, we demonstrate the transition from linear grating response to nonlinear enhancement. The experimental setup in Fig. 1 is modified so that the output of the Ti:Sapphire laser is focused into a photonic crystal fiber (Crystal Fibre NL-2.0-760, 70cm long) to generate SC, see Fig. 8(a). The SC light is then butt-coupled into the microstructure fiber grating, using the precision alignment station of an Ericsson fusion splicer. The excessive microstructure fiber on the input end of the grating is removed, and the coupling of SC light is controlled by tuning the air gap between the fibers. The photonic crystal fiber from Crystal Fibre has a hexagonal air-hole array pattern; it produces an SC output with reasonably high extinction ratio (i.e. predominantly polarized along one direction), allowing us to observe the grating bandgap in large depth (> 10dB) without the use of a polarizer. Also, the input polarization is tuned so that only one grating resonance is present.
Fig. 8. Study of transition from linear back-reflection to nonlinear grating enhancement. (a) Experimental setup, where SC is generated in PCF and then coupled into the grating, with coupling controlled by the variable air gap. PCF: Crystal Fibre NL-2.0-760. MSF: OFS Labs microstructure fiber. (b) Changes in transmission spectrum as coupling efficiency increases. The resolution of OSA is set to be 0.1nm.
Figure 8(b) shows how the grating responds as the intensity of the SC varies. With a small fraction of the light coupled into the grating, the transmission spectrum shows a dip at the bandgap, representing the linear response of a fiber Bragg grating. As the intensity of the coupled light increases, the spectral hole at the bandgap gradually fills, and the longer wavelength side of the spectrum begins to rise above the average transmission level. With sufficient SC light coupled into the grating, the spectral hole becomes completely filled and only a single peak shows up. The spectral peak in this experiment is not as high as in Fig. 4(b), even with the two fibers in contact with each other. This may be due to mode mismatch of the two fibers and alignment imperfections. Nevertheless, the experiment clearly shows the spectral enhancement is a nonlinear effect that appears at higher power levels, and the enhancement happens at the longer wavelength edge of the grating resonance.
3. Numerical modeling
We model the grating response in a manner similar to Ref [22]. Because the grating bandgap in our case (<1nm) is much narrower than the femtosecond pulse spectrum (>10nm), the Bragg reflection inside the bandgap may be neglected. On the other hand, grating-induced dispersion outside the bandgap can overwhelm waveguide and material dispersion over a significant region [22]. Therefore, we ignore the Bragg reflection here and assume the only grating effect for pulse propagation is additional dispersion outside the bandgap
Here βtotal(λ) is the final propagation constant after including grating effects, βfiber(λ) is the propagation constant for a given wavelength based on material and waveguide dispersion, and Δβgrating(λ) is the change of propagation constant due to the grating. To further simplify the calculations, the grating dispersion will be calculated from a one-dimensional model for uniform fiber gratings [28,29]
Where δ=βfiber(λ)-βfiber(λB) is the grating detuning parameter, κ is the coupling coefficient of the grating as defined earlier. This way the standard forward NLSE model [8] can still be used for pulse simulation, but with a different dispersion profile when propagating inside the grating section of the fiber. Since grating-induced dispersion changes very fast around the bandgap, the exact dispersion profile must be used, including all higher-order dispersion terms. Also, because the microstructure fiber is highly birefringent, the generalized polarization-coupled NLSE [31] is used in our simulation to include polarization effects.
Fig. 9. Simulation of grating in SC propagation. (a) Calculated dispersion profile in the grating section for two principal axes. X: Slow, Y: Fast. (b) Simulation of a 3cm grating inside a 6cm fiber using polarization-coupled NLSE. Input pulse energy is 1.5nJ, and polarization is 45° between X and Y. Grating coupling coefficient κ=0.6/mm.
Figure 9(a) shows the total dispersion profile including grating-induced dispersion. The grating resonance is at λB=950nm, and the coupling coefficient κ is assumed to be 0.6/mm. Grating dispersion clearly dominates the fiber dispersion around its bandgap. Figure 9(b) is the NLSE simulation result using these parameters, with the inset showing the spectra around 950nm. We assume the grating is 3cm long inside 6cm of microstructure fiber, and the input pulses are polarized at 45° between the two principal axes. From the inset of Fig. 9(b), we can see that the simulation has qualitatively reproduced the grating enhancement feature we observed in the experiment. Additional simulation shows that stronger peaks with larger bandwidth can be obtained for gratings with larger coupling coefficient.
We have also run the simulation for lower energy pulses using a simple NLSE model with only dispersion and self-phase modulation; the results are shown in Fig. 10. Even though Raman self-frequency shift is not included, the simulation shows clearly that the grating will introduce a picosecond tail to the main femtosecond pulse (Fig. 10(a)), which corresponds to the sharp peak in the pulse spectrum (Fig. 10(b)). The initial pulse is assumed to have a FWHM of 150fs and a peak power of 0.5kW centered at 950nm, and the coupling coefficient κ of the grating is still 0.6/mm. A sufficiently strong grating (κ>3/mm) would destroy the soliton completely and convert all the light into dispersive waves, according to our simulation (not shown).
Fig. 10. Simulation of grating interaction with femtosecond pulses under a simple NLSE model. Peak power is 0.5kW for the input pulse, and propagation length is 3cm. (a) Initial and final temporal pulse envelope, note the picosecond tail produced by the grating. (b) Initial and final pulse spectrum. The sharp peak in the final spectrum corresponds to the picosecond tail.
Dispersive perturbations of solitons have been discussed by J. P. Gordon in 1992 [32]. By solving NLSE with periodic perturbations, he showed that such perturbations could produce dispersive waves from the solitons passing through them. However, the effects described by Gordon’s treatment arise from perturbations with much longer periods than the gratings we use here. The wave number of the perturbations in Ref. [32] is meant to compensate the small difference in propagation constant between the forward-traveling soliton and the forward-traveling dispersive waves, while the wave number of our gratings is large enough to couple two counter-propagating waves at the wavelength of interest. Another significant point that warrants further study is that gratings at other wavelengths, especially those shorter than the pump, can also generate similar spectral enhancements, according to our numerical simulation as well as the HNLF experiments in IR supercontinua [22]. However, the soliton disruption interpretation we have considered would not be applicable in those cases, because there is no soliton formation in the normal dispersion region. In general, gratings will alter the phase matching process in the continuum generation, and grating enhancements can be derived from a solution of the NLSE with a modified propagation constant.
4. Summary
Through experiment and numerical modeling, we have studied the interaction of fiber Bragg gratings with supercontinuum light in microstructure optical fibers. We find that Bragg gratings can produce dispersive waves, showing up as sharp spectral peaks around their bandgap in the final SC spectrum, and that such spectral enhancements are strongly dependent on the input pulse energy level. Dispersive waves arise from grating dispersion in transmission outside the grating bandgap, which is able to disturb individual Raman solitons that form the continuum as they pass through the grating section. The transition of grating responses, from linear Bragg reflection to nonlinear enhancement, is also demonstrated by controlling the coupling of SC light into the grating. The nonlinear enhancement effect observed here may find applications in frequency metrology to selectively boost the spectral components of interest within a supercontinuum comb. In general, our results demonstrate that the addition of fiber gratings could bring more freedom for development of novel SC and soliton sources.
Acknowledgment
The authors thank Qiang Lin for some valuable discussions. This research was supported in part by the National Science Foundation under grant ECS-9816251.
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