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We report the generation of white light from a picosecond pump by efficient four-wave mixing processes. A 530 nm green source based on a frequency-doubled Yb-doped fiber laser generates strong red and blue sidebands in the secondary cores of a holey fiber with large air-filling factor. Phase matching is attributed to birefringence within the sub-micrometer-sized secondary cores induced by non-symmetric deformation during the fiber drawing.
©2007 Optical Society of America
1. Introduction
Photonic crystal fibers offer a wide range of design parameters and have therefore become a well established technology to provide tailorable dispersion profiles and exploit specific nonlinear effects. In recent years, supercontinuum generation in such fibers has attracted a lot of interest particularly for its potential to produce white light sources [1-4] for many applications. White light generation from a fiber can be implemented in a simple scheme and its main attraction resides in the remarkable spectral brightness achieved, compared to traditional white light sources [5].
A visible supercontinuum can be produced in a holey fiber from pulsed high-brightness bulk or fiber lasers emitting in the near infrared. Although this technique is very simple as it only involves a pump laser and a nonlinear fiber with adequate dispersion properties, it is relatively inefficient since generation of visible wavelengths is also accompanied by the transfer of a significant fraction of the pump power to longer wavelengths in the infrared. The same mechanism can be exploited with a pump beam centrally located in the visible spectrum to generate a supercontinuum restricted to the visible wavelengths. However, the fiber requirements are more stringent in this case because the technique requires a zero dispersion wavelength near the pump wavelength. So far, this has been achieved with tapered fibers [6, 7] and with the excitation of a higher order fiber mode [8].
Some applications such as laser projection displays require higher spectral density at specific wavelengths in the visible. An alternative to supercontinuum generation is therefore to distribute the pump intensity between discrete wavelengths so that the resulting spectral brightness is greatly enhanced. The generation of red, green, and blue radiation from a single near-infrared source combined with multiple frequency conversion steps has been demonstrated at high power [9]. Despite its potential for power scaling, this technique involves a large number of components with complex optical arrangements. A simpler approach is to exploit the large nonlinearities of holey fibers and, in particular, phase-matched four-wave mixing (FWM) to produce specific, narrow wavelength bands.
In this paper, we report the generation of white light in a short length of holey fiber by four-wave mixing. A green pump beam from a frequency doubled pulsed fiber laser is coupled into sub-micrometer-scale secondary cores in the cladding of a photonic bandgap fiber (PBGF) which act as highly nonlinear waveguides. The resulting output beam contains discrete red, green, and blue (RGB) spectral lines, with equal frequency spacing between the green pump and the red and blue sidebands characteristic of phase-matched FWM processes. Birefringence due to asymmetry of the secondary cores is identified to be the cause of this phase-matching. We present experimental investigations on various fibers and detailed model simulations to interpret these observations.
2. Experimental setup
The experimental set-up is presented in Fig. 1. The green pump laser is based on a fiber master-oscillator power amplifier (MOPA) source producing 80 ps pulses at 1060 nm, which is composed of four Yb-doped fiber amplifiers capable of amplifying the signal up to 200 W. These amplifiers are seeded by a gain-switched laser diode operating at repetition rates ranging from 32 MHz up to 1 GHz. The lowest frequency of 32 MHz is adopted to achieve maximum peak power with lowest average power. The collimated beam at 1060 nm passes through a half-wave plate to adjust its polarization and is then focused into a 15-mm long LBO crystal to a spot diameter of 56 μm for optimal frequency doubling. The frequency-doubled radiation at 530 nm is separated from the fundamental beam by a highly selective dielectric mirror. The green output beam then passes through a half wave plate to control the polarization and is launched into a nonlinear holey fiber as described below. Although power scaling of this system up to 80 W average power in a nearly diffraction limited beam (M2 = 1.15) is possible [10], in this experiment the output average power was restricted to 2 W corresponding to a peak power of 780 W to avoid damaging the holey fibers.
Fig. 1. Experimental arrangement for the generation of RGB in a single secondary core of a holey fiber. LBO: Lithium Triborate (LiB3O5) crystal, λ/2: half-wave plate at respective wavelengths.
3. Fiber design
The fibers considered in this study are photonic bandgap fibers (PBGFs) originally designed to achieve guidance in the hollow core in the following wavelength bands: 1070, 1210, 1550, 1800 and 2000 nm (fibers A, B, C, D, and E, respectively). The fibers were drawn from two different preforms: fibers A and B from one preform, fibers C-E from the other. The geometry is similar in all cases and the fibers differ essentially by the scale factor of the structure. For the work reported here, the fibers are not exploited for their air guiding properties but for the index guiding properties of the holey silica structure surrounding the hollow core. The fiber cladding is shown in Fig. 2. It is formed by a periodic arrangement of air holes on a triangular lattice. Each hole can be accurately represented as a hexagon with rounded corners [11] and the entire structure is completely determined by three parameters: the hole-to-hole spacing Λ, the hole diameter d, and the radius of the circles used to round the corners rc. Our fibers exhibit a relative hole size d/Λ ∼ 0.935 and a rc/d = 0.25, while the pitch Λ scales from 2.5 to 4.7 μm. In our study, we are interested in the light-guiding properties of the secondary cores in the cladding (indicated by the green circle in Fig. 2) whose dimensions, measured by the radius of an inscribed circle, vary between ∼200 and ∼400 nm. This corresponds to a nonlinear parameter γ between 394 and 200 W−1km−1 for green light.
4. Experimental results
The second-harmonic beam at 530 nm was carefully launched into a single secondary core in the cladding region of the different PBGFs using an objective lens. After propagation through 1 m in the holey fiber, the output beam and its spectrum were measured and analyzed. The output power typically reached in excess of 300 mW at 2 W of pump power.
Fig. 3. Normalized output spectra obtained from fibers A-E, and corresponding dispersion profiles calculated for a single secondary core as shown in Fig. 2.
Typical optical spectra measured directly from the output of the different fibers are presented in Fig. 3. We observe distinct spectral sidebands appearing around the pump wavelength in the blue and red parts of the visible wavelength range. The separation between the generated frequencies and the pump frequency satisfies energy conservation, i.e., 2ωgreen − ωred − ωblue = 0, which clearly points to a FWM process as the generating mechanism. The output spectra vary significally among fiber samples as well as from core to core within the same fiber. For instance, fiber C could generate blue and red components separated from 100 nm to 300 nm depending on the launch conditions and the choice of excited core. Slight qualitative changes in the spectra of fiber E can be observed, in particular a broadening of the red sidebands. In order to improve our understanding of these features, we also plot in Fig. 3 the dispersion of light propagating in individual secondary cores of fibers A-E, calculated for the idealized fiber structure as outlined in Sec. 3. We find that for all fibers the green pump is in the normal dispersion regime. However, for fiber E there exists a region of anomalous dispersion where soliton formation and subsequent Raman self-frequency shifting lead to broadening of the red sideband.
Fig. 4. Left: Diffracted picture of the RGB components generated by fiber D. Right: The fiber output observed in the green showing the location of the single excited core.
Figure 4 depicts the diffracted radiation emitted from fiber D. The use of red, green, and blue color filters to image the individual color mode at the fiber facet confirmed that all colors were generated in a single secondary core.
A cut-back measurement with fiber C revealed that the RGB generation takes place within the first 30 cm of the holey fiber. In fact, compared to the full length of 1 m, we observed a slight improvement in the FWM conversion efficiency at 30 cm, which we attribute to significant loss in the blue resulting from surface scattering for the longer fiber. The maxima of the blue and red sidebands were less than 10 dB below the residual green pump. In this configuration, a total of 360 mW average output power was obtained with 47, 292 and 21 mW of blue, green, and red average power, respectively.
In addition, a strong polarization dependence of the FWM process was observed. The conversion efficiency to the sidebands was found to be higly dependent on the alignment of the input polarization. In general, only one specific input polarization state resulted in RGB generation. The output polarization state of each spectral component was analyzed and this showed that the red as well as the blue components were polarized orthogonally to the green pump beam.
5. Modeling and interpretation
In order to interpret the experimental results and to understand the details of the underlying FWM process, it is important to identify the modes involved and to investigate the phase-matching conditions which determine the exact wavelengths of the red and blue sidebands. To this end, we performed numerical simulations on the fiber cross-section using a full-vectorial mode solver based on the hybrid edge-nodal Finite Element Method (FEM) [12]. A portion of the periodic cladding of our fibers, comprising either one or two silica cores with air holes was modeled with anisotropic perfectly-matched-layer (PML) boundary conditions. Propagation constants for the fundamental modes (FM) and for all higher order modes (HOMs) were evaluated at different wavelengths and relevant phase-matching curves were calculated. We studied four different hypotheses, which could all in principle explain the measurements. We hypothesize that coupling occurs either (a) between FM and HOMs within a single secondary core; (b) between even and odd supermodes in a system of two identical, adjacent secondary cores; (c) between two modes centered in two adjacent secondary cores that are slightly different in geometry; or (d) between the two orthogonally polarized FMs within a single birefringent secondary core.
Fig. 5. Idealized structure used in the simulations: single-core (a) and double-core (b). In this example Λ = 3.66 μm, d/Λ = 0.935, rc/d = 0.25. (c) High magnification SEM image of fiber C, and (d) detail of the simulated profile.
Because of the apparently large symmetry of the structures under investigation, we initially focused our attention on the idealized, perfectly symmetric, single-core structure shown in Fig. 5(a). The structural parameters were chosen to match the average features of fiber C (Λ = 3.66 μm, d/Λ = 0.935, rc/d = 0.25). Since such an ideal structure possesses a C3v symmetry, its FMs are doubly degenerate [13], and phase-matching is only possible between a fundamental and a higher order mode. The propagation constant mismatch between a FM and any HOM however is too large to generate phase matching between the experimentally observed wavelength bands, and therefore this process cannot be responsible for RGB generation.
We then studied the possible interactions between multiple cores, focusing on the elementary cell consisting of two adjacent, separate cores, as shown in Fig. 5(b). Such a structure possesses inversion symmetry with respect to the AA’ axis. Therefore, if the overlap between the modes guided in the two separate cores is not negligible, the structure supports either even or odd “supermodes”. Our calculations show that the splitting in propagation constant between even and odd “fundamental” supermodes is too small to explain the observed phase-matched peaks. On the other hand, good agreement of the measured sideband wavelengths with theory can be achieved by a number of specific even and odd higher order supermode pairs. However, a simple coupled-mode theory suggests that in this case light initially coupled into a single HOM would repeatedly couple into adjacent cores during the propagation and would eventually exit the fiber guided by multiple cores. This contradicts our experimental observation shown in Fig. 4, according to which light at the fiber output was always confined to a single core.
Fig. 6. Simulation results for the structure in Fig. 5(d): Effective indices of the first 12 modes (left); Mode intensity and polarization distribution of the first 4 modes at 530 nm (right).
Next, we investigated the effects of small structural fluctuations in a real fiber. Starting with a pair of secondary cores from a highly magnified SEM image of the cladding [Fig. 5(c)] and through image thresholding and splining we obtained the contour shown in Fig. 5(d), which was then meshed and used in the FEM simulation. The effective indices of the first 12 modes of such a structure and the mode fields and polarizations of the two pairs of orthogonal FMs centered in each core are shown in Fig. 6. The simulations show that as a result of minor structural deformations the difference in propagation constant between two modes centered on the different cores, for example between modes M1 and M3 (or between M2 and M4), would produce phase-matched wavelengths approximately in the observed spectral positions. However, the overlap between modes propagating in the different cores is very small, with ∼10% of the intensity propagating outside the central core at 700nm and much less than this in the green and blue, see Fig. 6 (right). The nonlinear conversion efficiency by FWM would therefore be extremely small and in particular would be well below the efficiency of Raman conversion within the central cores, in contrast to the spectra shown in Fig. 3.
On the other hand, the simulations also show that each core exhibits a significant modal birefringence B, as large as 2.5×10−4 at 530 nm, where B = ∣neff1 − neff2∣, and neff1 and neff2 are the effective indices of the two orthogonal FMs. Phase matching can thus occur if the polarization states of the signal and idler are orthogonal to that of the pump, which is in line with the experimentally observed polarization dependence of RGB generation. The corresponding phase matching curves are shown in Fig. 7. The phase-matched wavelengths agree well with the observed sidebands of Fig. 3. Repeating the procedure for other cores in the same and in other fibers confirmed a value of modal birefringence in the green between 10−4 and 2×10−3, with corresponding phase matching curves able to account for the range of sideband splittings observed in the experiment. Moreover, since all contributing modes are propagating within a single secondary core, their spatial overlap is close to 100% and we can expect efficient wavelength conversion. Because of the orthogonal polarizations of the pump and the sidebands required for birefringent phase matching in the normal dispersion regime, the nonlinear gain coefficient is reduced to 1/3 compared to the case of parallel polarizations. The peak gain for FWM processes is thus slightly below, but of the same order of magnitude as the peak Raman gain [14], in good agreement with the observed spectra where a Raman shifted peak of the pump is clearly visible and its maximum is comparable to or larger than the FWM sidebands. We thus interpret the mechanism leading to RGB generation in our fiber as a phase-matched FWM process between the polarization modes of highly birefringent fiber cores. Note that this process has also been termed “polarization modulation instability” in the literature and has been observed in holey fibers [15, 16], but no such large splitting and high conversion efficiency has been reported in the visible regime before.
Fig. 7. Phase matching curves for the modes of Fig. 6 (corresponding to fiber C): The pump is in mode M1, while signal and idler are in the orthogonally polarized mode M2. The yellow band refers to the pump used in the experiments.
Fig. 8. Simulated birefringence at 530 nm when a deformation (linear scaling) is applied along the x and y directions to a single core with structural parameters corresponding to 3 of the fibers under examination.
In order to investigate the unexpectedly large value of birefringence obtained from simulations on the realistic fiber structure, we calculated the form birefringence resulting from deliberately deforming the ideal single core shown in Fig. 5(a). The results of linear deformation along the x and y axes for fibers A, C and E are presented in Fig. 8. As expected, the smallest structure (fiber A) exhibits the largest sensitivity to asymmetric structural variations. However, even for larger structures a scaling factor between 10 and 20% is sufficient to generate B ∼ 5×10−4, which according to our model produces well spaced sidebands at ∼450 and ∼600 nm. Note that this analysis is based on longitudinally uniform fibers. Overall, the required asymmetry of 10-20% seems compatible with the structure of our fibers [see e.g. Fig. 5(c)], which especially in the first few rings outside the core exhibit small but significant deformation due to expansion of the air core during the fiber drawing process.
Finally, we want to comment on the conversion efficiency of the RGB generation reported here. FWM can be a very efficient process with, in principle, up to 100% conversion of the pump power into the sidebands. In practice, however, the conversion efficiency is limited by several factors: (i) Because of the large spectral separation of the sidebands and the large group velocity dispersion in the visible regime, the short pump, signal, and idler pulses experience considerable walk-off. For example, two pulses at 460 nm and 625 nm, respectively, will be spatially separated by ∼14 mm after 1 m of propagation. The length of 80 ps pulses, on the other hand, is ∼16 mm. Therefore, efficient nonlinear conversion can only take place over about 90 cm of fiber and the pump power must be high enough to achieve sufficient FWM gain over this length. (ii) Our fibers exhibit relatively large wavelength-dependent losses; in particular fibers A and B with the smallest structures exhibit large losses in the blue. Consequently, we observed slightly smaller losses of energy after 30 cm of fiber than after 1 m, as discussed before. (iii) Stimulated Raman scattering competes with FWM. As already mentioned, for orthogonally polarized pump and sidebands the peak Raman gain and the peak parametric gain are of comparable size. Therefore, a significant fraction of the pump power will be Raman shifted during the FWM process, which leads to a broadening of the pump spectrum and thus to lower FWM conversion efficiency. (iv) Fluctuations of the structural dimensions along the fiber lead to dephasing of pump and sidebands, and thus in turn reduce the energy conversion. (v) Finally, simulations of the nonlinear Schrödinger equation with coupled polarization states show that the nonlinear change of phase matching conditions as power is transferred to the sidebands restricts the conversion efficiency to less than ∼2/3 for an untapered fiber. A combination of all these effects is thought to have limited the maximum conversion efficiency in our experiments. Nevertheless, we observed up to ∼20% of the output power in the red and blue regions, see Sec. 4.
6. Conclusion
We have demonstrated the generation of RGB light from 80 ps pulses of green light. The pump was launched into sub-micrometer secondary cores in the cladding of a holey fiber with large air-filling factor. After 30 cm to 1 m of fiber propagation, discrete red and blue sidebands were observed. Detailed models of the fiber structure indicate that the RGB generation was based on FWM in single, birefringent cores, where the pump light and the sidebands propagating in orthogonally polarized fundamental modes are phase matched.
The observed spectral sidebands contained up to 20% of the total output power. Improving the coupling of the 530 nm pump light into a single secondary core would increase the pump peak power, which would allow for RGB generation in shorter fiber lengths and thus reduce the effects of spatial walk-off, propagation losses, and dephasing due to structural fluctuations. An optimized laser white light source with equal powers in the red, green, and blue spectral regions seems feasible in due course. The maximum power achievable from such a source will be limited by the damage threshold of the small fiber cores. For example, assuming a damage threshold fluence of 10 J/cm2 [17] for 80 ps pulses and a repetition rate of 100 MHz yields a maximum average output power of 2.5 W.
References and Links
1. J. C. Travers, S. V. Popov, and J. R. Taylor, “Extended blue supercontinuum generation in cascaded holey fibers,” Opt. Lett. 30,3132–3134 (2005). [CrossRef] [PubMed]
2. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19,753–764 (2002). [CrossRef]
3. P. -A. Champert, V. Couderc, P. Leproux, S. Février, V. Tombelaine, L. Labonté, P. Roy, C. Froehly, and P. Nérin, “White-light supercontinuum generation in normally dispersive optical fiber using original multi-wavelength pumping system,” Opt. Express 12,4366–4371 (2004). [CrossRef] [PubMed]
4. V. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800nm,” Opt. Lett. 25,25–27 (2000). [CrossRef]
5. G. Derra, H. Moench, E. Fischer, H. Giese, U. Hechtfischer, G. Heusler, A. Koerber, U. Niemann, F.-C. Noertemann, P. Pekarski, J. Pollmann-Retsch, A. Ritz, and U. Weichmann, “UHP lamp systems for projection applications,” J. Phys. D: Appl. Phys. 38,2995–3010 (2005). [CrossRef]
6. S. Leon-Saval, T. Birks, W. Wadsworth, P. St. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12,2864–2869 (2004). [CrossRef] [PubMed]
7. M. Rusu, S. Kivistö, C. Gawith, and O. Okhotnikov, “Red-green-blue (RGB) light generator using tapered fiber pumped with a frequency-doubled Yb-fiber laser,” Opt. Express 13,8547–8554 (2005). [CrossRef] [PubMed]
8. J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19,765–771 (2002). [CrossRef]
9. F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red-green-blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29,1921–1923 (2004). [CrossRef] [PubMed]
10. P. Dupriez, J. K. Sahu, A. Malinowski, Y. Jeong, D. J. Richardson, and J. Nilsson, “80 W green laser based on a frequency doubled, single-mode, linearly polarized fiber laser,” in Conference on Lasers and Electro-Optics (CLEO 2006), paper CThJ1, Long Beach, USA (2006).
11. N. A. Mortensen and M. D. Nielsen, “Modeling of realistic cladding structures for air-core photonic bandgap fibers,” Opt. Lett. 29,349–351 (2004). [CrossRef] [PubMed]
12. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13,3728–3736 (2005). [CrossRef] [PubMed]
13. P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Transactions on Microwave Theory and Techniques MTT-23,421–429 (1975). [CrossRef]
14. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, San Diego, CA, USA, 2001).
15. A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, “Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber,” Opt. Express 14,397–404 (2006). [CrossRef] [PubMed]
16. R. J. Kruhlak, G. K. L. Wong, J. S. Y. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Polarization modulation instability in photonic crystal fibers,” Opt. Lett. 31,1379–1381 (2006). [CrossRef] [PubMed]
17. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53,1749–1761 (1996). [CrossRef]
