news & views which path the radiative cascade occurs, the polarizations of the resulting pair of photons should have quantum correlations, or in other words, should be entangled. Although the scheme does indeed work, prior to the research of Mohan et al., self-assembled quantum dots that had been used always suffered from slight inherent asymmetry. The problem is that this asymmetry induces splitting of the intermediate single-exciton energy levels, distinguishing between the two decay paths of the biexciton. The two emitted photons become collinearly polarized either horizontally (parallel to the major in-plane symmetry axis of the quantum dot) or vertically (perpendicularly to that axis), and their colours (energies) are fully correlated with their polarizations. As the colours provide information about the decay path by which the quantum dot relaxes, the identity of the path disentangles the two photons and prevents them from being non-classically correlated (Fig. 1). Mohan and co-workers have now partially overcome this problem by developing a growth technique for InGaAs/GaAs quantum dots that greatly improves the efficiency of generating entangled photons. The work involves two important milestones. First, Mohan et al. developed a robust way of fabricating very uniform and highly symmetric quantum dots. Their dots are pyramidal in shape and offer three-fold rotational symmetry around an axis parallel to their growth direction. As a result, the splitting of the exciton energy levels is typically about an order of magnitude smaller than that in previously studied SCQDs and is comparable to its radiative widths (~1 2 μev). This is an important prerequisite for achieving any noticeable entanglement between the polarization state of the biexciton photon and that of the exciton photon. Second, but no less important, is that they have managed to control quite accurately the actual locations of the quantum dots. This is an attribute of their SCQD growth method, which makes use of growth in pre-etched patterned locations on the GaAs substrate surface. Accurate positioning or site control of the SCQDs opens the door to a wide range of additional advantages. Most notable is the ability to embed quantum dots within a photonic bandgap microcavity. A properly designed microcavity 12 can significantly increase the interaction between light and matter, improving SCQD performance by increasing the exciton radiative width significantly above its level splitting. This will substantially increase the degree of entanglement between the two photons in the radiative cascade. Additionally, a properly designed microcavity will result in a substantial increase in the light harvesting efficiency of the emitted light. A truly deterministic source of single and entangled photons on demand requires a light harvesting efficiency of close to 100%. Such a high efficiency has yet to be demonstrated, but the approach of Mohan et al. may bring us closer to that goal. David Gershoni is at the Physics Department and is the head of the Solid State Institute, Technion Israel Institute of Technology, Haifa, 32000, Israel. e-mail: dg@physics.technion.ac.il References 1. Zeilinger, A., Weihs, G., Jennewein, T. & Aspelmeyer, M. Nature 433, 230 238 (2005). 2. Einstein, A., Podolsky, B. & Rosen, N. Phys. Rev. 47, 777 780 (1935). 3. Peres, A. Phys. Rev. Lett. 77, 1413 1415 (1996). 4. Ekert, A. K. Phys. Rev. Lett. 67, 661 663 (1991). 5. Bennett, C. H. et al. Phys. Rev. Lett. 70, 1895 1899 (1993). 6. Kwiat, P. G., Waks, E., White, A. G., Appelbaum, I. & Eberhard, P. H. Phys. Rev. A 60, R773 R776 (1999). 7. Benson, O., Santori, C., Pelton, M. & Yamamoto, Y. Phys. Rev. Lett. 84, 2513 2516 (2000). 8. Mohan, A. et al. Nature Photon. 4, 302 306 (2010). 9. Michler, P. et al. Science 290, 2282 2285 (2000). 10. Yuan, Z. et al. Science 295, 102 105 (2001). 11. Akopian, N. et al. Phys. Rev. Lett. 96, 130501 (2006). 12. Badolato, A. et al. Science 308, 1158 1161 (2005). ULTRAFAST OPTICS Nonlinear attraction A new femtosecond fibre laser design combines two distinct regimes of nonlinear dynamic attraction within a single cavity to yield robust and low-noise performance. John M. Dudley Ultrafast science impacts nearly all areas of modern technology, and femtosecond lasers have proved themselves to be important tools in many different applications including materials processing, imaging and frequency metrology. Advances in ultrafast science have always gone hand-in-hand with the development of new ultrashort pulse lasers, but a crucial practical challenge is to make these lasers work reliably outside the laboratory in the real world. Fibrebased sources are widely considered as the solution to this problem, and a range of compact and robust femtosecond fibre lasers is now available. The propagation of short pulses in optical fibre, however, inevitably leads to high intensities, and hence learning how to manage and compensate nonlinear effects in fibre laser cavities is essential to ensure their stable operation. Reporting in Nature Photonics, Bulent Oktem and co-workers introduce a new approach to deal with nonlinear effects in a fibre laser 1. In fact, they do not attempt to avoid or compensate for nonlinearity at all; rather, they have designed a fibre laser with a cavity configuration that takes advantage of the nonlinearity to simultaneously support two different types of nonlinear shapepreserving pulses: solitons and similaritons. Their soliton similariton fibre laser operates around the important telecommunications wavelength of 1,550 nm and is based on two distinct branches, each of which sustains a fundamentally distinct type of nonlinear wave (Fig. 1). One branch uses standard telecommunicationsgrade single-mode fibre with anomalous group velocity dispersion (GVD), whereas the other branch uses a normal GVD erbium-doped fibre amplifier to provide gain. Propagation in the anomalous GVD fibre involves well-known soliton shaping dynamics, whereas propagation in the normal GVD gain fibre is fundamentally different and involves self-similar amplification. The latter is a special type of nonlinear propagation that preserves the shape of a pulse even as it increases in energy while it is amplified. In particular, an input pulse to the normal GVD gain segment will evolve with distance into a pulse that has a parabolic intensity 272 NATURE PHOTONICS VOL 4 MAY 2010 www.nature.com/naturephotonics 2010 Macmillan Publishers Limited. All rights reserved
news & views profile, and once the pulse has become parabolic, it remains so even as it continues to be amplified. Although the parabolic shape remains constant, the duration and bandwidth of this similariton pulse increase exponentially with distance. The two branches of the cavity soliton and similariton are matched by a strong dissipative transition that uses a frequency filter to select a portion of the similariton bandwidth for reinjection. The cavity also contains a saturable absorber to promote the emergence of pulses from noise, and to sustain mode-locking once initiated. From a fundamental viewpoint, the originality demonstrated by Oktem et al. lies in the coexistence of two completely different classes of localized nonlinear optical structure within the same cavity. Moreover, the pulse propagation in the amplifier branch represents the first observation of an amplifier similariton in a laser. In this regard, it is important to note that the authors used the PICASO characterization technique to confirm precisely the similariton and soliton pulse shapes in the cavity. Self-similar amplification itself was first discovered numerically in classic work by Tamura and Nakazawa 2 in 1996, but it was only after a rigorous theory was developed by Kruglov et al. that self-similarity was applied widely to improve amplifier design 3. Of course, the possibility of using selfsimilar amplification to make a laser was also immediately explored. But although numerical results were promising 4, building a laser in which genuine amplifier similaritons were generated has proved too challenging until now. Previous reports of self-similarity in a cavity configuration have used only passive similariton dynamics 5. The difficulty in making a cavity containing amplifier similaritons arises because of the need to precisely filter both the spectral and temporal properties of the amplified pulse to ensure self-consistent seeding of the amplifier on reinjection. It is the combination of strong dissipation and soliton reshaping in a second nonlinear branch, as shown by Oktem et al., that provides the solution, at last allowing amplifier similaritons to be seen in a cavity nearly a decade after their initial prediction. From a technology perspective, the fibre laser by Oktem et al. does not specifically target high-power operation, but the performance and specifications are nonetheless useful for many applications. After external compression of the portion of the similariton pulse that is out-coupled, the laser generates nanojoule energy pulses of 110 fs duration at a repetition rate of Similariton stage Amplifying fibre 30 60 MHz. In addition, a distinctive feature of the laser design is a very high degree of operating robustness and stability without, seemingly, any particular effort to design a low-noise cavity. The team measure intensity noise at the 10 4 level over a radiofrequency range of 1 250 khz, and the laser maintains stable modelocking for weeks. This is extremely impressive for what is, after all, a laboratory laser without the benefit of specific engineered packaging. A likely explanation for the operating stability of the soliton similariton laser lies in the intrinsic nonlinear dynamics of the cavity because similaritons and solitons are both attractive nonlinear pulses. In the similariton amplifier, this means that any input pulse of a given energy regardless of its shape will evolve towards the same linearly chirped parabolic pulse profile at the output. Although this insensitivity to the detailed initial conditions seems unintuitive, many processes exhibiting selfsimilarity also show this behaviour, and it has in fact been confirmed in fibre amplifier experiments 6. In the context of a cavity such as the one used by Oktem et al., the idea is that provided the intracavity energy is fixed, any fluctuations in the shape of the input pulse injected into the similariton amplifier simply would not be seen at the output; all input pulses of the same energy converge to the same parabolic output. In other words, the self-similar dynamics act as a nonlinear noise-eater, attracting any fluctuations that may be present towards a coherent asymptotic envelope. For the soliton branch of the cavity, the attraction is towards a fundamental soliton pulse, whose width and peak power are determined only by the pulse energy and the parameters of the single-mode fibre. The attractive soliton dynamics in this branch are very important because they build in natural robustness against imperfect filtering at the dissipation t Passive fibre β 2 > 0 β 2 < 0 Soliton stage Figure 1 Schematic of an ideal soliton similariton fibre laser. The normal GVD gain segment (dispersion β 2 > 0) supports shape-preserving self-similar amplification towards a parabolic pulse. Strong dissipation with spectral filtering (F) and saturable absorption (SA) match the similariton output to an anomalous GVD segment (β 2 < 0) where the pulse undergoes soliton propagation before reinjection in the amplifier. In the realistic case, even if the filtering does not immediately yield an ideal soliton, the pulse will evolve towards a fundamental soliton with propagation. F-SA t Temporal intensity step. That is, even if the filtering at the dissipation stage does not itself yield a perfect chirp-free pulse, propagation in the soliton branch will see nonlinear reshaping towards the fundamental soliton limit. Within this cavity then, both the input and the output of the similariton amplifier are structures towards which the fields within the different branches are nonlinearly driven. This seems to be a unique feature of the laser that yields the observed robustness. In addition, the cavity design borrows heavily from the study of dissipative soliton sources lasers in which loss does not act as a simple linear attenuation mechanism but rather plays a crucial role in shaping the intracavity field to ensure self-consistent pulse characteristics over a round trip 7. It is the combination of these two features, nonlinear attraction and strong dissipation, that allows stable oscillation even in the presence of extremely large intracavity breathing of the pulse characteristics. Both the temporal and spectral properties vary significantly over a cavity round trip, and indeed, up to an order of magnitude variation in the intracavity spectral bandwidth over a cavity round trip can be observed for some choices of cavity parameters. A natural question here is whether this design can be extended to higher energies. Here the answer is likely to be yes, but the dynamics in the soliton branch may need to be specifically tailored to exploit higher-order soliton compression. Perhaps new developments and designs of photonic crystal fibre could prove useful 8. Understanding how to scale the soliton similariton laser to higher energy will require new theoretical work to describe nonlinear laser oscillation in the presence of strong breathing and dissipation. Although previous classes of dissipative soliton laser have been amenable to analytic treatments based on the complex Ginzberg Landau NATURE PHOTONICS VOL 4 MAY 2010 www.nature.com/naturephotonics 273 2010 Macmillan Publishers Limited. All rights reserved
news & views models, the soliton similariton laser may require new approaches 9. On the other hand, certain aspects of the cavity design should be straightforward to optimize because, for a given intracavity energy, both similariton and soliton parameters can be predicted analytically. Thus, it may well be possible to use pulse manipulation techniques such as optical arbitrary waveform generation 10 to force the laser operation into any particular regime with either fundamental or higherorder soliton dynamics. The use of a genetic algorithm with feedback to the dissipation stage may be an approach to consider. The soliton similariton laser represents an important new addition to the family of mode-locked fibre format sources. It is of both fundamental and applied interest from a number of different perspectives as outlined above. It also provides an elegant example of how fibre-based systems remain an important and versatile testbed for the study of new concepts in nonlinear science. Finally, it seems very timely that these results are being reported in 2010, 50 years after the first report of laser oscillation. They underline that laser science itself remains a field of research that continues to yield new surprises. John Dudley is at the Department of Optics, Institut FEMTO-ST, University of Franche-Comté, 16 Route de Gray, Besancon 25000, France. e-mail: john.dudley@univ-fcomte.fr References 1. Oktem, B., Ülgüdür, C. & Ilday, F. Ö. Nature Photon. 4, 307 311 (2010). 2. Tamura, K. & Nakazawa, M. Opt. Lett. 21, 68 70 (1996). 3. Kruglov, V. I., Peacock, A. C., Harvey, J. D. & Dudley, J. M. J. Opt. Soc. Am. B 19, 461 469 (2002). 4. Peacock, A. C. et al. Conf. Opt. Fibre Commun. 2001, WP4, 1 3 (OSA Tech. Digest Series 3, 2001). 5. Ilday, F. Ö., Buckley, J. R., Clark, W. G. & Wise, F. W. Phys. Rev. Lett. 92, 213902 (2004). 6. Finot, C., Pitois, S., Millot, G., Billet, C. & Dudley, J. M. IEEE Sel. Top. Quant. Electron. 5, 1211 1218 (2004). 7. Akhmediev, N. & Ankiewicz, A. (eds) Dissipative Solitons (Springer, 2005). 8. Dudley, J. M. & Taylor, J. R. Nature Photon. 3, 85 90 (2009). 9. Bale, B. G. & Kutz, J. N. in Proc. World Congress Eng. 2009, Vol. 2, 1203 1208 (WCE, 2009). 10. Jiang, Z., Huang, C.-B., Leaird, D. E. & Weiner, A. M. Nature Photon. 1, 463 467 (2007). DISORDERED OPTICS Resonant dust The optics of disordered materials is rich and full of surprises. Researchers have now found a new form of stochastic resonance in which an image beam is resonantly amplified by noise. Diederik S. Wiersma Disorder is often associated with problems such as samples with imperfections, noise in data or dust on optics. Light waves undergo diffusive scattering when they encounter a disordered structure and this is often considered a nuisance in the realization of photonic devices. If treated and understood properly, however, disordered optical systems can give rise to beautiful physics as well as elegant applications. Recent examples include the trapping of light waves by strong disorder, and the use of opaque materials to create random lasers 1. In the field of imaging, as reported in Nature Photonics, Dmitry Dylov and Jason Fleischer use disorder in optics to scramble and de-scramble an optical image based on the fascinating effect of stochastic resonance 2. They show that it is possible to mix a clear image with an overwhelming noise signal and then use nonlinear optics to recover the image. The effect combines nonlinearity in an elegant way with the physics of disordered optics. Stochastic resonances were first proposed by Benzi et al. to explain the periodic recurrence of ice ages on Earth 3. It was found that the climate system of Earth can sustain two very different stable states; the current one, and one in which the temperature is significantly lower. Radiation from the sun, as such, is not Figure 1 Intensity distribution of light randomly scattered many times inside a disordered structure, called speckle. The pattern is due to interference among multiple scattered waves and contains information on the internal structure of the material. sufficient to force a change between one state and the other, but small stochastic climate changes can amplify the sun signal just enough to induce a change from one (meta-stable) state to another. Stochastic resonances occur, in general, in nonlinear systems when noise is added to a signal in such a way that it improves, instead of deteriorates, the signal-to-noise ratio. This can be easily understood in the case of a very weak signal that is below the threshold of a detector, and where the addition of noise makes it detectable 4. As this works best when the time scales of signal and noise match, one speaks of a resonant effect. Stochastic resonances have been found to have a role in many physical phenomena, and have also been observed in biology, neuroscience and medicine 5. Dylov and Fleischer use stochastic resonances in the following way. They mix an optical beam, carrying the information from an object, with a noise beam, and lead the combination to a CCD camera. The noise is created by directing the beam through a rotating diffuser. Due to the high intensity of the noise beam, the image is drowned in noise and cannot be observed. The researchers then introduce a tuneable nonlinear element in the beam path and observe that the image can be recovered at an appropriate level of nonlinear mixing. The geometry used in the initial experiment by Dylov and Fleischer was somewhat different from that of a regular imaging problem, as the diffuser was placed in the reference beam and not in front of the object. The noise was added via a separate laser beam and mixed with the image information in a nonlinear crystal. In a second series of experiments, however, image reconstruction was addressed using a configuration in which the diffuser was placed in front of the object. Dylov and Fleischer find that the object information 274 NATURE PHOTONICS VOL 4 MAY 2010 www.nature.com/naturephotonics 2010 Macmillan Publishers Limited. All rights reserved
LETTERS PUBLISHED ONLINE: 21 MARCH 2010 DOI: 10.1038/NPHOTON.2010.33 Soliton similariton fibre laser Bulent Oktem 1,Coşkun Ülgüdür 2 and F. Ömer Ilday 2 * Rapid progress in passively mode-locked fibre lasers 1 6 is currently driven by the recent discovery of new mode-locking mechanisms, namely, the self-similarly evolving pulse (similariton) 7 and the all-normal-dispersion (dissipative soliton) regimes 8,9. These are fundamentally different from the previously known soliton 10 and dispersion-managed soliton (stretched-pulse) 11 regimes. Here, we report a fibre laser in which the mode-locked pulse evolves as a similariton in the gain segment and transforms into a regular soliton in the rest of the cavity. To our knowledge, this is the first observation of similaritons in the presence of gain, that is, amplifier similaritons, within a laser cavity. The existence of solutions in a dissipative nonlinear cavity comprising a periodic combination of two distinct nonlinear waves is novel and likely to be applicable to various other nonlinear systems. For very large filter bandwidths, our laser approaches the working regime of dispersionmanaged soliton lasers; for very small anomalous-dispersion segment lengths it approaches dissipative soliton lasers. Passively mode-locked fibre lasers are being used in a diverse range of applications, including optical frequency metrology 12,13, material processing 14 and terahertz generation 15. Historically, major advances in laser performance have followed the discovery of new mode-locking regimes 1 6,16, so there is always a strong motivation to search for new regimes. The physics of mode-locked fibre lasers comprises a complex interaction of gain, dispersion and nonlinear effects 17. Such lasers are a convenient experimental platform for the study of nonlinear waves subject to periodic boundary conditions and dissipative effects. These characteristics profoundly alter the behaviour of nonlinear waves, so this area of research is interesting in its own right. In addition to the vast literature on optical solitons 18, optical similaritons have recently emerged as a new class of nonlinear waves 19.Other researchers 20 23 have demonstrated their existence in fibre amplifiers. These results have extended earlier predictions of parabolic pulse propagation in passive fibres by Anderson and colleagues 24 and experiments on amplification at normal dispersion 25. Similaritons were first observed in a laser cavity by Ilday and colleagues 7.These similaritons existed in segments of the cavity without any gain and loss to avoid the large spectral broadening that is characteristic of amplifier similaritons. Formation of a self-consistent solution in a laser cavity requires the compensation of spectral broadening, which has proved to be non-trivial 5. Despite numerical predictions of their existence dating back almost a decade 26, amplifier similaritons had yet to be observed in a laser cavity. Here, we present our experimental and theoretical work demonstrating an entirely new mode-locking regime, in which the pulse propagates self-similarly in the gain fibre with normal dispersion, and following spectral filtering, gradually evolves into a soliton in the rest of the cavity, where the dispersion is anomalous. All mode-locked lasers to date have had a single type of nonlinear wave propagating within the cavity; however, in our laser, distinctly different similariton and soliton pulses co-exist, demonstrating that transitions between these are possible. Remarkably, this construct is extremely robust against perturbations. Although the pulse experiences nonlinear effects strong enough to cause unprecedented, order-of-magnitude variations of the spectral bandwidth, the laser shows excellent short- and long-term stability. A schematic model for the laser is illustrated in Fig. 1a. Numerical simulations of the model laser, based on a modified nonlinear Schrödinger equation, are used to analyse its operation. Parameters are chosen to match the experimental values. (Further details can be found in the Methods.) The solution obtained for a filter bandwidth of 15 nm and net group velocity dispersion (GVD) of b (2) net ¼ 136 ps 2 illustrates the principle characteristics of the laser operation. The evolution is illustrated by plots of the pulse duration and spectral bandwidth as functions of position in the cavity (Fig. 1a). The gain fibre has normal GVD, where the incident pulse evolves into an amplifier similariton. A bandpass filter then filters the spectrum. Following the filter, the pulse enters a long segment of single-mode fibre (SMF) with anomalous GVD, and it evolves into a soliton in the long SMF segment. Because the pulse energy can easily exceed that of a fundamental soliton by up to a factor of 2, it undergoes soliton compression before its temporal and spectral widths stabilize. Similaritons have parabolic temporal profiles with linear chirp, and their temporal as well as spectral widths grow exponentially. In contrast, the first-order soliton pulse has a hyperbolic secant temporal profile and maintains a constant shape both in time and frequency, balancing nonlinear effects with dispersion. The transition from similariton to soliton is initiated by the bandpass filter, which filters both in the time and frequency domains due to the large chirp present. When the soliton re-enters the gain medium, it is shaped back into a similariton, which is an attractor state for any input pulse shape 22. A closer look confirms that a parabolic temporal profile with linear frequency chirp is obtained at the end of the gain fibre and a chirp-free hyperbolic secant profile is obtained at the end of the SMF (Fig. 2). Guided by the simulation results, we constructed an erbiumdoped fibre laser (Fig. 3). Characterization results for the laser operating with a 12-nm-wide filter and b (2) net ¼ 136 ps 2 are shown in Fig. 4. We measured full-width at half-maximum (FWHM) values of 12, 64 and 85 nm for the optical spectra from the 1%, 5% and polarization rejection ports, respectively (Fig. 4a,b). The corresponding spectral broadening ratio was 7.1. Figure 4a,b shows a good match between the simulations and the experiments. Pulse shapes were inferred from autocorrelation and spectrum measurements using the PICASO algorithm 27,28. The pulse shapes agree well with numerical simulations and match a parabolic (hyperbolic secant) temporal profile for the similariton (soliton-like) pulses shortly after the end of the gain fibre (near the end of the SMF section; Fig. 4c,d). The laser generates 750-fs-long chirped pulses from the nonlinear polarization evolution (NPE) port, which are compressed to 110 fs with a 1.2-m-long (23 ps 2 of dispersion) SMF fibre outside the laser cavity. A zero-phase Fouriertransform calculation yields a theoretical lower limit of 75 fs, as 1 Graduate Program of Materials Science and Nanotechnology, Bilkent University, 06800, Ankara, Turkey, 2 Department of Physics, Bilkent University, 06800, Ankara, Turkey. *e-mail: ilday@bilkent.edu.tr NATURE PHOTONICS VOL 4 MAY 2010 www.nature.com/naturephotonics 307
LETTERS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.33 a Spectral width (nm) 80 60 40 20 i ii iii iv Gain fibre SMF SMF similariton supporting soliton supporting SA+F 0 0 0.75 1.50 2.25 Position in cavity (m) 3.5 3.0 2.5 2.0 1.5 3.00 3.75 Pulsewidth (ps) b i 1.50 1.55 1.60 1.50 1.55 1.60 Wavelength ( m) Wavelength ( m) 2 0 2 2 0 2 iii iv 2 0 2 2 0 2 ii 1.50 1.55 1.60 1.50 1.55 1.60 Wavelength ( m) Wavelength ( m) Figure 1 Pulse evolution in the laser. a, Conceptual model of the laser with snapshots of different sections: at the end of the gain fibre (i), after the filter (ii), inside the SMF (iii), at the entrance of the gain fibre (iv). SA þ F denotes the saturable absorber and the optical bandpass filter. Evolution of the spectral width (FWHM, black circles) and the pulsewidth (FWHM, red triangles) is plotted along the cavity. The shaded regions correspond to the main sections of the conceptual model. b, Snapshots of the temporal (red, solid lines) and spectral (black, dash-dotted lines) profiles of the pulse at the indicated locations. a 10 0 60 0 60 δω (THz) b 10 0 60 0 60 δω (THz) 10 1 10 2 10 3 10 1 10 2 10 3 10 4 4 3 2 1 0 1 2 3 4 10 4 Figure 2 Numerical simulation results. a,b, Temporal intensity and chirp profiles obtained at the end of the gain fibre (a) and the SMF(b). Black solid curve, intensity profile obtained through simulation; curve formed from black open circles, chirp profile; blue dashed curve, sech 2 fit, red dash dotted curve, parabolic fit. shown in inset of Fig. 4f. The uncompressed FWHM widths of the pulses from the 5% and 1% ports are 0.82 ps (assuming parabolic shape) and 0.28 ps (assuming sech 2 (t) shape), respectively (Fig. 4e,f). The laser is very stable both in the short and long term. The RF spectrum shows 105 db (.120 db, limited by the measurement) suppression of noise, including (excluding) the sidebands at 50 and 100 Hz coupled from the power supply (inset of Fig. 4e). Also, the laser maintains uninterrupted mode-locked operation for many weeks. To gain a broader understanding of the mode-locking dynamics, we investigated the effect of net dispersion and filter bandwidth on the spectral breathing ratio. To investigate the effect of varying dispersion, the filter bandwidth was set at 12 nm and the net dispersion was varied as shown in Fig. 5a. Simulations and experiments indicate that a small positive dispersion of 13 ps 2 maximizes the spectral breathing. The behaviour of the laser at the large anomalous GVD limit follows the soliton-like regime, the pulses being significantly narrower in bandwidth and, correspondingly, the effect of the filter being weakened 29. In the case of large normal dispersion, the limiting behaviour is that of the all-normal dispersion fibre laser 8. The maximum bandwidth is ultimately limited by the gain, and the filter dictates the lower limit to the bandwidth. Decreasing the filter bandwidth increases the breathing SMF with anomalous dispersion 1% port Coupler WDM Collimator Pump diode QWP Filter Erbium-doped fibre with normal dispersion PBS HWP Polarization port QWP Collimator Isolator 5% port Figure 3 Experimental set-up. Simplified schematic of the erbium-doped fibre laser. QWP, quarter wave plate; HWP, half wave plate; PBS, polarizing beamsplitter; WDM, wavelength-division multiplexer; SMF, singlemode fibre. ratio up to a maximum of 9 for a filter bandwidth of 8 nm at b (2) net ¼ 136 ps 2 (Fig. 5b). A further decrease of the bandwidth increases the cavity losses and the regeneration of the spectrum becomes increasingly difficult. Mode-locking is unattainable for filter bandwidths lower than 3 nm. We numerically explored increasing the pulse energy, the lengths of the gain fibre and SMF 308 NATURE PHOTONICS VOL 4 MAY 2010 www.nature.com/naturephotonics
NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.33 LETTERS a b 1.50 1.55 1.60 Wavelength ( m) 1.50 1.55 1.60 Wavelength ( m) c d e 2 1 0 1 2 0 f Intensity (db) 40 80 120 0.4 0.2 0.2 Frequency (khz) 0.4 2 1 0 1 Time delay (ps) 2 2 0 2 4 6 8 Time delay (ps) 1 0 1 2 3 4 Time delay (ps) Figure 4 Comparison of experimental and numerical results for operation at b (2) net 5 136 ps 2.a,b, Measured (black solid curve) and corresponding numerically simulated (red dashed curve) spectra of the pulse from the 5% port (a) and the 1% port (b). The measured spectrum (green dash dotted curve, b) of the pulse from the NPE rejection port is also plotted to show the spectral breathing. c,d, PICASO retrieved (black solid curve) and numerically simulated temporal intensity profile (red dashed curve) of the pulse from the 5% port with a parabolic fit (blue dotted curve) (c) and from the 1% port with a sech 2 fit (blue dotted curve) (d). e,f, Intensity autocorrelation of the pulse from the 5% port (e), the 1% port (f) and NPE rejection port (f, inset),andtherf spectrum of the repetition of the laser with the central frequency shifted to zero for clarity (e, inset). a 8 b 10 Spectral breathing ratio 6 4 Spectral breathing ratio 8 6 4 2 c.w. regime 2 0 6 3 0 3 6 9 0.2 0.4 0.6 0.8 β (2) (ps 2 ) Normalized filter bandwidth net Figure 5 Spectral breathing ratio of the laser. a, Dependence on the net GVD of the laser cavity: the red stars (blue spheres) show the experimental (numerical) results. b, Dependence on filter bandwidth normalized to the gain bandwidth of 50 nm: the red stars indicate the experimental result at 10 and 12 nm filter bandwidth and the blue spheres represent the numerical results. for different values of the filter bandwidth and net dispersion to determine the maximum spectral breathing ratio. We obtained spectral breathing as much as 13 times greater for a 7-nm-wide filter, also at b (2) net ¼ 13 ps 2. In conclusion, we report a novel mode-locking regime of an erbium-doped fibre laser, with similariton and soliton propagation occurring in each half of the cavity. The similaritons are of the amplifier type, which constitutes their first experimental NATURE PHOTONICS VOL 4 MAY 2010 www.nature.com/naturephotonics 309
LETTERS observation inside a laser cavity. Indeed, we can interpret this mode of operation as a dissipative similariton, where the dissipation is viewed in a general sense of energy non-conservation and not necessarily only loss; in this way we may anticipate further links of this work with the wider class of nonlinear dynamics in non- Hamiltonian systems. The combination of an optical filter to undo the spectral broadening of the amplifier similariton and soliton formation to reshape the pulse into a chirp-free pulse, which can reseed the similariton formation, is the key step in overcoming the instabilities that have prevented the experimental demonstration of an amplifier similariton laser for nearly a decade 5,26. The transitions between the similariton and soliton-like pulses are inherently interesting due to their vastly different characteristics and lead to variations of the spectral width of the pulse by an order of magnitude, an unprecedented factor. In the limit of increasing filter bandwidth, the laser becomes identical to the dispersionmanaged soliton laser. In the other extreme of vanishing SMF section, the cavity becomes identical to that of an all-normal-dispersion laser. Thus, this new mode-locking regime sits at a nexus of all other known regimes of operation. Finally, it is remarkable that, in spite of the influence of these strong nonlinear effects, the laser is easier to mode-lock and more robust than any erbiumfibre laser incorporating NPE in our experience. The asymptotic attractive nature of the amplifier similariton may be key to the increased robustness against perturbations and low-noise operation of the laser (see Supplementary Information for the noise characterization of the laser). Methods Numerical simulations are based on a modified nonlinear Schrödinger equation: @U @z þ i bð2þ @ 2 U bð3þ @ 3 U 2 @t2 6 @t ¼ g 3 2 U þ igju @ juj 2 j2 U þ igt R @t U Here, U ¼ U(z, t) is the slowly varying amplitude of the pulse envelope, z the propagation coordinate, and t the time delay parameter. b (2) and b (3) are the secondorder (GVD) and third-order dispersion (TOD) parameters, respectively. g is the nonlinearity parameter given by g ¼ n 2 v 0 /ca eff,wheren 2 is the Kerr coefficient, v 0 the central angular frequency, c the velocity of light in vacuum, and A eff the effective mode area. T R ¼ 5 fs is related to the slope of the Raman gain spectrum, which is assumed to vary linearly with frequency around the central frequency. The gain is given by g SS g ¼ 1 þ W=W 0 þðv v 0 Þ 2 =Dv, 2 where g SS 3.45 is the small-signal gain (corresponding to 30 db in power and non-zero only for the gain fibre), Dv the gain bandwidth, which is chosen to correspond to 50 nm, and W(z) ¼ Ð juj 2 dt is the pulse energy. The gain is assumed to saturate over a large number of pulses with a response time much longer than the cavity roundtrip time. As such, the saturated values of the gain along the erbium fibre are assumed to depend on average power only. W 0 is an effective gain saturation energy corresponding to the saturation power (determined by pump power) for a given repetition rate. The saturable absorber is modelled by a transfer function that describes its transmittance q 0 TðtÞ ¼1, 1 þ PðtÞ=P 0 where q 0 is the unsaturated loss, P(z, t) ¼ ju(z, t)j 2 the instantaneous pulse power, and P 0 the saturation power. The specific shape of the transmittance function is found not to be important. The numerical model is solved with a standard symmetric split-step beam propagation algorithm, and the initial field is white noise. The same stable solutions are reached from different initial noise fields. The parameters used in the numerical simulations are the same as their experimental values. Experimentally, we are able to vary the net dispersion of the cavity (by varying the length of the SMF section), the pulse energy and use filters with bandwidth of either 10 or 12 nm, both of which are centred at 1,550 nm. The erbium-doped gain fibre is 1 m long, with a mode field diameter (MFD) of 3.57 mm, numerical aperture (NA) of 0.32, b (2) ¼ 76.9 fs 2 mm 21, b (3) ¼ 168 fs 3 mm 21, and g ¼ 0932 W 21 m 21 at 1,550 nm. The rest of the cavity comprises 3m (varied to adjust the net dispersion value) of SMF-28 just before the gain fibre and a total of 65 cm of OFS-980 as the lead fibres of the fibre components. SMF-28 NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.33 has an MFD of 10.4 mm, NA of 0.14, g ¼ 011 W 21 m 21, b (2) ¼ 222.8 fs 2 mm 21 and b (3) ¼ 86 fs 3 mm 21. The OFS-980 has an MFD of 7.5 mm, NA of 0.16, g ¼ 021 W 21 m 21, b (2) ¼ 4.5 fs 2 mm 21 and b (3) ¼ 109 fs 3 mm 21. We set P 0 ¼ 2.13 kw and W 0 ¼ 2.21 nj to obtain an intracavity pulse energy of 3.13 nj, which is the measured value for a 12-nm-wide filter, b (2) net ¼ 136 ps 2, and repetition rate of 39 MHz. For the results presented in Fig. 1 and Fig. 2, b (2) net ¼ 136 ps 2 and the filter bandwidth is 15 nm. For the results presented in Fig. 4, b (2) net ¼ 136 ps 2 and the filter bandwidth is 12 nm. Experimentally, a maximum of 350 mw of pump light at 980 nm from a laser diode is delivered to the cavity by means of a 980/1,550 nm wavelength division multiplexer. Although continuous-wave (c.w.) output power can be as high as 150 mw, the intracavity power is limited to 120 mw in mode-locked operation. An optical isolator ensures unidirectional operation. NPE, implemented with wave plates and a polarizer, functions as an artificial saturable absorber 30. Self-starting mode-locked operation is achieved readily and very stably by adjustment of the wave plates. The repetition rate of the laser varies between 29 MHz (at b (2) net ¼ 25 ps 2 ) and 58 MHz (at b (2) net ¼þ45 ps 2 ). The pulse energy is limited to 3.1 nj, limited by the self-similar evolution in the gain fibre, which has a value of g about a factor of 9 larger than that of regular fibre at 1,550 nm. At higher pulse energies, gain filtering starts to suppress further spectral broadening, which distorts self-similar propagation. It is easier to avoid overdriving the soliton propagation at higher energies because the output-coupling ratio can be increased. With the use of a suitably designed gain fibre, pulse energies exceeding 30 nj should be possible. We measure the intensity noise to be 08% (from 1 to 250 khz) and timing jitter to be 27 fs (from 1 khz to the Nyquist limit), even though no effort was made to improve the noise performance. These measurements suggest that this modelocking regime may lead to lower relative intensity noise and phase noise compared to conventional fibre lasers. Received 11 August 2009; accepted 8 February 2010; published online 21 March 2010 References 1. Buckley, J. R., Wise, F. W., Ilday, F. Ö. & Sosnowski, T. Femtosecond fiber lasers with pulse energies above 10 nj. Opt. Lett. 30, 1888 1890 (2005). 2. Kieu, K., Renninger, W. H., Chong, A. & Wise, F. W. Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser. Opt. Lett. 34, 593 595 (2009). 3. Ruehl, A., Hundertmark, H., Wandt, D., Fallnich, C. & Kracht, D. 0.7 W all-fiber erbium oscillator generating 64 fs wave breaking-free pulse. Opt. Express 13, 6305 6309 (2005). 4. Ortaç, B. et al. 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Soliton-Similariton Fibre Laser Bulent Oktem 1, Coşkun Ülgüdür 2 and F. Ömer Ilday 2 SUPPLEMENTARY INFORMATION doi: 10.1038/nphoton.2010.33 1 Graduate Program of Materials Science and Nanotechnology, Bilkent University, 06800, Ankara, Turkey 2 Department of Physics, Bilkent University, 06800, Ankara, Turkey Noise Performance and Stability of the Laser Long-term power stability was characterized by sampling the optical power output of the laser at 1 s intervals up to 10,000 s (upper panel of Fig. S1). It is found that the root-mean-square (RMS) variations in the power output are within 33% over this range. Even though this level of stability is already good, it appears to be pump laser dominated and hence can be improved. Presently, the pump diode is operating at a constant current and the specified output power stability of the diode is <%. Short-term power stability was characterized by measuring the relative intensity noise (RIN) (lower panel of Fig. S1) using the standard method [S1, S2]. A high-dynamic-range and low-noise baseband signal analyzer (Rohde & Schwarz, Audio Analyzer UPV) was used, following photodetection with a free-space InGaAs detector, and filtering off frequencies higher than 1.9 MHz. The integrated RIN is 08% (13%) over the frequency range 1 khz to 250 khz (3 Hz to 250 khz) for the laser operating at β (2) net = 136 ps 2. The single-side band phase noise and timing jitter of the laser system was characterized using direct photodetection (12 GHz photodetector, ET-3500 from Electro-Optics Technology). The RF signal at 1.3 GHz (corresponding to the 12 th harmonic of the repetition rate) was selected with a bandpass filter and characterized using a signal source analyzer (Rohde & Schwarz FSUP26). The measured phase noise and the equipment-limited noise levels are shown in Fig. S2. The corresponding timing jitter is 15.9 fs (27.3 fs) from 1 khz to 10 MHz (20 MHz), where 20 MHz is the Nyquist limit. This is among nature photonics www.nature.com/naturephotonics 1
supplementary information doi: 10.1038/nphoton.2010.33 the lowest values reported to date for an Er-doped fibre laser [S3, S4]. The measurement is clearly limited by the stability of the internal reference oscillator of the signal source analyzer as well as added timing jitter during photodetection. Figure S1. Short and long-term power stability. Upper panel: Output power fluctuations measured at 1 s intervals up to 10,000 s. The RMS power drift level is 33% over 10,000 s. Lower panel: Measured relative intensity noise (RIN) of the laser (black line) operating at β (2) net = 136 ps 2. Blue line shows the equipment noise floor. Red line shows the total noise as a function of frequency. We made no particular effort to improve the noise performance of the laser, which was constructed for the purpose of demonstrating the physics of the new mode-locking regime: the cavity was uncovered, it had extra output ports, and was modified numerous times leading to extra fibre splices. 2 nature photonics www.nature.com/naturephotonics
doi: 10.1038/nphoton.2010.33 supplementary information Figure S2. Phase noise and timing jitter. Solid black line: single-sideband phase noise of the laser measured at 1.3 GHz. Dashed red line: RMS timing jitter obtained by integrating the phase noise. Dotted blue line: instrument noise limit. Numerical experiment on long-range propagation of the intra-cavity soliton The pulse evolves gradually into a soliton upon entering the SMF section, while undergoing soliton compression. Since the SMF section is limited in length, it is natural to inquire about the stability of the pulse over much longer lengths to establish definitively that it is a fundamental soliton. Using numerical simulations, we checked that propagation over extended fibre lengths in the SMF segment yields nearly ideal fundamental soliton propagation, confirming our interpretation of these dynamics. Numerical simulations show that after the initial temporal compression and spectral broadening, the pulse propagates as a fundamental soliton for arbitrarily long distances (Fig. S3). nature photonics www.nature.com/naturephotonics 3
supplementary information doi: 10.1038/nphoton.2010.33 Figure S3. Soliton propagation. Evolution of the pulse into a fundamental soliton and propagation over an extended SMF section (total length of 10 m). Pulse energy as a function of net cavity dispersion Maximizing the intracavity pulse energy maximizes the spectral breathing ratio at any given setting of the cavity. Consequently, pulse energy and spectral breathing ratio have similar dependence on the cavity dispersion (Fig. S4). The optical spectra measured at the polarization port are shown for select dispersion values in Fig. S5. 4 nature photonics www.nature.com/naturephotonics