Nonlinear propagation of ultrafast near infrared pulses in anomalous dispersion region of dual-core photonic crystal fiber was studied. Polarization tunable soliton-based nonlinear switching at multiple non-excitation wavelengths was demonstrated experimentally for fiber excitation by 100 fs pulses at 1650 nm. The highest-contrast switching was obtained with the fiber length of just 14 mm, which is significantly shorter compared to the conventional non-solitonic in-fiber switching based on nonlinear optical loop mirror. Advanced numerical simulations show good agreement with the experimental results, suggesting that the underlying dual-core soliton fission process supports nonlinear optical switching and simultaneous pulse compression to few-cycle durations at the level of 20 fs.
© 2014 Optical Society of America
Realization of an all-optical switching device in a simple fiber format is one of the great challenges of the nonlinear fiber optics which holds promise for many applications that require very compact and very fast optical switching free from free-space optics and electric currents. The use of the fiber format also allows potential straightforward integration into fiber-based communication systems. Moreover, an all-optical switch is an indispensable building block of both an optical RAM and optical logic - the main enabling elements of a digital optical computer. The concept of nonlinear directional couplers (NLDCs) for all-optical signal switching was first introduced in the early 1980s [1,2]. Since then considerable attention was devoted to a deeper theoretical analysis and optimization of the device performance in dual-core optical fibers . A promising demonstration of ultrafast nonlinear switching has been exploited utilizing femtosecond pulses in normal dispersion region of the step-index silica optical fiber coupler . The main limitations of ultrafast all-optical switching in conventional silica fiber NLDCs are relatively high powers required for signal redirection and the pulse temporal breakup leading to degradation of the switching performance as well as of the signal itself . In order to prevent signal degradation, Trillo et al. suggested utilization of temporal solitons due to their resistance to weak perturbations . Even though the subject has been treated extensively on a theoretical level [3,7–9], there is a notable absence of successful experimental configurations because the tight requirements imposed on the dispersion, coupling and nonlinear characteristics are not accessible in conventional fiber structures.
Photonic crystal fiber (PCF) technology offers extended possibilities for fiber dispersion tailoring, nonlinearity boosting and simple realization of multi-core structures . Utilization of dual-core (DC) PCFs as nonlinear directional couplers thus opens a new space for enhancing and controlling of soliton-based switching. First experimental realization of nonlinear switching in PCF based NLDC was performed by Betlej et al. for femtosecond pulses in the telecommunication C-band . Soon afterwards, numerical analysis of soliton switching performance dedicated to the presented experimental conditions has been published . The outcomes of these studies revealed that the switching performance was deteriorated due to the nonlinearly induced multi-frequency generation and consequent pulse breakup. Later, Lorenc et al. demonstrated soliton fission propagation scenario in a special square lattice DC PCF under 1240-nm femtosecond excitation . Subsequently, potential of this fiber as a compact NLDC for non-excitation wavelengths has been demonstrated based on coupling behavior of individual soliton-like pulses generated during the soliton fission process . Most recently, ultrafast nonlinear switching at multiple non-excitation wavelengths was reported in the same DC PCF under optimized excitation conditions . In this paper we present solitonic multi-wavelength switching in a DC PCF under 1650 nm excitation. We study, for the first time, the fiber length dependence of nonlinear dual-core field evolution which allows us to recreate the pulse propagation dynamics in detailed numerical simulations based on coupled generalized nonlinear Schrödinger equations (GNLSE), that clearly point towards a solitonic mechanism of nonlinear switching. The complex analysis of the proof-of-concept experiment utilizing DC PCF opens the way for development of new generation of all-optical switches for applications where very short resp. broadband pulses are required.
2. Experimental conditions
The experimental study was performed on a special square-lattice DC PCF made of an in-house synthesized multicomponent silicate glass PBG01 . Fiber microstructure consisting of 9 × 9 capillaries with two cores having similar sizes of 1.9 × 1.9 μm is depicted in Fig. 1(a). Fiber linear properties required for further nonlinear simulations were investigated by commercial eigenmode solver software utilizing the SEM image of the fiber cross section and the glass dispersion. Our theoretical model for nonlinear propagation is based on coupled-mode theory (CMT) for dual-core fiber couplers , which requires separate characterization of individual fiber cores. Model single-core structures were created and analyzed by assuming an artificial circular hole at the position of the opposite core while retaining the periodicity and dimensions of the surrounding air-hole structure. Dispersion characteristics of the fiber upper core obtained this way are illustrated in Fig. 1(b).
Dispersion of the lower fiber core differs from the presented one only minimally . For higher input pulse energies and longer fiber lengths, slight fiber asymmetry causes nonreciprocal behavior under different core excitations, which has been analyzed in our previous publication . For brevity, only the results where the upper core was excited are presented in this paper. Focus is on the analysis of the fiber length and the underlying physical processes influence on the switching performance. The qualitative mechanism of nonlinear propagation is the same regardless of whether the upper or the lower core is excited. To address fiber birefringence, we will refer to linear polarization orientation parallel to the two-core axis as Y-polarization and to the orthogonal orientation as X-polarization.
The DC PCF was excited by pulses from an amplified Yb-based femtosecond laser system driving an IR optical parametric amplifier . In order to minimize fundamental soliton breakup, excitation wavelength of 1650 nm was chosen as it lies at a broad flattened peak of the fiber anomalous dispersion region. The laser system delivers 100 fs pulses at 3.7 kHz repetition rate with the maximum pulse energy at the level of 10 μJ. In experiment, the maximal applied pulse energy was 55 nJ (measured before coupling optics) to prevent fiber facet damage. The fiber facet damage threshold was empirically estimated at the level of 100 nJ. The input radiation intensity and polarization were controlled with a pair of half-wave plates and a Glan polarizer inserted between them. 40x and 50x microobjectives were used to couple radiation in and out of the fiber, respectively. Selective excitation and spectral registration of individual fiber cores were ensured. All presented spectra were recorded with an IR optical spectrum analyzer (OSA) - NIR Quest, Ocean Optics, using a 200 ms integration time and 5x averaging. Utilizing this setup, systematic investigation of the pulse energy dependent fiber output spatial and spectral intensity redistribution for different fiber lengths and input polarization directions (X vs. Y) was performed.
3. Numerical model
The theoretical model based on CMT  was developed specially for numerical analysis of pulse propagation in the DC PCF and was introduced in more details in reference . In the frame of this study, the model was refined in order to achieve better correspondence with the experimental results. Ultrashorshort pulse evolution along dual-core structure can be modeled by a pair of coupled GNLSE in retarded time frame taking form18], is the speed of light and is the effective mode area. Material nonlinear response function accounts for instantaneous Kerr and delayed Raman response of medium  and is the small cross-phase modulation (XPM) contribution coefficient. The optical shock wave formation time scale19], where is the core mode effective refractive index. Equations are solved by split-step Fourier method. Linear properties of the fiber were calculated with the aid of a commercial eigenmodes solver in the range of 0.4 - 3.0 μm and then inter- and extrapolated on the whole wavelength grid used in the simulations. This enables efficient calculation of a linear step in the frequency domain which permits us to include full spectral dependence of fiber losses, propagation and coupling characteristics. For clarity, an overview of selected basic propagation parameters from Eq. (1) can be found in Table 1. Theoretically calculated wavelength dependent fiber losses were scaled to the value of 50 dB/m measured in the telecommunication C-band . As the PBG01 is essentially silicate glass with only minor composition changes in order to improve drawing conditions, the Raman response was assumed to be identical to that of conventional fused silica . Compared to our previous numerical results , new terms describing wavelength dependent fiber losses, XPM and additional correction to nonlinearity dispersion in were included in the model. Also, fiber linear properties were calculated more precisely and in the broader wavelength range. These improvements should lead to higher precision and relevance of the simulation results especially in the cases when ultra-short broadband solitons are generated during the pulse propagation in the fiber.
Operating at 1650 nm, deep inside the fiber’s anomalous dispersion region, soliton fission scenario is expected for propagation of femtosecond pulses . For sufficiently high energies initial phase of propagation is associated with temporal compression and spectral broadening of the pulse and is culminated by generation of higher-order soliton. Based on the numerical simulations for our experimental conditions, even moderate pulse energies at the level of 20 nJ are sufficient to generate higher order solitons on sub-centimeter fiber lengths. Figure 2 presents dual-core propagation maps of 100 fs, 24 nJ pulse both in the temporal and spectral domain along 50 mm fiber length, which allows us to visualize the stability of the generated soliton-like pulses. After the initial compression distance (~7 mm) the fission process results in emergence of three separate solitonic features preserving their pulse-shape. As a result of the wavelength dependent inter-core coupling, individual soliton-like pulses oscillate between the cores with different wavelength-dependent periods. An increase of the input pulse energy strongly affects the pattern of the propagation maps, mainly because of the increase of the initial soliton order and the nonlinearly altered coupling behavior. Increase in the input pulse energy results in shorter initial compression distance and increased soliton order and temporal compression ratio .
For 55 nJ, which corresponds to the maximal experimentally applied energy, the initial compression distance is reduced to 5 mm as can be seen in Fig. 3. Due to higher-order perturbations, the generated soliton breaks up into fundamental soliton-like pulses as well as some narrow-band non-solitonic components. The theoretical estimation of the soliton order is 3 and 6 for 24 nJ and 55 nJ pulse energies, respectively. According to the simulations, influence of the optical losses on pulse propagation up to 15 mm is negligible and few-cycle soliton-like pulses with sub-20 fs duration are formed for both 24 nJ and 55 nJ excitation. After the breakup, individual temporal features continue to propagate through the fiber separately. The wavelength dependent inter-core oscillations of different temporal features can give rise to simultaneous nonlinear switching at multiple non-excitation wavelengths, which we demonstrated previously . The current study is focused on experimenta identification of the minimal propagation length necessary for redirection of soliton-like pulses between the fiber cores with the high contrast. Moreover, the dedicated simulations presented here offer a very credible explanation of the fiber length effect on the switching performance.
Systematic experimental investigation of nonlinearly induced fiber output intensity redistribution between the cores was performed with an aim to demonstrate an optimized soliton-based nonlinear switching. Fiber samples were kept as short as possible for the sake of compactness and minimization of losses. The initial fiber length in the experiments was 5 mm, which corresponded to the minimal soliton compression distance predicted numerically for the highest applied input energy. The length of investigated samples was then gradually increased. For every fiber length, the output spectrum dependence on input pulse energy was measured individually for both cores and orthogonal polarization directions. For the sake of better visualization of narrowband switching possibilities, results will be presented in the form of excited core output spectral intensity normalized to the overall spectral intensity registered from both cores. These will be presented in whole spectral region covering pulse broadening under maximal applied pulse energy. Such graphs provide comprehensive information about redistribution of spectral intensity between the cores, where values above 0.5 (equilibrium) indicates dominancy of the spectral feature in the excited core while values lower than 0.5 indicates dominancy in non-excited. Figure 4 utilizes this representation to illustrate evolution of switching possibilities with increasing sample length in the case of upper core excitation with X-polarized pulses.
For 5 mm sample, spectral intensity distribution plots generally have a smooth character as a result of a smooth pulse spectral profile before the soliton fission point which was predicted by numerical simulations at longer propagation distance. Also, the short propagation distance is not sufficient to induce more abrupt changes in the spectral intensity of the inter-core distribution due to spectral dependent coupling as the number of oscillations between the cores is small. Nonlinearly altered coupling leads to 16 dB switching at for 5 nJ vs. 55 nJ excitation. However, switching performance is not ideal because the spectral intensity ratio at given is not symmetrically mirrored between the cores. In general, excited core is obviously dominant for this fiber length. For longer 10 mm sample, relative distribution of spectral intensity between the cores has a more structured character and is better balanced between the cores. The fission process evolving after the initial compression distance gives rise to new switching possibilities at non-excitation wavelengths for the lower order soliton-like pulses. Only moderate switching at the level of 5 dB at remains for 5 nJ vs. 55 nJ excitation. However, for 15 nJ vs. 35 nJ excitation, new possibility of simultaneous switching at 1800 nm and 1570 nm emerges with 8 dB and 6 dB extinction ratio contrast, respectively. The switching direction between the cores is different for red- and blue-side switching wavelengths. With the increase of input pulse energy, wavelengths around 1800 nm are being redirected from the non-excited to the excited core, while wavelengths around 1570 nm are switched in the opposite direction. The switching in opposite direction is hardly accessible in the normal dispersion region, because it benefits from the high contrast solitonic coupling oscillations between the cores. Knowing the dependence of the coupling length on the wavelength, the intended switching performance is controllable by the fiber length and pulse energy. As a result, the switching of designated wavelength can be achieved by the pulse energy control for a given fiber length, which constitutes a wavelength-tunable nonlinear switch.
Further increasing the fiber length to 14 mm, switching at excitation wavelength vanishes completely as depicted in Fig. 4(c). On the other hand, switching contrast at 1560 nm reaches 9 dB for 20 nJ vs. 50 nJ excitation . Moreover, solely by changing the input pulse polarization to orthogonal state (Y-pol), better conditions for simultaneous multi-wavelength switching can be achieved as shown in Fig. 5(a). Switching at 1540 nm expresses 6 dB contrast, while switching contrast at 1730 nm reaches up to 15 dB. In this case, switching direction between the cores is the same for both switching wavelengths. As switching energy levels are kept the same for both polarization settings at 14 mm fiber length, polarization tunable switching performance at non-excitation wavelengths was achieved after optimization of all the experimental conditions. The X-polarization provides optimized switching at 1560 nm, while the Y-polarization at 1730 nm. With pulse energy increase, the switching direction is from excited core to the non-excited one for both cases. It is worth mentioning that the complex multi-solitonic dual-core propagation offers redistribution of the dominant soliton-like pulses with different spectral contents into the different output ports. One clear example of this performance is in Fig. 4(c) for 35 nJ excitation (blue-dashed curve), where the blue-side spectral feature dominates in the excited core, while the red-side feature in the non-excited core, respectively. The extinction ration contrast between these two features reaches 13 dB. Moreover, this spatial splitting of the few-cycle soliton-like pulses takes place advantageously in coherent manner, because the split pulses are derived from the same initial pulse entering one single port of the dual-core PCF. Such switching would be useful in the field of ultrafast photonics where spatial redistribution of broadband pulses is required, for example, for synchronization of two-color femtosecond oscillators.
For comparison, Fig. 5(b) shows simulated normalized excited core output spectral intensity for same propagation length (14 mm) and polarization conditions (Y-pol). Lower energy level is at 24 nJ corresponding to the pulse propagation presented in Fig. 2 and upper energy level is at 55 nJ corresponding to Fig. 3. Accounting for an uncertainty in the radiation coupling efficiency into the fiber and laser source fluctuations, these values roughly correspond to experimental ones (20/50 nJ). The central part of presented simulation results, covering excitation and both switching wavelengths, exhibit a relatively good qualitative agreement with the experimental observations. The simulations predict even higher switching contrast extremes at wavelengths that are only slightly shifted from the experimentally determined ones. Pronounced features on both edges of presented spectral window do not appear in experimental results. These features, however, correspond to low intensity regions on the edges of nonlinearly broadened spectra, which are already below experimental detection threshold, especially at the red side, where the spectrometer sensitivity decreases significantly. Considering single-shot character of simulations, one can also expect that laser source power fluctuation, measurement averaging as well as limited OSA resolution (6.3 nm FWHM) will lead to considerable smoothing of sharp narrowband features present in the simulated results. Taking into account complex propagation behavior which is highly sensitive to all the input parameters, the performed simulations yield very good agreement with experimental results. It is true even for the spectral intensity distribution plots expressing the same switching directions for all three central spectral features.
This represents significant progress in comparison with previously published similar study . Better agreement was achieved due to the refined theoretical model, when especially incorporation of the fiber nonlinearity dispersion correction strongly affected obtained propagation maps. Beside the effect of additional fiber nonlinear parameter dispersion correction term, also impact of other key nonlinear processes were evaluated by repeatedly performing simulations while separately ignoring Raman, XPM and complete self-steepening term of the basic equation. According to these results, the effect of the XPM is negligible, however both the Raman and self-steepening terms has significant contribution to the overall spectral bandwidth and the frequency-evolution of the soliton-like pulses. On the other hand, the strong influence of the Raman and self-steepening processes do not compromise the integrity of the individual solitonic components. It is worth mentioning, the optimal excitation wavelength chosen within the flat area in the vicinity of the maximal dispersion reduces the effect of the third order dispersion (represented byin Table 1.). Therefore, only negligible part of the pulse energy is coupled to the dispersive waves, which is very advantageous from the point of view of stability of the soliton-like features. As a result, high contrast coupling oscillations take place and the strong nonlinear interaction induces sufficient spectral shift even at short fiber distances leading to the observed non-conventional switching performance.
5. Summary and outlook
In summary, in this paper proof-of-principle study of ultrafast soliton-based nonlinear multi-wavelength switching in DC PCF was presented. According to our knowledge, the experimental work is the first realization of high contrast nonlinear solitonic switch in DC optical fiber. Overcoming our previous publication  detailed experimental-numerical analysis of the field evolution along the DC PCF was presented enabling deeper insight to the roles of the physical processes behind and optimization of the fiber length for high contrast switching. The experimentally identified optimal length of 14 mm was confirmed also by the simulation results together with the role of Raman and self-steepening nonlinearities which enhance the wavelength tuning by optimization of the fiber length and input pulse energy. The optimal short fiber length enables to maintain the overall losses at the level of 85% which has a negligible effect on the nonlinear propagation and on the energy content of the switched soliton-like pulses. By the numerical simulation tool we estimated the ratio of input energy carried by the individual switched soliton-like pulses at the output of the fiber. For 24 nJ excitation, it was at the level 20-30% and about 15% for the 55 nJ excitation. Considering 10% in-coupling efficiency, the output soliton-like features have in the both cases roughly 1 nJ, which is applicable level even for further free space utilization. Moreover, the accompanied pulse compression behavior enables the application of these pulses also in the area of excitation of various nonlinear processes. Due to improved numerical model, reasonable agreement with the experimental results was achieved. This tool can be thus used in the future for fiber design optimization for diverse switching-splitting schemes.
Further advantageous aspect of the presented approach is that after the coupling efficiency improvement (for example by properly managed splicing procedure ), switching performance requires only sub-10 nJ level 100 fs laser pulses, what is already accessible by simple and commercially available oscillators at MHz repetition rates. Furthermore, the demonstrated switching performance evolves at simultaneous wavelength-shift offering simple solution for optical data processing. Lee et al. reported optically controlled buffer in the telecommunication C-band, where wavelength shifted counterpropagating control wavepacket was used in a nonlinear optical loop mirror in order to realize phase shift without interference with the signal . Coupling of both signal and control wavepacket into the loop mirror in opposite directions would be realized by our approach in an easier way using a short piece of DC PCF eliminating the requirement of separated shifted wavelength generator. The second application area emerges from the fact, that the presented ultrafast propagation in DC PCF can ensure high contrast spatial separation of two broadband solitons with different spectral content. This feature would be beneficial for optical synchronization of two femtosecond oscillators with different spectral content, thus decreasing the timing jitter between the oscillators in the field of sub-femtosecond pulse synthesis . One properly designed DC PCF sample could be inserted into a femtosecond master resonator, in which one channel ensures only spectral broadening of the pulses and the second channel provides spectrally shifted broadband pulses for the slave resonator with the same repetition rate as the master oscillator. Prospectively the multi-wavelength ultrafast switching would be useful also for optical data processing applications, however in the case of the demonstrated switching performance the applied energies are rather high. Interesting questions from this point of view is the scalability of our approach for sub-nJ energy levels, what we already addressed by the numerical simulations. Our preliminary results in this area revealed that designing DC PCF made of highly nonlinear glass materials opens the way even for single soliton switching with enhanced efficiency requiring only sub-100 pJ excitation .
Experimental and numerical study of nonlinear propagation of NIR femtosecond pulses in anomalous dispersion region of special dual-core PCF was performed. Interplay between soliton fission process and inter-core coupling was analyzed with focus on ultrafast nonlinear switching. Soliton-based polarization tunable nonlinear switching at multiple non-excitation wavelengths was demonstrated under excitation of fiber samples with different lengths in the range of 5-14 mm with 100 fs, 1650 nm pulses. The performed complex study enabled deeper analysis of the influence of fiber length and key physical processes on the dual-core nonlinear field evolution. The best switching performance was achieved at 14 mm fiber length. Depending on the input polarization, 9 dB or 15 dB narrowband switching was obtained at 1560 nm or 1730 nm, respectively, by simple change of the input pulse energies on the order of few nJ. Furthermore, the advanced theoretical model developed in the frame of this study provided results with good correspondence with experimental data and indicated further space for switching performance improvement.
The authors thank Ryszard Buczynski and Martin Koys for their invaluable help in accomplishing this work. The presented work was supported by the Austrian Research Promotion Agency (FFG) via Eurostars MIRANDUS 834722 project, Austrian Science Fund (FWF) via NextLite SFB F4903-N23 project, Slovak Scientific Grant Agency via VEGA 1/1187/12 research project and by the National Science Centre in Poland in the scope of the Harmonia project DEC2012/ 06/M/ST2/00479. Pavol Stajanca was sponsored by a scholarship grant by the Aktion Österreich Slowakei.
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