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We experimentally demonstrate a convenient technique for in situ fine group velocity dispersion (GVD) tailoring in optical microfibers via dielectric nanocoatings. This was elaborated by successively depositing poly-dimethylsiloxane (PDMS) nanocoatings around a 1.2 μm-diameter optical microfiber with a modified dip-coating method. In situ dispersion measurements showed that the GVD was tailored by 55 ps/nm•km at 1580 nm, and the zero-dispersion wavelength (ZDW) was red shifted by 30 nm. Numerical simulations showed that GVD tailoring in optical microfibers could bring signal (idler) tuning in spontaneous four-wave mixing (FWM) and spectral bandwidth expanding in supercontinuum (SC) generation, implying that this in situ fine GVD tailoring technique would offer optical microfibers with many new opportunities for applications in nonlinear optics.
© 2014 Optical Society of America
1. Introduction
Dispersion is one of the most important features of optical waveguides, and is crucial for many nonlinear optical processes and ultrashort pulse propagation in optical waveguides [1, 2]. Advances in dispersion engineering of optical waveguides including dispersion shifted fibers, dispersion compensation fibers, photonic crystal fibers and waveguides [3–6], silicon waveguides [7, 8], to name a few, unveil many otherwise unobservable physics [9–11] and find wide applications in optical communications [1], ultrafast optics [12, 13], nonlinear wave generation [14–20], and quantum optics [21, 22].
Optical microfibers have drawn great attentions in recent years because of the wavelength/subwavelength diameters, high fractional evanescent field, easy fabrication, low-loss, and full integration with fiber systems. This progress enabled a broad range of applications such as miniature optical devices, optical sensing, highly efficient light launching and coupling, and atom trapping [23–26]. Besides, optical microfibers can offer a tight optical confinement and the group velocity dispersion (GVD) profile is diameter-dependant. Hence, optical microfibers can be used for many nonlinear processes such as self-phase modulation (SPM), optical soliton generation, stimulated Raman scattering, four-wave mixing (FWM) and supercontinuum (SC) generation [7, 8, 16–19]. Since GVD is always involved in many nonlinear processes, fine GVD tailoring promises great agility in optical spectrum tuning in these nonlinear processes. For example, fine tailoring of the GVD may allow the tuning of phase-matched signal and idler wavelengths in spontaneous FWM [16, 17]. GVD profile also shows impact on the pump scheme and output spectra in SC generation [18, 19]. Therefore, fine GVD tailoring of optical microfibers would offer new opportunities for applications in nonlinear optics.
The dispersion profile of microfibers depends on the refractive index of the core and the environment [19, 20], and can also be engineered by controlling the microfiber’s diameter. However, the GVD of an optical microfiber is very sensitive to the diameter, and eventually a diameter control accuracy of nanometers is required for fine tunability, which is a nontrivial task for the drawing process. A modification of the microfiber’s cross section can also offer dispersion tailoring [27, 28]. However, to our knowledge, no relevant experiment has been reported yet.
In this work, we experimentally demonstrate for the first time, as far as we know, a convenient technique for in situ fine GVD tailoring in optical microfibers. We deposited poly-dimethylsiloxane (PDMS) nanocoatings layer-by-layer around a 10 cm-long microfiber via a modified dip-coating method. In situ dispersion measurements showed that the group delay dispersion (GDD) was gradually changed and a shift of −0.0078 ps2 could be obtained for a 20 nm-thick PDMS nanocoating. Measurement results and numerical simulations showed that the GVD was changed by more than 55 ps/nm•km at 1580 nm and the zero-dispersion wavelength (ZWD) was red shifted by more than 30 nm. To show new opportunities offered by this GVD tailoring technique, we use numerical simulations to show signal (idler) tuning in spontaneous FWM and spectral bandwidth expanding in SC generation.
2. Fabrication and measurement approach
The travelling-flame taper-drawing scheme [17] was employed to fabricate a 10 cm-long silica optical microfiber with a uniform diameter of about 1.2 μm on a home-made taper-drawing workstation. The total insertion loss was measured to be less than 0.1 dB. The as-fabricated microfiber was kept straight under a weak tension for the subsequent coating procedure.
We have demonstrated a modified dip-coating technique to functionalize microfibers with thin coatings. Benefited from the versatility of this technique, many transparent materials can be adopted here for dispersion tailoring. We chose PDMS (RTV 615, 10:1, GE) for illustration, since it could be conveniently dissolved in organic solvent, and high temperature annealing was unnecessary.
The in situ coating process is illustrated in Fig. 1, somewhat resembling that reported in [29]. PDMS was dissolved in toluene and the resultant solution was then fed into a syringe for suspending the solution droplets. The syringe was mounted onto a translation stage for the scanning started after the microfiber was immersed in the droplet. After each travel, the oxygen-butane flame, used in the microfiber drawing process, now could be employed to accelerate the solvent evaporation and the cure of PDMS. It should be noted that temperature at the polymer coating should be kept less than 200°C to prevent it from possible damage. In this way, PDMS coatings with a thickness of several nanometers, determined by the concentration of the solution, can be obtained on the microfibers. The optical loss induced by the coating was thickness-dependent, and was less than 1 dB for the thickness of 10 nm.
Fig. 1 Schematic for the coating process via a modified dip-coating method. The as-fabricated microfiber is connected with untapered fibers through taper sections. The PDMS: toluene solution droplet suspended from the syringe scans along the microfiber to deposit nanocoatings. The oxygen-butane flame (not shown here), used in the microfiber drawing process, is employed to accelerate the solvent evaporation and the cure of PDMS. The inset shows the cross section of the coated microfiber.
To demonstrate the capability of successive in situ dispersion tailoring, we deposited three coatings around the microfiber in succession. Two PDMS: toluene solutions with different concentrations were used in the coating process to obtain different coating thickness, and thus to show the possibility of fine GVD tailoring.
White-light interferometry based on a broadband source and a Michelson interferometer (MI) is a powerful method for dispersion characterizations [30–32], and we use it for in situ measurement of GVD tailoring for each PDMS nanocoating. The measurement setup is shown in Fig. 2(a). An amplified spontaneous emission (ASE) source in the C band was employed for illumination and a 3 dB fiber coupler (FC) was used as the beam splitter and combiner in the balanced MI. The reference arm of the interferometer was a movable broadband mirror in free space, and the measuring arm was the as-fabricated microfiber under test (MFUT) (including the microfiber, taper sections and untapered fibers), terminated with a fixed broadband mirror. We recorded the interference spectrum and that of each arm by blocking the other one on an optical spectrum analyzer (OSA) (86142b, Agilent). The recorded spectra are shown in Fig. 2(b). For each coating, the interference spectrum were recorded repeatedly on the OSA to give the error bars and thus to verify the reliability of the measurements.
Fig. 2 (a) The white-light interferometry setup for microfiber GVD measurements. An ASE source in the C band is employed to illuminate the balanced MI, in which a 3 dB FC is used as the beam splitter and combiner. The reference arm is free space with a movable broadband mirror and the measuring arm was the MFUT terminated with a fixed broadband mirror. (b) The recorded interference spectrum and spectrum of each arm. (c) The relative phase delay extracted from the interference spectrum via phase retrieval methods [26].
The intensity of the interference spectrum was given by
where I1(ω), I2(ω), and φ(ω) are the spectral density and the relative phase delay of the two beams, respectively. The symbols βf and βa stand for the propagation constants of the fiber and free space, and L and d for the lengths of them, respectively.The relative phase delay φ(ω) can be extracted from the interference spectrum of MI via well-known phase retrieval methods [30], which is presented in Fig. 2(c), and the group delay dispersion (GDD) and the GVD of the MUFT can be calculated from the relative phase delay according to Eqs. (3) and (4),
3. GVD measurement results
The mean values and the error bars of the GDD for each coating are shown in Fig. 3(a). It can be seen that the GDD of the bare MFUT (including a 10 cm-long microfiber, two 2 cm-long taper sections and a 20 cm-long untapered fiber) was measured to be 0.0556 ± 0.00035 ps2, and that the GDD shifted by −0.0022 ps2, −0.0043 ps2, and −0.0078 ps2 at 1580 nm for the three coatings, respectively.
Fig. 3 (a) The measured GDD of the MFUT (including a 10 cm-long microfiber, two 2 cm-long taper sections and a 20 cm-long untapered fiber). The error bars gives a standard deviation of less than 1%. (b) The measured (solid lines) and the simulated (scatters) GVDs of the bare and coated microfiber. In the simulation, the refractive index of PDMS assumed to be 1.406 and its material dispersion is ignored. Note that the GDD contributions from the taper sections and the untapered fibers should be subtracted from (a) in the calculations of GVD profiles.
It is a nontrivial task to measure the coating thickness with an accuracy of nanometers directly. Therefore, we determined it using numerical simulations. Shown in Fig. 3(b) are the measured (solid lines) and the simulated (scatters) GVDs of a 1.2 μm-diameter bare microfiber and that with PDMS coatings with a thickness of 8 nm, 12 nm and 20 nm, respectively. Note that the measured GDDs shown in Fig. 3(a) included the contributions of the microfiber, the taper sections and untapered fibers, which should be subtracted in the calculations of microfiber GVDs in Fig. 3(b) based on Eqs. (3) and (4). It is quite remarkable that the GVD was changed by 55 ps/nm•km at 1580 nm and that the ZDW was red shifted by more than 30 nm, i.e., from less than 1510 nm to about 1540 nm, for the 20 nm-thick PDMS coated microfiber compared with the bare one. It also should be noted that this fine in situ tailoring of GVD and ZDW of the microfiber is almost impossible for the drawing process.
4. Possible applications of GVD tailoring in optical microfibers
Measurement results shown above clearly demonstrate the capability of in situ fine GVD tailoring using nanocoatings around microfibers. Benefited from its convenience and versatility, this technique offers possibilities of optical spectrum tuning in many GVD-involved nonlinear optical processes.
4.1 Signal (idler) wavelength tuning in spontaneous FWM
In spontaneous FWM, the dispersion profile and the ZDW of the microfiber have a significant impact on the frequency difference between the pump and signal (idler), which is very small when the pump lies in the regime of normal dispersion, and that it increases dramatically for the pump in the regime of anomalous dispersion [16]. Hence, fine GVD tailoring in optical microfibers would enable a great tuning of signal (idler) wavelength in spontaneous FWM.
This is illustrated with Fig. 4. For a bare 1.2 μm-diameter microfiber and that with an 8 nm-thick PDMS nanocoating, a pump at 1535 nm lies in the regime of normal dispersion, and thus the signal (idler) is almost coincident with the pump and the wavelength difference is unobservable and negligible in Fig. 4. When the coating thickness is increased to 20 nm, the dispersion profile of the microfiber is red shifted, as shown in Fig. 3(b), and the pump now lies in the regime of anomalous dispersion. This leads to a signal with a wavelength of 1632 nm. A further increase of the coating thickness would lead to a signal with an even longer wavelength. It can be seen in Fig. 4 that the signal wavelength can be increased to 2033 nm for the microfiber with a 50 nm-thick PDMS coating.
Fig. 4 The phase matching curves of a bare and coated optical microfiber. The diameter of the bare microfiber is assumed to be 1.2 μm in the calculations.
4.2 Spectral bandwidth expanding in supercontinuum generation
SC generation is observed in many optical waveguides, and many physical mechanisms are involved therein, such as SPM, soliton generation and high-order soliton fission, Raman soliton self-frequency shifting, and many other parametric processes [See Ref. 14 for an extensive review]. It has been shown that the position of the ZDW relative to the pump has a great impact on the spectral bandwidth and the coherence properties of the output supercontinuum [14]. Therefore, fine GVD tailoring of optical microfibers would bring a tailoring of the extent of the spectral broadening and the detailed spectral shape of the SC radiation.
We illustrate this with numerical simulations of SC generation in a 1.2 μm bare optical microfiber and that with PDMS nanocoatings using split-step Fourier method, shown in Fig. 5. Compared with the situation in the bare microfiber, the bandwidths of the supercontinuum extend 30 nm and 70 nm in the microfibers with 20 nm and 50 nm coatings, respectively. This can be explained by the fact that the GVD tailoring of the microfiber causes the pump at 1535 nm to shift from normal to anomalous dispersion regime [14, 15], and that the dominant physical mechanisms involved are different.
Fig. 5 The SC generated in the bare and coated optical microfiber. The bare microfiber diameter is 1.2 μm and the length is 10 cm. We chose typical parameters of a femtosecond fiber laser for the simulation, i.e., wavelength: 1535 nm, pulse duration: 250 fs, peak power: 2000 W. The nonlinear coefficient is calculated to be 0.074 W−1m−1 and the nonlinear effects of PDMS coatings are ignored.
In the bare microfiber, the pump at 1535 nm lies in the regime of normal dispersion and SPM dominates at the beginning of the spectral broadening process, accompanied by transferring spectral components into the anomalous dispersion region. For the microfiber with a 20 nm coating, the ZDW is shifted to around 1540 nm, which is in the vicinity of the pump, as shown in Fig. 3(b). In this case, the soliton dynamics play a more important role in the SC generation. For the microfiber with a 50 nm coating, the pump lies in the anomalous GVD regime, and soliton dynamics dominate the SC generation. The long-wavelength edge of the SC is further broadened by 40 nm, arising from the phase-matched dispersive wave generation. The dynamics in the SC generation are much clearer in the temporal evolution, as discussed exhaustively in [14], and will not be shown here. Although the physics is well-understood, it is emphasized in Fig. 5 that GVD tailoring in microfibers would bring a spectral bandwidth broadening in SC generation.
5. Conclusion
We demonstrate a technique for in situ GVD tailoring in optical microfibers via PDMS nanocoatings. The GDD shifts of a 10 cm-long optical microfiber with a diameter of 1.2 μm were measured to be −0.0022 ps2, −0.0043 ps2, and −0.0078 ps2 for PDMS coatings with a thickness of 8 nm, 12 nm and 20 nm, respectively. The ZDW of the microfiber was shifted by more than 30 nm with a 20 nm-thick coating. Benefited from the versatility of the coating technique, many other materials can also be adopted here. This technique can be used for fine and successive GVD tailoring in optical microfibers, enabling diverse applications in nonlinear optics. We illustrate this with signal (idler) wavelength tuning in spontaneous FWM and spectral bandwidth expanding in SC generation using numerical simulations. We believe that the technique of in situ fine GVD tailoring reported in this work would offer optical microfibers with many new opportunities for applications in nonlinear optics.
Acknowledgments
We thank Liang Cui from Tianjin University for helpful discussions in numerical simulations. This work is supported by the National Basic Research Program (973) of China (No. 2010CB22901).
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