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For the first time to our knowledge, we demonstrate a coherent supercontinuum in silica fibers reaching 2.2 µm in a long wavelength range. The process of supercontinuum generation was studied experimentally and numerically in two microstructured fibers with a germanium doped core, having flat all-normal chromatic dispersion optimized for pumping at 1.55 µm. The fibers were pumped with two pulse lasers operating at 1.56 µm with different pulse duration times equal respectively to 23 fs and 460 fs. The experimental results are in a good agreement with the simulations conducted by solving the generalized nonlinear Schrödinger equation with the split-step Fourier method. The simulations also confirmed high coherence of the generated spectra and revealed that their long wavelength edge (2.2 µm) is related to OH contamination. Therefore, improving the fibers purity will result in further up-shift of the long wavelength spectra limit.
© 2016 Optical Society of America
1. Introduction
Since the first demonstration of a microstructured optical fiber (MOF) in 1996 [1], this class of fibers found numerous applications thanks to high freedom in engineering their transmission and sensing properties. A possibility of shaping chromatic dispersion was particularly useful for supercontinuum (SC) generation. Although supercontinuum generation in optical fibers was reported as early as 1976 [2], only after the first demonstration in a microstructured optical fiber it gained much interest [3]. Ranka et al. showed in 2000 the SC spectrum extending from 0.39 to 1.60 μm, which was generated in the microstructured fiber with zero dispersion wavelength shifted below 0.8 μm by injecting femtosecond pulses close to zero dispersion wavelength [3].
Pumping at an anomalous chromatic dispersion range results in an ultra-broad spectrum, but such SC is not uniform in terms of spectral energy density and splits in many pulses in the time domain. On the contrary, pumping the all-normal dispersion (ANDi) fibers results in generation of a single pulse SC exhibiting a high level of coherence as shown by Heidt et al. [4]. The all-normal dispersion SC spectrum broadens maximally when pumped at the wavelength corresponding to the low absolute value of chromatic dispersion. In other words, pumping should be close to the maximum dispersion wavelength and chromatic dispersion should be flat and slightly negative. Hartung et al. analyzed different designs of silica microstructured fibers and concluded that the maximum dispersion wavelength can be up-shifted by simultaneously increasing the pitch and decreasing the air filling factor [5]. The limit for the maximum dispersion wavelength is around 1.3 μm, because further changes in the pitch and the air filling factor cause vanishing of the dispersion maximum and its monotonic increase into the anomalous regime [5]. As a result, the experimentally generated ANDi SC in silica fibers reached at most 1.5 μm [4], which is very far from the long wavelength limit of the silica transparency window (2.8 μm). There have been many efforts reported in literature to shift the long wavelength limit of the ANDi SC towards the mid infrared but they have all been based on the fibers not compatible with the telecommunication technology. A design of a heavily doped silica fiber with the GeO2 concentration in the core ranging from 60 to 100 mol% was proposed and numerically analyzed by Wang et al. [6]. Another approach based on lead-silicate glass fiber was discussed by Chatterjee et al. [7]. The only fabricated fiber reported so far was made of borosilicate glass with flint glass inclusions [8–10]. A low-noise SC was generated by Hori et al. in hybrid fibers combining sections with different (anomalous and normal) dispersion [11], but fibers designs were not disclosed.
In this work, we present the all-normal dispersion supercontinuum reaching 2.2 μm generated in specially designed silica microstructured fibers with chromatic dispersion flattened in a normal regime. The desired fibers properties were achieved thanks to the application of the germanium doped core which provides an additional degree of freedom in engineering the chromatic dispersion and allows to obtain flattened dispersion in the spectral range reaching 2.3 µm, as described in our earlier work [12].
According to our knowledge, this is the most up-shifted all-normal dispersion SC generated in silica microstructured fibers reported so far. It should be stressed that the developed fibers are made of pure silica with the core moderately doped with GeO2 (18 mol%) and therefore they are compatible with present optical telecommunication technology. This fact makes them particularly interesting in comparison to other recently proposed approaches aiming at similar wavelength ANDi SC range based on the fibers fabricated from more exotic glasses [6–10].
The generation of ANDi SC in the developed fibers was investigated both experimentally and numerically. First, we measured the chromatic dispersion in the fabricated fibers using an interferometric method and confirmed the experimental results by numerical simulations conducted using a finite element method (FEM). In the second step, we pumped the fabricated fibers using two femtosecond lasers with different pulse durations, respectively 23 fs and 460 fs, operating at 1.56 μm. Next, we simulated the supercontinuum generation process by solving the generalized nonlinear Schrödinger equation with the split-step Fourier method. The experimental and numerical results are in a good agreement showing that the generated highly coherent spectra are significantly shifted towards the long wavelength edge of a silica transparency window.
2. Microstructured silica fibers for ANDi SC
The silica fibers were fabricated by Laboratory of Optical Fiber Technology, Maria Curie-Sklodowska University, Lublin, Poland, according to the idea presented in [12]. Thanks to the balance of the fiber geometrical parameters, it is possible to obtain flattened normal dispersion in a broad wavelength range. The fiber preforms were stacked from silica rods (cladding) and the germanium doped rod was fabricated by the MCVD method (core). In Figs. 1(a), 1(b), 1(e) and 1(f), we show images of the fibers obtained in a scanning electron microscope (SEM). Basing on the SEM images, we estimated the microstructure geometrical parameters in fiber A (fiber B), which are as follows: ddo – diameter of the germanium doped core 3.4 µm (3.3 µm), dr – diameter of the first air holes ring 5.8 µm (6.2 µm), dh – averaged diameter of the air holes in the first ring 0.26 µm (0.38 µm). The GeO2 doping level cdo is the same in both fibers and equals to 18 mol%.
Fig. 1 Images of fabricated fibers: (a)-(d) fiber A, (e)-(h) fiber B. (a), (b), (e), (f) SEM images; (c), (g) post-processed images used in FEM model: white – air, light grey – silica, dark grey – germanium doped silica; (d), (h) calculated electric field distributions at 1.55 μm.
First, we post-processed the SEM images to determine the fibers geometry for FEM simulations. Different materials constants were assigned to distinguished domains, Figs. 1(c) and 1(g). Next, the numerical models were developed with Comsol Multiphysics Wave Optics Module. Solving the wave equation, we found effective refractive indices and electric field distribution of guided fundamental modes in a broad wavelength range, Figs. 1(d) and 1(h). The material dispersion of pure and doped silica glass was accounted for during numerical simulations [13, 14]. Finally, we calculated the chromatic dispersion and effective mode area of the fundamental modes in both fibers.
To show the influence of germanium doping on characteristics of the proposed fibers, we have calculated a chromatic dispersion and an effective mode area of the fundamental mode in the idealized fiber having almost the same geometry as fiber B (circular hole and only four rings of air holes) and different GeO2 doping levels in the core (12, 15, 18 mol%). The calculated chromatic dispersion is shown in Fig. 2 for a wavelength range at which the effective mode area is smaller than 40 µm2.
Fig. 2 Calculated characteristics of the idealized fiber with the geometry as fiber B (circular core and four air holes rings) and different GeO2 doping levels: (a) chromatic dispersion (b) effective mode area.
Thanks to germanium doping, the four air holes rings are enough to keep mode confinement at long wavelengths in the fabricated fibers. Much more rings (>15) of small air holes were needed in the case of a pure silica PCF reported in [5] to shift maximum dispersion wavelength at 1.3 µm and keep mode confinement. In our fibers, the small air holes introduce significant waveguide dispersion to push down the overall chromatic dispersion to negative values at pump wavelength and consequently to up-shift zero dispersion wavelength. Increasing the doping level in the proposed fibers limits the influence of the microstructure and increases the chromatic dispersion. Moreover, greater GeO2 level lowers the effective mode area and increases the nonlinear coefficient. By balancing the contribution of microstructure and doped core, one can obtain normal dispersion with low absolute value in a wide spectral range [12].
An analysis of the effect of germanium doping on dispersion of a microstructured fiber with a high air filling factor was also presented by Modotto et al. [15] and Kudlinski et al. [16]. It was shown that depending on a cladding microstructure a zero dispersion wavelength can be shifted by more than 100 nm (from 1001 nm to 1115 nm) [15], but also it is possible to make fiber dispersion insensitive to germanium concentration in the core [16]. Two fibers with very high air filling factor, one fabricated from pure silica, while the other with germanium doping, were compared. The zero dispersion wavelength remained unchanged, while the nonlinear coefficient increased over four times with germanium doping [16]. As it is shown in Fig. 2, in our fibers, due to the low air filling factor of the cladding holes, the germanium doped core simultaneously up-shifts the flat part of the dispersion characteristics and increases the nonlinear coefficient.
In parallel with the numerical simulations, we also measured the spectral dependence of the chromatic dispersion in the two fibers. For this purpose we employed the white light interferometric technique described in [17–19]. We placed the investigated fiber of the known length (1.2 m) in one arm of a dispersion-balanced Mach-Zehnder interferometer, while the reference arm was with the adjustable path length in the air. We used the supercontinuum source (NKT Photonics SuperK Versa), which allowed to perform measurements in the spectral range up to 2.1 µm. To measure the equalization wavelength λeq as a function of the path length difference ΔL(λ), a series of spectral interferograms were registered using an optical spectrum analyzer (OSA Yokogawa AQ6375). Finally, we applied two methods to calculate the spectral dependence of the chromatic dispersion, i.e., the five-term power series fit to the obtained data ΔL(λ) [17] and the method based on resolving the spectral interferogram from which the phase difference (the spectral positions of interference extrema) can be plotted as a function of wavelength [18, 19]. Fitting this dependence with the polynomial function allows to determine the chromatic dispersion at particular wavelength λeq. Next, by varying the delay in the reference arm, it is possible to measure the chromatic dispersion in a broader spectral range.
We obtained a very good agreement between the experimental and numerical data in both fibers, Fig. 3. According to the measurement results, in the fiber A there is a local maximum of chromatic dispersion reaching −7 ps/km/nm@1.63 μm and the dispersion remains flat (measured values are between −8.5 up to −6.5 ps/km/nm) from 1.48 μm up to at least 2.0 μm. In the fiber B, the maximum value of dispersion is −0.5 ps/km/nm at around 1.7 μm. A slight discrepancy between the experimental and numerical results (the difference of 3 ps/km/nm) may be related to the inaccuracy in reproducing fibers geometries from SEM images for numerical simulations. For the fiber B, the experimental points are spectrally more distant since the interference fringes obtained for this fiber were very broad. This observation confirms indirectly that a very low absolute value of chromatic dispersion occurs in this fiber in a broad spectral range.
Fig. 3 The chromatic dispersion in fabricated fibers – comparison between experimental and numerical data: (a) fiber A, (b) fiber B. Solid lines and points correspond to numerical and experimental data, respectively. The insets show same plot in wider wavelength range.
Using a bending method [20], we measured the cut-off wavelength, which is around 1.3 µm in both fibers. We also measured spectral attenuation in both fabricated fibers using a cut-back method. The obtained results revealed that, similarly as for cut-off wavelength, there is no significant loss difference between the two fibers. The representative measurement data shown in Fig. 4 exhibit the OH absorption band at 1.38 µm with the maximum of 2.4 dB/m. We were not able to conduct the attenuation measurements in the spectral range beyond 2.1 µm because of the supercontinuum source limit. We estimated the fibers loss in the long wavelength range assuming that it is related mainly to OH absorption band at 2.21 µm. Basing on the relative attenuation curve given by Humbach et al. [21], we estimated the OH absorption related losses to 7.8 dB/m at 2.21 µm. The extrapolated attenuation data were later used in numerical simulations of SC generation.
Fig. 4 The attenuation coefficient of fabricated fibers: circles – measured up to 2.1 µm, solid line – extrapolated up to 2.4 µm.
Finally, in Fig. 5, we present the calculated spectral dependences of the effective mode area Aeff in both fibers, which are necessary to conduct nonlinear simulations. Due to a larger diameter of air holes, the mode confinement is slightly higher in the fiber B than in the fiber A. In both fibers, the effective mode area at 1.56 µm is Aeff = 14 µm2, which results in effective nonlinear coefficient γ = 7.7 W−1km−1 for nonlinear refractive index n2 = 2.6∙10−20 m2/W [22].
Fig. 5 Calculated spectral dependence of the effective mode area of the fundamental mode in the fabricated fibers.
3. Coherent supercontinuum generation
In order to investigate the supercontinuum generation process, we performed both the experimental and the numerical studies. In the experimental part, we pumped both fibers with two pulse fiber lasers. The first one was a commercially available TOPTICA Photonics FemtoFiber pro IRS laser [23] providing ultra-short 23 fs pulses with the repetition rate of frep = 80 MHz, an average power of Pav = 230 mW and a central wavelength λ0 = 1.56 µm. The second one was a subpicosecond mode-locked fiber laser with a saturable graphene absorber [24] with 460 fs pulses (frep = 100 MHz, Pav = 1.8 W and λ0 = 1.56 µm). To adjust pulse energy while preserving a pulse shape, we use a half-wave plate (WPH05M-1550, Thorlabs Inc.) and polarizer (WP25M-UB, Thorlabs Inc.).
The numerical studies were performed with self-developed software for solving the generalized nonlinear Schrödinger equation (GNLSE) using the split-step Fourier method [20, 25]. In the simulations, we used the chromatic dispersions calculated with FEM showed in Fig. 3 and the extrapolated fibers attenuation showed in Fig. 4. Additionally, knowing the mode field distribution from FEM calculations (Fig. 5), we accounted for the effective mode area dispersion in GNLSE [26]. For the coherence calculations, one photon per mode noise [20] and Raman noise [25, 27] were taken into account.
3.1 Pumping with 23 fs pulses
It was already demonstrated in [12] that shortening the pump pulse results in flatter and broader SC spectrum. For this reason, we used the ultra-short pulse laser as a pump for the SC generation. In Fig. 6 we show the initial pulse spectrum and the interferometric autocorrelation [28] registered for this pulse. Since the full characterization of this pulse was not possible, we performed time pulse shape fitting to restore the interferometric autocorrelation trace. We considered two cases: ideal and non-ideal pulse shape. In the first case, we fitted the autocorrelation trace assuming sech pulse shape (E(A) – amplitude, T(A) – time width):
for the second, we assumed linearly chirped sech pulse (E(A) – amplitude, T(A) – time width, C(A) – chirp) with two sech side-pulses (E(B), E(C) – amplitudes; T(B), T(C) – time widths; t(B), t(C) – time shifts):Fig. 6 Characteristics of initial ultra-short pulse: (a) measured pulse spectrum, (b) measured and calculated interferometric autocorrelation.
The results of pulse fitting are presented in Fig. 6(b). For the ideal pulse represented by Eq. (1), the full width at half maximum was estimated to be 23 fs. In case of ultra-short pulses, very broad and flat SC spectra were expected. In Fig. 7 we present the SC spectra registered with an optical spectrum analyzer for two fiber pieces of different lengths, respectively 10 cm and 80 cm. The SC generated for the highest pulse energy 1.008 nJ in the 80 cm long fiber B reached up to 2.2 μm. The pulse energy was measured at the fiber output, thus this value accounts for the coupling and propagation loss.
Fig. 7 Supercontinuum spectra registered at the output of: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B, all pumped with 23 fs pulses.
The simulations of SC generation in both fibers were performed assuming pumping with ideal pulses represented by Eq. (1) and distorted pulses represented by Eq. (2). The results are showed in Figs. 8 and 9, respectively. We modeled the nonlinear propagation for different pump pulse energy, respectively 1.45, 1.20, 0.95, 0.70, 0.45, and 0.20 nJ (solid color lines). In the simulations, the pump pulse energy is set at the beginning of nonlinear propagation. For comparison, we show also the simulation results obtained for the highest pulse energy in the fibers with losses disregarded (dashed black line).
Fig. 8 Supercontinuum spectra calculated for ideal 23 fs pulse pump (Eq. (1)) by solving GNLSE: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B. Solid color lines correspond to the fibers with the loss level evaluated experimentally, while black dashed line to lossless fibers.
Fig. 9 Pulse shapes calculated for ideal 23 fs pulse pump (Eq. (1)) by solving GNLSE: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B. Solid color lines correspond to the fibers with the loss level evaluated experimentally, while black dashed line to lossless fibers.
The results presented in Fig. 8 are in a qualitative agreement with the experimental spectra. The broadening is similar in terms of spectral width but the simulation curves are smooth in contrast to the measured ones. The pulse shapes presented in Fig. 9 are also smooth. The dip in time profiles visible for 80 cm long propagation distance is related to fiber attenuation.
Non-uniformity in the experimental spectra can be attributed to non-ideal pulse characteristics. By accounting for a distorted pulse shape in the numerical simulations, we achieved a very good agreement between experimental and calculated SC spectra (Fig. 10). In both fibers the generated SCs are broad and show characteristic ripples already after 10 cm of propagation length. Similarly, the ripples are also present in pulse shapes presented in Fig. 11. The process of enhancing the fine structure is visualized in Fig. 12. The spectrograms were calculated at different propagation distances 1, 5, 10, 80 cm, in both fibers for ideal and distorted 23 fs pulse pumping. The gating function was a hyperbolic secant with full width half maximum equal to 23 fs. Increasing the propagation distance up to 80 cm does not change the spectra significantly. The most distinct difference between spectra generated on short and long distances is an appearance of OH absorption dips, particularly visible for the fiber B at 2.2 µm. The corresponding dip was observed in the experiments. To confirm that it originates from the fiber losses, we calculated the SC spectra for 1.45 nJ pulses with fiber attenuation disregarded (dashed black line). Basing on these simulation results, we conclude that by decreasing OH contamination, the long wavelength limit of ANDi SC in silica fibers can be up-shifted to at least 2.3 µm.
Fig. 10 Supercontinuum spectra calculated for distorted 23 fs pulse pump (Eq. (2)) by solving GNLSE: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B. Solid color lines correspond to the fibers with the loss level evaluated experimentally, while black dashed line to lossless fibers.
Fig. 11 Pulse shapes calculated for distorted 23 fs pulse pump (Eq. (2)) by solving GNLSE: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B. Solid color lines correspond to the fibers with the loss level evaluated experimentally, while black dashed line to lossless fibers.
Fig. 12 Spectrograms comparing SC generation at 1, 5, 10, 80 cm propagation distance: (a), (b) fiber A; (c), (d) fiber B; (a), (c) ideal 23 fs pulse; (b), (d) distorted 23 fs pulse.
The complex shape of the output pulse could be a limiting factor for potential pulse compression. However, the simulation results obtained for an ideal pulse prove that SC generated in the presented fibers using a pump pulse of better quality can be compressed and used in ultra-fast spectroscopy.
Finally, we performed a series of simulations to calculate the spectra coherence for ultra-short pulses. For each fiber, we run 100 simulations with 1.45 nJ pulse energy and calculated the first-order coherence degree g as defined in [25] after 1 m propagation distance for an ideal and distorted pulse pump. The results of simulations presented in Fig. 13 confirm that the SC spectra generated in both fibers are highly coherent. The high coherence range spreads wider than SC spectra shown in Figs. 8 and 10. This is because we display in these plots only the part of the SC spectra with power density greater than −40 dB which matches to 1-2.2 µm range. In the simulations there are some spectral components of low power density outside the 1-2.2 µm range, which show high coherence.
Fig. 13 First-order coherence degree g calculated for supercontinuum spectra based on 100 simulation runs for 23 fs pulse pumping: (a), (c) fiber A; (b), (d) fiber B; (a), (b) ideal pulse pump; (c), (d) distorted pulse pump.
3.2 Pumping with 460 fs pulses
We also performed measurements and simulation for pumping with a subpicosecond mode-locked laser. We decided to conduct such studies to provide experimental data for comparison between ultra-short (23 fs) and subpicosecond (460 fs) pumping regimes. In Fig. 14, we present the SC spectra registered with an optical spectrum analyzer for both fibers of different lengths (10 cm and 80 cm). Like in the case of the ultra-short pumping regime, the SC generated over the same distance is broader in the fiber B than in the fiber A.
Fig. 14 Supercontinuum spectra registered at the output of: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B, all pumped with 460 fs pulses.
The simulations results presented in Fig. 15 are in a good agreement with the experimental data as the registered and calculated SC spectra have similar flatness and shape. We modeled the nonlinear propagation for different pump pulse energies, respectively 8.0, 6.0, 4.0, 2.0, 1.0, and 0.5 nJ (solid color lines). For comparison, we show also the simulation results obtained for the highest pulse energy in the fibers with losses disregarded (black dashed line). However, in both fibers almost two times higher pulse energies were needed to reach in the simulations of the SC widths similar to the measured ones. This is partly related to fiber loss as the pulse energy was measured at the fiber output while in the simulations the pulse energy was set at the beginning of propagation. A second reason could be a discrepancy between the calculated and measured chromatic dispersion dependences (Fig. 3). In Fig. 16 we show the simulated pulse shapes corresponding to spectra displayed in Fig. 15.
Fig. 15 Supercontinuum spectra calculated by solving GNLSE for: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B. Solid color lines correspond to the fibers with the loss level evaluated experimentally, while black dashed line to lossless fibers.
Fig. 16 Pulse shapes spectra calculated by solving GNLSE for: (a) 10 cm long fiber A, (b) 10 cm long fiber B, (c) 80 cm long fiber A, (d) 80 cm long fiber B. Solid color lines correspond to the fibers with the loss level evaluated experimentally, while black dashed line to lossless fibers.
To evaluate the first order coherence degree of the SCs generated in the subpicosecond regime, we performed a series of 100 simulation runs with 8 nJ pulse for 1 m long propagation distance. The calculation results shown in Fig. 17 prove that the generated SC remains coherent in the full spectral range (1.2-1.9 µm). Similarly, as in the case of 23 fs pumping, there are some coherent spectral components outside this range. They are visible in Fig. 17 but they are not present in the SC spectra showed in Fig. 15 due to low spectral power density. The observed degradation of coherence in the normal dispersion regime for subpicosecond pulses is most probably related to Raman scattering [29].
Fig. 17 First-order coherence degree g calculated for supercontinuum spectra based on 100 simulation runs with subpicosecond pumping of: (a) fiber A; (b) fiber B.
4. Summary
In this work, we studied experimentally and numerically a possibility of covering long wavelength part of the transparency window of silica fibers with coherent supercontinuum generated in all-normal dispersion regime. We fabricated and characterized two microstructured fibers with a germanium doped core. As predicted in [12], it was possible to achieve all-normal chromatic dispersion with an extremely low absolute value in the wide spectral range. The maximum value of the chromatic dispersion in the fiber B is only −0.5 ps/km/nm. The supercontinuum generated using 23 fs pulses reached in this fiber 2.2 µm. According to our simulation results, this limit is related to OH absorption peak at 2.21 µm. Therefore, reducing the OH contamination will allow to shift SC long wavelength edge up to at least 2.3 μm. By numerical simulations conducted using the split-step Fourier method, we confirmed that the generated SCs are highly coherent, as expected for all-normal dispersion regime. Our results prove that the proposed design of a silica fiber is a good solution for coherent SC generation with 1.56 µm pumping.
Funding
National Science Centre, Poland (2014/13/D/ST7/02090 – fibers design, fabrication and characterization with respect to linear and nonlinear properties, 2014/13/D/ST7/02143 –development of graphene-based fiber pulse laser).
Acknowledgments
We acknowledge Bertrand Kibler for comments and advice on numerical simulations of supercontinuum generation.
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