We fabricated a microstructured optical fiber with a dispersion profile that, according to calculations, is near-zero and flat, with 3 zero dispersion wavelengths in the mid-IR. To the best of our knowledge this is the first report of the fabrication of such a fiber. Simulations of multimode supercontinuum generation were performed using a simplified approach. Strong agreement between experiments and simulations were observed using this approach.
© 2011 OSA
The capacity for tailoring dispersion profile is one of the most important features of microstructured optical fibers (MOFs). This brings benefits not only for raising the transmission capacity in telecommunication applications, but is also crucial for many nonlinear fiber systems. For example, the phase matching condition of optical parametric processes , soliton and dispersive wave generation  are all determined by the dispersion profile of the fiber. Previous research has demonstrated that a flat near-zero dispersion profile can be very useful for these applications [3–7]. Many design from previous reports [3–7] involve of dispersion profiles with three zero dispersion wavelengths (ZDWs), however, to the best of our knowledge, no fiber with three ZDWs has ever been fabricated. This is because the successful demonstration of such fibres not only requires careful design of the structure, but also high precision control of the MOF fabrication.
In our previous study , a fiber with flat and near-zero dispersion profile was designed for the purpose of generating supercontinuum (SC) with large bandwidth and high coherence. The design was selected by using a genetic algorithm, and the result was a dispersion profile with three ZDWs (2, 2.5 and 3 μm). In this paper, we report the fabrication of such fiber, and present SC experiments using this fiber.
The effect of higher order modes (HOMs) on the generation of SC has been explored previously, and, for example, HOMs have been used to generate UV spectral content . A multimode pulse propagation model has also been developed [10,11] to investigate the dynamics of femtosecond SC generation in multimode fibers. In Ref. , measured SC spectra were compared to simulations for both fundamental and first high order modes respectively, and while qualitative agreement was obtained, these simulations could not accuruately describe the experiments over a broad spectral range. The multimode pulse propagation model used in Ref.  considered not only the broadening in each mode but also the interactions between modes, which enabled better agreement between predictions and experiments , with reasonable agreement over a spectral width approximately 200 nm.
Here we explore SC generation in a multimode fiber using an intermediate approach that considers the supercontinuum generated by multiple modes but without using a multimode pulse propagation model. Using this simple approach, good agreement is observed between experimental and simulation results over a wavelength range from 1.2 ∼ 2.2 μm. In addition, we report the fabrication details of a bismuth glass fiber designed to have three ZDWs and the experimental results of SC generation within this fiber. We find that large SC output bandwidth can be easily achieved in this fiber for a large range of pumping wavelengths.
In previous work  a fibre was designed to support supercontinuum generation with large bandwidth and high coherence. The fiber consisted of a small core, high NA microstructured soft glass optical fiber with a number of small (sub-wavelength) holes within the core region. The fiber was designed to have high nonlinearity and a low flat dispersion profile. Here we report the fabrication of this new form of fiber for the first time.
While the original fiber design was based on tellurite glass, here we made use of bismuth glass supplied by Asahi Glass Co. The use of the bismuth has its advantage over the tellurite glass. According to previous work , the existence of anomalous dispersion in the dispersion profile of the tellurite fiber is the main source of coherence degradation. To maintain high coherence, a flat dispersion profile with slight negative dispersion value is preferred. Using bismuth glass for the fiber allows us to achieve this dispersion feature without redesign the fibre structure. The detail of the dispersion profile of our bismuth fiber is discussed in Section 3.1. In addition, the bismuth glass is a high quality glass that enables high quality and robust fiber fabrication . Comparing to tellurite glass, the bismuth glass has a somewhat higher softening temperature and shallower viscosity versus temperature slope, relaxing the requirements for temperature control during the fabrication processes. The transmission window of the bismuth glass used in this work extends to approximately 3 μm which is narrower than that of tellurite glass . Despite the difference in transmission window, the two types of glass have reasonably similar optical properties. The refractive indices of the two types of glass are similar (1.98 for bismuth and 2.00 for tellurite, both at 1550 nm) as well as their material dispersion profiles (especially from 1 to 3 μm region) and zero dispersion wavelengths at 2.22 and 2.21 μm for bismuth and tellurite glass, respectively. The nonlinear refractive index of the bismuth glass (5.954×10−19 m2/W)  is also similar to that of this tellurite glass (5.5×10−19 m2/W measured with Z-scan method ).
The design of the structure has also been simplified from the structure proposed in Ref.  to reduce the complexity for fabrication purposes. The outer-most ring of the structure (Fig. 1) is removed due to its negligible effects on dispersion from our observation in simulations. The diameter of the inner holes was set to an average value of 0.36 μm (in the original design there were two sets of hole sizes 0.32 and 0.4 μm).
The fiber was fabricated in three steps: (1) preform and tube extrusion, (2) caning and (3) drawing. The preform was fabricated using the extrusion technique . The extruded preform is shown in Fig. 2a. In the next step it is pulled down to 1 mm diameter cane on a fiber drawing tower and inserted into a 10 mm diameter tube with a 1 mm hole in the center. Finally, the cane and the tube are pulled together into the final fiber. Figure 2b shows a scanning electronic microscopy (SEM) image of the cross section of the fabricated fiber.
Note that in the preform (Fig. 2a) that the ring of inner six holes are slightly non-circular, and are somewhat offset within the suspended core region. This distortion is transferred into the fabricated fiber (Fig. 2b). The core (defined as the area enclosed by the outer six holes) has a diameter of approximately 6.4 μm, as designed. The radius of the inner ring of holes (1.75 μm) and the diameter of the inner holes (0.4 μm) are about 10% larger than the designed sizes.
The fabricated fiber is close to the design. To study the effect of the slight distortions in the fabricated fiber on the nonlinearity and dispersion profile, calculations based on the SEM images of the fiber and simulations of ultra-short pulse propagation are described as a prelude to experimental measurements on this fiber in the following section.
3.1. Ideal structure with Bismuth glass
The dispersion and nonlinearity profiles of the fundamental mode of the bismuth fiber are calculated and plotted in Fig. 3.
A finite element method package COMSOL was used for solving the eigenmodes of the fiber. We also employed the Sellmeier equation of the glass, provided by Asahi Glass Co., and the nonlinear refractive index n2 into the calculation. The same value of n2 was also used for other wavelengths since the change in n2 as a function of wavelength is small. The nonlinearity profile is similar to that of the designed fiber . The dispersion profile of this fiber no longer show three ZDWs, however, it is flat and slightly negative in value, which it more preferred. The dispersion profile has a flat region from approximately 1.8 to 3.2 μm with a maximum of −3 ps/km/nm around 2.1 μm and a minimum of −11 ps/km/nm around 2.9 μm.
3.2. The fabricated structure
The nonlinearity and dispersion profiles of the fabricated fiber were also calculated using the SEM image of the fabricated fiber. The calculated nonlinearity and dispersion profiles of the fiber are shown in Fig. 4.
In Fig. 4, the thick green and blue lines show the results for the orthogonal polarized fundamental modes. The nonlinearity is approximately 250 W−1km−1 at 2 μm which is approximately 43% larger than for the original design (175W−1km−1) . This is mainly due to reduced mode area caused by the ∼10% increase in the diameter of the inner six holes, which increases the index contrast between the inner core and the first ring of holes. The calculated dispersion of the fabricated fiber shows three ZDWs. This result is not surprising because the dispersion profile of the ideal structure is flat and close to zero, and has a minimum and a maximum in the wavelength range of interest. Thus a shift in this dispersion profile in the right direction due to the distortion moves parts of the profile into anomalous regime resulting in 3 ZDWs. The calculated 3 ZDWs are located at 1.7, 2.7 and 3.6 μm. The maximum difference in the dispersion values over the range of 1.7 and 3.6 μm is only 20 ps/nm/km.
As a result of the slight structural asymmetry present in the fabricated fiber, birefringence is observed in the form of the difference between the two curves in the nonlinearity plot (|Δneff| = 2 × 10−4 at 1.7 μm calculated based on the SEM image). Note that there is negligible difference in the dispersion profiles of the two fundamental modes (two polarizations) as shown in the figure. However, the dispersion and nonlinearity profiles of the high-order modes (dashed lines) exhibit rather different characteristics. As shown in Fig. 4a and 4b, the nonlinearity profiles of all high order modes are lower than the fundamental ones. The first ZDWs of all high order modes (≤∼1500 nm) are shorter than those of fundamental modes, therefore modulation instability (MI) and soliton fission processes can be expected if the fiber is pumped at wavelengths longer than 1500 nm.
Applying a pulse propagation method for the above fiber including multiple modes can be computational intensive, and requires the solution of tens of coupled nonlinear Schrödinger equations . Here, we consider an alternative approach in which we make two assumptions. Firstly, in experiments the alignment of the laser beam and the fiber is optimized such that the majority of the light is coupled into the fundamental mode along one of the principle axes. Therefore the nonlinear pulse broadening is dominated by the fundamental mode. Secondly, if we consider that (1) there are temporal walk-off between pulses in high order modes and fundamental mode (total walk-off occurs within 2 mm in our fiber according to calculations), (2) the likelihood of achieving good phase matching condition are low for certain nonlinear effects such as four-wave mixing (FWM) and cross-phase modulation (XPM), (3) we only simulate pulse propagation for a short length ( 2 cm) in order to observe early stage of SC generation., then it is reasonable to assume that nonlinear cross-talk between modes including FWM and XPM do not have significant effects on the fundamental mode. Therefore we ignore these effects in the simulations. Furthermore, the fiber we used in the experiments is highly birefringent, so the coherent coupling is also ignored. With these assumptions, we write that the total electric field at the fiber output as a superposition of the electric fields of all modes. The fraction of pulse power in each mode is then determined by the coupling between the input beam and that mode. We calculate the coupling efficiency between an input beam and the modes based on the mode field pattern calculated from COMSOL. The coupling efficiency can be described by Eq. (1) which is a simplified form derived based on Ref. . Approximations that are implicit within this definition include the assumption that the modes are purely transverse and there is no coupling to radiation modes.Eq. (1), ηn is the coupling efficiency of n-th mode, Ein is the electric field of the input beam and En is the electric field of n-th mode inside the fiber. Assuming the input field distribution is Gaussian, the coupling efficiencies from the input field to the different modes can be found for a range of input beam diameters (focal spot size in experiments) as shown in Fig. 5a.
The first 16 modes contain the majority (∼94%) of energy of the input beam that is coupled in the fiber (calculated based on Fig. 5b) where the coupling efficient of each mode is averaged over input beam diameters from 2 to 16 μm. We simulated the pulse propagation for each of these modes independently with power determined by the coupling coefficients and for a range of input beam diameters. Following this, the electric fields of all the modes at the output of the fiber are superimposed. The superimposed electric fields interfere with each other, resulting in changes in the generated spectra.
During the experiments, the only confirmation of good alignment is the intensity distribution output on the IR camera. With the 10% power fluctuation in the laser (see Section 4), large NA of the fiber (≳ 0.5, which indicates short focal length) and possible beam diameter fluctuation, it is difficult to know the exact spot size on the fiber tip, especially for pump wavelengths longer than 1.7 μm due to the coupling difficulties which will be discussed later. Therefore, the simulated spectra were compared to the measured ones and only the best fit was selected as the delegates.
In the simulations, 100-fs 10-kW peak power hyperbolic secant pump pulses were used. The coupling efficient was set to 25% according to measurements. The propagation length is set to 2 cm. The fiber loss is 4 dB/m. Since we used only 2 cm of fiber, the loss was not included in the simulation. Simulations were carried out for a range of different pump wavelengths. The following wavelengths are chosen by considering the dispersion profile of the fundamental mode: a pump wavelength of 1300 nm is in normal dispersion region, pump wavelengths of 1550 and 1650 nm are in normal dispersion region but close to ZDW, and a pump wavelength of 1800 nm lies in the anomalous dispersion region. The output of the pulse propagation model is shown in Fig. 6a. As expected, when the pump wavelength is in normal dispersion region, the output spectrum is smooth and narrow since the broadening is dominated by self-phase modulation only. As the pump wavelength moves towards the first ZDW, the spectral bandwidth become wider and less smooth. This transition in the spectra can be attributed to the change of the dominant nonlinear processes. When the pump wavelength is varied from the normal to anomalous dispersion region, the dominant nonlinear process changes from SPM to MI and solitonal dynamics. Making use of these qualitative differences, we are able to estimate the first zero dispersion wavelength using the experimental data such as, in this case, around 1500 nm or longer since, on one side, spectra are smooth (SPM) and, on the other side, spectra are rough (MI and solitonal dynamics).
The spectral broadening in these simulations is dominated by the fundamental mode as it contains most of the energy. Therefore, despite the multimodeness of the fiber, the single-mode-based design directives of this fiber are still reasonable. Figure 6b shows the spectral output of the fundamental mode only. When the transmission window of the glass is not considered, the broadening of the fundamental modes extends over 4 μm width for almost all the pump wavelengths. This is achieved through the low flat dispersion profile of this fiber. The most significant differences between multimode (Fig. 6a) and single-mode (Fig. 6b) simulations are the peaks around the pump wavelengths [the highest peaks at 1300 (blue), 1550 (green), 1650 (red) and 1800 (cyan) nm]. These peaks are coming from power that coupled into the high order modes. Since the power coupled into the high order modes are low, these is no significant nonlinear processes took place in high order modes. Apart from that, the rest of the spectra are similar to the spectra generated by the fundamental mode alone.
Since the spectral broadening simulations are dominated by the fundamental mode, it is possible to link the multimode spectrum to the fundamental mode. If the measured spectra match with these simulations then the actual fundamental mode of the fiber should also be the same as the simulated one. Direct dispersion measurement of this fiber is challenging due to its multimode nature and low dispersion values. In the next section, experimental investigations of the influence of fiber’s tailored dispersion profile on SC generation were performed. By comparing the experimental results to the simulation predictions, we are able to estimate the dispersion profile of the fabricated fiber.
4. Ultra-short pulse experiments
The laser source used in these experiments is a wavelength tunable, 1-kHz repetition rate, 100-fs pulsed laser system (includes Spectra Physics Tsunami Ultrafast Ti:Sapphire Lasers, Spitfire Pro XP Ultrafast Ti:Sapphire Amplifier and TOPAS Automated Ultrafast OPA). This laser exhibits approximately 10% power fluctuation at all wavelengths according to our measurements. Averages of 10,000 pulses are taken for each wavelength point in the measurements. Taking into account the coupling efficiencies achieved in the experiments (approximately 25%), we measured the output spectra for different pump wavelengths as shown in Fig. 7. Due to the fact that this is a multimode fiber, one can not guarantee the coupling is optimized for the fundamental modes by maximizing the output power only. An infrared camera was used to monitor the optimization and ensure that predominantly the fundamental mode was excited. In experiments, 2-cm fiber pieces were used and the peak power of the pump pulses was approximately 10 kW.
Considering the assumptions described previously, Fig. 7 shows good agreement between simulations (thin red curve) and experiments (thick blue curve), especially for pumping wavelengths shorter than 1700 nm. As we expected, intensive peaks appeared in the measured spectra around the pumping wavelengths which can be attributed to high order modes. The remaining of the spectra correspond principally to the fundamental modes. Wavelengths longer than 1700 nm are difficult to observe using a IR camera (GOODRICH SU320M-1.7RT, wavelength ranging from 0.9 μm to 1.7 μm), therefore the coupling to the fundamental mode is difficult to verify using this camera. However, by aligning the beam using light with wavelength shorter than 1700 nm and gradually increasing the pump wavelength and maximizing the fiber output, we managed to align the fiber, to a certain extend, using the part of light generated through pulse broadening at short wavelengths. Figure 7d shows the spectra from the experiment and simulations pumped at 1800 nm. In this case, the simulation only partially matches with the measured spectrum. Further analysis indicates this was due to poor alignment of input light to the fundamental mode. This is likely to be due to significant contribution from higher order modes.
Figure 7 shows that there is strong agreement between the spectral peaks in simulated and measured spectra. Since the fundamental modes contain most of the energy, this indicates that the SC spectra of the fundamental modes also agrees well with the simulated results (Fig. 6b), which underpin most important physical effects of the spectral broadening. These results confirm that the fabricated fiber has a dispersion profile close to the predicted one which has three ZDWs.
5. Discussion and conclusions
In this paper we fabricated what we believe to be the first bismuth MOF with flat and near-zero dispersion in the mid-IR. According to the calculation, the fabricated fiber has a dispersion profile with three ZDWs in the mid-IR from 1.7 to 3.6 um and a maximum variation of 20 ps/nm/km. Using a simplified approach to include high order modes into the simulations, we simulated the multimode pulse broadening and achieve good agreements with experimental results and therefore the fundamental mode in the fabricated fiber behaves as predicted. The fabrication results described here demonstrate that it is feasible to produce complex fibre cross-sections in soft glass materials for the purpose of dispersion tailoring, and future work will focus on reducing the ∼10% increase in the inner hole diameters which would significantly reduce the number of modes in the fiber and improve the coupling to the fundamental mode.
A better coupling efficiency model can be used to include cladding modes and radiation modes and a finite difference method can be applied at the fiber interface to solve coupling for different phase front, angle and shape of the input beams. It is also worth using a multimode pulse propagation model to predict SC generations in the fiber which will facilitate deeper insight into the underlying physics. Also, recent work [19, 20] have pointed out that a vectorial form of nonlinear Schrödinger equation is necessary when high index material and sub-wavelength features are involved in a fiber. Developing such model with multimode capability is critical for future work.
The results here demonstrate the successful fabrication of a bismuth glass microstructured optical fiber with a flat low dispersion, and investigations of SC generation (up to 2.6 μm) through simulation and experiment pave the way to measurements of SC beyond 2.6 μm and exploring the relationship between the dispersion and nonlinear characteristics of these fibers and the characteristics of the generated supercontinuum. Direct measurement of dispersion in the mid-IR would be useful to support the further development of these fibers.
This work was supported by ARC LIEF grant ( LE0989747) and ARC DP grant ( DP110104247). We also would like to acknowledge ARC funding support (DP110104247), Naoki Sugimoto ASAHI GLASS CO., LTD for providing the bismuth glass and Tanya M. Monro acknowledges the support of an ARC Federation Fellowship.
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