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We report about a new type of nonlinear photonic crystal fibers allowing broadband four-wave mixing and supercontinuum generation. The microstructured optical fiber has a structured core consisting of a rod of highly nonlinear glass material inserted in a silica tube. This particular structure enables four wave mixing processes with very large frequency detuning (>135 THz), which permitted the generation of a wide supercontinuum spectrum extending over 1650 nm after 2.15 m of propagation length. The comparison with results obtained from germanium-doped holey fibers confirms the important role of the rod material properties regarding nonlinear process and dispersion.
©2009 Optical Society of America
1. Introduction
The nonlinear effects in standard optical fibers are strongly limited by the low Kerr index of silica (n2 = 2.6 × 10−20 m2/W). The use of photonic crystal fibers (PCF) has partially improved the efficiency of nonlinear effects because of the high confinement of the electro-magnetic field in a small core size. In a more direct way, other glass materials with higher nonlinear coefficients could be used. Therefore, several fibers have been fabricated with non silica glasses such as tellurite [1,2], bismuth [3], chalcogenide [4], sapphire [5] and also SF6 [6–8]. The nonlinear Kerr coefficients of such glasses are at least five times higher than that of silica. Moreover, these kinds of glasses often provide an improved transparency in the infrared (IR) wavelength range and a large modification of dispersion properties. Fiber fabrication with exotic glasses is complex especially when different types of glasses are mixed. Recently, a numerical study was reported where PCFs with different glass compositions were compared in order to modify the dispersion properties of the microstructured fibers and to increase the generation of blue wavelengths [9–11]. Additionally, it has already been demonstrated that the presence of a central air hole in the PCF core enables stabilization of the soliton self-frequency shift (SSFS) and generation of a broadband four-wave mixing process (FWM) [12]. Another solution for structuring the core of a PCF consists in using local doping. This possibility has been reported with the use of germanium (Ge) ions to control the dispersion, the modal cut-off and the nonlinearity of the fibers [13–15]. Such a PCF with a highly Ge-doped rod in the core center has been reported to achieve broadband supercontinuum (SC) [16].
In this paper we investigate a new type of PCF with a particular design using a highly nonlinear multi-component material. The glass fabricated for this purpose is composed of lanthanum oxide, aluminum oxide and silica in order to achieve a high nonlinearity in the fiber core. The variation of the mode areas versus the wavelength leads to a differential overlapping between the multi-component glass (MCG) region and the guided modes propagating in the fiber. In this way, broadband phase matching with regard to an efficient FWM process can be obtained. This parametric phenomenon can be used in different applications such as correlated photon pair generation [17], conversion of laser rays and SC generation [18]. The results obtained with this new multi-component guide are also compared to highly Ge-doped silica PCF.
After a description of the specific fiber structure, we investigate the nonlinear fiber properties by observing the efficient broadband FWM (> 135 THz) obtained by using a sub-ns laser source. Next we show how the particular FWM process can give birth to an SC extending from 500 nm to 2220 nm. Finally, we compare the SC generation obtained both in the MCG PCF and in highly Ge-doped silica PCF.
2. Experimental setup and characteristics of the nonlinear PCF
The nonlinear multi-component optical fiber used in our experiments is a holey fiber fabricated by the stack-and-draw technique [Fig. 1(a) ]. The particularity of this optical fiber is the presence of a glass rod with a high refractive index in the central area of the core as shown in the schematic diagram of the index profile of Fig. 1(b). This high index glass is composed of lanthanum oxide, aluminum oxide and silica in order to achieve a high nonlinearity of the PCF. A complete description of the melting glass fabrication is given in reference [19]. The core is surrounded by a silica capillary structure resulting in good compatibility with more conventional PCFs and other solid silica fibers.
Fig. 1 (a) Cross sectional scanning electron microscope (SEM) image of the fiber; (b) Schematic of the refractive index profile of the PCF; (c) Measured values (squares) and fitting curve (red solid) of the multi-component glass refractive index; (d) Measured group velocity dispersion of the PCF for the LP01 mode (black triangles) and the LP11 mode (red squares). Dispersion curves for the LP01 mode (black solid) and the LP11 mode (red solid), calculated by using the approximated refractive index curve.
The specific composition of the glass is as follows: 70 mol% SiO2, 20 mol% Al2O3 and 10 mol% La2O3. This glass exhibits a high refractive index [Fig. 1(c)], compared with the silica glass (Δn ~0.14). The preparation of the microstructured preform is made by using a MCG rod for the fiber core center and adapted silica tubes for holey cladding and overcladding (silica F300). Due to the different melting temperatures of the glasses and a great difference in viscosity, critical control of the drawing parameters is essential. The outer diameter of the used holey fiber is 210 µm, the average hole diameter d is close to 8 µm and the hole-to-hole spacing Λ is 8.4 µm. The fiber core is slightly elliptical with diameters of 5.4 µm for the slow axis and 4.5 µm for the fast one. In these conditions the MCG area exhibits an elliptical shape with diameters of 3.5 µm and 2.95 µm for the two principal axes. By using the cutback technique, we obtain the propagation loss of the fundamental mode (LP01) at 1064 nm (α = 1.3 dB/m). This high value can be explained by the inhomogeneity of the MCG induced during glass fabrication and by interface scattering effects between MCG and pure silica glass.
The chromatic dispersion properties of our MCG fiber have been investigated. Figure 1(d) presents the calculated and measured chromatic dispersion of the LP01 and LP11 modes of the PCF. The calculations are made with a program based on the finite element method. For the linear refractive index curve of the multi-component material, we have approached our experimental values with an approximated curve [Fig. 1(c)]. Thanks to using this approximated refractive index curve and taking into account the real cross section structure of the holey fiber, the calculations are in good agreement with the chromatic dispersion measurements obtained by a low-coherent interferometric method. The small difference between calculations and measurements can be explained by errors in the dimensions of the MCG area and on the MCG index [Fig. 1(d)]. The zero dispersion wavelengths (ZDW) are located at 1140 nm and 970 nm for the LP01 and LP11 modes, respectively. We have also estimated the nonlinear refractive index n2 of the MCG at close to 7 × 10−20 m2/W by taking advantage of previous results published in the reference [20].
The nonlinear properties of the PCF were investigated with a setup for SC generation as shown in Fig. 2 . The pump source is a passively Q-switched Nd:YAG microchip-laser delivering pulses of 650 ps at 1064 nm. The pulses are emitted at a repetition rate of 23.5 kHz and with a peak power equal to 14 kW. The pump power is controlled by the combination of a half-wave plate (λ/2) and a polarizer (P). The second half-wave plate allows controlling the linear polarization orientation of the pump light. The radiation is launched into the PCF with an aspheric lens allowing a coupling efficiency of 70%. Different systems are used to characterize the output beam at the optical fiber end. To measure the visible spectrum, we use an Ando AQ-6315A optical spectrum analyzer (OSA) with a multimode fiber to collect the output radiations, whereas in the IR domain a Yokogawa AQ6375A OSA is used. With the Yokogawa OSA, a long pass filter is applied to remove the pump wave in order to avoid artefacts induced by the high pump power. Moreover, the near field patterns are observed in the visible and IR ranges with the help of a × 100 microscope objective, a filter and a CCD camera.
3. Experimental results and discussion
The sub-ns pump wave is coupled into the optical fiber both in the fundamental mode (LP01) and the second mode (LP11). The energy propagating at 1064 nm in the LP01 mode undergoes normal dispersion whereas the energy in the LP11 mode is in anomalous dispersion regime. The near field patterns recorded at the output fiber end clearly show the repartition of the pump power [Fig. 3(a) ]. After 0.2 m of propagation length, the output spectrum exhibits peaks due to a frequency conversion at 715 nm and 2094 nm [Fig. 3(a)–(b)]. This phenomenon is clearly due to a degenerated FWM process with a frequency detuning between the pump and the generated waves of 138 THz.
Fig. 3 (a) Experimental output spectrum as a function of fiber length for a pump peak power of 7 kW coupled into the PCF (inset: output near field patterns); (b) Measured spectrum at the fiber output after 0.2 m of propagation length (Pin = 7 kW); (c) Measured spectrum at the fiber output after 2.15 m of propagation length (Pin = 7 kW).
Because of the limited spectral band of our CCD cameras, we observed output field patterns only at the anti-Stokes and pump wavelengths. The wave at 715 nm was generated in the fundamental mode, while two modes were observed at 1064 nm. The near field diameters of the pump and anti-Stokes waves have a diameter of 4.6 µm and 3.2 µm, respectively. With these conditions, several parametric processes could account for the frequency conversion. To determine precisely the nonlinear behavior we carried out numerical simulations. We calculated the energy conservation (1) and the phase matching conditions (2) [21] for several coupled transverse modes:
where, is the nonlinear coefficient of the optical fiber and P the input peak power. We assume a 7 kW peak pump power and n2 = 7 × 10−20 m2/W as nonlinear refractive index. For the effective area, we use values obtained from the calculations of the effective index of the modes propagating in the fiber core. At 1064 nm, the effective area is equal to 10 µm2 for the fundamental mode and 15 µm2 for the LP11 one. Figure 4(a) shows the phase matching diagram for the scalar FWM process involving the LP01 mode only. The dashed lines represent the pump wavelength at 1064 nm with the corresponding phase-matched wavelengths. The calculated Stokes and anti-Stokes wavelengths are located at 2370 nm and 686 nm, respectively. The frequency detuning between the pump wave and the generated wavelength is 138 THz for the experimentation and 155 THz for the numerical calculations. The difference between these two values can be explained by the use of the approximated glass indices and by a possible error concerning the exact size of the MCG zone. Nevertheless, this theoretical approach confirms that the FWM at the origin of this nonlinear conversion is a scalar FWM process using only LP01 transverse mode. No numerical solution was obtained by mixing LP01 and LP11 modes.Fig. 4 (a) Phase matched wavelengths versus pump wavelength in the case of scalar FWM process using LP01 transverse mode; (b) Measured output spectrum for an input polarization oriented along the fast axis of the PCF. (c) Phase matched wavelengths versus pump wavelength in the case of scalar FWM process using LP11 transverse mode; (d) Measured output spectrum when the input polarization is oriented along the slow axis of the PCF (inset: near field patterns recorded at 532 nm and 632 nm). The dashed line indicates the pump wavelength located at 1064 nm with the corresponding Stokes and anti-Stokes wavelengths.
The generation of the broadband scalar FWM is directly due to the fiber core structure and composition. Then, the differential overlapping between the guided modes and the central MCG zone for the pump, the Stokes and anti-Stokes radiations allowed us to obtain broadband phase matching and, therefore, to achieve efficient single scalar FWM effect. Indeed, for visible wavelengths, the fundamental guided mode covers mainly the MCG region, whereas the mode at higher wavelengths covers areas both of the silica and the MCG material, as it is shown by the mode field diameter measurements. So the average effective index of the visible fundamental mode is mainly determined by the MCG refractive index, while the effective index of the IR fundamental mode is more influenced by the silica ring around the MCG region.
By further increasing the fiber length we observe a continuum generation mainly developed towards the higher IR wavelengths. The MI effect induced in the LP11 mode leads to a modulation of the temporal profile of the pulse and breaks up the pulse into several solitons [22]. These solitons undergo a large SSFS effect under the influence of the Raman gain. At the same time, a visible spectral enlargement is generated from the anti-Stokes wavelength. The temporal overlapping combined with the group velocity difference between the visible and infrared waves induces both a red and a blue shift because of the cross phase modulation (XPM) effect [23–26].
We note also that the output radiation is 90% polarized along the fast axis of the fiber core. Indeed, the elliptical shape of the core induces a form birefringence. By consequence, the spectrum profile is directly affected by the input polarization state. If the input polarization is oriented along the slow axis, the spectrum shape is modified. Figure 4(d) shows the output spectrum for a linear polarization oriented along the slow axis. The modification of the polarization orientation induces a change of the phase matching condition. In this case, the FWM process is obtained in the LP11 mode [see Fig. 4(d)]. The Stokes and anti-Stokes radiations are located at 1434 nm and 845 nm, respectively. The phase matching diagram, calculated for a polarization orientation along the slow axis [see Fig. 4(c)], shows a solution in the LP11 mode. For a pump at 1064 nm, the phase-matched wavelengths are located at 860 nm and 1395 nm, which is in good agreement with the experimental result. In a second step, and mainly because of the XPM process between infrared radiations and anti-Stokes wave, a SC is generated in the visible range.
Beyond 2.15 m of propagation in the nonlinear fiber, no additional extension of the output spectrum is observed. Only the output power level is decreasing due to the loss of the MCG. Therefore a 2.2-2.5 m propagation length has shown to be the optimal fiber length with regard to the spectral broadening. In Fig. 5(a) , the output spectrum is superimposed with the measured MCG loss curve in order to understand the limitations of the spectral broadening of the SC. The blue areas indicate the location of the main MCG losses which shape the spectrum profile and limit it beyond 500 nm and 2220 nm. Additionally, another limitation of the broadening of the SC spectrum in the blue-green domain can be attributed to the group velocity matching between the IR solitons and the visible radiations as it was demonstrated in many publications [9,27]. Figure 5(b) presents the group velocity curves for the fundamental and the second modes propagating into the PCF. The green dashed line shows the group velocity matching between waves at 2220 nm and 510 nm in the LP11 and LP01 modes, respectively, calculated from the approximated refractive index curve. In our experiments the IR broadening is limited at 2220 nm, whereas the visible blue shift is stopped at around 500 nm. The agreement between the experimental and calculation results is quite good. However, recent improvements of the MCG fabrication method have allowed the decreasing of propagation losses (α ≈0.6 dB/m at 1.1 µm) and, in particular, the decreasing of the absorption peak at 800 µm.
Fig. 5 (a) Measured SC output spectrum superimposed with the measured MCG loss (blue zones indicate the positions where the MCG losses are important). (b) Group velocity curves calculated respectively for the LP01 and the LP11 modes by using the approximated refractive index curve. The dashed line indicates the group velocity matching between the 2220 nm IR wave and the 510 nm visible wave.
By changing the fiber dimensions (core, hole diameter, pitch and rod size) it is possible to tune the phase-matched wavelengths. A second MCG PCF was made with core diameters of 4.2 µm × 7.2 µm. By pumping this holey fiber at 1064 nm we obtained an FWM process in the LP01 transverse mode with an anti-Stokes wave located at 677 nm and a Stokes wave close to 2483 nm (frequency detuning ~161 THz). The nonlinear behavior obtained here is close to the one observed with the preceding MCG PCF. A spectral broadening between 500 nm and 2200 nm is then obtained.
4. Comparison with germanium-doped PCF
This type of broadband scalar FWM process can also be obtained by structuring the fiber core with doping ions. The high index rod composed of an MCG is replaced by a highly germanium-doped region localized in the central part of the fiber core. The doping is effected by the MCVD technique. In order to obtain a high refractive index difference with respect to the silica material, the doping concentration is set to 36 mol% at the core center. It represents an index difference of ~0.05 compared to pure silica at 1064 nm. The diameter of this high index zone is 600 nm. The nonlinear index of this highly doped central zone is estimated to be 4.35 × 10−20 m2/W at λ = 1550 nm [28]. A ring-shaped base between the high index region and the surrounding silica is obtained. The linear refractive index in this region is almost linearly decreasing between 1.47 (13.5 mol% Ge-doping) and 1.45 (pure silica). The complete fabrication method and the profile of the refractive index curve are described in references [16,19]. The cladding composed of silica and air holes is characterized by the average hole diameter and the average hole-to-hole spacing of 3.6 µm and 4.4 µm, respectively. Due to the expansion of a single hole of the first ring, the core shape is not circular; however, the average diameter of the fiber core is around 3.5 µm. A cross section of the holey fiber is presented in Fig. 6(a) . The ZDWs are measured at 1140 nm for the fundamental mode and 870 nm for the LP11 mode.
Fig. 6 (a) SEM image of the Ge-doped PCF. (b) Experimental output spectrum as a function of fiber length for a pump peak power of 5 kW coupled into the Ge-doped PCF. (c) Phase mismatch curve for intermodal FWM in the Ge-doped PCF.
The same experimental setup as before is used but with a lower input peak power (5 kW) because of the input face destruction threshold of the Ge-doped PCF. The spectral broadening evolution as a function of the propagation length at constant peak power is obtained by the cut-back technique and is shown in Fig. 6(b). After 0.4 m propagation length, a visible wave is generated at 700 nm due to efficient FWM. The Stokes wave is therefore located at 2216 nm. The FWM in the Ge-doped PCF is an intermodal FWM process. Indeed, the pump radiation is launched both onto the LP01 and LP11 modes. The anti-Stokes wave is generated in the fundamental mode, whereas the Stokes is generated in the LP11 mode [29]. Phase-matching calculations show the possibility to satisfy the phase-matching condition when the Stokes wavelength is in the LP11 mode and the anti-Stokes wave is in the LP01 mode. The phase mismatch curve obtained by using the Eqs. (1) and (2) is presented in Fig. 6(c). The Stokes and anti-Stokes radiations are obtained at 2237 nm and 698 nm, respectively, which is in good agreement with the experimental result.
For 1 m of propagation, we note that a Raman cascade is induced by the pump wave towards the higher wavelengths. When the broadening reaches the ZDW of the fundamental mode, solitonic effects are generated allowing a broadening towards the higher IR wavelengths. In the visible domain, we observed first an asymmetric spectral broadening of the anti-Stokes wave because of the XPM effect induced by infrared radiations. Afterwards, the same nonlinear behavior leads to a blue shift giving birth to a smooth and continuous broadening extending from 540 nm up to 2400 nm.
By comparing the behavior of the two fibers, we note in both cases that the SC generation in the visible region is obtained from an anti-Stokes wave arising from a broadband FWM process. This parametric nonlinear effect transfers, in a first step, a significant part of the pump wave toward the visible spectrum. In a second step, the XPM process goes on and spreads this energy in the vicinity of the anti-Stokes wavelength.
These experiments with two different fiber types confirm the role played by the complex index profile of the core fiber in the generation of broadband FWM processes. Indeed, a microstructuring of the fiber core with higher index part allows the control of specific degenerated parametric processes and the generation of visible spectral broadening. The modifications of the rod size and/or doping concentration permit also the tuning of the Stokes and anti-Stokes wavelengths. The different loss properties between the two fibers play also an important role concerning the flatness of the SC spectra obtained at the fiber end. The loss of the MCG in high IR wavelengths obviously limits the broadening of the SC at 2220 nm, whereas longer wavelengths have been observed up to 2400 nm with the Ge-doped PCF. We note also that the fiber length to obtain an optimal SC is different. We need only 2.2 m for MCG versus 5 m for Ge-doped PCF. This difference can be explained in part by a slightly different pump power but also mainly by the nonlinear coefficients of the two fibers.
4. Conclusions
We propose a new type of highly nonlinear PCF, consisting of a structured core with a high refractive index rod. The fiber core is composed of MCG or a highly Ge-doped rod surrounded by pure silica capillaries. The core structure allows increasing the nonlinearity of the fiber and permits at the same time the phase matching conditions for a broadband FWM process to be satisfied. The mechanism relies on the fact that the Stokes and anti-Stokes waves have different overlappings with the high index region. In the case of the MCG PCF, the measured maximum frequency detuning is 161 THz with Stokes and anti-Stokes waves propagating in the fundamental mode. By modifying the air cladding and/or the high index area dimensions, it is possible to tune the generated waves. The efficient FWM effect easily obtained by using this type of fibers can be used for correlated photon pair generation and SC generation. In this last case, the SC is particularly modulated by the specific loss properties of the nonlinear additional material. It is important to note that the MCG PCF losses in the near IR can be slightly lower than those of nonlinear PCFs composed with tellurite glass or extruded SF6 material (respectively 2.3 dB/m at 1055 nm [2] and 2 dB/m at 1200 nm [8]). Nevertheless, the latter are clearly appealing for lower loss at wavelengths longer than 2 µm.
Acknowledgements
The authors thank the European Commission for its support through the FP6 integrated project “NextGenPCF”, and the Thuringian Ministry of Education and Cultural Affairs for its funding.
References and links
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