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Hybrid large mode area Ytterbium-doped double-cladding photonic crystal fibers with anti-symmetric high refractive index inclusions provide efficient amplified spontaneous emission spectral filtering. Their performances have been analyzed by numerical simulations and experimental measurements. In particular, the fiber single-mode behaviour has been studied, by taking into account the fundamental and the first higher-order mode. Two approaches, the core down-doping and the reduction of the air-hole diameter in the inner cladding, have been successfully applied to reduce the higher-order mode content, regardless of the bending of the doped fiber, without significantly affecting its spectral filtering properties.
© 2010 Optical Society of America
1. Introduction
The design of Yb-doped Photonic Crystal Fibers (PCFs) for highly-efficient pulsed fiber amplifiers has to match opposite requirements of lowering nonlinear threshold, essentially by an increased core size, and mantaining single-mode operation [1, 2]. Moreover, suppression of Amplified Spontaneous Emission (ASE) is very important, in order to obtain high signal gain and slope efficiency, especially in low repetition rate systems. ASE filtering can be done in multi-stage amplifiers with discrete filters, but their typically low damage threshold represents a serious issue for high-power operation. Distributed Spectral Filtering (DSF) of ASE can be performed exploiting the transmission features of photonic bandgap fibers, as already demonstrated for Yb-doped fiber amplifiers [3] and lasers [4], with suppression of the long-wavelength and short-wavelength ASE, respectively. The main drawback of this solution is that the high index regions of the bandgap structure may guide some of the pump light, to the detriment of the slope efficiency of the amplifier. Hybrid PCFs [5, 6, 7], where light confinement is provided by both modified total internal reflection, due to the presence of an array of air-holes, and by antiresonant reflection, obtained with high-index inclusions, can be used in order to overcome this problem. Recently, large mode area passive DSF PCFs, which exploit anti-symmetric resonant structures to provide narrow spectral filtering, have been proposed [8], and their polarization-maintaing and bending characteristcs have been deeply analyzed. Moreover, a large mode area Yb-doped anti-symmetric DSF PCF with air-cladding has been fabricated.
The hybrid double-cladding DSF PCF has been demonstrated experimentally to have 65% slope efficiency, and ASE and stimulated Raman scattering filtering. Moreover, the effectiveness of the DSF PCF in suppressing the pulsed preamplifier ASE in a two-stage amplifier configuration, without the need of any other filtering component, has been proved [9]. Furthermore, DSF fiber has reduced bend sensitivity compared to a conventional PCF with similar mode size [8]. Finally, the DSF PCF bandgap guidance can be tuned so that the fiber only guides in parts of the Yb band, having substantially less gain then at conventional wavelengths. This idea has been demonstrated in [10], where a similar bandgap design is utilized to obtain 167 W at an otherwise inaccessible wavelength of 1178 nm. Accordingly, the DSF design has enormous potential for booster amplifiers and high-power lasers, both at conventional wavelengths around 1064 nm and more exotic wavelengths beyond 1100 nm, and thus further investigation is important.
In this paper the guiding properties of the Yb-doped double-cladding DSF PCF presented in [8] have been investigated. In particular, since the core refractive index change due to the Yb doping can influence the fiber single-mode behaviour [8], the Higher-Order Mode (HOM) content has been analyzed through a full-vector modal solver based on the finite element method [11]. After comparing the simulation results obtained with the transmission spectra experimentally measured, two different techniques, such as core down-doping and air-hole diameter reduction in the inner cladding, have been proposed in order to perform the HOM suppression. Results have shown that the HOM guiding can be effectively reduced through core down-doping, even in the straight fiber, without negatively affecting the spectral filtering of the DSF PCF. Moreover, a strong reduction of the HOM content can be obtained also by adjusting the air-hole size in the bent fiber, without detriment to the Fundamental Mode (FM) guiding properties.
2. Single-mode regime analysis
In this analysis a PCF very similar to the A1 DSF fiber fabricated by NKT Photonics A/S and presented in [8], shown in Fig. 1(left), has been considered. The PCF cross-section is characterized by a 30 μm-diameter core surrounded by a photonic crystal cladding made of 6 rings of air-holes, with hole-to-hole spacing Λ = 10 μm and air-hole diameter d = 1.5 μm. The refractive index of undoped silica has been set to 1.45. Two opposite rows of air-holes have been replaced with graded-index Germanium-doped rods, with parabolic index profile and NA = 0.29, whose refractive index has been modeled for the simulations as a staircase function with maximum value nmax = 1.4787. The rods on each side of the core have different diameter, which is 5.89 μm for the smallest resonant structure, and 7.1 μm for the largest one, yielding to two different sets of bandgap conditions. The whole structure is surrounded by a 9 μm-thick air-cladding with inner diameter of 191 μm. Notice that the air-cladding presence provides this DSF fiber with all the positive aspects typical of double-cladding fibers made with PCF technology, such as an extremely high numerical aperture for the pump core/inner cladding, and an all-glass design with high damage threshold [1]. Moreover, with respect to conventional double-cladding fibers, the DSF PCF has an added filtering capability, given by the combination of two different guiding mechanisms, that is total internal reflection and photonic bandgap effect [8].
Fig. 1 (Left) Optical micrograph of the manufactured A1 DSF PCF. (Right) Simulated cross-section half of the DSF fiber.
Simulations have been performed with a complex full-vector modal solver based on the finite element method, which exploits conformal mapping transformation [12] to analyze the fiber bending. In particular, with this technique the bent fiber can be studied as an equivalent straight one, with a proper refractive index profile, changed accordingly to the bending radius. In order to avoid spurious reflections, a perfectly match layer has been considered as the boundary condition for the computational domain [12]. The fiber cross-section half taken into account for the numerical analysis is depicted in Fig. 1(right). The overlap integral Γ between the guided mode field and the Yb-doped 30 μm core has been considered to evaluate the confinement for the FM and the HOM into the DSF fiber core, in order to investigate its spectral filtering features. It has been calculated as
where i(x, y) is the mode normalized intensity distribution and Sd the core active section [13]. Two almost-degenerate HOMs belonging to the LP11-like family, with orthogonal spatial orientation, have been taken into account in the analysis, that is the HOM11, whose field distribution on the cross-section has the zero level lying along the same axis of the high-index rods, and the HOM12, with zero level along the axis normal to the Germanium rods. Simulations have been carried out for both straight and bent fiber.2.1. Straight and bent silica core fiber
Fig. 2(a) reports the measured transmitted output power for the straight and for the 40 cm-bent passive DSF fiber with the same geometrical parameters of the A1 PCF, excepted for the absence of the air-clad. These experimental values were obtained by coupling white light from a tungsten halogen lamp into a standard multimode fiber, followed by a collimating lens. The output was focused into the core of a 2 m sample of the DSF PCF, and the transmitted radiation was collected by a butt-coupled high-NA fiber with 20 μm core, which also formed a spatial filter for suppression of the non-core light.
Fig. 2 (a) Experimentally measured transmitted output power for straight and bent (with 40 cm coil diameter) DSF fiber. (b) Calculated overlap integral Γ for the FM of the straight and bent (with 40 cm coil diameter) DSF fiber.
Fig. 2(b) shows the overlap integral Γ calculated for the FM in the wavelength range spanning from 900 nm to 1200 nm, by considering the A1 PCF both straight and bent with a coil diameter of 40 cm on the Ge rods plane, with the largest features oriented towards the coil center. The computed overlap integral of the FM of the bent fiber shows a transmission band spanning from about 980 nm to 1050 nm, with values steadily above 0.93. The short-wavelength edge of the passband is determined by the resonance of the structure with the largest Ge features, while the long-wavelength one depends on the smaller Germanium rods, as shown by the FM magnetic field distribution reported in Fig. 3(left) and (right), respectively. The simualted transmission band can be inferred from the overlap integral. It is blue-shifted 50 nm and reduced 20% compared to the experimental results. The uncertainty on the actual refractive index profile of the Germanium-doped rods in the manufactured fiber, due to the drawing-induced stress, can explain the discrepancy in the positions of the bandgaps. High Γ values have been obtained also in the wavelength range between 900 nm and 915 nm, which are related to the secondary peak in the transmitted output power spectra of Fig. 2(a), centered at about 920 nm and 930 nm for the straight and 40-cm bent DSF PCF, respectively. By comparing the FM overlap integral computed for the straight fiber with the Γ values obtained for the bent one, both shown in Fig. 2(b), it can be noticed that the bent DSF PCF passband is broader than the one of the straight fiber, whose short wavelength edge is shifted to 1000 nm. Experimental results, reported in Fig. 2(a), have confirmed this unusual behaviour, which is probably due to the reduced filtering efficiency of the high-index rod structure oriented towards the coil center in the bent fiber.
Fig. 3 FM magnetic field modulus distribution at (left) 970 nm and (right) 1050 nm for the 40 cm-bent DSF fiber.
In order to evaluate the HOM content in the DSF PCF, the overlap integral of the first two HOMs previously described has been calculated in the same wavelength range for the straight and the bent fiber. As shown in Fig. 4(a), in the straight fiber both HOMs are well confined, with an overlap integral of about 0.8 in the 1000–1050 nm range, and a slight red shift of the transmission band with respect to the FM. Consequently, as already observed in [8], there is a small window, about 10 nm wide, near the short-wavelength edge where the fiber is single-mode, being only the FM supported. By bending the fiber with a diameter of 40 cm, the HOM confinement is reduced, and Γ values for the most detrimental HOM, that is the HOM12 in this case, decreases to about 0.65 at 1030 nm, as shown in Fig. 4(b). It is important to underline that the resonant structures are very effective in cutting HOM12 at all the wavelengths above 1100 nm, while HOM 11 remains better confined in both the straight and the coiled fiber cases. This behaviour is due to the different spatial distribution of the two HOMs. Since the HOM11 has the field minimum along the Germanium rods direction, it is less sensitive to the resonances than HOM12, whose maxima are directed towards the high-index features. This effect is clearly visible considering the HOM magnetic field modulus distribution for the straight fiber at the wavelength of 1130 nm, shown in Fig. 5. In this case, HOM11 is well confined in the fiber core, with an overlap integral even higher than the FM one, while HOM12 leaks out, due to the resonance of the small Germanium rods structure.
Fig. 4 Overlap integral Γ of the first HOMs (a) for the straight fiber and (b) for the fiber bent with a diameter of 40 cm.
Fig. 5 Magnetic field modulus distribution at 1130 nm of the (left) HOM11 and (right) HOM12 of the straight DSF fiber.
2.2. Core down-doped fiber
Two approaches to reduce the HOM content have been investigated. At first, uniform down-doping of 1.5×10−4 has been applied on the fiber core in order to obtain a single-mode behaviour. The confinement of FM and HOMs for the both the straight and the 40 cm-bent fiber has been evaluated, again by considering the overlap integral Γ on the core region. In fact, even if the down-doping technique has been already successfully applied to large-mode-area unflexible double-cladding rod-type PCFs [14], its effectiveness is not straightforward for a DSF fiber, which can be bent and has a more complicated guiding mechanism, strongly based on the resonance provided by the Ge rods [8].
For the straight fiber the change in the core refractive index has a negligible impact on the FM, whose overlap integral remains above 0.9 in the 1000–1050 nm band, as shown in Fig. 6(a). Moreover, the depth of the two stopbands due to the resonances of the high-index features is not influenced, thus the spectral filtering characteristics of the DSF PCF are substantially unaffected. As shown in Fig. 6(b), the core down-doping is very effective in suppressing both the considered HOMs. HOM11, which is the most detrimental one, has a maximum Γ value of 0.6 at 1200 nm, and it has a reduced overlap integral of 0.5 at 1030 nm. Even lower Γ values can be obtained for HOM12, ranging between 0.2 and 0.4 in the 1000–1050 nm span. With respect of the PCF without down-doping, the lowered core index entails a reduction of the overlap integral of about 35% and 55% at 1030 nm, for the HOM11 and HOM12 respectively. Moreover, the straight DSF fiber with low index core performs a better HOM suppression even with respect of the 40 cm-bent fiber without down-doping, with a overlap integral reduction at 1030 nm from 0.6 to 0.5, and from 0.65 to 0.35 for HOM11 and HOM12, respectively.
Fig. 6 Overlap integral Γ (a) of the FM for straight and 40 cm-bent down-doped core DSF fiber, and (b) of the HOMs for the straight fiber.
When the down-doped core DSF fiber is bent, the confinement of the HOMs definitely worsens in all the wavelength range considered for the simulations, and they are no longer guided into the fiber core. On the contrary, as shown by the red curve in Fig. 6(a), there is still a main transmission band 50 nm wide for the FM, even if the Γ values are slightly lower with respect to the straight fiber case.
2.3. Air-hole scaling
As an alternative to the core down-doping, the HOM suppression can be obtained by reducing the air-hole diameter and exploiting the leakage of the HOMs due to the fiber bending, provided that a suitable confinement for the FM is maintained. A new silica core DSF fiber has been designed in order to explore this possibility. The original pitch, air-clad diameter and Germanium-doped rods characteristics of the A1 fiber have been kept unchanged, while modifying the cladding air-hole diameter to 1 μm, yielding to a d/Λ value of 0.1. Simulations have been carried out for FM and the first HOMs of the new fiber, bent with a 40 cm diameter, in the wavelength range spanning from 900 nm to 1200 nm. As shown by Fig. 7(a), the overlap integral of the FM is only slightly affected by the change of the relative air-hole size, being close to 0.9 on the whole transmission band. The same conclusion can be drawn by taking into account the FM magnetic field distribution at 1030 nm, reported in Fig. 8(left) and (right) for the 40 cm-bent DSF fiber with d/Λ = 0.15 and d/Λ = 0.1, respectively. Moreover, by comparing these overlap integral results with the ones reported in Fig. 2(b), it can also be noted that the edges of the passband do not shift in wavelength, showing that the resonance conditions of the high-index rods are not significantly affected. A sharp decrease of the overlap integral, with a minimum centered near 1020 nm and a total width of about 5 nm, can also be observed, which is due to bend-induced leakage of the FM in the silica region between the inner cladding and the air-clad. As expected, the new cladding design is effective in reducing HOM content. A decrease of Γ values of both the HOMs, reported in Fig. 7(b), with respect to the ones of the starting DSF PCF, shown in Fig. 4(b), is clearly visible in the full wavelength range. In particular, the HOM11 overlap integral is lower than 0.4 in the whole wavelength range, while the HOM12 overlap integral shows few narrow peaks with maximum values of about 0.5, remaining below 0.4 in most of the passband.
Fig. 7 Overlap integral Γ (a) of the FM and (b) of the HOMs for the DSF PCF with d/Λ=0.1, bent with a diameter of 40 cm.
Fig. 8 FM magnetic field modulus distribution at 1030 nm for the 40 cm-bent DSF fiber with (left) d/Λ = 0.15 and (right) d/Λ = 0.1.
3. Conclusions
A thorough numerical analysis has been performed on the properties of Yb-doped hybrid PCFs with air-cladding, which provide narrow distributed spectral filtering with anti-symmetric high-index inclusions. Numerical results have shown a good agreement with experimental measurements. Since the single-mode behaviour is a mandatory requirement for high-power fiber amplifiers and lasers, the spectral filtering properties have been evaluated by considering the HOM suppression. Two different approaches have been proposed in order to reduce the HOM confinement, that is the core down-doping and the air-hole diameter reduction. Simulation results have demonstrated that HOMs can be effectively suppressed by applying both the techniques, without worsening the spectral filtering properties of the fiber.
Acknowledgments
The Authors acknowledge the support of the EU funded FP7 ALPINE Project, n. 229231.
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