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We propose a new technique to selectively excite the fundamental mode in a few mode fiber (FMF). This method of excitation is made from a single mode fiber (SMF) which is inserted facing the FMF into an air-silica microstructured cane before the assembly is adiabatically tapered. We study theoretically and numerically this method by calculating the effective indices of the propagated modes, their amplitudes along the taper and the adiabaticity criteria, showing the ability to achieve an excellent selective excitation of the fundamental mode in the FMF with negligible loss. We experimentally demonstrate that the proposed solution provides a successful mode conversion and allows an almost excellent fundamental mode excitation in the FMF (representing 99.8% of the total power).
© 2016 Optical Society of America
1. Introduction
The selective excitation of the fundamental mode in a few modes fiber (FMF) from a single mode fiber (SMF) has particular interest for the design and implementation of fiber lasers with high performance [1,2 ]. To procure a low loss joint between two dissimilar optical fibers, the mode fields of the involved fibers have to match at the splice. This means that the fibers must have identical mode field repartition with no relative tilt or offset between them. To obtain a high efficiency fundamental mode excitation in a multimode fiber, many techniques have already been presented in the literature. One technique uses the modal filtering to suppress higher order modes (e.g. winding the fiber and the exploitation of the greater sensitivity to the bend loss of high order modes) [1], a second is the excitation of a multimode fiber and a FMF from a SMF by adiabatically tapering the fusion splice [3,4 ]. The techniques mentioned above, although efficient, are limited. The first one is not easy to efficiently fit and implement for many kind of fibers and the second technique may suffer from a lack in robustness because of the small size of the processed splice.
In this paper we propose a new technique for the fundamental mode excitation in a FMF from a SMF. This technique can be applied for all optical fiber with large core and the component takes the form of a single robust element. The proposed solution is based on a tapered transition between the two optical fibers inserted in the central hole (from both end) of an air-silica microstructured cane. The technique achieves a gradual mode transformation which converts the fundamental mode of one fiber to that of the other with an excellent beam quality and low loss. In a tapered structure, the adiabatic evolution of the fundamental mode is ensured with sufficiently gentle slope [5]. The component is fabricated by using the flame-brushing technique.
First, after a short description of the component design and implementation, we study through Beam Propagation Method (BPM) numerical simulations (using the commercial RSoft package) the optimal geometry of the component to efficiently excite the fundamental mode LP01 in the FMF and thus validate the principle of operation of the device. Then, we present a calculation of the modal effective indices and adiabaticity criterion to describe the phenomenon of the fundamental mode cutoff in the structure and the modal conversion process. Finally, we present and discuss the experimental results.
2. Geometry
Our solution is based on insertion of two fibers face to face in the central hole of a microstructured cane consisting of several rings of air holes as shown in Fig. 1 . The hexagonal rings of air holes of the cane are surrounded by a silica cladding. The biconical tapering of this set is done by using a flame-brushing technique to obtain the desired reduction coefficient RC representing the ratio between the dimension of the waist and the initial size of the structure. The tapering laws for both tapers are assumed to be linear along the direction of propagation for a given value of RC.
The core diameter of the SMF and FMF are 8.2µm and 15µm respectively, the outer diameter being 125µm for the two fibers. The air hole diameter of the microstructured cane is 145µm with a pitch equal to 161µm. The refractive index of the SMF and FMF cores are equal to 1.4491 and 1.4537 respectively, while both SMF and FMF cladding refractive indices are equal to 1.444 corresponding to the pure fused silica value (λ = 1550 nm).The FMF can support four modes (LP01, LP11, LP02 and LP21) when the operational wavelength is 1550 nm. The parameter L represents the length of each taper. In the numerical calculations, we take a symmetric linear biconical taper which is a good approximation of our real conditions as presented in the experimental description part.
Before tapering, the total length of the cane is 70 mm. Each fiber is individually inserted in the cane, the point of contact between the two fibers being located at the middle of the cane.
3. Modal analysis of the device
We performed simulations of a two air-hole ring geometry component using the finite difference beam propagation method (FD-BPM). The field injected into the structure is the fundamental mode of the SMF. The wavelength is set to 1550nm. The conversion and propagation loss of the fundamental mode of FMF were evaluated for various values of L and RC, by overlap integrals calculated from output field and fundamental mode of the FMF.
We present in Fig. 2 the light propagation simulation results for a biconical taper with L = 30mm and RC = 0.1. At the input of the structure, the fundamental mode propagates as a SMF core mode and its effective index lies between the core and cladding indices. During the tapering, the guided mode expands and its effective index decreases [6,7 ]. For a particular value of radius, this effective index is equal to the cladding index value (this situation is sometimes referred to as core mode cutoff) and becomes lower while continuing the tapering process [8]. At this level, the microstructured cane takes over the guidance and the propagation is done by the waveguide formed by the surrounding air holes which now act as a new optical cladding. At the waist position, the fundamental mode of SMF is now transformed into the fundamental mode of microstructured cane. In the second taper, the core of the FMF core progressively takes over the guidance and the microstructured cane gradually loses its influence.
The length L of the tapers and the RC value must be chosen in order to excite properly the microstructure fundamental mode at the waist position. It is essential not only for the input taper with the SMF, but also for the output taper too. The component principle is based on a two-steps mode conversion, first from the SMF fundamental mode to the microstructure fundamental mode, and then from microstructure fundamental mode to FMF fundamental mode. Assuming the adiabaticity of these conversions, each taper-induced mode conversion is then supposed to be reversible. Thus, the output taper will be correctly designed when it will be able to efficiently and adiabatically convert the FMF fundamental mode to the microstructure fundamental mode in a reverse path propagation. A symmetric biconical component with each taper length L = 30 mm and RC = 0.1 respects this principle. In this case, BPM simulations show that the fundamental mode at the output of the component is cleanly excited and its value α2 = 0.9984 shows excellent modal selectivity with negligible loss (0.03dB). This value must be compared to the 2dB conversion loss (α2 = 0.631) of the fundamental mode using a direct end-butt connection between the two fibers. The overlap integral is given by the Eq. (1):
Where and are the scalar fields distribution of the two calculated modes.4. Adiabaticity criteria
In this section we exploit physical principles to know the delineation criterion for ascertaining the taper shapes ensuring adiabatic propagation with low loss. Along a taper, power leakage is explained by the coupling of the fundamental core mode with higher order guided or unguided modes [6]. In a cylindrical geometry component, the fundamental mode LP01 can couple power only to modes with the same circular symmetry (i.e. to the higher order LP0m modes) [5]. The power coupling occurs mainly to the higher order mode showing an effective index closest to that of the fundamental mode. For a more quantitative description of these coupling effects, we determined the normalized coupling coefficients (Eq. (2)) between the modes [9].
This coupling coefficient expression involves an overlap integral over the taper-induced refractive index variations, with and are the normalized scalar fields of the modes with and their respectivepropagationconstants. We calculated these coefficients between the first three LP0m modes which may be involved in the coupling process and their effective indices as function of RC. As previously, calculations are performed using FD-BPM in scalar mode. The adiabaticity criterion is respected whenever the condition described by Eq. (3) is satisfied, where r is the local fiber radius and is the normalized slope [5]:We plot in Fig. 3 the mode effective indices as a function of RC to identify the coupling regions and to analyze power exchange between modes. The fundamental core-mode cutoff in the SMF and FMF occurs for a reduction coefficient 0.4 and 0.16 respectively. Thus, in order that the microstructured cane ensures the guiding in the two tapers, it is necessary that the reduction of the core diameter is below RC = 0.16. At this level of reduction ratio, the two fiber cores have no more effect on the light guidance. Therefore, the mode obtained at waist represents the fundamental mode of the microstructure at this position.
The effective indices of the LP01 mode in the two tapers (SMF and FMF tapers) are almost identical at RC = 0.1 in accordance to the fact that the cores have now lost their guiding capacity (LP01 cutoffs). We calculate the overlap integral between the two fields derived respectively from SMF and FMF taper, we obtain α2 ≈1, hence the principle is valid in both directions.
The LP01, LP02 and LP03 modes and the mode of the microstructured guide are calculated for the different sections of the SMF (Fig. 3(a)) and FMF (Fig. 3(b)) tapers. As seen in Fig. 3(a), the modal effective indices separation between LP01 and LP02 modes becomes small at RC = 0.38. This level of reduction represents the coupling region between the LP01 and LP02 modes indicating the zone of the power exchange between the modes. For the FMF taper, this occurs at RC = 0.16 (Fig. 3(b)).
To study and analyze this coupling phenomenon, we plot the value of as function of RC, and compared this value to the normalized slope of a taper (Eq. (3)).
At the beginning of the component, as shown in Fig. 4(a) , all the energy is guided by the fundamental SMF LP01 mode. Along the SMF taper, the black curve representing the adiabatic criterion between the LP01 and LP02 modes is above the normalized slope that should theoretically ensure adiabaticity, or at least limited power exchange.
In the second taper (cf. Fig. 4(b)), as the LP01-LP02 and LP01-LP03 curves are far above the normalized slope, the propagation of the LP01 mode is believed to be adiabatic and without coupling to other modes. The blue curve (LP02-LP03) does not matter since there is no possible power transfer from the LP01 to the LP02 mode. To give a more quantitative description of this coupling phenomenon and to validate the interpretations extracted from Fig. 4, we plot the amplitudes of the modes in the component (Fig. 5 ). The calculations of modal powers are evaluated by calculating the overlap integral between the propagated mode in the structure and the three first local scalar LP0m modes.
The amplitude variation of the modes along the component (Fig. 5) shows localized power transfer from LP01 to LP02in the SMF Taper. This partial power transfer finds a justification from Fig. 4(a) by the small gap between the black curve and the normalized slope close to L = 21mm that seems to allow slight power transfer. As the taper length is longer than this critical 21mm length, and because the modes power transfer is reciprocal, the power is coupled back to the LP01 mode before the waist position, where all the energy is finally kept guided by the LP01 mode (fundamental mode) of the microstructure. In the FMF taper, the power transfer between LP01 and LP02 is negligible confirming the results presented in Fig. 4(b) and the adiabaticity of the output FMF taper.
5. Experimental results and discussion
We present a schematic diagram of the tapering setup in Fig. 6 . The microstructured cane including the two fibers is clamped and pulled on either side by two motors while a flame brushes along the cane. The total elongation, the flame size, the brushing duration and the translation speed of the two computer-controlled servo motors can all be varied to obtain various shapes of tapers. An InGaAs camera associated to a 100x magnification ratio imaging setup was used in order to grab and analyze the FMF output near-field.
The parameters of the untapered cane, manufactured at Xlim, are as follows: the outer diameter is D = 3.9 mm, the hole diameter of microstructured cane is d = 145µm, the pitch of the lattice of air holes is Λ = 161µm, thus d/Λ = 0.9 and the initial length of the cane is L = 70mm. There are four rings of air holes. A microscope image of the cross-section is shown in Fig. 7(b) with the longitudinal section (Fig. 7(a)).
Fig. 7 a) Longitudinal section of the cane with two inserted fibers and b) the cross-section of the cane before tapering.
During the fabrication process, we use an air-pump to control pressure in the air holes to preserve the aspect ratio of the cross-sectional profile along the microstructured cane. Using a profile measuring bench, we plot the diameter variation of the cane as a function of the length of the biconical taper (Fig. 8(b) ). The obtained RC value is 0.13, as expected below the RC cutoff value of the FMF LP01 mode.
Fig. 8 a) Illustration of the cane after the tapering process, showing the input SMF and output FMF b) the profile of a real biconical taper versus the distance along the component.
The LP01 fundamental mode of the FMF was successfully excited as illustrated by the near-field image of the FMF output face (Fig. 9(b) ) after a 20m-long propagation. It is compared to an image of the LP01 mode of the SMF (Fig. 9(a)) illustrating their difference in size. A qualitative analysis indicates a high selectivity singlemode excitation. This was shown stable when manipulating the input SMF or the whole component. The propagation loss of the component is 1.6dB at 1550nm wavelength, higher than expected. The cause is believed to be due to small imperfections of the microstructure geometry after drawing at waist position leading to unwanted radiation loss. Drawing process optimization should help to enhance power transmission.
Fig. 9 Fundamental mode profiles of a) SMF (component input) and b) the FMF (output of the component).
In order to quantify the number and type of modes really excited and propagating in the FMF, we use the spatially and spectrally resolved imaging (S2 imaging) technique at the output of the FMF [10]. The measurement provides high quality images of the propagated modes as well as their respective weight. The light of our ASE source (50mW) is launched into the component through the SMF. The beam at the output of the FMF is collimated and 2D spatially scanned and sampled by a single mode fiber coupled to an optical spectrum analyzer. The optical spectrum is measured at each (x, y) point of the beam with a spatial resolution equal to 10µm. For each point, the acquired optical spectrum is processed by a Fourier transform to analyze spectral beatings induced by the modes group delay differences (Fig. 10 ).
The figure shows the sum of all Fourier transforms on the entire plan. The unit of the x-axis is in ps because the group delay differences between the LP11 mode and the LP01are not renormalized by the fiber length (~20m). Consequently, the group delay difference (LP01-LP11) is equal 86ps for 20m which leads to 4.3ps/m. Finally, we obtain informations about the presence of the guided modes and their relative weights in the speckle given by the multi-path-interference (MPI) parameter defined by where P1 and P2 are the power of propagating modes.
The S2 analysis demonstrates a very high purity LP01 mode excitation in the FMF. The only higher order mode detected is the LP11 with a MPI below −26 dB as shown by Fig. 11(b) . This mode represents only 0.19% of the total output power of the fiber. The residual presence of the non-azimuthal symmetry mode LP11 is a consequence of a slight non-axial deformation of the component issued from the drawing process. One can note that neither LP21, nor LP02 modes are detected. Therefore, we demonstrate a good fundamental mode beam quality in the output FMF.
Fig. 11 Beam profiles obtained by integrating the optical spectrum at each pixel a) the total beam resembling the LP01 mode intensity distribution b) The LP11 image and MPI level.
7. Conclusion
We presented a new method to selectively excite the fundamental mode in a few mode fiber from a single mode fiber using an adiabatically tapered microstructured cane. A high purity LP01 mode was obtained representing 99.8% of the guided power. We have numerically and experimentally validated the principle of operation of the component based on an original optical guided structure involving an intermediate microstructured guiding section leading to an efficient mode conversion between the input and the output fibers. This principle is believed to be sufficiently general to be applicable to many couples of different fibers and mode conversions.
Acknowledgments
We would like to acknowledge, Prof. Jacques Bures of the Polytechnic School of Montreal, Quebec, Canada for his help about the mode coupling phenomena and the adiabaticity criteria in tapers. We would like to thank also, Dr. Simon Laflamme and Dr. Xavier Daxhelet for their assistance in the numerical calculations, and Dr. Philippe Roy for his help with cane drawing. Part of this work was funded, from the French Agence Nationale de la Recherche, on the one hand through grant ANR-13-BS09-0018 UBRIS2, and on the other hand through grants OC1AE041Z and OC1AE013 from the Région Limousin.
References and links
1. M. E. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett. 23(1), 52–54 (1998). [CrossRef] [PubMed]
2. H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, “High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber,” Opt. Lett. 23(21), 1683–1685 (1998). [CrossRef] [PubMed]
3. Y. Jung, Y. Jeong, G. Brambilla, and D. J. Richardson, “Adiabatically tapered splice for selective excitation of the fundamental mode in a multimode fiber,” Opt. Lett. 34(15), 2369–2371 (2009). [CrossRef] [PubMed]
4. W. S. Tsai, C. K. Chang, F. W. Sheu, Y. H. Wang, and S. H. Chen, “Refractive index profiling of a few-mode fiber from fundamental mode excitation,” Opt. Commun. 323, 138–142 (2014). [CrossRef]
5. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibers and devices. Part 1: Adiabaticity criteria,” IEEE J. Optoelectron. 138(5), 343–354 (1991). [CrossRef]
6. B. T. Kuhlmey, H. C. Nguyen, M. J. Steel, and B. J. Eggleton, “Confinement loss in adiabatic photonic crystal fiber tapers,” J. Opt. Soc. Am. B 23(9), 1965–1974 (2006). [CrossRef]
7. R. J. Black and R. Bourbonnais, “Core-mode cutoff for finite-cladding light guides,” IEEE J. Optoelectron. 133(6), 377–384 (1986). [CrossRef]
8. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997). [CrossRef] [PubMed]
9. S. Laflamme, S. Lacroix, J. Bures, and X. Daxhelet, “Understanding power leakage in tapered solid core microstructured fibers,” Opt. Express 15(2), 387–396 (2007). [CrossRef] [PubMed]
10. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008). [CrossRef] [PubMed]
