Design of High Order Mode-multiplexers Using Multiplane Light Conversion

Fabrication and Characterization of a Mode-selective 45-Mode Spatial Multiplexer based on Multi-Plane Light Conversion

Satyanarayana Bade, Bertrand Denolle, Gauthier Trunet, Nicolas Riguet, Pu Jian, Olivier Pinel, Guillaume Labroille

Abstract

The fabrication of 45 spatial mode multiplexers is reported for the first time. The multiplexers based on Multi-Plane Light Conversion show an average 4 dB insertion loss and -28 dB cross-talk across the C band.

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CAILabs, 38 boulevard Albert 1er, 35200 Rennes, France \email

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060.4230, 060.4510, 080.4295, 080.2720.

1 Introduction

One promising approach for using spatial diversity to increase the capacity of optical fibers is Mode Division Multiplexing (MDM) in few-mode or multi-mode fibers (MMFs)[1]. Implementing MDM requires mode selective spatial multiplexer (MUX) and demultiplexer (DEMUX) in order to excite independently and unitarily the propagation modes of the MMF. Several techniques have been proposed for mode selective MUX. Mode selective photonic lantern, deriving from photonic lantern with dissimilar input single-mode fibers (SMFs), has been largely investigated[2].

Multi-Plane Light Conversion (MPLC) is a multiplexing technique based on conversion in free-space between sets of spatial modes through spatial phase transforms. MPLC is interesting since it offers low insertion loss (IL), low mode dependent loss (MDL) and highest reported mode selectivity for a large number of arbitrary modes. Previous experimental implementations of 6-, 10- and 15-mode MUX over MMF[3, 4, 5] have demonstrated the high performance of this approach. MPLC-based MUX can also be optimized for orbital angular momentum modes[6] and have been used in record-breaking transmission experiments[7].

Previous works have shown that increasing the number of multiplexed modes increases the number of phase transforms required in the MPLC, thus complexifying the assembly of the MUX and decreasing its IL. [8] has showed that the specific case of converting a triangle array of SMFs to Hermite-Gaussian modes requires a much smaller number of phase transforms than the general case. Here, we generalize this approach and we show that the number of phase transforms can be drastically reduced for a special class of spatial modes, namely a separable basis of modes. We demonstrate how MPLC with separable bases in input and output enables the design of multiplexers selectively addressing modes of graded-index fibers with a reduced number of phase transforms, and report the fabrication of a pair of 45-mode multiplexer and demultiplexer addressing all the 45 modes of a 50 m core graded-index multi-mode fiber with an average IL of 4 dB and cross-talk (XT) of -28 dB across the full C-band.

2 Multi-Plane Light Conversion with separable mode basis

Multi-Plane Light Conversion (MPLC) is a technique that allows performing any unitary spatial transform. Theoretically, MPLC enables the lossless conversion of any set of orthogonal spatial modes into any other set of orthogonal modes through a succession of transverse phase profiles separated by propagation. For a given conversion, the phase profiles can be calculated by a wavefront matching algorithm[9].

In particular, MPLC enables mode selective spatial multiplexing, i.e. the conversion of spatially separate input Gaussian beams into orthogonal propagation modes of a few-mode or multi-mode fiber[3]. Practically, MPLC is implemented using a multi-pass cavity, in which the successive phase profiles are all manufactured on a single reflective phase plate (see Fig.0(a)). The cavity is formed by a mirror and the reflective phase plate, and performs the successive phase profiles. A MPLC used in the reverse direction implements the demultiplexing operation. The number of phase profiles required for a given MPLC is a trade-off between the number of modes, the complexity of the phase and amplitude profile of the modes, the ease of assembly of the multi-pass cavity, and the performance of the MPLC. In particular, the IL increases with the number of phase profiles due to coating losses on the phase plate. We have previously demonstrated an increase in the number of phase profiles required for -mode multiplexers with constant performance when increases: for average IL 5 dB and average XT  dB, the number of phase profiles required for 6, 10 and 15 mode MUX were respectively 7, 14 and 20[3, 4, 5].

(a) Photo of a 45-mode MUX based on MPLC of separable variable modes. The beam path is shown in red.

(b) Experimentally measured free-space output modes of the 45-mode multiplexer.

Figure 1: Implementation of a 45-mode MUX based on MPLC.

The number of phase profiles can be strongly reduced for a special class of input and output modes: when the input mode basis and the output mode basis are both separable. We call a separable variable mode if at a given plane can be written as:

One can show that in the Fresnel approximation, as the field propagates, it stays separable at any and can be written as with and independent of each other[10]. Moreover, if one applies a separable phase profile to the field, i.e. a phase profile that can be written as , the resulting field remains separable.

Consequently, conversion of a separable basis of modes to a separable basis of output modes can be achieved with separable phase profiles, and the complexity of the MPLC reduces to that of an -mode problem. Indeed, it is possible to find a collection of 1D phase profiles enabling the MPLC of into , and similarly a collection enabling the MPLC of into . Therefore, the collection of 2D phase profiles enables the MPLC of into . Therefore, the MPLC of a separable basis of modes requires approximately the same number of phase profiles as the multiplexing of arbitrary modes, thus greatly reducing the implementation complexity of the multiplexer without compromising the performance.

3 Design and fabrication of a 45-mode multiplexer with separable mode basis

The guided modes of a multi-mode fiber with a parabolic refractive index profile, such as a standard 50 m core graded-index multi-mode fiber (so-called 50/125 m fiber or OM2 fiber) can be analytically written as Hermite-Gaussian modes [11, 12]. Modes with a same value have the same propagation constants and are therefore degenerate. One can easily show that HG modes form a separable basis of modes.

For the input mode basis, we have built a separable basis of spatially separate SMFs with a 2D array of single-mode fibers arranged in a square configuration ( matrix of single-mode fibers) and we have chosen 45 SMFs arranged in a triangle inscribed in the square. Given that all the input SMFs are identical and that the grid of fibers has a fixed pitch, it is easy to see that the input modes also form a separable basis.

It follows that the MPLC transforming a 2D array of SMFs to all the 45 modes (9 mode groups) of a 50/125 m MMF requires approximately the same number of phase profiles as multiplexing 9 arbitrary spatial modes. This demonstrates why the choice of a triangle configuration of SMFs in input and HG modes in output can lead to a reduced number of profiles, as was found in[8].

Thus, we fabricated two 45-mode multiplexers, each composed of: a 45 single-mode fiber array in which the 45 SMFs in triangle formation are used at the input; a multi-pass cavity with 11 phase profiles on the reflective phase plate; a 50/125 m fiber at the output. The 45 spatial modes in free-space, before coupling into the multi-mode fiber, are shown in Fig.0(b), measured with a superluminescent diode centered at 1550 nm with FWHM of 50 nm as the light source and captured by a near-infrared camera with Indium Gallium Arsenide sensor.

4 Performance of the 45-mode multiplexer and demultiplexer

The 45-mode MUX and DEMUX are characterized by measuring the transmission matrix of a back-to-back system comprising a MUX, 20 meters of MMF and a DEMUX. The measurement setup is similar to the one described in[4]. The light source used is a tunable distributed feedback laser (DFB). An output power matrix at 1550 nm is shown in Fig.1(a). By measuring the input power and the matrix of output powers, we retrieve the insertion loss and the modal cross-talk for all modes. In order to neglect the effect of intra-mode group mixing inside the fiber in the calculation of MUX performance, output powers from modes of the same mode group are summed up for IL estimation, and averaged for XT calculation.

(a) Output power matrix at 1550 nm in dBm. The input power is 5.1 dBm.

(b) IL (in blue), MDL (in red), average XT (in green) and maximum XT (in orange) of a single MUX for all measured transmission matrices.

Figure 2: Performance of the 45-mode MUX measured with a DFB source.

Assuming that the MUX and DEMUX are identical, we measured that the IL per MUX at 1550 nm ranges from 3.1 dB to 6.1 dB with an average of 4 dB, and that the average mode-to-mode XT is -28 dB. We also measured the performance across the full C+L band (1530 to 1630 nm) by measuring for each wavelength 50 transmission matrices while bending and twisting the MMF in order to test various multi-path interference conditions. The IL, MDL and XT for the 50 measurements at each wavelength are shown in Fig.1(b). Over the C band (1530 to 1570 nm), the average insertion loss is 4 dB, the average XT is -28 dB, and the maximum MDL and XT observed over all the 450 measurements are respectively 3.6 dB and -18 dB.

5 Conclusion

We have built a 45-mode multiplexer based on Multi-Plane Light Conversion addressing all the modes of a 50 m core graded-index fiber with an average insertion loss of 4 dB and an average cross-talk of -28 dB across the C-band. The performance, similar to previous 10 or 15-modes MPLC multiplexer, is enabled by using separable mode basis as the target output modes, which significantly reduced the required number of phase profiles.

References

• [1] R. Ryf et al. , ECOC 2015, PDP 3.3.
• [2] R. Amezcua Correa, OFC 2016, Tu3I.3.
• [3] G. Labroille et al. , Opt. Express 22 , 15599 (2015).
• [4] G. Labroille et al. , OFC 2016, Th3E.5.
• [5] N. Barré et al. , OFC 2017, Th2A.7.
• [6] R. Saad et al. , ECOC 2017, P1.SC1.15.
• [7] D. Soma et al. , ECOC 2017, Th.PDP.A.1.
• [8] N. Fontaine et al. , ECOC 2017, Tu.1.F.4.
• [9] J.-F. Morizur et al. , U.S. Patent 9,250,454 B2 (2016)
• [10] J. Goodman, "'Introduction to Fourier Optics"' (2005)
• [11] S. Choudary & L. B. Felsen, JOSA A 67, 1192 (1977)
• [12] M. W. Beijersbergen et al. , Optics Comm. 96, 123 (1993)

Design of High Order Mode-multiplexers Using Multiplane Light Conversion

Source: https://www.arxiv-vanity.com/papers/1803.07907/

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