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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2955–2964
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Adaptive control of waveguide modes in a two-mode-fiber

Peng Lu, Matthew Shipton, Anbo Wang, Shay Soker, and Yong Xu  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2955-2964 (2014)
http://dx.doi.org/10.1364/OE.22.002955


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Abstract

We experimentally demonstrate an adaptive-optics-based approach that allows selective excitation of waveguide modes and their mixtures in a two-mode fiber (TMF). A phase-only spatial light modulator is used for wavefront control, using feedback signals provided by the correlation between the experimentally measured field distribution and the desired mode profiles. Experimental results show the optical field within the TMF can be shaped to be pure linearly polarized (LP) modes or their combinations. Analysis shows selective mode excitation can be achieved using only 5 × 5 independent phase blocks. With proper feedback signals, this method should enable one to precisely control the optical field within any multimode fiber or other types of waveguides in real time.

© 2014 Optical Society of America

1. Introduction

Recently, spatial division-multiplexing (SDM) has attracted much attention in optical communications [1

1. P. J. Winzer, “Optical networking beyond WDM,” IEEE Photonics J. 4(2), 647–651 (2012). [CrossRef]

3

3. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]

]. A major goal of SDM is to use space as a multiplexing parameter to overcome the capacity limit of single mode fibers [4

4. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

, 5

5. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]

]. One approach of SDM is mode division multiplexing (MDM), which utilizes individual waveguide modes within multimode fiber (MMF) as communication channels for signal multiplexing and demultiplexing. A key component of MDM is the excitation of specific waveguide mode in a MMF. In existing literature, this task can be accomplished using multiple techniques, such as stress fiber [6

6. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s COOFDM signal over a two-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11) (2011), PDPB8.

], spot-based coupler or spatial beam sampler [7

7. R. Ryf, N. K. Fontaine, and R.-J. Essiambre, “Spot-based mode coupler for mode-multiplexed transmission in few mode fiber,” in Proc. IEEE Summer Topical (2012), TuC3.2. [CrossRef]

, 8

8. H. Bulow, H. Al Hashimi, and B. Schmauss, “Spatial-mode multiplexers and MIMO processing,” in Proc. Opto-Electronics and Communication Conference (OECC 2012) (2012), 5E4–1. [CrossRef]

], photonic lanterns [9

9. S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010). [CrossRef] [PubMed]

11

11. R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen, and R. Lingle, “12 x 12 MIMO transmission over 130-km few-mode fiber,” in Proc. Frontiers in Optics Conference (FiO’12) (2012), FW6C.4. [CrossRef]

], phase masks [12

12. S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982). [CrossRef] [PubMed]

, 13

13. N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). [CrossRef] [PubMed]

] or spatial light modulators (SLM) [14

14. D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2. [CrossRef]

18

18. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef] [PubMed]

].

Despite impressive progress so far, most of the existing methods for mode control have certain drawbacks. For example, the phase mask approaches described in [12

12. S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982). [CrossRef] [PubMed]

, 13

13. N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). [CrossRef] [PubMed]

] are static in nature and cannot be easily adjusted in real time. Other research groups have utilized SLM to achieve selective mode excitation [14

14. D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2. [CrossRef]

18

18. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef] [PubMed]

]. However, the method described here is different from existing approaches in [14

14. D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2. [CrossRef]

18

18. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef] [PubMed]

]. Specifically, our adaptive optics (AO) based approach requires no prior knowledge of the optical system or the intermodal coupling within the fiber network. In fact, our method treats the entire optical system, including both the input coupling system and the few-mode fiber (FMF) itself, as a “black box”. In contrast, the method reported in [15

15. J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010). [CrossRef]

17

17. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

] requires knowledge of the optical system and is based on linking optical near field to far field through a Fourier transform [15

15. J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010). [CrossRef]

]. Furthermore, the method in [15

15. J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010). [CrossRef]

17

17. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

] is implemented using computer generated holography, which is both computationally intensive and time consuming. As an additional example, the method reported in [18

18. J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef] [PubMed]

] requires careful optical alignment and pre-calibration of the SLM to achieve pre-determined phase and amplitude modulation for selective mode excitation.

For many applications in optical communications and sensing, one needs to ensure that the optical field at a given location within a MMF network becomes either a specific linearly polarized (LP) mode, or a mixture of LP modes with proper amplitudes and phases for individual LP components. For a MMF network with strong and time-dependent intermodal coupling, we may not even know how optical waves propagate within such a network. Therefore, there is an urgent need to develop a technique that can achieve selective mode excitation within a fiber network that support multiple LP modes, without any prior knowledge of the underling optical systems. The main purpose of the present paper is to demonstrate the feasibility of use AO techniques to achieve this goal. Additionally, the method presented here is generic, easy to implement, requires a relatively few number of independent phase control elements, and can deliver mode control in real time.

The AO-based approach, as illustrated in Fig. 1(a)
Fig. 1 (a) Principle of AO-based mode control. (b) Schematic of the setup: λ/2, half-wave plate; Expander, 1:5 beam expander comprise of two lenses; M, mirror; SLM, phase-only spatial light modulator; P1, P2 and P3, polarizers; L1, 20 × objective lens, NA = 0.40; Fiber, Thorlabs 980HP, ~1.5m; L2, 100 × objective lens, NA = 0.70; CCD, CCD camera. (c) Optimization sequence of SLM blocks (N = 13).
, requires a feedback signal that is directly associated to the desired mode properties. For example, in present paper, the desired outcome is that the optical field at the fiber output becomes specific LP modes or their combinations. For the convenience of implementation, the feedback signal in present work is simply the correlation between the desired mode profile and the optical field distribution captured by a CCD camera. Potential candidates for feedback signals, however, are by no means restricted to this particular choice. For future applications, the feedback signal could be the reflection peak of a fiber Bragg grating, the coupling ratio of a directional coupler, or even nonlinear signals generated by processes such as Brillouin scattering, Raman scattering, and four wave mixing. After choosing the proper feedback, we use the SLM to modify the wavefront and measure the feedback signal produced by the new wavefront. The modified wavefront is retained (or rejected) depending on whether the feedback signal suggests better (or worse) match between the measured outcome and the desired target. This optimization cycle is repeated until the desired target is reached.

In this work, we demonstrate AO-based selective excitation of LP modes in a two-mode fiber (TMF). In Section 2, we describe the experiment setup. In Section 3, we introduce our adaptive algorithm for wavefront shaping. In Section 4, we present different experimental results of selective mode excitation. Examples include selective excitation of only the LP01 mode, only the LP11 mode, or a specific mixture of the LP01 and the LP11 modes. In Section 5, we describe several important features of the AO-based selective mode excitation processes. Additionally, we show that it is possible to utilize only 5 × 5 phase blocks to achieve highly selective mode excitations. Finally, we summarize our work in Section 6.

2. Experiment setup

Our experimental system is shown in Fig. 1(b). Light from a linearly polarized He-Ne laser (632.8nm) is collimated and expanded. The expanded beam is reflected by a phase-only SLM (Holoeye, Pluto) and focused into a silica fiber (Thorlabs 980HP, length approximately 1.5m). According to the specification of the fiber, the fiber V-number is V = 3.57 at the operation wavelength. Thus the fiber is a TMF that supports the LP01 and the LP11 modes.

The light polarization is controlled by a half-wave plate and three polarizers in the setup. The first two polarizers (P1 and P2) select optical waves with polarization direction parallel to the optical table, which happens to be the same as the phase modulation axis of the SLM. The polarizer in front of the CCD (P3) ensures that we only monitor a single polarization component of the optical output. The polarization direction of P3 is randomly chosen, excluding the obvious case where P2 and P3 are orthogonal to each other. The expanded He-Ne laser beam (FWHM ~8 mm) is projected onto the SLM and forms an optical beam of similar size. (The total area of the SLM pixels that are phase modulated is approximately 6.2 mm by 6.2 mm.) This area is evenly divided into 13 × 13 phase blocks to control the wavefront of the incident beam. Within each phase block, the phase shifts produced by the SLM are identical. An objective lens (20 × , NA = 0.40) is used to focus the beam into the fiber. At the output end of the fiber, a second objective lens (100 × , NA = 0.70) and a CCD camera are used to measure the output intensity profile. From the measured intensity profile, we calculate its correlation with the desired target mode profile as the feedback signal for SLM control.

3. AO-based mode control

AO-based mode control is carried out as follows. From the fiber specification, we can theoretically calculate the desired target profile at the fiber output. More specifically, a linear combination of the LP01 and the LP11 mode with a specific polarization can be expressed as:
I(r,φ)=|A01E01(r,φ)ejβ+A11E11(r,φ)|2=A012E012(r,φ)+A112E112(r,φ)+2A01A11cosβE01(r,φ)E11(r,φ)
(1)
Here E01(r, φ) and E11(r, φ) denote electric fields of the LP01 and LP11 modes with a specific polarization, respectively. A01 and A11 are the amplitudes of two modes, and β represents their relative phase difference. To simplify the procedure for mode decomposition in later sections, we assume both E01(r, φ) and E11(r, φ) to be real.

With the theoretical mode profile known, we can calculate the correlation between the target intensity profile and the measured intensity profile at the fiber output, and use this correlation function as the feedback for mode control. Specifically, we define an objective function based on the CCD intensity profile Ik and the target intensity profile I0:
f(k)=1(I0(x,y)I0¯)(Ik(x,y)Ik¯)(I0(x,y)I0¯)2(Ik(x,y)Ik¯)2
(2)
where Ik¯ and I0¯are the average of I0 and Ik, respectively. According to Eq. (2), it is clear that the optimization function f(k) quantitatively described the difference between the actual CCD intensity profile and the desired target, with smaller f(k) indicating better match. Ideally, if the CCD intensity profile forms a perfect match with the target profile, f(k) should become 0.

The time required for one optimization cycle with 13 × 13 phase blocks is roughly 192 s. For a proof-of-concept demonstration, there is no need for using faster but more complex optimization algorithms. In future, we expect the faster algorithms and methods described in [21

21. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010). [CrossRef] [PubMed]

, 22

22. M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett. 36(6), 870–872 (2011). [CrossRef] [PubMed]

, 24

24. D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012). [CrossRef] [PubMed]

27

27. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013). [CrossRef] [PubMed]

] should significantly improve the speed of selective mode excitation.

4. Experimental results

By using the experimental setup and adaptive algorithm described above, we have adaptively controlled optical mode content at the fiber output. During the experiment, only the optical field within or near the fiber core (approximately 5.4 µm × 5.4 µm in size) is used in the evaluation of the optimization function. (It corresponds to a 61 × 61 pixel block in the CCD image. The fiber core, with a radius of 1.8 µm, is completely contained within this region.) In our studies, we considered three different cases. In case 1 and 2, we adaptively covert the optical mode at the fiber output to be either purely LP01 (in case 1) or purely LP11 (in case 2). Then, in case 3, we excite a mixture of LP01 and LP11 with pre-determined mode coefficients.

The results for case 1, i.e., exciting only the LP01 mode, are shown in Fig. 2
Fig. 2 Selective excitation of the LP01 mode. Images in (a) are the initial field distributions. Results in (b) are the images captured after the optimization process. Figures with the same sequence number belong to the same optimization process; (c) and (d) show the horizontal and the vertical cross-section of the intensity profiles (along the dashed blue line in the inset) of both the theoretical target (solid line) and the experiment results (dots), respectively.
. Figures 2(a) and 2(b) show the “before” and the “after” optimization images for four experiments with randomly selected initial intensity profiles. In Figs. 2(a) and 2(b), the “before” and “after” images that belong to the same optimization process are denoted using the same sequence number. The difference between the optimized intensity distribution and the theoretical target is less than 0.19% for all four cases. The cross-sections of the optimized field intensity (as captured by the CCD camera, represented as dots) and the theoretical target (represented as solid lines) are shown in Figs. 2(c) and 2(d). After optimization, the agreement between the actual mode profile and the theoretical target is excellent.

Figure 3
Fig. 3 Selective excitation of the LP11 mode. Intensity profiles in (a) and (b) denotes the “before” and “after” optimization of four different optimization processes; (c) and (d) show the horizontal and the vertical cross-section (along the dashed blue line in the inset) of the intensity profiles for both the theoretical target (solid line) and the experiment results (dots), respectively.
shows experimental results for case 2, where we excite only the LP11 mode at the fiber output. Again, Figs. 3(a) and 3(b) show the “before” and “after” optimization images for four experimental studies with different initial intensity profiles. After optimization, the difference between the actual CCD camera image and the theoretical target is less than 0.75% for all four cases. As previously, the cross-sections of theoretical and actual “after” optimization mode profiles are shown in Figs. 3(c) and 3(d).

Results in Figs. 2 and 3 demonstrate that the AO-based approach can produce either the LP01 or the LP11 mode with very high selectivity, regardless of the initial mode profiles. Next, we consider, in some sense, the worst case scenario, where we deliberately choose the LP01 mode as the initial profile and select the LP11 mode as our target. The “before” and “after” optimization images, as captured by the CCD camera, are shown in Figs. 4(a)
Fig. 4 Converting the LP01 mode (shown as the initial distributions in (a)) to the LP11 mode (shown as the optimized intensity profiles in (b)). Figures labeled as the same sequence number belong to the same optimization process.
and 4(b). Again, it is clear that we can achieve complete mode conversion from the LP01 to the LP11 mode.

Finally, we consider case 3, where we use the adaptive algorithm to excite a superposition of LP01 and LP11 modes. The results are shown in Fig. 5
Fig. 5 Excitation of a specific mixture of the LP01 and the LP11 modes. Targets in (a) to (d) are obtained through theoretical calculations, with specific amplitude ratios (AR = A01/A11) and phase differences β, as defined in Eq. (1). (a) AR = 0.5, β = π/2. (b) AR = 0.5, β = π/4 (c) AR = 0.2, β = π/2. (d) AR = 0.2, β = π/4. In (e)-(f), we choose four representative CCD camera images, captured experimentally, as the targets used in the optimization process.
. In Figs. 5(a)5(d), the target intensity profiles are generated using the theoretical LP01 and LP11 mode profile with different amplitude ratios and phase contrasts. The difference between theoretical targets and actual CCD camera images are less than 1%. In Figs. 5(e)5(h), we use some arbitrarily chosen CCD camera images as target profiles. The differences between the target profile and the “optimized” results are less than 0.7% for all four cases.

5. Optimization process analysis

In this section, we discuss several important aspects of the optimization processes. Figure 6
Fig. 6 The variation of the objective function obtained during the optimization process: (a) Optimize the mode to LP01 mode; (b) Optimize the mode to LP11 mode; (c) Optimize towards a mixed LP01/LP11 mode.
shows the variations of objective functions during 7 optimization cycles. We consider three different cases, with the LP01 mode being the target in Fig. 6(a), the LP11 mode as the target in Fig. 6(b), and a mixed mode as the target in Fig. 6(c). All results in Fig. 6 are divided into individual cycles, as indicated by the dashed lines. Within each cycle, the objective function exhibits significant variations as we adjust the phase shift for each of the 13 × 13 SLM blocks. This is to be expected, since for any SLM block, a “wrong” phase shift can certainly increase the difference between the captured CCD image and the target profile. Furthermore, recall that for each optimization cycle, we use the minimum value of the objective function to determine the optimal phase shift for the desired incident wavefront. Consequently, the results in Fig. 6 suggest that it only takes 3 to 4 cycles to reach the optimal wavefront for selective mode excitation. And after 7 optimization cycles, the deviation between the actual CCD image and the target profile are less than −27 dB for the LP01 case and fewer than −20 dB case for the LP11 case. Several factors may account for the differences between the theoretical targets and the actual optimized field distributions. For example, the actual index distribution of the fiber may not be the simple step-index profile assumed in our theoretical calculations. Additionally, the fiber output facet may not be perfectly flat, which can also cause deviations between the theoretical target profiles and the CCD camera images.

We also analyze the mode profiles captured by the CCD camera after each optimization cycle. Specifically, we decomposed the CCD image into a linear superposition of the LP01 and the LP11 mode components. The square of the amplitude ratios of LP01 mode to LP11 mode are shown in Fig. 7
Fig. 7 The variations of mode ratio A012/A112 during the optimization cycles. Mode is shaping to (a) LP01 mode, (b) LP11 mode, and (c) mixed modes. The legend in (c) shows the mode ratios A012/A112 of the targets used in optimization.
. Figures 7(a) and 7(b) confirms that after optimization, the optical mode at the fiber output is clearly dominated by the desired target, i.e., LP01 for Fig. 7(a) and LP11 for Fig. 7(b). Figure 7(c) shows the mode decomposition results of the four cases shown in Figs. 5(a)5(d), where we use a mixed mode as the optimization target. In Figs. 5(a) and 5(b), the target mode amplitude ratio between the LP01 and the LP11 mode is A01/A11 = 0.5. The corresponding values of A012/A112 measured during the optimization process, are shown as the red and green lines in Fig. 7(c). In Figs. 5(c) and 5(d) the target mode amplitude ratio is A01/A11 = 0.2, and the corresponding values of A012/A112 measured during the optimization processes, are represented as the blue and magenta lines in Fig. 7(c). Results in Fig. 7 also suggest that we can reach the LP modes or their mixtures after only 3-4 optimization cycles.

Finally, for certain applications in optical communications and sensing, it is often desirable to reduce the amount of independent SLM phase blocks used in selective mode excitation. (For example, fewer independent blocks should increase optimization speed and reduce system cost.) Here, we show that it is possible to use only the central 5 × 5 SLM blocks (out of the 13 × 13 phase blocks) to achieve highly selective mode excitation. Three different sets of “before” and “after” optimization images, as well as their corresponding target intensity distributions, are shown in Figs. 8(a)
Fig. 8 Results of selective mode excitation using 5 × 5 blocks with different initial and target intensity profiles. The initial intensity distributions, the target intensity distributions, and the optimized images are labelled accordingly in (a)-(c). The optical output field is shape to (a) the LP01 mode, (b) the LP11 mode and (c) a mixture of the LP01/LP11 modes (the target is an experimentally captured CCD camera image). The objective functions obtained during the optimization process are also shown in (a)-(c).
8(c). For all three cases, the deviation between the target and the optimized image is less than 0.6%. The variations of objective functions during 7 optimization cycles are also shown in Figs. 8(a)8(c). Comparing the results shown in Fig. 8 (5 × 5 blocks) with the results obtained using 13 × 13 blocks in Figs. 6(a)6(c), there is no significant degradation in the performance of SLM-based optimization.

We further reduce the independent SLM phase blocks from 5 × 5 to 3 × 3 central blocks (out of the 13 × 13 phase blocks). With fewer phase blocks, the performance of SLM optimization degrades noticeably. Figure 9
Fig. 9 Results of selective mode excitation using 3 × 3 blocks with different target intensity profiles. The initial intensity distributions, the target intensity distributions, and the optimized images are labelled accordingly in (a)-(b). The optical output field is shape to (a) the LP01 mode, (b) the LP11 mode. The objective functions obtained during the optimization process are also shown in (a) and (b).
shows two representative examples, where the target mode is the LP01 and the LP11 mode, respectively. The difference between the target mode and the optimized intensity distribution is ~7.5% and ~6.0% respectively, and is noticeable through visual comparison.

6. Discussion and conclusion

Three aspects of our method deserve further comments. First, in present work, we do not consider the issue of coupling efficiency. Primarily, this is because for applications such as optical sensing, coupling efficiency is not as critical as in optical communications, where every dB counts. Additionally, it should not be too difficult to incorporate coupling efficiency into the optimization process. For example, we may first choose total output power as the optimization parameter and increase it to the largest possible extent. Then, we may apply the method described here for selective mode excitation. We may also alternate optimization parameters in different optimization cycles. For example, we may select optical output power as the to-be-optimized parameter for the odd optimization cycles, and choose the objective function in Eq. (2) as the optimization parameter for the even cycles. We may also define a different optimization parameter that depends on both the coupling efficiency and the correlation with the desired mode patterns. Given the fact that the algorithm described here has been widely used for optical focusing through diffusive media [19

19. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007). [CrossRef] [PubMed]

27

27. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013). [CrossRef] [PubMed]

], where optical power is a critical factor, the issue of coupling efficiency should not become a major hurdle for our AO-based approach.

Additionally, we consider only a single polarization component for both the input and the output optical fields. For more general scenarios, we may replace P2 in Fig. 1(b) with a polarization beam splitter (PBS) and P3 with another PBS. In this case, the study carried out here corresponds to a specific combination (out of four possible choices) for the input / output polarization channels [17

17. J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

]. We can add more bulk optics components so that all four input / output polarization channels are monitored simultaneously using the same SLM and CCD camera. The added complexity, however, is unlikely to reveal anything new. This is because in our studies, the orientation of P3 is randomly chosen, excluding the obvious case where P2 and P3 are orthogonal to each other. We did not observe any dependence or correlation between the optimization results and P3 orientation.

Finally, the results presented here are obtained using a TMF. For a FMF that supports a limited number of modes (for example, 4 or 6), the results reported here should remain applicable. However, for a MMF that supports hundreds of modes, some of the conclusions may no longer apply. For example, we may need to use more phase control elements to distinguish different LP modes within the MMF. However, the overall framework of the AO-based approach should still apply. Again, this expectation is based on the successful demonstration of AO-based focusing [19

19. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007). [CrossRef] [PubMed]

27

27. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013). [CrossRef] [PubMed]

], which involves hundreds, if not tens of thousands independent scattering channels.

In summary, we experimentally demonstrate the feasibility of using AO to achieve highly selective mode excitations in a TMF. In this proof-of-concept demonstration, we use the correlation between the CCD camera image and the theoretical target profile as the feedback for SLM control. The target profile can be purely LP01, purely LP11, or a mixture of the two modes. Furthermore, selective mode control can be accomplished using as few as 5 × 5 independent phase elements.

The method developed here can be easily generalized to cases where the feedback is provided by signals produced by mode-selective elements, including fiber Bragg gratings and mode selective couplers. The AO-based approach may find applications in MDM-based fiber communications and optical sensing.

Acknowledgments

The research is partially funded by NIH (NIBIB, HL098912, 1R21EB017819-01), whose support is gratefully acknowledged.

References and links

1.

P. J. Winzer, “Optical networking beyond WDM,” IEEE Photonics J. 4(2), 647–651 (2012). [CrossRef]

2.

R.-J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013). [CrossRef]

3.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]

4.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

5.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]

6.

A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s COOFDM signal over a two-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11) (2011), PDPB8.

7.

R. Ryf, N. K. Fontaine, and R.-J. Essiambre, “Spot-based mode coupler for mode-multiplexed transmission in few mode fiber,” in Proc. IEEE Summer Topical (2012), TuC3.2. [CrossRef]

8.

H. Bulow, H. Al Hashimi, and B. Schmauss, “Spatial-mode multiplexers and MIMO processing,” in Proc. Opto-Electronics and Communication Conference (OECC 2012) (2012), 5E4–1. [CrossRef]

9.

S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010). [CrossRef] [PubMed]

10.

N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in Proc. European Conference on Optical Communication (ECOC’12) (2012), Th.2.D.6. [CrossRef]

11.

R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen, and R. Lingle, “12 x 12 MIMO transmission over 130-km few-mode fiber,” in Proc. Frontiers in Optics Conference (FiO’12) (2012), FW6C.4. [CrossRef]

12.

S. Berdagué and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982). [CrossRef] [PubMed]

13.

N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). [CrossRef] [PubMed]

14.

D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2. [CrossRef]

15.

J. Carpenter and T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010). [CrossRef]

16.

J. Carpenter and T. D. Wilkinson, “All-optical mode multiplexing using holography and multimode fiber couplers,” J. Lightwave Technol. 30(12), 1978–1984 (2012). [CrossRef]

17.

J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]

18.

J. von Hoyningen-Huene, R. Ryf, and P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef] [PubMed]

19.

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007). [CrossRef] [PubMed]

20.

I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008). [CrossRef]

21.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010). [CrossRef] [PubMed]

22.

M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett. 36(6), 870–872 (2011). [CrossRef] [PubMed]

23.

R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011). [CrossRef] [PubMed]

24.

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012). [CrossRef] [PubMed]

25.

R. N. Mahalati, D. Askarov, J. P. Wilde, and J. M. Kahn, “Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling,” Opt. Express 20(13), 14321–14337 (2012). [CrossRef] [PubMed]

26.

C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, and T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20(14), 15086–15092 (2012). [CrossRef] [PubMed]

27.

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013). [CrossRef] [PubMed]

28.

I. M. Vellekoop and C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35(8), 1245–1247 (2010). [CrossRef] [PubMed]

29.

G. Ghielmetti and C. M. Aegerter, “Scattered light fluorescence microscopy in three dimensions,” Opt. Express 20(4), 3744–3752 (2012). [CrossRef] [PubMed]

30.

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nat. Commun. 3, 1027 (2012). [CrossRef]

31.

R. N. Mahalati, R. Y. Gu, and J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21(2), 1656–1668 (2013). [CrossRef] [PubMed]

32.

T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011). [CrossRef] [PubMed]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.2340) Fiber optics and optical communications : Fiber optics components
(060.4230) Fiber optics and optical communications : Multiplexing
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Fiber Optics

History
Original Manuscript: December 4, 2013
Revised Manuscript: January 23, 2014
Manuscript Accepted: January 24, 2014
Published: January 31, 2014

Citation
Peng Lu, Matthew Shipton, Anbo Wang, Shay Soker, and Yong Xu, "Adaptive control of waveguide modes in a two-mode-fiber," Opt. Express 22, 2955-2964 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2955


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References

  1. P. J. Winzer, “Optical networking beyond WDM,” IEEE Photonics J. 4(2), 647–651 (2012). [CrossRef]
  2. R.-J. Essiambre, R. Ryf, N. K. Fontaine, S. Randel, “Breakthroughs in photonics 2012: Space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photonics J. 5(2), 0701307 (2013). [CrossRef]
  3. D. J. Richardson, J. M. Fini, L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
  4. P. P. Mitra, J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]
  5. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]
  6. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s COOFDM signal over a two-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11) (2011), PDPB8.
  7. R. Ryf, N. K. Fontaine, and R.-J. Essiambre, “Spot-based mode coupler for mode-multiplexed transmission in few mode fiber,” in Proc. IEEE Summer Topical (2012), TuC3.2. [CrossRef]
  8. H. Bulow, H. Al Hashimi, and B. Schmauss, “Spatial-mode multiplexers and MIMO processing,” in Proc. Opto-Electronics and Communication Conference (OECC 2012) (2012), 5E4–1. [CrossRef]
  9. S. G. Leon-Saval, A. Argyros, J. Bland-Hawthorn, “Photonic lanterns: A study of light propagation in multimode to single-mode converters,” Opt. Express 18(8), 8430–8439 (2010). [CrossRef] [PubMed]
  10. N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in Proc. European Conference on Optical Communication (ECOC’12) (2012), Th.2.D.6. [CrossRef]
  11. R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen, and R. Lingle, “12 x 12 MIMO transmission over 130-km few-mode fiber,” in Proc. Frontiers in Optics Conference (FiO’12) (2012), FW6C.4. [CrossRef]
  12. S. Berdagué, P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt. 21(11), 1950–1955 (1982). [CrossRef] [PubMed]
  13. N. Bai, E. Ip, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. T. Lau, H.-Y. Tam, C. Lu, Y. Luo, G.-D. Peng, G. Li, T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). [CrossRef] [PubMed]
  14. D. Sperti, M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, A. Boutin, P. Sillard, and G. Charlet, “Experimental investigation of modal crosstalk using LCOS-based spatial light modulator for mode conversion,” in Proc. European Conference on Optical Communications 2011 (ECOC 2011) (2011), Th.12.B.2. [CrossRef]
  15. J. Carpenter, T. D. Wilkinson, “Graphics processing unit–accelerated holography by simulated annealing,” Opt. Eng. 49(9), 095801 (2010). [CrossRef]
  16. J. Carpenter, T. D. Wilkinson, “All-optical mode multiplexing using holography and multimode fiber couplers,” J. Lightwave Technol. 30(12), 1978–1984 (2012). [CrossRef]
  17. J. Carpenter, B. C. Thomsen, T. D. Wilkinson, “Degenerate mode-group division multiplexing,” J. Lightwave Technol. 30(24), 3946–3952 (2012). [CrossRef]
  18. J. von Hoyningen-Huene, R. Ryf, P. Winzer, “LCoS-based mode shaper for few-mode fiber,” Opt. Express 21(15), 18097–18110 (2013). [CrossRef] [PubMed]
  19. I. M. Vellekoop, A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007). [CrossRef] [PubMed]
  20. I. M. Vellekoop, A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008). [CrossRef]
  21. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010). [CrossRef] [PubMed]
  22. M. Cui, “Parallel wavefront optimization method for focusing light through random scattering media,” Opt. Lett. 36(6), 870–872 (2011). [CrossRef] [PubMed]
  23. R. Di Leonardo, S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express 19(1), 247–254 (2011). [CrossRef] [PubMed]
  24. D. B. Conkey, A. M. Caravaca-Aguirre, R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012). [CrossRef] [PubMed]
  25. R. N. Mahalati, D. Askarov, J. P. Wilde, J. M. Kahn, “Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling,” Opt. Express 20(13), 14321–14337 (2012). [CrossRef] [PubMed]
  26. C. Stockbridge, Y. Lu, J. Moore, S. Hoffman, R. Paxman, K. Toussaint, T. Bifano, “Focusing through dynamic scattering media,” Opt. Express 20(14), 15086–15092 (2012). [CrossRef] [PubMed]
  27. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013). [CrossRef] [PubMed]
  28. I. M. Vellekoop, C. M. Aegerter, “Scattered light fluorescence microscopy: imaging through turbid layers,” Opt. Lett. 35(8), 1245–1247 (2010). [CrossRef] [PubMed]
  29. G. Ghielmetti, C. M. Aegerter, “Scattered light fluorescence microscopy in three dimensions,” Opt. Express 20(4), 3744–3752 (2012). [CrossRef] [PubMed]
  30. T. Čižmár, K. Dholakia, “Exploiting multimode waveguides for pure fiber-based imaging,” Nat. Commun. 3, 1027 (2012). [CrossRef]
  31. R. N. Mahalati, R. Y. Gu, J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21(2), 1656–1668 (2013). [CrossRef] [PubMed]
  32. T. Čižmár, K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011). [CrossRef] [PubMed]

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