Source: https://www.osapublishing.org/oe/abstract.cfm?uri=oe-27-4-5570
Timestamp: 2019-04-25 01:57:17+00:00

Document:
To meet the demand for higher capacity fiber-optic communication, multimode fibers have gradually attracted attention, but they introduce spatial distortions. To overcome this limitation, wavefront shaping technology promises to control scattered light after it is transmitted through multimode fibers. In this work, we introduce a Hadamard encoding algorithm (HEA) to control 1550-nm light that has passed through a multimode fiber. A series of Hadamard bases is iteratively added to the current optimum phase map, and the coefficient of each order is determined through a simple four-step phase-shifting mechanism. Using a laser source at 1550-nm wavelength, we experimentally achieved an optical focus through a 2-meter-long multimode fiber. With 1024 orders, the experimental enhancement reached 690, which is 86% of the theoretical value. As far as we know, this is the best result ever reported in focusing 1550-nm light through a multimode fiber. Moreover, we note that the HEA can also be used to reduce the intensity of the targeted light, suggesting broad applications in glare suppression. These results demonstrate superior performance in controlling targeted light transport through a multimode fiber at a telecommunication wavelength. We anticipate that this work will open new possibilities in a variety of applications in fiber optics.
I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).
I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008).
Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
M. Cui and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18(4), 3444–3455 (2010).
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).
S. M. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13(12), 123021 (2011).
C.-L. Hsieh, Y. Pu, R. Grange, G. Laporte, and D. Psaltis, “Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle,” Opt. Express 18(20), 20723–20731 (2010).
X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics 6(10), 657–661 (2012).
Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3(1), 928 (2012).
T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3(1), 1909 (2013).
B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE),” Nat. Photonics 7(4), 300–305 (2013).
E. H. Zhou, H. Ruan, C. Yang, and B. Judkewitz, “Focusing on moving targets through scattering samples,” Optica 1(4), 227–232 (2014).
C. Ma, X. Xu, Y. Liu, and L. V. Wang, “Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media,” Nat. Photonics 8(12), 931–936 (2014).
H. Ruan, M. Jang, and C. Yang, “Optical focusing inside scattering media with time-reversed ultrasound microbubble encoded light,” Nat. Commun. 6(1), 8968 (2015).
E. E. Morales-Delgado, S. Farahi, I. N. Papadopoulos, D. Psaltis, and C. Moser, “Delivery of focused short pulses through a multimode fiber,” Opt. Express 23(7), 9109–9120 (2015).
D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728–735 (2015).
B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11(8), 684–689 (2015).
Y. Shen, Y. Liu, C. Ma, and L. V. Wang, “Sub-Nyquist sampling boosts targeted light transport through opaque scattering media,” Optica 4(1), 97–102 (2017).
Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4(2), 280–288 (2017).
Z. Yu, J. Huangfu, F. Zhao, M. Xia, X. Wu, X. Niu, D. Li, P. Lai, and D. Wang, “Time-reversed magnetically controlled perturbation (TRMCP) optical focusing inside scattering media,” Sci. Rep. 8(1), 2927 (2018).
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).
T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, “Controlling light in scattering media non-invasively using the photoacoustic transmission matrix,” Nat. Photonics 8(1), 58–64 (2014).
M. Kim, W. Choi, Y. Choi, C. Yoon, and W. Choi, “Transmission matrix of a scattering medium and its applications in biophotonics,” Opt. Express 23(10), 12648–12668 (2015).
J. Yoon, K. Lee, J. Park, and Y. Park, “Measuring optical transmission matrices by wavefront shaping,” Opt. Express 23(8), 10158–10167 (2015).
W. Xiong, P. Ambichl, Y. Bromberg, B. Redding, S. Rotter, and H. Cao, “Spatiotemporal Control of Light Transmission through a Multimode Fiber with Strong Mode Coupling,” Phys. Rev. Lett. 117(5), 053901 (2016).
O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011).
M. Cui, “A high speed wavefront determination method based on spatial frequency modulations for focusing light through random scattering media,” Opt. Express 19(4), 2989–2995 (2011).
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).
D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express 20(5), 4840–4849 (2012).
P. Lai, L. Wang, J. W. Tay, and L. V. Wang, “Photoacoustically guided wavefront shaping for enhanced optical focusing in scattering media,” Nat. Photonics 9(2), 126–132 (2015).
M. Jang, H. Ruan, H. Zhou, B. Judkewitz, and C. Yang, “Method for auto-alignment of digital optical phase conjugation systems based on digital propagation,” Opt. Express 22(12), 14054–14071 (2014).
M. Azimipour, F. Atry, and R. Pashaie, “Calibration of digital optical phase conjugation setups based on orthonormal rectangular polynomials,” Appl. Opt. 55(11), 2873–2880 (2016).
A. S. Hemphill, Y. Shen, J. Hwang, and L. V. Wang, “High-speed alignment optimization of digital optical phase conjugation systems based on autocovariance analysis in conjunction with orthonormal rectangular polynomials,” in (SPIE, 2018), 11.
X. Cheng, B. Li, B. Zhang, Q. Feng, C. Lin, and Y. Ding, “Deeply focusing light at 1550 nm through strongly scattering media,” Opt. Commun. 405, 412–415 (2017).
H. Huang, Z. Chen, C. Sun, J. Liu, and J. Pu, “Light Focusing through Scattering Media by Particle Swarm Optimization,” Chin. Phys. Lett. 32(10), 104202 (2015).
L. Fang, H. Zuo, Z. Yang, X. Zhang, L. Pang, W. Li, Y. He, X. Yang, and Y. Wang, “Particle swarm optimization to focus coherent light through disordered media,” Appl. Phys. B 124(8), 155 (2018).
L. Fang, X. Zhang, H. Zuo, and L. Pang, “Focusing light through random scattering media by four-element division algorithm,” Opt. Commun. 407, 301–310 (2018).
Y. Wu, X. Zhang, and H. Yan, “Focusing light through scattering media using the harmony search algorithm for phase optimization of wavefront shaping,” Optik (Stuttg.) 158, 558–564 (2018).
A. Hedayat and W. D. J. T. A. O. S. Wallis, “Hadamard matrices and their applications,” 6, 1184–1238 (1978).
J. Seberry, B. Jwysocki, and T. Awysocki, “On some applications of Hadamard matrices,” Metrika 62(2-3), 221–239 (2005).
J. W. Goodman, Speckle Phenomena In Optics: Theory And Applications (Roberts and Company Publishers, 2007).
B. Blochet, L. Bourdieu, and S. Gigan, “Focusing light through dynamical samples using fast continuous wavefront optimization,” Opt. Lett. 42(23), 4994–4997 (2017).
Y. Liu, Y. Shen, H. Ruan, F. L. Brodie, T. T. Wong, C. Yang, and L. V. J. J. O. b. O. Wang, “Time-reversed ultrasonically encoded optical focusing through highly scattering ex vivo human cataractous lenses,” 23, 010501 (2018).
E. H. Zhou, A. Shibukawa, J. Brake, H. Ruan, and C. Yang, “Glare suppression by coherence gated negation,” Optica 3(10), 1107–1113 (2016).
A. Daniel, L. Liberman, and Y. Silberberg, “Wavefront shaping for glare reduction,” Optica 3(10), 1104–1106 (2016).
Fig. 1 Illustration of feedback-based wavefront shaping. (a) Light with a planar wavefront is transformed into a speckle pattern after passing through a multimode fiber. (b) After many rounds of iterations, a shaped wavefront can form a focus at the targeted position. D: detector; MMF: multimode fiber; PC: personal computer; SLM: spatial light modulator.
Fig. 2 (a) A series of Hadamard bases is reshaped into two-dimensional matrices. (b) A phasor diagram to illustrate the optimization principle. (c) A flowchart of the phase optimization process.
Fig. 3 Experimental setup of the system. BB: beam block; BS: beam splitter; CCD: charge-coupled device; HWP: half-wave plate; L1, L2: lens; M: mirror; MMF: multimode fiber; OBJ1, OBJ2: objective lens; PBS: polarizing beam splitter; PC: personal computer; SLM: spatial light modulator.
Fig. 4 Results of focusing 1550-nm light through a multimode fiber. (a) A random speckle pattern before optimization. (b) A bright focus formed after optimization, with an enhancement of 690. (c) Enhancement as a function of the number of measurements (the number of iterations × 4). The enhancements are 274, 638, and 690 at the end of each round, reaching 34%, 79%, and 86% of the theoretical value, respectively. (d) The optimum phase map that corresponds to the final focus in (b). (e) A focus achieved through HEA in the simulation. (f) Simulated enhancements as a function of the number of measurements by using HEA (blue), GA (red), and PA (cyan). In (c) and (f), different rounds of iterations are separated by dashed yellow lines.
Fig. 5 Experimental results of focusing 1550-nm light through two stacked ground diffusers. (a) A random speckle pattern before optimization. (b) A sharp focus formed after optimization with an enhancement of 620. (c) Enhancement as a function of the number of measurements (the number of iterations × 4). After three rounds of optimization, the enhancement reaches 620, which is 77.3% of the theoretical value. Different rounds of iterations are separated by dashed yellow lines. (d) The optimum phase map that corresponds to the final focus in (b).
Fig. 6 (a) An illustration of HEA for glare suppression. (b) A typical speckle pattern before optimization, with the targeted position encircled in red (c) The optimized intensity pattern after 1024 iterations. For visualization, the color bars in (b) and (c) are in logarithmic scale. (d) A logarithmic scale plot of the normalized intensity variation of the targeted position as a function of the number of iterations.
(1) E out ( j )= ∑ k t( j,k ) E in ( k ) = ∑ k A( j,k ) .
(3) I n,m ( j )= | ∑ k t( j,k ) e i φ n,m ( k ) | 2 = | ∑ k ( t( j,k ) e i ψ n−1 ( k ) e i( mπ/2 )( H n ( k )+1 )/2 ) | 2 = | ( E n−1,opt ( j )+ E n,mod ( j ) e imπ/2 ) | 2 .
(4) ϕ n =Arg[ ( I n,1 ( j )− I n,3 ( j ) )+i( I n,2 ( j )− I n,4 ( j ) ) ].
(6) η≡ I foc / 〈 I avg 〉 .

References: V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V.