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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 2 — Jan. 27, 2014
  • pp: 1990–1996
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Acousto-optic resonant coupling of three spatial modes in an optical fiber

Hee Su Park and Kwang Yong Song  »View Author Affiliations


Optics Express, Vol. 22, Issue 2, pp. 1990-1996 (2014)
http://dx.doi.org/10.1364/OE.22.001990


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Abstract

A fiber-optic analogue to an externally driven three-level quantum state is demonstrated by acousto-optic coupling of the spatial modes in a few-mode fiber. Under the condition analogous to electromagnetically induced transparency, a narrow-bandwidth transmission within an absorption band for the fundamental mode is demonstrated. The presented structure is an efficient converter between the fundamental mode and the higher-order modes that cannot be easily addressed by previous techniques, therefore can play a significant role in the next-generation space-division multiplexing communications as an arbitrarily mode-selectable router.

© 2014 Optical Society of America

1. Introduction

State transfer by coherent coupling is a key element of many optical devices as well as various quantum mechanical phenomena. Analogies between optical interference and temporal evolution of coupled quantum states have led to designing novel photonic waveguide devices inspired by coherent quantum effects in atomic or molecular physics [1

1. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009). [CrossRef]

, 2

2. D. Dragoman and M. Dragoman, Quantum-Classical Analogies(Springer, Berlin, 2004). [CrossRef]

]. For example, optical analogues to a multi-level atom have reproduced electromagnetically induced transparency (EIT) [3

3. C. Ciret, M. Alonzo, V. Coda, A. A. Rangelov, and G. Montemezzani, “Analog to electromagnetically induced transparency and Autler-Townes effect demonstrated with photoinduced coupled waveguides,” Phys. Rev. A 88, 013840 (2013). [CrossRef]

7

7. L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626–628 (2004). [CrossRef] [PubMed]

], stimulated Raman adiabatic passage [8

8. E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006). [CrossRef]

11

11. H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev., doi: [CrossRef] (2013).

], and quantum Zeno effect [12

12. K. T. McCusker, Y.-P. Huang, A. S. Kowligy, and P. Kumar, “Experimental demonstration of interaction-free all-optical switching via the quantum Zeno effect,” Phys. Rev. Lett. 110, 240403 (2013). [CrossRef]

], resulting in novel photonic devices. These examples controlled the coupling strength and the selection rule solely by the proximity and/or the phase matching between the optical modes, unlike the original atomic level configuration whose coupling is controlled by external driving fields. This work realizes external resonant couplings between the spatial modes of a few-mode fiber (FMF) by flexural acoustic waves propagating along the fiber. The symmetry of the transverse mode profiles determines the allowed or forbidden couplings between the spatial modes, as the selection rule of the dipole transition between the atomic states. Narrow-bandwidth transmission analogous to EIT and Autler-Townes splitting (ATS) is experimentally demonstrated. To our knowledge, this is the first demonstration of acousto-optic (AO) three-mode coherent coupling as well as the first implementation of an optical analogue to a three-level atom with resonant coupling fields. The demonstrated structure is an efficient mode converter that is applicable to space-division multiplexing (SDM) communications [13

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

, 14

14. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013). [CrossRef] [PubMed]

]. For example, one can implement an arbitrarily mode-selectable router to a multi-mode fiber transmission line when combined with a multi-mode fiber directional coupler that couples the same spatial modes of two fibers.

2. Device structure and operation principle

The fiber in this work has a step-index elliptic-core (numerical aperture 0.16, core diameter 11 μm × 7 μm) with a cladding diameter 100 μm. Around the wavelength of 1550 nm, the fiber guides in its core two spatial modes, the fundamental LP01 mode and the ‘even’ LP11 mode whose intensity lobes are aligned along the major axis of the core. The ‘odd’ LP11 mode is cut off from the core [15

15. H. S. Park, K. Y. Song, S. H. Yun, and B. Y. Kim, “All-fiber wavelength-tunable acoustooptic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20, 1864–1868 (2002). [CrossRef]

]. The third mode is the LP03 mode, which is a ‘cladding mode’ that is guided not by the core-cladding boundary but by the cladding-air boundary of an unjacketed fiber section. Advantage of using the LP03 mode among available modes is that the refractive index difference between the LP11 and the LP03 modes is close to the difference between the LP01 and the LP11 modes in the given fiber such that the required driving frequencies for both transitions lie in the effective bandwidth of our acoustic transducer.

A piezoelectrically driven acoustic transducer generates two flexural acoustic waves of different frequencies along the fiber as shown in Fig. 1(a). The flexural acoustic waves introduce antisymmetric perturbation to the optical path length throughout the fiber cross section, thus the symmetric LP0i modes can be coupled to the antisymmetric LP1j modes, and the antisymmetric LP1j modes can be coupled to the doubly antisymmetric LP2k or the symmetric LP0l modes (i, j, k, l = 1, 2, 3,...) [16

16. The indices i and j of a linearly polarized LPij mode denote the number of asymmetry axes and the number of lobes along the radius, respectively, of the transverse field distribution.

, 17

17. T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996). [CrossRef]

]. Coherent mode conversion occurs when the acoustic wavelength matches the intermodal beat length λ/|n1n2|, where λ is the optical wavelength and n1, n2 are effective refractive indices of the two modes, respectively. Propagation of each mode under the influence of the AO coupling is described by the following coupled mode equations [18

18. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, USA, 2007).

]:
dA01dz=iκpA11e2iδpz,dA11dz=iκp*A01e2iδpz+iκcA03e2iδcz,dA03dz=iκc*A11e2iδcz,
(1)
where z is the propagation distance along the fiber, A01, A11, and A03 are respectively the field amplitudes of the three modes, κp (κc) is the coupling coefficient between modes LP01 and LP11 (LP11 and LP03), and δp (δc) is the phase mismatch of the coupling δp = π(n01n11)/λ±πp (δc = π(n11n03)/λ ± πc), where Λp,c is the acoustic wavelength. The above equations are equivalent to the master equation for the lambda-type laser-driven atomic states with no dephasing or decaying terms for pure initial states [19

19. S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990). [CrossRef] [PubMed]

22

22. Although our scheme is closer to the ladder-type configuration considering the order of the propagation constants, we relate the current scheme to the lambda-type configuration to avoid unnecessary confusion. Whereas the dark state in a ladder-type atomic configuration is not strictly stable, our implementation does not contain decaying processes and therefore has a steady dark state leading to an efficient induced transparency.

]. Temporal evolution of the atomic state is replaced by spatial propagation of the light along the fiber. This equivalence is illustrated in Fig. 1(b). Each spatial mode corresponds to one energy level of the lambda-type configuration, and different phase velocities play a role of different energies between the states. AO coupling coefficients κ’s are equivalent to the Rabi frequencies by the external driving fields in the lambda scheme. As our system has no decaying terms, in a strict sense [23

23. P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011). [CrossRef] [PubMed]

] the configuration is in the ATS regime rather than in the EIT regime.

Fig. 1 Experimental scheme. (a) Structure of the acoustooptic three-mode coupler. (b) Equivalent lambda-type atomic state configuration. Labels in the parentheses denote corresponding parameters in our scheme. (c) Measured far field patterns of the spatial modes. ωp (ωc): the electromagnetic frequency of the probe (coupling) field, Ωpc): the Rabi frequency by the probe (coupling) field, fp (fc): the probe (coupling) acoustic frequency, Λpc): the probe (coupling) acoustic wavelength, κp (κc): the coupling coefficient by the probe (coupling) acoustic wave. FMF: few-mode fiber, SMF: single-mode fiber, MS: mode stripper, PZT: piezoelectric transducer.

Figure 1(c) shows the far field patterns of the spatial modes measured with cleaving the end part of the unjacketed AO interaction region. To generate the LP11 mode and the LP03 mode from the initial LP01 mode, acoustic amplitudes are set as κp = κ0, κc = 0 and κpκc2κ0, respectively, where κ0 = π/(2L) with L being the AO interaction length. Here two identical coupling efficiencies enable complete transfer to the LP03 mode. This can also be interpreted as an analogy to the spin-1 rotation of a qutrit [24

24. M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. D. O’Connel, D. Sank, H. Wang, J. Wenner, A. N. Cleland, M. R. Geller, and J. M. Martinis, “Emulation of a quantum spin with a superconducting phase qubit,” Science 325, 722–725 (2009). [CrossRef] [PubMed]

].

3. Experimental results and discussions

For characterization of the induced transparency, the LP01 mode enters the FMF from a lead single-mode fiber, and, after the AO interaction region, a mode stripper (MS) that is a tightly bound fiber section removes the more weakly guided LP11 mode while preserving the LP01 mode. The efficiency of the mode removal is ≥ 99%. The LP03 mode is removed by the fiber jacket just after the AO interaction. The AO interaction length L is 50 cm. The probe acoustic frequency fp for the LP01-LP11 conversion is 3.733 MHz with the corresponding acoustic wavelength Λp of 436.3 μm. The conversion efficiency is set as 100% by adjusting the coupling coefficient κc = π/(2L). The FMF has been designed to match the group velocities of the LP01 mode and the LP11 mode around the wavelength of 1580 nm [15

15. H. S. Park, K. Y. Song, S. H. Yun, and B. Y. Kim, “All-fiber wavelength-tunable acoustooptic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20, 1864–1868 (2002). [CrossRef]

]. Therefore the phase matching for the LP01-LP11 conversion is preserved in the first order of the wavelength difference, and the transmission spectrum shows a broad-bandwidth notch as shown in Fig. 2(a).

Fig. 2 Transmission spectra of the LP01 mode: (a) with only the probe acoustic wave that makes 100% coupling between the LP01 mode and the LP01 mode (κp = κ0 = 2π/L). (b) with the coupling wave additionally applied between the LP11 mode and the LP03 mode (κc ≅ 3κ0).

The coupling acoustic frequency fc (wavelength Λc) for the LP11-LP03 conversion is 2.883 MHz (505.0 μm). The transmission spectrum while applying the coupling acoustic wave with the coupling coefficient κc = 3κ0 is shown in Fig. 2(b). The transparency induced by the LP11-LP03 coupling shows a narrow half-maximum bandwidth (2 nm) due to a non-zero group index difference between the LP11 and LP03 modes, which is estimated to be 0.005. The small side lobes of the transmission peak are attributed to the nonuniformity of the fiber geometry along the interaction length.

The magnitude of the peak transmission is measured while varying the two coupling coefficients as shown in Figs. 3(a) and 3(b). The transmission due only to the LP01-LP11 probe field is shown in Fig. 3(a). Maximum mode conversion occurs at the applied voltage of 4 Vpp with reaching the minimum transmission of 0.9%, and the higher voltage range shows the over-coupling behavior [25

25. The retained maximum transmission (83%) and the voltage (9.5 Vpp) of the next minimum transmission, however, deviate from 100% and 2 × 4 Vpp, respectively. These discrepancies arise mainly from an off-resonant coupling due to non-uniformity of the fibre and also from the saturation of the acoustic transducer efficiency.

]. The magnitude of the induced transparency by the coupling field is shown in Fig. 3(b) with the theoretical fit based on the solution of Eq. (1) expressed as
T=|κc|2+|κp|2cos(|κp|2+|κc|2z)|κp|2+|κc|2.
(2)
A constant 0.814 is multiplied to Eq. (2) as an attenuation factor, and the fitted voltage for κc = κ0 is 4.81 V.

Fig. 3 Transmission of the LP01 mode at the center wavelength: (a) when only the probe acoustic wave is applied, and (b) when the coupling acoustic wave is applied with the probe amplitude fixed at the voltage of 4 Vpp. The solid line is the fitting result based on Eq. (2).

To more clearly reveal the coherent nature of the induced transparency, the transparency is undone by detuning the probe field. In a dressed state picture, the coupling field in Fig. 1(b) converts the state |3〉 into two superposed states whose energy levels are higher or lower than that of |3〉 by the Rabi frequency Ω, respectively, between |2〉 and |3〉. Therefore detuning the probe frequency by ±Ω retains the coherent absorption from |1〉 [3

3. C. Ciret, M. Alonzo, V. Coda, A. A. Rangelov, and G. Montemezzani, “Analog to electromagnetically induced transparency and Autler-Townes effect demonstrated with photoinduced coupled waveguides,” Phys. Rev. A 88, 013840 (2013). [CrossRef]

, 26

26. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955). [CrossRef]

]. The current system realizes this Autler-Townes effect by shifting the acoustic propagation constant 2πp by κc. Transmission of the LP01 mode while tuning the acoustic frequency is shown in Fig. 4(a). κc is fixed as in Fig. 2(b) (κc ≅ 3κ0). Two notches appear on both sides of the central transmission peak with the separation 2Δfp = 8 kHz.

Fig. 4 Induced absorption of the LP01 mode with the probe frequency fp detuned by Δfp: (a) transmission at the center wavelength, (b) transmission spectrum for Δfp = +4 kHz, and (c) transmission spectrum for Δfp = −4 kHz. Dashed lines denote the spectra with the coupling acoustic wave turned off.

The presented scheme can be extended to more than three modes. Generally an LPlm mode can be coupled to an LP(l−1)m′ mode or an LP(l+1)m′ mode (m, m′ = 1, 2, 3,···) considering the symmetry of the mode profiles and the acoustic perturbation to the local refractive index [17

17. T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996). [CrossRef]

]. Coupling between two core modes is generally more efficient than between a core mode and a cladding mode because of a greater mode overlap. Therefore a fiber that guides a greater number of core modes will be useful for realizing a more complex level configuration. Moreover, a lower-NA fiber is generally desirable because the required acoustic frequencies are lower, and accordingly the acoustic amplitudes are higher for a fixed input power of the acoustic transducer.

4. Conclusions

In conclusion, AO three-mode coupling in an optical fiber has been successfully demonstrated. AO conversion from the fundamental LP01 mode to the LP03 mode has been demonstrated for the first time to our knowledge. As an analogy to EIT in a lambda-type atom, transmission of the LP01 mode has been induced by the coupling between the LP11 mode and the LP03 mode. This three-level coupling can also be conceptually compared to the interaction-free measurement [28

28. P. Kwiat, H. Weinfurter, T. Herzog, and A. Zeilinger, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995). [CrossRef] [PubMed]

], whose repeated interrogation of interferometers is replaced by continuous coherent coupling between the copropagating modes. The presented scheme can be extended to visualize the coherent nature of a multi-level atomic structure, and inspire the development of novel devices that perform unique functions for multiplexing and demultiplexing the spatial modes in future communication systems.

Acknowledgments

This work has been supported by the KRISS project ‘Convergent Science and Technology for Measurements at the Nanoscale.’ The authors thank K. J. Park and Prof. B. Y. Kim in KAIST for help with the experimental setup.

References and links

1.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009). [CrossRef]

2.

D. Dragoman and M. Dragoman, Quantum-Classical Analogies(Springer, Berlin, 2004). [CrossRef]

3.

C. Ciret, M. Alonzo, V. Coda, A. A. Rangelov, and G. Montemezzani, “Analog to electromagnetically induced transparency and Autler-Townes effect demonstrated with photoinduced coupled waveguides,” Phys. Rev. A 88, 013840 (2013). [CrossRef]

4.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71, 043804 (2005). [CrossRef]

5.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006). [CrossRef] [PubMed]

6.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004). [CrossRef] [PubMed]

7.

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626–628 (2004). [CrossRef] [PubMed]

8.

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006). [CrossRef]

9.

S.-Y. Tseng and M.-C. Wu, “Mode conversion/splitting by optical analogy of multistate stimulated Raman adiabatic passage in multimode waveguides,” J. Lightwave Technol. 28, 3529–3534 (2010).

10.

X. Xiong, C.-L. Zou, X.-F. Ren, and G.-C. Guo, “Integrated polarization rotator/converter by stimulated Raman adiabatic passage,” Opt. Express 21, 17097–17107 (2013). [CrossRef] [PubMed]

11.

H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev., doi: [CrossRef] (2013).

12.

K. T. McCusker, Y.-P. Huang, A. S. Kowligy, and P. Kumar, “Experimental demonstration of interaction-free all-optical switching via the quantum Zeno effect,” Phys. Rev. Lett. 110, 240403 (2013). [CrossRef]

13.

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

14.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013). [CrossRef] [PubMed]

15.

H. S. Park, K. Y. Song, S. H. Yun, and B. Y. Kim, “All-fiber wavelength-tunable acoustooptic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20, 1864–1868 (2002). [CrossRef]

16.

The indices i and j of a linearly polarized LPij mode denote the number of asymmetry axes and the number of lobes along the radius, respectively, of the transverse field distribution.

17.

T. A. Birks, P. S. J. Russell, and D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996). [CrossRef]

18.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, USA, 2007).

19.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990). [CrossRef] [PubMed]

20.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]

21.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005). [CrossRef]

22.

Although our scheme is closer to the ladder-type configuration considering the order of the propagation constants, we relate the current scheme to the lambda-type configuration to avoid unnecessary confusion. Whereas the dark state in a ladder-type atomic configuration is not strictly stable, our implementation does not contain decaying processes and therefore has a steady dark state leading to an efficient induced transparency.

23.

P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011). [CrossRef] [PubMed]

24.

M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. D. O’Connel, D. Sank, H. Wang, J. Wenner, A. N. Cleland, M. R. Geller, and J. M. Martinis, “Emulation of a quantum spin with a superconducting phase qubit,” Science 325, 722–725 (2009). [CrossRef] [PubMed]

25.

The retained maximum transmission (83%) and the voltage (9.5 Vpp) of the next minimum transmission, however, deviate from 100% and 2 × 4 Vpp, respectively. These discrepancies arise mainly from an off-resonant coupling due to non-uniformity of the fibre and also from the saturation of the acoustic transducer efficiency.

26.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955). [CrossRef]

27.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, “Propagation and optical interaction of guided acoustic waves in two-mode optical fibers,” J. Lightwave Technol. 6, 428–436 (1998). [CrossRef]

28.

P. Kwiat, H. Weinfurter, T. Herzog, and A. Zeilinger, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995). [CrossRef] [PubMed]

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(230.1040) Optical devices : Acousto-optical devices
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Fiber Optics

History
Original Manuscript: December 6, 2013
Revised Manuscript: January 10, 2014
Manuscript Accepted: January 12, 2014
Published: January 23, 2014

Citation
Hee Su Park and Kwang Yong Song, "Acousto-optic resonant coupling of three spatial modes in an optical fiber," Opt. Express 22, 1990-1996 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1990


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References

  1. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009). [CrossRef]
  2. D. Dragoman, M. Dragoman, Quantum-Classical Analogies(Springer, Berlin, 2004). [CrossRef]
  3. C. Ciret, M. Alonzo, V. Coda, A. A. Rangelov, G. Montemezzani, “Analog to electromagnetically induced transparency and Autler-Townes effect demonstrated with photoinduced coupled waveguides,” Phys. Rev. A 88, 013840 (2013). [CrossRef]
  4. A. Naweed, G. Farca, S. I. Shopova, A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71, 043804 (2005). [CrossRef]
  5. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006). [CrossRef] [PubMed]
  6. M. F. Yanik, W. Suh, Z. Wang, S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004). [CrossRef] [PubMed]
  7. L. Maleki, A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626–628 (2004). [CrossRef] [PubMed]
  8. E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006). [CrossRef]
  9. S.-Y. Tseng, M.-C. Wu, “Mode conversion/splitting by optical analogy of multistate stimulated Raman adiabatic passage in multimode waveguides,” J. Lightwave Technol. 28, 3529–3534 (2010).
  10. X. Xiong, C.-L. Zou, X.-F. Ren, G.-C. Guo, “Integrated polarization rotator/converter by stimulated Raman adiabatic passage,” Opt. Express 21, 17097–17107 (2013). [CrossRef] [PubMed]
  11. H. Suchowski, G. Porat, A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev., doi: (2013). [CrossRef]
  12. K. T. McCusker, Y.-P. Huang, A. S. Kowligy, P. Kumar, “Experimental demonstration of interaction-free all-optical switching via the quantum Zeno effect,” Phys. Rev. Lett. 110, 240403 (2013). [CrossRef]
  13. D. J. Richardson, J. M. Fini, L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013). [CrossRef]
  14. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013). [CrossRef] [PubMed]
  15. H. S. Park, K. Y. Song, S. H. Yun, B. Y. Kim, “All-fiber wavelength-tunable acoustooptic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20, 1864–1868 (2002). [CrossRef]
  16. The indices i and j of a linearly polarized LPij mode denote the number of asymmetry axes and the number of lobes along the radius, respectively, of the transverse field distribution.
  17. T. A. Birks, P. S. J. Russell, D. O. Culverhouse, “The acousto-optic effect in single-mode fiber tapers and couplers,” J. Lightwave Technol. 14, 2519–2529 (1996). [CrossRef]
  18. A. Yariv, P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, USA, 2007).
  19. S. E. Harris, J. E. Field, A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990). [CrossRef] [PubMed]
  20. K.-J. Boller, A. Imamoğlu, S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]
  21. M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005). [CrossRef]
  22. Although our scheme is closer to the ladder-type configuration considering the order of the propagation constants, we relate the current scheme to the lambda-type configuration to avoid unnecessary confusion. Whereas the dark state in a ladder-type atomic configuration is not strictly stable, our implementation does not contain decaying processes and therefore has a steady dark state leading to an efficient induced transparency.
  23. P. M. Anisimov, J. P. Dowling, B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011). [CrossRef] [PubMed]
  24. M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. D. O’Connel, D. Sank, H. Wang, J. Wenner, A. N. Cleland, M. R. Geller, J. M. Martinis, “Emulation of a quantum spin with a superconducting phase qubit,” Science 325, 722–725 (2009). [CrossRef] [PubMed]
  25. The retained maximum transmission (83%) and the voltage (9.5 Vpp) of the next minimum transmission, however, deviate from 100% and 2 × 4 Vpp, respectively. These discrepancies arise mainly from an off-resonant coupling due to non-uniformity of the fibre and also from the saturation of the acoustic transducer efficiency.
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