OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 24085–24092
« Show journal navigation

Mode conversion using optical analogy of shortcut to adiabatic passage in engineered multimode waveguides

Tzung-Yi Lin, Fu-Chen Hsiao, Yao-Wun Jhang, Chieh Hu, and Shuo-Yen Tseng  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 24085-24092 (2012)
http://dx.doi.org/10.1364/OE.20.024085


View Full Text Article

Acrobat PDF (2332 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A shortcut to adiabatic mode conversion in multimode waveguides using optical analogy of stimulated Raman adiabatic passage is investigated. The design of mode converters using the shortcut scheme is discussed. Computer-generated planar holograms are used to mimic the shaped pulses used to speed up adiabatic passage in quantum systems based on the transitionless quantum driving algorithm. The mode coupling properties are analyzed using the coupled mode theory and beam propagation simulations. We show reduced device length using the shortcut scheme as compared to the common adiabatic scheme. Modal evolution in the shortened device indeed follows the adiabatic eigenmode exactly amid the violation of adiabatic criterion.

© 2012 OSA

1. Introduction

Mode-division multiplexing (MDM) is a promising technique where multiple optical modes are used as independent data channels to transmit optical data [1

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

]. Several basic building blocks for MDM, such as the mode add/drop multiplexer [2

2. M. Greenberg and M. Orenstein, “Multimode add-drop multiplexing by adiabatic linearly tapered coupling,” Opt. Express 13, 9381–9387 (2005). [CrossRef] [PubMed]

] and the mode generator [3

3. J. B. Park, D.-M. Yeo, and S.-Y. Shin, “Variable optical mode generator in a multimode waveguide,” IEEE Photon. Technol. Lett. 18, 2084–2086 (2006). [CrossRef]

], have been proposed. Mode converter is another important building block for MDM systems. Two major routes to realize mode conversion in integrated optics devices are resonant coupling and adiabatic coupling. By designing the coupling region of a resonant mode converter to be half the beat length, light is converted from one mode to the other [4

4. T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14, 1288–1290 (2002). [CrossRef]

]. While resonant mode converter can be made very short; the difficulty is to determine the exact beat length due to device parameter variations from fabrication. Recently, due to the analogies between quantum mechanics and wave optics, light propagation in waveguide structures has been exploited as a tool to visualize or investigate many adiabatic coherent quantum phenomena which may otherwise be difficult to observe. In particular, coupled waveguide system has proven to be a useful tool for such realizations. Examples include optical analogy of stimulated Raman adiabatic passage (STIRAP) [5

5. S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E 73, 026607 (2006). [CrossRef]

, 6

6. S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76, 201101(R) (2007). [CrossRef]

], optical analogies of multi-level STIRAP [7

7. G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008). [CrossRef]

], and etc [8

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

]. Device applications include broadband beam splitter [9

9. F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” Appl. Phys. Lett. 95, 261102 (2009). [CrossRef]

], directional coupler [10

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

], and others. In these devices, light passage among coupled single mode waveguides resembles population transfer in quantum systems, and the waveguides are curved such that the coupling rates resemble that of the coupling pulses in STIRAP. However, due to restrictions of the planar lightwave circuit (PLC) technology, only adjacent waveguides can be efficiently coupled, and it is difficult to implement more elaborate coupling schemes with PLC waveguide arrays. Other interesting variations of STIRAP, such as STIRAP via a continuum [11

11. E. Paspalakis, M. Protopapas, and P. L. Knight, “Time-dependent pulse and frequency effects in population trapping via the continuum,” J Phys. B 31, 775–794 (1998). [CrossRef]

, 12

12. R. G. Unanyan, N. V. Vitanov, B. W. Shore, and K. Bergmann, “Coherent properties of a tripod system coupled via a continuum,” Phys. Rev. A 61, 043408 (2000). [CrossRef]

] and tripod STIRAP [13

13. H. Theuer, R. G. Unanyan, C. Habscheid, K. Klein, and K. Bergmann, “Novel laser controlled variable matter wave beamsplitter,” Opt. Express 4, 77–83 (1999). [CrossRef] [PubMed]

15

15. F. Vewinger, M. Heinz, R. Garcia Fernandez, N. V. Vitanov, and K. Bergmann, “Creation and measurement of a coherent superposition of quantum states,” Phys. Rev. Lett. 91, 213001 (2003). [CrossRef] [PubMed]

], involve more complex coupling schemes; to realize these analogies with coupling schemes other than nearest-neighbor coupling, single mode waveguides in 3D arrangement is needed [16

16. A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85, 055803 (2012). [CrossRef]

, 17

17. F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009). [CrossRef] [PubMed]

]. We have previously proposed adiabatic mode conversion/splitting devices using computer-generated planar holograms (CGPHs) in multimode waveguides based on STIRAP [18

18. S.-Y. Tseng and M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” IEEE Photon. Technol. Lett. 22, 1211–1213 (2010). [CrossRef]

] and multistate STIRAP [19

19. 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).

] ; in which multiplexed long-period gratings with coupling coefficient variations along the propagation direction are used to mimic the delayed laser pulses in STIRAP, and the light passage among the guided modes resembles population transfer in quantum systems. These devices are based on the PLC technology, but the multimode nature of the waveguides makes it possible to implement arbitrary coupling scheme among the guided modes.

In atomic and molecular physics, STIRAP refers to the adiabatic transfer of population between two energy levels in a three-level system via two delayed optical pulses [20

20. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998). [CrossRef]

], and the system is characterized by its robustness to pulse parameter variations. This is of particular importance to waveguide devices based on optical analogies of STIRAP. Such devices have good fabrication tolerance because they do not require a precise definition of coupling length and coupling strength due to the adiabatic nature. On the other hand, they need to be sufficiently long to satisfy the adiabatic condition. Otherwise, unwanted coupling among the adiabatic modes would deteriorate the device efficiency. However, long device length reduces device density and induces more transmission losses. It is desirable to combine the compactness of resonant devices and the robustness of adiabatic devices.

Efforts have been made to optimize the pulses used in STIRAP to minimize nonadiabatic coupling in the process and to speed up the passage [21

21. G. S. Vasilev, A. Kuhn, and N. V. Vitanov, “Optimum pulse shapes for stimulated Raman adiabatic passage,” Phys. Rev. A 80, 013417 (2009). [CrossRef]

, 22

22. G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, “Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses,” Phys. Rev. A 80, 043408 (2009). [CrossRef]

]. One interesting approach is the shortcut to adiabatic passage (SHAPE) [23

23. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010). [CrossRef] [PubMed]

] using the transitionless quantum driving algorithm [24

24. M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009). [CrossRef]

]. For a system with a time-dependent Hamiltonian H0(t) initially in an eigenstate |Ψn(0)〉, the adiabatic theorem states that it will follow the same instantaneous eigenstate |Ψn(t)〉 closely, as long as the evolution of the Hamiltonian is slow enough [25

25. M. H. S. Amin, “Consistency of the adiabatic theorem,” Phys. Rev. Lett. 102, 220401 (2009). [CrossRef] [PubMed]

]. SHAPE is based on the reverse engineering approach that one can always find Hamiltonians H(t), associated with any chosen H0(t), that drive the instantaneous eigenstates |Ψn(t)〉 exactly. The Hamlitonian H(t) can be found as [23

23. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010). [CrossRef] [PubMed]

, 24

24. M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009). [CrossRef]

]
H(t)=H0(t)+H1(t),
(1)
where
H1(t)=ih¯n|tΨn(t)Ψn(t)|.
(2)
Of course, prior knowledge of the instantaneous eigenstates is required to implement the SHAPE algorithm. Due to the potential complexity of H(t), elaborate coupling schemes might be required to realize optical analogies of such systems. In this paper, we propose a optical realization of the SHAPE scheme using CGPH in multimode waveguides. The designed mode converter could find applications in MDM systems.

2. Shortcut to adiabatic passage in multimode waveguides

In a step-index multimode waveguide supporting N ≥ 3 forward-propagating modes, we consider three distinct modes |Ψ1〉, |Ψ2〉, and |Ψ3〉, coupled by a CGPH. The CGPHs are multiplexed long-period gratings which couple the guided modes depending on the grating shape and periodicity [26

26. S.-Y. Tseng, S. K. Choi, and B. Kippelen, “Variable-ratio power splitters using computer-generated planar holograms on multimode interference couplers,” Opt. Lett. 34, 512–514 (2009). [CrossRef] [PubMed]

]. We can design the CGPH to mimic the STIRAP process, with modes |Ψ1〉 and |Ψ2〉 and modes |Ψ2〉 and |Ψ3〉 coupled by gratings Λ12 and Λ23 with coupling coefficients κ12 and κ23. Figure 1 shows the level scheme of STIRAP, the schematic of a CGPH loaded multimode waveguide, and amplitude profiles of the three guided modes. When only Λ12 and Λ23 are present, the evolution of mode amplitudes Ai(i = 1, 2, 3) obey the coupled mode equations
iddz[A1A2A3]=[0κ12(z)0κ21(z)0κ23(z)0κ32(z)0][A1A2A3]=H0(z)[A1A2A3].
(3)
Replacing the spatial variation z with the temporal variation t, (3) is used to describe the probability amplitudes of a three-level atomic system driven by two laser pulses shown in Fig. 1(a) using the Schrödinger equation (h̄ = 1) under the rotating-wave approximation, in which A represents the probability amplitudes of the states being populated, κmn is the Rabi frequency of the pulse coupling states |Ψm〉 and |Ψn〉. Solving for the eigenmodes |ΨD〉, |Ψ+〉, and |Ψ〉, we can find a dark eigenmode as
|ΨD=1κ122+κ232(κ23|Ψ1κ12|Ψ3).
(4)
When the two spatially variable coupling coefficients κ12(z) and κ23(z) are applied in a counterintuitive scheme to mimic the laser pulses in STIRAP, |ΨD〉 can be used to convert |Ψ1〉 to |Ψ3〉. If the device length is not sufficiently long, unwanted couplings happen among |ΨD〉, |Ψ+〉, and |Ψ〉, resulting in low conversion efficiency.

Fig. 1 (a) Level scheme of STIRAP (b) Schematic of a CGPH loaded multimode waveguide composed of three multiplexed gratings (c) Amplitude profiles of the three guided modes which correspond to levels 1, 2, and 3 in the level scheme (a).

With knowledge of the eigenmodes, we can use the SHAPE scheme to obtain a new coupling matrix, such that the system will follow |ΨD〉 exactly. Replace t with z in (2), let h̄ = 1, and substitute |ΨD〉, |Ψ+〉, and |Ψ〉 in to (2), we obtain
H1(z)=[00iκ13(z)000iκ13(z)00],
(5)
with
κ13(z)=κ˙12(z)κ23(z)κ˙23(z)κ12(z)κ122(z)+κ232(z).
(6)
The shortcut here is thus to add a grating Λ13 coupling |Ψ1〉 and |Ψ3〉 to the original CGPH implementing the STIRAP scheme H0(z) in (3) as shown in Fig. 1(b). We also note that grating Λ13 is 90° out of phase with gratings Λ12 and Λ23 due to the presence of i in (5). To implement H(z) = H0(z) + H1(z) in a coupled PLC waveguide system would be difficult, because the waveguides representing |Ψ1〉 and |Ψ3〉 are not adjacent to each other. In a multimode waveguide, by designing a CGPH to implement H(z) with the addition of a grating Λ13 coupling modes |Ψ1〉 and |Ψ3〉 using the coupling coefficient in (6), we can realize optical analogy of the SHAPE scheme as shown in Fig 1(b). In the following, we use a numerical example to demonstrate SHAPE in an engineered multimode waveguide and compare it with STIRAP in the same system.

3. Numerical results

We consider a 3 μm wide, five-moded polymer waveguide similar to the one in [19

19. 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).

] for mode conversion from |Ψ1〉 to |Ψ3〉 via |Ψ2〉. The CGPHs used to implement the SHAPE and STIRAP schemes are designed at the zero-detuning wavelength λ0=1.55 μm and the TE polarization. The maximum effective index modulation is assumed to be Δn = 0.003. Figure 2 shows Gaussian shaped coupling coefficients κ12(z) = k12 exp[−(z0/z − 2)2/c2] and κ23(z) = k23 exp[−(z + z0/2)2/c2], with k12 and k23 directly proportional to Δn, chosen arbitrarily to mimic the counterintuitive optical pulses used in STIRAP. The parameter c is chosen to be the same as the delay z0 to minimize nonadibatic coupling [20

20. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998). [CrossRef]

], and we define it to be a function of the total device length L (mm) as c = z0 = 3L/20. To implement SHAPE, the coupling coefficient κ13(z) corresponding to the additional Λ13 is calculated using (6) and also shown in Fig. 2.

Fig. 2 Evolution of the coupling coefficients for STIRAP (κ12, κ23) and SHAPE (κ13) schemes.

Fig. 3 Calculated CGPH pattern to implement the SHAPE scheme for mode conversion. Dashed lines indicate the waveguide core.
Fig. 4 BPM simulation of light propagation in a 5 mm SHAPE mode converter using CGPH. Dashed lines indicate the waveguide core.
Fig. 5 BPM simulation of light propagation in a 5 mm STIRAP mode converter using CGPH. Dashed lines indicate the waveguide core.
Fig. 6 Modal power evolution in a 5 mm mode converter using (a) SHAPE and (b) STIRAP scheme.

Fig. 7 Normalized modal power at the mode converter output for different device lengths. |Ψ1〉 is used as the input. (a) STIRAP (b) SHAPE.

4. Conclusion

Acknowledgment

This work was supported in part by the National Science Council of Taiwan under contracts NSC 100-2221-E-006-176-MY3 and NSC 100-2622-E-006-013-CC2 and by the Industrial Technology Research Institute.

References and links

1.

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

2.

M. Greenberg and M. Orenstein, “Multimode add-drop multiplexing by adiabatic linearly tapered coupling,” Opt. Express 13, 9381–9387 (2005). [CrossRef] [PubMed]

3.

J. B. Park, D.-M. Yeo, and S.-Y. Shin, “Variable optical mode generator in a multimode waveguide,” IEEE Photon. Technol. Lett. 18, 2084–2086 (2006). [CrossRef]

4.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14, 1288–1290 (2002). [CrossRef]

5.

S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E 73, 026607 (2006). [CrossRef]

6.

S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76, 201101(R) (2007). [CrossRef]

7.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008). [CrossRef]

8.

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

9.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” Appl. Phys. Lett. 95, 261102 (2009). [CrossRef]

10.

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

11.

E. Paspalakis, M. Protopapas, and P. L. Knight, “Time-dependent pulse and frequency effects in population trapping via the continuum,” J Phys. B 31, 775–794 (1998). [CrossRef]

12.

R. G. Unanyan, N. V. Vitanov, B. W. Shore, and K. Bergmann, “Coherent properties of a tripod system coupled via a continuum,” Phys. Rev. A 61, 043408 (2000). [CrossRef]

13.

H. Theuer, R. G. Unanyan, C. Habscheid, K. Klein, and K. Bergmann, “Novel laser controlled variable matter wave beamsplitter,” Opt. Express 4, 77–83 (1999). [CrossRef] [PubMed]

14.

R. G. Unanyan, B. W. Shore, and K. Bergmann, “Preparation of an N-component maximal coherent superposition state using the stimulated Raman adiabatic passage method,” Phys. Rev. A 63, 043401 (2001). [CrossRef]

15.

F. Vewinger, M. Heinz, R. Garcia Fernandez, N. V. Vitanov, and K. Bergmann, “Creation and measurement of a coherent superposition of quantum states,” Phys. Rev. Lett. 91, 213001 (2003). [CrossRef] [PubMed]

16.

A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A 85, 055803 (2012). [CrossRef]

17.

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009). [CrossRef] [PubMed]

18.

S.-Y. Tseng and M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” IEEE Photon. Technol. Lett. 22, 1211–1213 (2010). [CrossRef]

19.

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).

20.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998). [CrossRef]

21.

G. S. Vasilev, A. Kuhn, and N. V. Vitanov, “Optimum pulse shapes for stimulated Raman adiabatic passage,” Phys. Rev. A 80, 013417 (2009). [CrossRef]

22.

G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, “Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses,” Phys. Rev. A 80, 043408 (2009). [CrossRef]

23.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett. 105, 123003 (2010). [CrossRef] [PubMed]

24.

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009). [CrossRef]

25.

M. H. S. Amin, “Consistency of the adiabatic theorem,” Phys. Rev. Lett. 102, 220401 (2009). [CrossRef] [PubMed]

26.

S.-Y. Tseng, S. K. Choi, and B. Kippelen, “Variable-ratio power splitters using computer-generated planar holograms on multimode interference couplers,” Opt. Lett. 34, 512–514 (2009). [CrossRef] [PubMed]

OCIS Codes
(000.1600) General : Classical and quantum physics
(090.1760) Holography : Computer holography
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices

ToC Category:
Integrated Optics

History
Original Manuscript: July 23, 2012
Revised Manuscript: September 26, 2012
Manuscript Accepted: September 27, 2012
Published: October 5, 2012

Citation
Tzung-Yi Lin, Fu-Chen Hsiao, Yao-Wun Jhang, Chieh Hu, and Shuo-Yen Tseng, "Mode conversion using optical analogy of shortcut to adiabatic passage in engineered multimode waveguides," Opt. Express 20, 24085-24092 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-24085


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. Berdague and P. Facq, “Mode division multiplexing in optical fibers,” Appl. Opt.21, 1950–1955 (1982). [CrossRef] [PubMed]
  2. M. Greenberg and M. Orenstein, “Multimode add-drop multiplexing by adiabatic linearly tapered coupling,” Opt. Express13, 9381–9387 (2005). [CrossRef] [PubMed]
  3. J. B. Park, D.-M. Yeo, and S.-Y. Shin, “Variable optical mode generator in a multimode waveguide,” IEEE Photon. Technol. Lett.18, 2084–2086 (2006). [CrossRef]
  4. T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett.14, 1288–1290 (2002). [CrossRef]
  5. S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E73, 026607 (2006). [CrossRef]
  6. S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B76, 201101(R) (2007). [CrossRef]
  7. G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett.92, 011106 (2008). [CrossRef]
  8. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev.3, 243–261 (2009). [CrossRef]
  9. F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” Appl. Phys. Lett.95, 261102 (2009). [CrossRef]
  10. E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun.258, 30–34 (2006). [CrossRef]
  11. E. Paspalakis, M. Protopapas, and P. L. Knight, “Time-dependent pulse and frequency effects in population trapping via the continuum,” J Phys. B31, 775–794 (1998). [CrossRef]
  12. R. G. Unanyan, N. V. Vitanov, B. W. Shore, and K. Bergmann, “Coherent properties of a tripod system coupled via a continuum,” Phys. Rev. A61, 043408 (2000). [CrossRef]
  13. H. Theuer, R. G. Unanyan, C. Habscheid, K. Klein, and K. Bergmann, “Novel laser controlled variable matter wave beamsplitter,” Opt. Express4, 77–83 (1999). [CrossRef] [PubMed]
  14. R. G. Unanyan, B. W. Shore, and K. Bergmann, “Preparation of an N-component maximal coherent superposition state using the stimulated Raman adiabatic passage method,” Phys. Rev. A63, 043401 (2001). [CrossRef]
  15. F. Vewinger, M. Heinz, R. Garcia Fernandez, N. V. Vitanov, and K. Bergmann, “Creation and measurement of a coherent superposition of quantum states,” Phys. Rev. Lett.91, 213001 (2003). [CrossRef] [PubMed]
  16. A. A. Rangelov and N. V. Vitanov, “Achromatic multiple beam splitting by adiabatic passage in optical waveguides,” Phys. Rev. A85, 055803 (2012). [CrossRef]
  17. F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett.34, 2405–2407 (2009). [CrossRef] [PubMed]
  18. S.-Y. Tseng and M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” IEEE Photon. Technol. Lett.22, 1211–1213 (2010). [CrossRef]
  19. 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).
  20. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys.70, 1003–1025 (1998). [CrossRef]
  21. G. S. Vasilev, A. Kuhn, and N. V. Vitanov, “Optimum pulse shapes for stimulated Raman adiabatic passage,” Phys. Rev. A80, 013417 (2009). [CrossRef]
  22. G. Dridi, S. Guérin, V. Hakobyan, H. R. Jauslin, and E. Eleuch, “Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses,” Phys. Rev. A80, 043408 (2009). [CrossRef]
  23. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010). [CrossRef] [PubMed]
  24. M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor.42, 365303 (2009). [CrossRef]
  25. M. H. S. Amin, “Consistency of the adiabatic theorem,” Phys. Rev. Lett.102, 220401 (2009). [CrossRef] [PubMed]
  26. S.-Y. Tseng, S. K. Choi, and B. Kippelen, “Variable-ratio power splitters using computer-generated planar holograms on multimode interference couplers,” Opt. Lett.34, 512–514 (2009). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited