## All-optical microdisk switch using EIT |

Optics Express, Vol. 21, Issue 5, pp. 6169-6179 (2013)

http://dx.doi.org/10.1364/OE.21.006169

Acrobat PDF (1076 KB)

### Abstract

We present theoretical results of a low-loss all-optical switch based on electromagnetically induced transparency and the quantum Zeno effect in a microdisk resonator. We show that a control beam can modify the atomic absorption of the evanescent field which suppresses the cavity field buildup and alters the path of a weak signal beam. We predict more than 35 dB of switching contrast with less than 0.1 dB loss using just 2 *μ*W of control-beam power for signal beams with less than single photon intensities inside the cavity.

© 2013 OSA

## 1. Introduction

1. N. Kim, T. Austin, D. Baauw, T. Mudge, K. Flautner, J. Hu, M. Irwin, M. Kandemir, and V. Narayanan, “Leakage current: Moore’s law meets static power,” Computer **36**, 68 – 75 (2003) [CrossRef] .

2. A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science **308**, 672–674 (2005) [CrossRef] [PubMed] .

6. M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion coulomb crystals,” Nat. Photonics **5**, 633–636 (2011) [CrossRef] .

7. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**, 36–42 (1997) [CrossRef] .

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

9. J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. **32**, 1317–1319 (2007) [CrossRef] [PubMed] .

11. M. Fleischhauer, “Switching light by vacuum,” Science **333**, 1228–1229 (2011) [CrossRef] [PubMed] .

12. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. **86**, 783–786 (2001) [CrossRef] [PubMed] .

15. M. D. Lukin, “*Colloquium* : Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. **75**, 457–472 (2003) [CrossRef] .

16. B. Misra and E. Sudarshan, “The Zeno’s paradox in quantum theory,” J. of Math. Phys. **18**, 756 – 763 (1977) [CrossRef] .

17. B. C. Jacobs and J. D. Franson, “All-optical switching using the quantum zeno effect and two-photon absorption,” Phys. Rev. A **79**, 063830 (2009) [CrossRef] .

18. S. M. Hendrickson, C. N. Weiler, R. M. Camacho, P. T. Rakich, A. I. Young, M. J. Shaw, T. B. Pittman, J. D. Franson, and B. C. Jacobs, “All-optical-switching demonstration using two-photon absorption and the zeno effect,” Phys. Rev. A **87**, 023808 (2013) [CrossRef] .

19. Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. **36**, 1413–1415 (2011) [CrossRef] [PubMed] .

20. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse raman scattering in liquid-core optical fibers,” Opt. Lett. **37**, 942–944 (2012) [CrossRef] [PubMed] .

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

23. T. J. Kippenberg, S. M. Spillane, D. K. Armani, B. Min, L. Yang, and K. J. Vahala, *Fabrication, Coupling and Nonlinear Optics of Ultra-High-Q Microcavities* (World Scientific Publishing, 2004, vol. 5, Chap. 5, pp. 177–238) [CrossRef] .

*E*will be almost completely transferred to the drop-port as a result of destructive interference between the resonant build-up of the cavity field and the light in the input waveguide. Next, consider how this system would change with the addition of a strong loss mechanism in the cavity, such as shown in Fig. 1(a). The resonant field buildup of the signal beam will be suppressed which dramatically reduces the destructive interference in the input waveguide and results in nearly all of the incident light exiting the through-port.

_{in}17. B. C. Jacobs and J. D. Franson, “All-optical switching using the quantum zeno effect and two-photon absorption,” Phys. Rev. A **79**, 063830 (2009) [CrossRef] .

24. J. D. Franson, B. C. Jacobs, and T. B. Pittman, “Quantum computing using single photons and the zeno effect,” Phys. Rev. A **70**, 062302 (2004) [CrossRef] .

*S*

_{1/2}, 5

*P*

_{3/2}and 5

*D*

_{5/2}states of Rb. We take the signal beam to be resonant with the 5

*S*

_{1/2}→ 5

*P*

_{3/2}transition near 780 nm and the control beam to be resonant with the 5

*P*

_{3/2}→ 5

*D*

_{5/2}transition near 776 nm. When the 776 nm EIT control beam is present, a transmission window is created in the 780 nm single-photon absorption line. This allows the signal beam to build in the resonator and exit through the drop port, as shown schematically in Fig. 1(b).

## 2. Theoretical model

_{3}N

_{4}disk with a free spectral range equal to the 4 nm difference between the 5

*S*

_{1/2}→ 5

*P*

_{3/2}

*D*

_{2}line at 780 nm and the 5

*P*

_{3/2}→ 5

*D*

_{5/2}line at 776 nm, allowing for simultaneous resonance at 776 nm and 780 nm (for an example of a similar device operating at a higher wavelength see Ref. [18

18. S. M. Hendrickson, C. N. Weiler, R. M. Camacho, P. T. Rakich, A. I. Young, M. J. Shaw, T. B. Pittman, J. D. Franson, and B. C. Jacobs, “All-optical-switching demonstration using two-photon absorption and the zeno effect,” Phys. Rev. A **87**, 023808 (2013) [CrossRef] .

### 2.1. Atomic Model

*P*

_{3/2}level. In the steady-state approximation, the population of that level can be neglected, when no fields are near resonance with it, and replaced by just the decay rate from the excited state to the intermediate state. Therefore it is included in our atomic model only as a decay term. The Hamiltonian of this system is the standard three-level cascade model given by We denote all variables associated with the 776 nm control field and 780 nm signal field with the subscripts c and s respectively. The Rabi frequency is Ω = 2〈

*d⃗*·

*ε*̂〉

*ℰ*/

*h*̄, where

*d⃗*is the dipole moment,

*ℰ*is the slowly varying electric field amplitude,

*ε*̂ is the polarization vector, and Δ is the detuning of the field from its associated transition. The angular brackets denote an averaging over the random orientation of the dipole moment with respect to the electric field polarization that reduces the Rabi frequency due to random atomic orientations [25

25. D. A. Steck, “Rubidium 87 d line data,” http://steck.us/alkalidata/ (2009).

*is the homogeneous decay term associated with the*

_{mn}*m*→

*n*transition, and

*γ*is the transverse decay term associated with the off-diagonal elements. We take

_{mn}*γ*

_{12}= Γ

_{12}/2,

*γ*

_{13}= (Γ

_{13}+ Γ

_{23})/2, and

*γ*

_{23}= (Γ

_{12}+ Γ

_{13}+ Γ

_{23})/2. These off-diagonal decay rates assume that all decoherence is due to population decay, which is suitable for atomic vapors. The values were chosen to be physically consistent with a positive density matrix, which does not always hold for arbitrary decoherence terms [26

26. S. G. Schirmer and A. I. Solomon, “Constraints on relaxation rates for *n*-level quantum systems,” Phys. Rev. A **70**, 022107 (2004) [CrossRef] .

27. P. R. Berman and R. C. O’Connell, “Constraints on dephasing widths and shifts in three-level quantum systems,” Phys. Rev. A **71**, 022501 (2005) [CrossRef] .

_{23}and Γ

_{13}decay channels was set to 0.65 : 0.35 as given in Ref. [28

28. O. S. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am. **51**, 1058–1061 (1961) [CrossRef] .

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

29. R. G. Brewer and E. L. Hahn, “Coherent two-photon processes: Transient and steady-state cases,” Phys. Rev. A **11**, 1641–1649 (1975) [CrossRef] .

30. J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment,” Phys. Rev. A **51**, 576–584 (1995) [CrossRef] [PubMed] .

*=*

_{s,c}*ω*−

_{s,c}*ω*

_{12,23}±

*k*

_{v}*z*is the laser field detuning of the signal and control field respectively due to the thermal velocity of the atom,

*k*is the wave-vector due to the Doppler shift,

_{v}*z*is taken to be the dimension of propagation inside the resonator,

*σ*is the Doppler linewidth, given by the Maxwell-Boltzmann velocity distribution, and

_{D}*h*̄

*ω*

_{12,23}is the energy difference between the |1〉 → |2〉 and |2〉 → |3〉 transitions respectively. Because the signal and control fields are counter-propagating in the resonator, the signal and control experience opposite Doppler shifts as denoted by the opposite signs within the detuning coefficient.

### 2.2. Cavity – Waveguide Coupling Model

*Q*

_{0}=

*ω*

_{0}/

*κ*

_{0}and the external quality factor is

*Q*=

_{ext}*ω*

_{0}/(

*κ*+

_{e}*κ*

_{1}+

*κ*

_{2}). By controlling the atomic absorption rate

*κ*we can modify the external

_{e}*Q*of the atom-resonator system causing the coupling conditions to change, resulting in the ability to switch between the drop port and through port.

### 2.3. Cavity Field – Atomic Interaction Model

*κ*in the waveguide–resonator coupling model above. To give performance estimates for the switch, we calculate the average absorption coefficient of the signal beam in the resonator.

_{e}*α*̄ is given by where the integral is taken to extend over the volume external to the resonator, denoted by

*V*, and the weighting function scales with the signal beam intensity.

_{e}*V*, including the region interior to the resonator, as opposed to the integral in Eq. (10) which is only over the region exterior to the resonator. This accounts for the fact that the field inside the resonator does not interact with the Rubidium thus reducing the overall strength of the interaction. This weighting also accounts for the fact that the scattering cross section is larger near regions of high signal beam intensity than regions of low intensity. We assume that both beams are contained in the same cavity mode for this calculation.

_{t}*α*̄ to the external cavity loss rate

*κ*through the simple relation

_{e}*κ*=

_{e}*c*

*α*̄, where

*c*is the speed of light in the cavity. Thus, by changing the atomic absorption coefficient

*α*̄ through EIT, we can modify the total cavity Q, resulting in changing coupling conditions and switching.

## 3. Results

*κ*

_{1}and

*κ*

_{2}roughly two orders of magnitude larger than

*κ*

_{0}. The coupling rates were chosen to equalize the bandwidth on the through-port and drop-port. With this constraint, we estimate the on-resonant switching contrast to be 50 dB in the through-port and 25 dB in the drop-port, along with only 0.5 dB and 0.02 dB of loss in each respectively. We define the bandwidth as the point at which the switching contrast reaches 20 dB, on Figs. 5(a) and 5(b). This gives a bandwidth of approximately 516 MHz for each output port. These results are tabulated in Table 2.

## 4. Conclusions

## Acknowledgments

## References and links

1. | N. Kim, T. Austin, D. Baauw, T. Mudge, K. Flautner, J. Hu, M. Irwin, M. Kandemir, and V. Narayanan, “Leakage current: Moore’s law meets static power,” Computer |

2. | A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science |

3. | X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics |

4. | M. Waldow, T. Plötzing, M. Gottheil, M. Först, J. Bolten, T. Wahlbrink, and H. Kurz, “25ps all-optical switching in oxygen implanted silicon-on-insulator microring resonator,” Opt. Express |

5. | D. Miller, “Are optical transistors the logical next step?” Nat. Photonics |

6. | M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion coulomb crystals,” Nat. Photonics |

7. | S. E. Harris, “Electromagnetically induced transparency,” Phys. Today |

8. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. |

9. | J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett. |

10. | M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. |

11. | M. Fleischhauer, “Switching light by vacuum,” Science |

12. | D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. |

13. | A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. |

14. | A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A |

15. | M. D. Lukin, “ |

16. | B. Misra and E. Sudarshan, “The Zeno’s paradox in quantum theory,” J. of Math. Phys. |

17. | B. C. Jacobs and J. D. Franson, “All-optical switching using the quantum zeno effect and two-photon absorption,” Phys. Rev. A |

18. | S. M. Hendrickson, C. N. Weiler, R. M. Camacho, P. T. Rakich, A. I. Young, M. J. Shaw, T. B. Pittman, J. D. Franson, and B. C. Jacobs, “All-optical-switching demonstration using two-photon absorption and the zeno effect,” Phys. Rev. A |

19. | Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. |

20. | K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse raman scattering in liquid-core optical fibers,” Opt. Lett. |

21. | S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. |

22. | H. A. Haus, |

23. | T. J. Kippenberg, S. M. Spillane, D. K. Armani, B. Min, L. Yang, and K. J. Vahala, |

24. | J. D. Franson, B. C. Jacobs, and T. B. Pittman, “Quantum computing using single photons and the zeno effect,” Phys. Rev. A |

25. | D. A. Steck, “Rubidium 87 d line data,” http://steck.us/alkalidata/ (2009). |

26. | S. G. Schirmer and A. I. Solomon, “Constraints on relaxation rates for |

27. | P. R. Berman and R. C. O’Connell, “Constraints on dephasing widths and shifts in three-level quantum systems,” Phys. Rev. A |

28. | O. S. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am. |

29. | R. G. Brewer and E. L. Hahn, “Coherent two-photon processes: Transient and steady-state cases,” Phys. Rev. A |

30. | J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment,” Phys. Rev. A |

31. | L. Stern, B. Desiatov, I. Goykhman, and U. Levy, “Evanescent light-matter interactions in atomic cladding wave guides,” arXiv:1204.0393 (2012). |

**OCIS Codes**

(230.1150) Optical devices : All-optical devices

(270.1670) Quantum optics : Coherent optical effects

(130.4815) Integrated optics : Optical switching devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: January 16, 2013

Revised Manuscript: February 22, 2013

Manuscript Accepted: February 24, 2013

Published: March 4, 2013

**Citation**

B.D. Clader, S.M. Hendrickson, R.M. Camacho, and B.C. Jacobs, "All-optical microdisk switch using EIT," Opt. Express **21**, 6169-6179 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6169

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### References

- N. Kim, T. Austin, D. Baauw, T. Mudge, K. Flautner, J. Hu, M. Irwin, M. Kandemir, and V. Narayanan, “Leakage current: Moore’s law meets static power,” Computer36, 68 – 75 (2003). [CrossRef]
- A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science308, 672–674 (2005). [CrossRef] [PubMed]
- X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics2, 185–189 (2008). [CrossRef]
- M. Waldow, T. Plötzing, M. Gottheil, M. Först, J. Bolten, T. Wahlbrink, and H. Kurz, “25ps all-optical switching in oxygen implanted silicon-on-insulator microring resonator,” Opt. Express16, 7693–7702 (2008). [CrossRef] [PubMed]
- D. Miller, “Are optical transistors the logical next step?” Nat. Photonics4, 3–5 (2010). [CrossRef]
- M. Albert, A. Dantan, and M. Drewsen, “Cavity electromagnetically induced transparency and all-optical switching using ion coulomb crystals,” Nat. Photonics5, 633–636 (2011). [CrossRef]
- S. E. Harris, “Electromagnetically induced transparency,” Phys. Today50, 36–42 (1997). [CrossRef]
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005). [CrossRef]
- J. Zhang, G. Hernandez, and Y. Zhu, “All-optical switching at ultralow light levels,” Opt. Lett.32, 1317–1319 (2007). [CrossRef] [PubMed]
- M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett.102, 203902 (2009). [CrossRef] [PubMed]
- M. Fleischhauer, “Switching light by vacuum,” Science333, 1228–1229 (2011). [CrossRef] [PubMed]
- D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett.86, 783–786 (2001). [CrossRef] [PubMed]
- A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett.88, 023602 (2001). [CrossRef]
- A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A65, 031802 (2002). [CrossRef]
- M. D. Lukin, “Colloquium : Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys.75, 457–472 (2003). [CrossRef]
- B. Misra and E. Sudarshan, “The Zeno’s paradox in quantum theory,” J. of Math. Phys.18, 756 – 763 (1977). [CrossRef]
- B. C. Jacobs and J. D. Franson, “All-optical switching using the quantum zeno effect and two-photon absorption,” Phys. Rev. A79, 063830 (2009). [CrossRef]
- S. M. Hendrickson, C. N. Weiler, R. M. Camacho, P. T. Rakich, A. I. Young, M. J. Shaw, T. B. Pittman, J. D. Franson, and B. C. Jacobs, “All-optical-switching demonstration using two-photon absorption and the zeno effect,” Phys. Rev. A87, 023808 (2013). [CrossRef]
- Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett.36, 1413–1415 (2011). [CrossRef] [PubMed]
- K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse raman scattering in liquid-core optical fibers,” Opt. Lett.37, 942–944 (2012). [CrossRef] [PubMed]
- S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev.100, 703–722 (1955). [CrossRef]
- H. A. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, 1984).
- T. J. Kippenberg, S. M. Spillane, D. K. Armani, B. Min, L. Yang, and K. J. Vahala, Fabrication, Coupling and Nonlinear Optics of Ultra-High-Q Microcavities (World Scientific Publishing, 2004, vol. 5, Chap. 5, pp. 177–238). [CrossRef]
- J. D. Franson, B. C. Jacobs, and T. B. Pittman, “Quantum computing using single photons and the zeno effect,” Phys. Rev. A70, 062302 (2004). [CrossRef]
- D. A. Steck, “Rubidium 87 d line data,” http://steck.us/alkalidata/ (2009).
- S. G. Schirmer and A. I. Solomon, “Constraints on relaxation rates for n-level quantum systems,” Phys. Rev. A70, 022107 (2004). [CrossRef]
- P. R. Berman and R. C. O’Connell, “Constraints on dephasing widths and shifts in three-level quantum systems,” Phys. Rev. A71, 022501 (2005). [CrossRef]
- O. S. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am.51, 1058–1061 (1961). [CrossRef]
- R. G. Brewer and E. L. Hahn, “Coherent two-photon processes: Transient and steady-state cases,” Phys. Rev. A11, 1641–1649 (1975). [CrossRef]
- J. Gea-Banacloche, Y.-q. Li, S.-z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment,” Phys. Rev. A51, 576–584 (1995). [CrossRef] [PubMed]
- L. Stern, B. Desiatov, I. Goykhman, and U. Levy, “Evanescent light-matter interactions in atomic cladding wave guides,” arXiv:1204.0393 (2012).

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