Abstract

The ability to modulate an optical field via an electric field is regarded as a key function of electro-optic interconnects, which are used in optical communications and information-processing systems. One of the main devices required for such interconnects is the electro-optic modulator (EOM). Current EOMs based on electro-optic and electro-absorption effects often are bulky and power-inefficient due to the weak electro-optic properties of their constituent materials. Here, we propose a new mechanism to produce an arbitrary-waveform EOM based on quantum interference, in which both real and imaginary parts of the susceptibility are engineered coherently with super-high efficiency. Based on this EOM, a waveform interconnect from the voltage to the modulated optical absorption is realized. We expect that such a new type of electro-optic interconnect will have a broad range of applications, including in optical communications and networks.

© 2017 Chinese Laser Press

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References

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2016 (1)

L. G. Qin, Z. Y. Wang, G. W. Lin, J. Y. Zhao, and S. Q. Gong, “Electrically controlled quantum memories with a cavity and electro-mechanical system,” IEEE J. Quantum Electron. 52, 9300106 (2016).
[Crossref]

2015 (4)

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).

K. Liu, C. R. Ye, S. Khan, and V. J. Sorger, “Review and perspective on ultrafast wavelength-size electro-optic modulators,” Laser Photon. Rev. 9, 172–194 (2015).
[Crossref]

R. Yu, V. Pruneri, and F. J. G. de Abajo, “Resonant visible light modulation with graphene,” ACS Photon. 2, 550–558 (2015).
[Crossref]

K. Ying, Y. Niu, D. Chen, H. Cai, R. Qu, and S. Gong, “White light cavity via modification of linear and nonlinear dispersion in an N-type atomic system,” Opt. Commun. 342, 189–192 (2015).
[Crossref]

2014 (2)

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, J. Frigerio, D. Chrastina, J.-R. Coudevylle, X. L. Roux, S. Edmond, G. Isella, and L. Vivien, “Recent progress in GeSi electro-absorption modulators,” Sci. Technol. Adv. Mater. 15, 014601 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

2013 (2)

C. Huang, R. Lamond, S. K. Pickus, Z. R. Li, and V. J. Sorger, “A sub-λ-size modulator beyond the efficiency-loss limit,” IEEE Photon. J. 57, 2202411 (2013).
[Crossref]

Z. Wang, B. Yu, S. Zhen, and X. Wu, “Large refractive index without absorption via quantum interference in a semiconductor quantum well,” J. Lumin. 134, 272–276 (2013).
[Crossref]

2012 (1)

V. J. Sorger, N. D. Lanzillotti-Kimura, R. M. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1, 17–22 (2012).
[Crossref]

2011 (4)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

V. Venkataraman, K. Saha, P. Londero, and A. L. Gaeta, “Few-photon all-optical modulation in a photonic band-gap fiber,” Phys. Rev. Lett. 107, 193902 (2011).
[Crossref]

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]

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).
[Crossref]

2010 (2)

G. Nikoghosyan and M. Fleischhauer, “Photon-number selective group delay in cavity induced transparency,” Phys. Rev. Lett. 105, 013601 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

2009 (5)

C. Batten, A. Joshi, J. Orcutt, and C. Holzwarth, “Building manycore processor-to-DRAM networks with monolithic CMOS silicon photonics,” IEEE Micro 29, 8–21 (2009).
[Crossref]

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

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]

D. Barettin, J. Houmark, B. Lassen, M. Willatzen, T. R. Nielsen, J. Mørk, and A.-P. Jauho, “Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures,” Phys. Rev. B 80, 235304 (2009).
[Crossref]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[Crossref]

2008 (2)

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic networks-on-chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57, 1246–1260 (2008).
[Crossref]

2006 (1)

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[Crossref]

2005 (1)

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

2004 (2)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref]

M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A 70, 053806 (2004).
[Crossref]

2002 (2)

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314 (2002).
[Crossref]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, “Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium,” Phys. Rev. A 66, 013805 (2002).
[Crossref]

2001 (3)

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, “Observation of transient gain without population inversion in a laser-cooled rubidium Λ system,” Phys. Rev. A 64, 055801 (2001).
[Crossref]

A. V. Turukhin, V. S. Sudarhanam, 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]

M. Yan, E. G. Rickey, and Y. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A 64, 041801(R) (2001).
[Crossref]

2000 (2)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[Crossref]

D. A. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88, 728–749 (2000).
[Crossref]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

1998 (2)

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[Crossref]

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium system,” Phys. Rev. A 58, 1545–1548 (1998).
[Crossref]

1995 (2)

S. E. Harris and Z.-F. Luo, “Preparation energy for electromagnetically induced transparency,” Phys. Rev. A 52, R928 (1995).
[Crossref]

Y.-Q. Li and M. Xiao, “Transient properties of an electromagnetically induced transparency in three-level atoms,” Opt. Lett. 20, 1489–1491 (1995).
[Crossref]

1991 (1)

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

1986 (1)

D. A. B. Miller, D. S. Chemla, and S. Schmitt-Rink, “Relation between electroabsorption in bulk semiconductors and in quantum wells: the quantum-confined Franz-Keldysh effect,” Phys. Rev. B 33, 6976–6982 (1986).
[Crossref]

1984 (2)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined stark effect,” Phys. Rev. Lett. 53, 2173–2176 (1984).
[Crossref]

K. Aihara, G. Matsumoto, and Y. Ikegaya, “Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator,” J. Theoret. Biol. 109, 249–269 (1984).
[Crossref]

1966 (1)

M. Cardona and F. H. Pollak, “Energy-band structure of Germanium and Silicon: the k · p method,” Phys. Rev. 142, 530–543 (1966).
[Crossref]

Aihara, K.

K. Aihara, G. Matsumoto, and Y. Ikegaya, “Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator,” J. Theoret. Biol. 109, 249–269 (1984).
[Crossref]

Albert, M.

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]

Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[Crossref]

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).

Bajcsy, M.

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]

Balic, V.

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]

Barettin, D.

D. Barettin, J. Houmark, B. Lassen, M. Willatzen, T. R. Nielsen, J. Mørk, and A.-P. Jauho, “Optical properties and optimization of electromagnetically induced transparency in strained InAs/GaAs quantum dot structures,” Phys. Rev. B 80, 235304 (2009).
[Crossref]

Batten, C.

C. Batten, A. Joshi, J. Orcutt, and C. Holzwarth, “Building manycore processor-to-DRAM networks with monolithic CMOS silicon photonics,” IEEE Micro 29, 8–21 (2009).
[Crossref]

Beals, M.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2, 433–437 (2008).
[Crossref]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Bergman, K.

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic networks-on-chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57, 1246–1260 (2008).
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Figures (3)

Fig. 1.
Fig. 1. Proposed opto- and electro-mechanical hybrid system composed of a tunable cavity with a charged mirror operating as a CMO and a mechanically variable capacitor. A Λ-type three-level medium confined inside the cavity interacts with two optical fields: a constant optical field ϵc, which is resonantly injected into the cavity along the x axis to form the cavity field, and the probe field Ep, which is externally injected into the cavity along the z axis at frequency ωp.
Fig. 2.
Fig. 2. Imaginary part of the susceptibility of the probe field in the medium as a function of the square of the voltage U2 and the detuning Δp. The inset shows the real part of the susceptibility. Here, the units of the voltage and the detuning axis are the square of the voltage (V2) and hertz (Hz), respectively. The parameters are used from the experiments in Ref. [32] as ϵc=4×1010  Hz, γ=2π×5.75  MHz, γs=0.0001γ, g=0.001γ, κ=0.2γ, ωm=γ, m=145  ng, G0=2π×1.5×1016  Hz/m, S=0.6  mm2, r=0.21  μm, δ=0, and atomic density 1019  m3. The modulative material is Rb87 with Λ-type three-level configuration.
Fig. 3.
Fig. 3. Numerical results of the EOM. (a) Modulation of the sine wave: (a1) shows the target absorptive waveform and numerical results, and (a2) shows the square of voltage waveform U2 applied to the capacitor. (b) Modulation of the sawtooth wave: (b1) shows the target absorptive waveform and numerical results, and (b2) shows the square of voltage waveform U2 applied to the capacitor. (c) Modulation of the square wave: (c1) shows the target absorptive waveform and numerical results, and (b2) shows the square of voltage waveform U2 applied to the capacitor. The simulation parameters are ϵc=0.5×1010  Hz, γm=3γ, and κ=0.4γ; the other parameters are the same as in Fig. 2.

Equations (8)

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q¨+γmq˙+ωm2q=(G0nc(t)+U2η)/m,a˙=(κiΔcmo)a+ϵc,
R˙=MR+A,
R=(σbaσbc),M=(γ+iΔpigaigaγs+i(Δpδ)),A=(igpϵp0).
R=eMtR0+(1eMt)M1AM1A.
σbas=igpϵp[γs+i(Δpδ)](γ+iΔp)[γs+i(Δpδ)]+g2(nc+1).
Im(χ)=χ0γsγγs+g2[ϵc2κ2+(2G0ηmwm2U2)2+1],
U2=mωm22G0ηg2ϵc2χ0γsIm(χ)sγγsg2κ2,
RdB=10logIm(χ)maxIm(χ)min,

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