Abstract

Photonic crystal waveguides (PCWs) are promising candidates for the basic building blocks of quantum information processing because they support circular polarization points that can unbalance the directionality of an integrated quantum emitter (QE). Nevertheless, the Purcell effect at circular polarization points saturates near the band edge, the preferred region for quantum electrodynamics. Consequently, chirality and ultra-strong light–matter interaction are difficult to combine. Here, we detract from the vicinity of the band edge, and couple modes with different parities by breaking the mirror symmetry. Using the three-dimensional finite-difference time-domain method, simulated band structures of the implemented photonic bonding states (PBS) display single-mode anomalous zero-group-velocity (ZGV) points far from the band edge. The electric field patterns of these points feature circular polarization points at high field intensity regions where a QE would acquire uni-directional emission behavior. Fabricated devices in silicon (Si) slabs demonstrate the predicted coupling energy between the modes and the signature of single-mode anomalous ZGV points. This method to engineer PBS in PCWs paves the way for outperforming chiral light–matter experiments on-chip.

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References

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2017 (1)

2016 (1)

B. Lang, D. M. Beggs, and R. Oulton, “Time-reversal constraint limits unidirectional photon emission in slow-light photonic crystals,” Philos. Trans. R. Soc. A 374, 20150263 (2016).
[Crossref]

2015 (3)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref]

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

2014 (2)

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

S. Haddadi, P. Hamel, G. Beaudoin, I. Sagnes, C. Sauvan, P. Lalanne, J. A. Levenson, and A. Yacomotti, “Photonic molecules: tailoring the coupling strength and sign,” Opt. Express 22, 12359–12368 (2014).
[Crossref]

2013 (1)

W. Liu, D. Yang, G. Shen, H. Tian, and Y. Ji, “Design of ultra compact all-optical XOR, XNOR, NAND and OR gates using photonic crystal multi-mode interference waveguides,” Opt. Laser Technol. 50, 55–64 (2013).
[Crossref]

2011 (2)

2010 (3)

2009 (2)

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Y. S. Kivshar, “Slow-light vortices in periodic waveguides,” J. Opt. A 11, 094016 (2009).
[Crossref]

M. Burresi, R. Engelen, A. Opheij, D. Van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

2008 (1)

2007 (2)

V. M. Rao and S. Hughes, “Single quantum-dot Purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

2006 (1)

2005 (1)

2004 (5)

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[Crossref]

M. Ibanescu, S. Johnson, D. Roundy, C. Luo, Y. Fink, and J. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref]

H. Nakamura, Y. Sugimoto, K. Kanamoto, N. Ikeda, Y. Tanaka, Y. Nakamura, S. Ohkouchi, Y. Watanabe, K. Inoue, H. Ishikawa, and K. Asakawa, “Ultra-fast photonic crystal/quantum dot all-optical switch for future photonic networks,” Opt. Express 12, 6606–6614 (2004).
[Crossref]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

S. Hughes, “Enhanced single-photon emission from quantum dots in photonic crystal waveguides and nanocavities,” Opt. Lett. 29, 2659–2661 (2004).
[Crossref]

2003 (1)

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, “Photonic crystal optical filter based on contra-directional waveguide coupling,” Appl. Phys. Lett. 83, 5121–5123 (2003).
[Crossref]

2002 (1)

M. Notomi, A. Shinya, K. Yamada, J.-I. Takahashi, C. Takahashi, and I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[Crossref]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref]

1999 (1)

Alfano, R.

G. Milione, H. Sztul, D. Nolan, and R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Anand, S.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, “Photonic crystal optical filter based on contra-directional waveguide coupling,” Appl. Phys. Lett. 83, 5121–5123 (2003).
[Crossref]

Androvitsaneas, P.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref]

Arcari, M.

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

Asakawa, K.

Atature, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Baba, T.

M. Burresi, R. Engelen, A. Opheij, D. Van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Beaudoin, G.

Beggs, D. M.

B. Lang, D. M. Beggs, and R. Oulton, “Time-reversal constraint limits unidirectional photon emission in slow-light photonic crystals,” Philos. Trans. R. Soc. A 374, 20150263 (2016).
[Crossref]

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenović, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J.-P. Hugonin, and H. Lalanne, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[Crossref]

Borel, P. I.

Bradley, C.

C. Bradley and A. Cracknell, The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Oxford University, 2010).

Burresi, M.

M. Burresi, R. Engelen, A. Opheij, D. Van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

Citrin, D.

Cracknell, A.

C. Bradley and A. Cracknell, The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Oxford University, 2010).

de Sterke, C. M.

Deppe, D.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Desyatnikov, A. S.

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Y. S. Kivshar, “Slow-light vortices in periodic waveguides,” J. Opt. A 11, 094016 (2009).
[Crossref]

Eich, M.

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[Crossref]

El-Ella, H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Engelen, R.

M. Burresi, R. Engelen, A. Opheij, D. Van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of polarization singularities at the nanoscale,” Phys. Rev. Lett. 102, 033902 (2009).
[Crossref]

Fage-Pedersen, J.

Falt, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Fink, Y.

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref]

M. Ibanescu, S. Johnson, D. Roundy, C. Luo, Y. Fink, and J. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref]

Forchel, A.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, “Photonic crystal optical filter based on contra-directional waveguide coupling,” Appl. Phys. Lett. 83, 5121–5123 (2003).
[Crossref]

Frandsen, L. H.

Gao, D.

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Gibbs, H.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Gomez-Iglesias, A.

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Ha, S.

Haddadi, S.

Hamel, P.

Hansen, S. L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Hou, J.

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Hughes, S.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref]

V. M. Rao and S. Hughes, “Single quantum-dot Purcell factor and β factor in a photonic crystal waveguide,” Phys. Rev. B 75, 205437 (2007).
[Crossref]

S. Hughes, “Enhanced single-photon emission from quantum dots in photonic crystal waveguides and nanocavities,” Opt. Lett. 29, 2659–2661 (2004).
[Crossref]

Hugonin, J.-P.

Ibanescu, M.

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref]

M. Ibanescu, S. Johnson, D. Roundy, C. Luo, Y. Fink, and J. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref]

Ikeda, N.

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Inoue, K.

Ishikawa, H.

Jaskorzynska, B.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, “Photonic crystal optical filter based on contra-directional waveguide coupling,” Appl. Phys. Lett. 83, 5121–5123 (2003).
[Crossref]

Javadi, A.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. L. Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

Ji, Y.

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

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Figures (5)

Fig. 1.
Fig. 1. Schematic of the PCWs with lattice constant a, the waveguide width W (i.e., the distance between the center of the first circular hole rows). The figures introduce the definition of the mismatch m between both parts of the PhC regions. (a) For no mismatch, the structure can be constructed with one side and its mirror image by the plane (xOz^) placed at y=0. (b) For a mismatch m, one side has been translated by a distance m along the propagation axis. Presented here is the maximum mismatch m/a=0.5.
Fig. 2.
Fig. 2. Photonic band structure of the TE guided modes PCW with the parameters a=450  nm, W=1.23a for different mismatches between PhC sides. The mismatch parameter m/a is scanned from 0 to 0.5 in steps of 0.125. For m/a=0, odd and even modes are respectively represented in solid and dashed black lines. The TE1+, TE1, TE2+, TE2 modes are represented in shades of blue, red, green, and magenta, respectively. The light line is represented in orange and the PhC bulk modes in gray.
Fig. 3.
Fig. 3. Normalized transmission spectra of the waveguides with different (m/a) values from 0 (red) to 0.5 (blue) in steps of 0.05. The simulated wavelengths of the anomalous ZGV points (orange and black for bonding and anti-bonding at k0+ and k0, respectively) have been superimposed onto the measurements as well as the frequency of the anti-bonding mode at the end of the BZ (in green).
Fig. 4.
Fig. 4. Relevant properties of the odd and even mode profiles at the k0 and of TE1+ and TE1 modes at k0+ and k0, respectively. The mismatch parameter m/a has been scanned between 0 and 0.5 in steps of 0.125. (a) The normalized Stokes parameter S0,norm(r)=(|Ex(r)|2+|Ey(r)|2)/max(|Ex|2+|Ey|2). (b) The Stokes parameter S3(r), describing the degree of elliptic polarization across the PCWs unit cell. Green crosses have been superimposed at |S3|=1 positions for mismatches where the anomalous ZGV points are single-mode.
Fig. 5.
Fig. 5. Scanning electron microscopy imaging of the fabricated devices: (a) no mismatch and (b) m/a=1/2.

Equations (12)

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Ex=±iEy,
Ψπ/a(x,y,z)=Ψπ/a*(x,y,z)=Ψπ/a+2π/a*(x,y,z)=Ψπ/a*(x,y,z),
Pf(r)|ng|E2(r),
limkπaPf(rc)0.
ΨK(x+a,y,z)=ΨK(x,y,z)eiKa,
R^yEy(x,y,z)=±Ey(x,y,z),
G^mEk=T^x=mR^yEk,
Eπ/a(x+a/2,y,z)=±iEπ/a(x,y,z),
E1,π/a=E2,π/a*.
λTE1(πa)>λTE1+(k0+)
δ2δk2(aλ)k0±0.
S0(r)=(|Ex(r)|2+|Ey(r)|2),S3(r)=2Im(Ex*(r)Ey(r))S0(r),

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