Abstract

We demonstrated lasing in two-dimensional trivalent network structures with short-range order. Despite the lack of translational and rotational symmetries, such structures possess a large isotropic photonic bandgap. Different from those of a photonic crystal, the band-edge modes are spatially localized and have high quality factor.

© 2011 Optical Society of America

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  1. C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
    [CrossRef]
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  3. C. Rockstuhl, U. Peschel, and F. Lederer, Opt. Lett. 31, 1741 (2006).
    [CrossRef] [PubMed]
  4. Y. Wang and S. Jian, Phys. Lett. A 352, 550 (2006).
    [CrossRef]
  5. C. Rockstuhl and F. Lederer, Phys. Rev. B 79, 132202(2009).
    [CrossRef]
  6. M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
    [CrossRef] [PubMed]
  7. M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA 106, 20658 (2009).
    [CrossRef] [PubMed]
  8. K. Edagawa, S. Kanoko, and M. Notomi, Phys. Rev. Lett. 100, 013901 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
    [CrossRef]
  11. C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635(1995).
    [CrossRef]

2011 (1)

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

2010 (2)

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

2009 (2)

M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA 106, 20658 (2009).
[CrossRef] [PubMed]

C. Rockstuhl and F. Lederer, Phys. Rev. B 79, 132202(2009).
[CrossRef]

2008 (1)

K. Edagawa, S. Kanoko, and M. Notomi, Phys. Rev. Lett. 100, 013901 (2008).
[CrossRef] [PubMed]

2006 (2)

2001 (1)

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

1999 (1)

J. Ballato, J. Dimaio, A. James, and E. Gulliver, Appl. Phys. Lett. 75, 1497 (1999).
[CrossRef]

1995 (1)

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635(1995).
[CrossRef]

Ballato, J.

J. Ballato, J. Dimaio, A. James, and E. Gulliver, Appl. Phys. Lett. 75, 1497 (1999).
[CrossRef]

Cao, H.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Chan, C. T.

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635(1995).
[CrossRef]

Cheng, B.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Dimaio, J.

J. Ballato, J. Dimaio, A. James, and E. Gulliver, Appl. Phys. Lett. 75, 1497 (1999).
[CrossRef]

Dreisow, F.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Edagawa, K.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

K. Edagawa, S. Kanoko, and M. Notomi, Phys. Rev. Lett. 100, 013901 (2008).
[CrossRef] [PubMed]

Florescu, M.

M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA 106, 20658 (2009).
[CrossRef] [PubMed]

Gulliver, E.

J. Ballato, J. Dimaio, A. James, and E. Gulliver, Appl. Phys. Lett. 75, 1497 (1999).
[CrossRef]

Guy, M. I.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Heinrich, M.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Ho, K. M.

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635(1995).
[CrossRef]

Imagawa, S.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

James, A.

J. Ballato, J. Dimaio, A. James, and E. Gulliver, Appl. Phys. Lett. 75, 1497 (1999).
[CrossRef]

Jian, S.

Y. Wang and S. Jian, Phys. Lett. A 352, 550 (2006).
[CrossRef]

Jin, C.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Kagawa, Y.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

Kanoko, S.

K. Edagawa, S. Kanoko, and M. Notomi, Phys. Rev. Lett. 100, 013901 (2008).
[CrossRef] [PubMed]

Keil, R.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Lederer, F.

Li, Z.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Liew, S.-F.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Meng, X.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Morita, K.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

Niino, T.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

Noh, H.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Nolte, S.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Notomi, M.

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

K. Edagawa, S. Kanoko, and M. Notomi, Phys. Rev. Lett. 100, 013901 (2008).
[CrossRef] [PubMed]

O’Hern, C. S.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Peschel, U.

Rechtsman, M.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Rockstuhl, C.

Schreck, C.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Segev, M.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Steinhardt, P. J.

M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA 106, 20658 (2009).
[CrossRef] [PubMed]

Szameit, A.

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

Torquato, S.

M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA 106, 20658 (2009).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang and S. Jian, Phys. Lett. A 352, 550 (2006).
[CrossRef]

Yang, J.-K.

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Yu, Q. L.

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635(1995).
[CrossRef]

Zhang, D.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

J. Ballato, J. Dimaio, A. James, and E. Gulliver, Appl. Phys. Lett. 75, 1497 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

Y. Wang and S. Jian, Phys. Lett. A 352, 550 (2006).
[CrossRef]

Phys. Rev. A (1)

J.-K. Yang, C. Schreck, H. Noh, S.-F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, Phys. Rev. A 82, 053838 (2010).
[CrossRef]

Phys. Rev. B (4)

C. T. Chan, Q. L. Yu, and K. M. Ho, Phys. Rev. B 51, 16635(1995).
[CrossRef]

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

S. Imagawa, K. Edagawa, K. Morita, T. Niino, Y. Kagawa, and M. Notomi, Phys. Rev. B 82, 115116 (2010).
[CrossRef]

C. Rockstuhl and F. Lederer, Phys. Rev. B 79, 132202(2009).
[CrossRef]

Phys. Rev. Lett. (2)

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, Phys. Rev. Lett. 106, 193904(2011).
[CrossRef] [PubMed]

K. Edagawa, S. Kanoko, and M. Notomi, Phys. Rev. Lett. 100, 013901 (2008).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA 106, 20658 (2009).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Black solid circles are the center positions of polydisperse cylinders produced by jammed packing in a computer simulation. The blue thin lines represent the Delaunay tessellation that leads to the formation of a trivalent network structure shown by the red thick lines. (b) Spatial Fourier spectra (inset) and spatial correlation function C ( Δ r ) (main panel) of the trivalent network structure (scale bar: 2 π / a ). (c) Calculated density of optical states for a trivalent network structure (blue dashed curve) and an amorphous array of air cylinders (black solid curve) with the same air filling fraction f = 0.53 and dielectric refractive index n e = 2.68 . (c) Calculated Q factor of the resonant modes in the trivalent network structure as a function of the normalized frequency a / λ . (e) and (f) are calculated intensity distributions of two modes [circled in (d)] at the low and high frequency sides of the bandgap.

Fig. 2
Fig. 2

(a) Plane-view SEM image of the fabricated trivalent network structure in a GaAs membrane with a = 315 nm . The scale bar is 2 μm . (b) Measured intensity (black circles) and spectral width (blue squares) of one emission peak at λ = 1000 nm as a function of the incident pump power P.

Fig. 3
Fig. 3

Measured emission spectra for the trivalent network structures of (a)  a = 315 nm and (b)  275 nm . The two spectra in each panel are taken from different configurations. With decreasing a, the lasing modes blueshift.

Fig. 4
Fig. 4

(a) Optical image of the lasing mode in Fig. 2b. (b) Spatial intensity distribution of the dielectric BE mode calculated in a 3D FDTD simulation of the real structure.

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