Abstract

One of the possibilities of increasing optical gain of a light emitting source is by embedding it into a photonic crystal (PhC). If the properties of the PhC are tuned so that the emission wavelength of the light source with gain falls close to the photonic band edge of the PhC, then due to low group velocity of the light modes near the band edge caused by many multiple reflections of light on the photonic structure, the stimulated emission can be significantly enhanced. Here, we perform simulation of the photonic band edge effect on the light intensity of spectrally broad source interacting with a diamond PhC with low optical gain. We show that even for the case of low gain, up to 10-fold increase of light intensity output can be obtained for the two-dimensional PhC consisting of only 19 periodic layers of infinitely high diamond rods ordered into a square lattice. Moreover, considering the experimentally feasible structure composed of diamond rods of finite height - PhC slab - we show that the gain enhancement, even if reduced compared to the ideal case of infinite rods, still remains relatively high. For this particular structure, we show that up to 3.5-fold enhancement of light intensity can be achieved.

© 2012 OSA

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2011 (4)

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nature Photon. 5, 397–405 (2011).
[CrossRef]

L. Ondič, K. Dohnalová, M. Ledinský, A. Kromka, O. Babchenko, and B. Rezek, “Effective extraction of photoluminescence from a diamond layer with a photonic crystal,” ACS Nano 5, 346–350 (2011).
[CrossRef]

Q. Wang, S. Stobbe, and P. Lodahl, “Mapping the local density of optical states of a photonic crystal with single quantum dots,” Phys. Rev. Lett. 107, 167404 (2011).
[CrossRef] [PubMed]

J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[CrossRef]

2010 (2)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

J. Grgic, J. Pedersen, S. Xiao, and N. Mortensen, “Group index limitations in slow-light photonic crystals,” Photon. Nano. 8, 56–61 (2010).
[CrossRef]

2009 (3)

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photon. 3, 163–169 (2009).
[CrossRef]

K. Dohnalová, K. Žídek, L. Ondič, K. Kůsová, O. Cibulka, and I. Pelant, “Optical gain at the F-band of oxidized silicon nanocrystals,” J. Phys. D: Appl. Phys. 42, 135102 (2009).
[CrossRef]

M. Nomura, S. Iwamoto, A. Tandaechanurat, Y. Ota, N. Kumagai, and Y. Arakawa, “Photonic band-edge micro lasers with quantum dot gain,” Opt. Express 17, 640–648 (2009).
[CrossRef] [PubMed]

2008 (2)

A. Kromka, B. Rezek, Z. Remes, M. Michalka, M. Ledinsky, J. Zemek, J. Potmesil, and M. Vanecek, “Formation of continuous nanocrystalline diamond layers on glass and silicon at low temperatures,” Chem. Vap. Deposition 14, 181–186 (2008).
[CrossRef]

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622–626 (2008).
[CrossRef]

2007 (3)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D: Appl. Phys. 40, 2666–2670 (2007).
[CrossRef]

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. A. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nanotech. 2, 515–520 (2007).
[CrossRef]

2006 (3)

J. W. Baldwin, M. Zalalutdinov, T. Feygelson, J. E. Butler, and B. H. Houston, “Fabrication of short-wavelength photonic crystals in wide-band-gap nanocrystalline diamond films,” J. Vac. Sci. Technol. B 24, 50 (2006).
[CrossRef]

S. Tomljenovic-Hanic, M. J. Steel, C. M. de Sterke, and J. Salzman, “Diamond based photonic crystal microcavities,” Opt. Express 14, 3556–3562 (2006).
[CrossRef] [PubMed]

A. F. Koenderink, M. Kafesaki, C. M. Soukoulis, and V. Sandoghdar, “Spontaneous emission rates of dipoles in photonic crystal membranes,” JOSA B 23, 1196–1206 (2006).
[CrossRef]

2005 (1)

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296–1298 (2005).
[CrossRef] [PubMed]

2004 (1)

2001 (2)

2000 (2)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

D. Wiersma, “The smallest random laser,” Nature 406, 132–135 (2000).
[CrossRef] [PubMed]

1999 (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals,” Opt. Express 4, 167–176 (1999).
[CrossRef] [PubMed]

1998 (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef] [PubMed]

1997 (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[CrossRef]

Y. A. Vlasov, K. Luterova, I. Pelant, B. Honerlage, and V. N. Astratov, “Enhancement of optical gain of semiconductors embedded in three-dimensional photonic crystals,” Appl. Phys. Lett. 71, 1616 (1997).
[CrossRef]

1996 (1)

R. Sprik, B. A. van Tiggelen, and A. Lagendijk, “Optical emission in periodic dielectrics,” Europhys. Lett. 35, 265 (1996).
[CrossRef]

1995 (1)

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52, 7982–7986 (1995).
[CrossRef]

1992 (1)

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Aharonovich, I.

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nature Photon. 5, 397–405 (2011).
[CrossRef]

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Andreasen, J.

Arakawa, Y.

Arjavalingam, G.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296–1298 (2005).
[CrossRef] [PubMed]

Asatryan, A.

Asatryan, A. A.

Astratov, V. N.

Y. A. Vlasov, K. Luterova, I. Pelant, B. Honerlage, and V. N. Astratov, “Enhancement of optical gain of semiconductors embedded in three-dimensional photonic crystals,” Appl. Phys. Lett. 71, 1616 (1997).
[CrossRef]

Awschalom, D. D.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).

Babchenko, O.

L. Ondič, K. Dohnalová, M. Ledinský, A. Kromka, O. Babchenko, and B. Rezek, “Effective extraction of photoluminescence from a diamond layer with a photonic crystal,” ACS Nano 5, 346–350 (2011).
[CrossRef]

Baets, R.

Baldwin, J. W.

J. W. Baldwin, M. Zalalutdinov, T. Feygelson, J. E. Butler, and B. H. Houston, “Fabrication of short-wavelength photonic crystals in wide-band-gap nanocrystalline diamond films,” J. Vac. Sci. Technol. B 24, 50 (2006).
[CrossRef]

Barrelet, C. J.

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nat. Photon. 2, 622–626 (2008).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Bienstman, P.

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef] [PubMed]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75, 1896 (1994).

Botten, L.

Botten, L. C.

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75, 1896 (1994).

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef] [PubMed]

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Phys. Rev. Lett. 68, 2023–2026 (1992).
[CrossRef] [PubMed]

Busch, K.

Butler, J. E.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).

J. W. Baldwin, M. Zalalutdinov, T. Feygelson, J. E. Butler, and B. H. Houston, “Fabrication of short-wavelength photonic crystals in wide-band-gap nanocrystalline diamond films,” J. Vac. Sci. Technol. B 24, 50 (2006).
[CrossRef]

Byrne, M. A.

Cao, H.

Chen, H.

H. Chen, J. H. Shin, and P. M. Fauchet, “Optical gain in silicon nanocrystal waveguides,” in Silicon Nanophotonics: Basic Principles, Present Status and Perspectives, L. Khriachtchev, ed. (World Scientific Publishing, 2009), pp. 89–117.

Chow, E.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. A. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nanotech. 2, 515–520 (2007).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef] [PubMed]

Cibulka, O.

K. Dohnalová, K. Žídek, L. Ondič, K. Kůsová, O. Cibulka, and I. Pelant, “Optical gain at the F-band of oxidized silicon nanocrystals,” J. Phys. D: Appl. Phys. 42, 135102 (2009).
[CrossRef]

Cunningham, B. T.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. A. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nanotech. 2, 515–520 (2007).
[CrossRef]

David, A.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photon. 3, 163–169 (2009).
[CrossRef]

de Sterke, C. M.

de Sterke, M.

Dohnalová, K.

L. Ondič, K. Dohnalová, M. Ledinský, A. Kromka, O. Babchenko, and B. Rezek, “Effective extraction of photoluminescence from a diamond layer with a photonic crystal,” ACS Nano 5, 346–350 (2011).
[CrossRef]

K. Dohnalová, K. Žídek, L. Ondič, K. Kůsová, O. Cibulka, and I. Pelant, “Optical gain at the F-band of oxidized silicon nanocrystals,” J. Phys. D: Appl. Phys. 42, 135102 (2009).
[CrossRef]

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75, 1896 (1994).

Fabre, S.

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78, 3294–3297 (1997).
[CrossRef]

Fauchet, P. M.

H. Chen, J. H. Shin, and P. M. Fauchet, “Optical gain in silicon nanocrystal waveguides,” in Silicon Nanophotonics: Basic Principles, Present Status and Perspectives, L. Khriachtchev, ed. (World Scientific Publishing, 2009), pp. 89–117.

Feygelson, T.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).

J. W. Baldwin, M. Zalalutdinov, T. Feygelson, J. E. Butler, and B. H. Houston, “Fabrication of short-wavelength photonic crystals in wide-band-gap nanocrystalline diamond films,” J. Vac. Sci. Technol. B 24, 50 (2006).
[CrossRef]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007).
[CrossRef]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296–1298 (2005).
[CrossRef] [PubMed]

Ganesh, N.

N. Ganesh, W. Zhang, P. C. Mathias, E. Chow, J. A. N. T. Soares, V. Malyarchuk, A. D. Smith, and B. T. Cunningham, “Enhanced fluorescence emission from quantum dots on a photonic crystal surface,” Nature Nanotech. 2, 515–520 (2007).
[CrossRef]

Ge, L.

Greentree, A. D.

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nature Photon. 5, 397–405 (2011).
[CrossRef]

Grgic, J.

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ACS Nano (1)

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Figures (5)

Fig. 1
Fig. 1

Photonic diagrams for TM modes in the Γ-X (a) and Γ-M (b) directions of the square array of infinitely high diamond rods (2D PhC) with radius r = 0.3a, where a is the lattice constant. The insets show the electric field (parallel to the rods, z-direction) patterns of the modes for each band at the wavevector marked by the red spot. Bands whose mode patterns are symmetric and asymmetric with respect to the mirror plane (a black line in each field pattern) are plotted with solid and dashed line, respectively. The left-hand side of the photonic band diagram in each panel shows the computational domain used for computation of the transmission spectra shown on the right-hand side of the band diagram. The blue and red rectangles represent a light source and a detector, respectively.

Fig. 2
Fig. 2

(a) Transmission spectra of the 2D PhC in the Γ-X direction simulated considering 3, 9 and 19 lattice periods of infinite diamond columns with the lattice constant a. (b) Detail of the transmission spectra - formation of photonic states near the band edge with increasing number of lattice periods. (c) Transmission (T) and reflection (R) spectra of the PhC with 9 lattice periods demonstrating the correctness of the FDTD simulation. The red curve shows the absorption (A) calculated by the formula A=1–T–R.

Fig. 3
Fig. 3

Gain-influenced transmission spectra (black curve) computed for the TM polarized plane wave incident in the Γ-X (a) and Γ-M (b) crystal directions of the square array of 19 layers of infinitely high diamond rods possessing optical gain. The red horizontal line depicts the single pass light amplification when the periodicity is not present.

Fig. 4
Fig. 4

Projected photonic band diagrams for TM modes in the Γ-X (a) and Γ-M (b) crystal directions of the PhC slab consisting of a square array of diamond rods with radius r = 0.3a and height h = 2a, where a is a lattice constant. Modes that are symmetric (asymmetric) with respect to the mirror plane parallel to the direction of mode propagation are plotted with black solid (dashed) lines. The air lightline is depicted with the red line. On the left side of each panel, a computational domain is depicted (a top-view and a side-view) used for simulation of transmission spectra plotted on the right side of each panel. Blue rectangles represent a source of TM polarized light incident in the relevant direction for 19 layers of rods. Red rectangles represent detector plane. Origin of the coordinate system is in the middle of the computational domain.

Fig. 5
Fig. 5

Photon flux enhancement spectra (black curve) in the Γ-X (a) and Γ-M (b) crystal directions of the PhC slab depicted in Fig. 4, computed as a ratio of the gain-influenced and ordinary transmission spectra. The red horizontal line depicts the single pass enhancement.

Tables (1)

Tables Icon

Table 1 Fraction of electric field energy confined in the rods computed for the mode at the band edge.

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