## Low-threshold lasing in photonic-crystal heterostructures |

Optics Express, Vol. 22, Issue 6, pp. 6229-6238 (2014)

http://dx.doi.org/10.1364/OE.22.006229

Acrobat PDF (910 KB)

### Abstract

We study a photonic crystal (PhC) heterostructure cavity consisting of gain medium in a three-dimensional (3D) PhC sandwiched between two identical passive multilayers. For this structure, based on Korringa-Kohn-Rostoker method, we observe a decrease in the lasing threshold of two orders of magnitude, as compared with a stand-alone 3D PhC. We attribute this remarkable decrease in threshold gain to the overlap of the defect cavity mode with the reduced group velocity region of the PhC’s dispersion, and the associated enhancement in the distributed feedback from the ordered layers of the PhC. The obtained results show the potency for designing PhC-based, compact on-chip lasers with ultra-low thresholds.

© 2014 Optical Society of America

## 1. Introduction

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

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. **58**, 2486–2489 (1987). [CrossRef] [PubMed]

3. R. Herrmann, T. Snner, T. Hein, A. Lffler, M. Kamp, and A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. **31**, 1229–1231 (2006). [CrossRef] [PubMed]

4. H. Y. Ryu and M. Notomi, “Enhancement of spontaneous emission from the resonant modes of a photonic crystal slab single-defect cavity,” Opt. Lett. **28**, 2390–2392 (2003). [CrossRef] [PubMed]

5. L.-T. Shi, F. Jin, M.-L. Zheng, X.-Z. Dong, W.-Q. Chen, Z.-S. Zhao, and X.-M. Duan, “Threshold optimization of polymeric opal photonic crystal cavity as organic solid-state dye-doped laser,” Appl. Phys. Lett. **98**, 093304 (2011). [CrossRef]

8. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. OBrien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science **284**, 1819–1821 (1999). [CrossRef] [PubMed]

9. N. Susa, “Threshold gain and gain-enhancement due to distributed-feedback in two-dimensional photonic-crystal lasers,” J. Appl. Phys. **89**, 815–823 (2001). [CrossRef]

11. 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**, 1896–1899 (1994). [CrossRef]

12. K. Sakoda, K. Ohtaka, and T. Ueta, “Low-threshold laser oscillation due to group-velocity anomaly peculiar to two and three-dimensional photonic crystals,” Opt. Express **4**, 481–489 (1999). [CrossRef] [PubMed]

13. P.-H. Weng, T.-T. Wu, T.-C. Lu, and S.-C. Wang, “Threshold gain analysis in GaN-based photonic crystal surface emitting lasers,” Opt. Lett. **36**, 1908–1910 (2011). [CrossRef] [PubMed]

14. M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. **38**, 1046–1048 (2013). [CrossRef] [PubMed]

16. M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, “Spatial and spectral distributions of emission from dye-doped photonic crystals in reflection and transmission geometries,” J. Nanophotonics **6**, 063526 (2012). [CrossRef]

17. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. **113**, 49–77 (1998). [CrossRef]

18. N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. **132**, 189–196 (2000). [CrossRef]

## 2. Proposed design

*ε*=

*ε′*+

*iε″*with

*ε″*< 0 [10

10. 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]

7. J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid onedimensional photonic crystal,” Appl. Phys. Lett. **88**, 091102 (2006). [CrossRef]

15. M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photonics J. **5**, 4700409 (2013). [CrossRef]

19. M. N. Shkunov, Z. V. Vardeny, M. C. DeLong, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, “Tunable, gap-state lasing in switchable directions for opal photonic crystals,” Adv. Funct. Mat. **12**, 2126, (2002). [CrossRef]

21. F. Yu. Sychev, I. E. Razdolski, T. V. Murzina, O. A. Aktsipetrov, T. Trifonov, and S. Cheylan, “Vertical hybrid microcavity based on a polymer layer sandwiched between porous silicon photonic crystals,” Appl. Phys. Lett. **95**, 163301 (2009). [CrossRef]

*xy*plane and of finite thickness in the z direction. It is well known that the available DOS is higher at the defect mode frequency due to the multilayer cavity, and also near the band edge frequencies of the sandwiched 3D PhC [7

7. J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid onedimensional photonic crystal,” Appl. Phys. Lett. **88**, 091102 (2006). [CrossRef]

11. 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**, 1896–1899 (1994). [CrossRef]

*ε′*= 2.53) doped with a gain medium. The multilayers are composed of 5 double layers each, with

*ε*

_{1}= 7 (TiO

_{2}),

*ε*

_{2}= 2.37 (SiO

_{2}) in the visible range [22], and thicknesses

*t*

_{1}= 0.25

*a*and

*t*

_{2}= 0.16

*a*, where

*a*is the lattice constant. The period and the number of layers of the multilayer structure are chosen in such a way that the stopband is broad enough to cover the stopband of the 3D PhC. The stop band of the PhC is centered at the normalized frequency

*ωa*/2

*πc*= 0.6.

## 3. Numerical method

17. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. **113**, 49–77 (1998). [CrossRef]

17. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. **113**, 49–77 (1998). [CrossRef]

*i*=

*x*,

*y*,

*z*of the electric field vector are obtained from polarization direction and magnitude of the field associated with a given beam

*g′*[17

**113**, 49–77 (1998). [CrossRef]

*A*(

_{L}*A*) is the appropriate origin on the top (bottom) side of the structure and the

_{R}*Q*,

^{I}*Q*,

^{II}*Q*,

^{III}*Q*are the matrix elements of the transmission/reflection matrix with a definite sequence in the ordering of indices:

^{IV}*g*

_{1}

*x*,

*g*

_{1}

*y*,

*g*

_{1}

*z*,

*g*

_{2}

*x*,

*g*

_{2}

*y*,

*g*

_{2}

*z*,...... They are obtained using the matrix elements of the single layer via layer doubling method, which is given explicitly in [17

**113**, 49–77 (1998). [CrossRef]

*û*is the unit vector (

_{i}*i*,

*i′*=

*x*,

*y*,

*z*) and

*g*(

*g′*) is the two-dimensional (2D) reciprocal lattice vector in the

*xy*plane given by where

*m*

_{1},

*m*

_{2}= 0, ±1, ±2, ±3,.... and

*b*,

_{x}*b*are defined by Here

_{y}*a*(

_{j}*j*=

*x*,

*y*) are the primitive vectors of the lattice in

*xy*plane with lattice constant

*a*. The wave vector of the incident plane wave with parallel wave vector component

*q*

_{||}=

*k*

_{||}+

*g*is given by where

*μ*, and

*ε*are the complex permeability and complex dielectric constant of the sphere and

*c*is the speed of light in vacuum. The parameter

*ε*with a negative imaginary part gives gain, and the positive imaginary part of

*ε*gives absorbance of the medium.

*k*

_{||}is the reduced wave vector in the surface Brillouin zone and

*g′*is one of the reciprocal lattice vectors. +, − defines the sign of the

*z*component of the wave vector.

*T*) and the reflectance (

*R*) of the PhC heterostructure can be obtained using the calculated transmitted and reflected wave using Eqs. (1),(2) for a corresponding incident wave. The ratio between the flux of transmitted (reflected) wave and the flux of incident wave is called as

*T*(

*R*). It can be obtained by integrating the Poynting vector over the

*xy*plane with a time average over the period 2

*π/ω*on each side of the slab. The transmittance and reflectance are given by Here * denotes the complex conjugation.

*T*and

*R*never exceed one. In a crystal with a gain medium, the

*T*and

*R*may be greater than unity due to stimulated emission, which will be discussed in the next section. In the calculations, we assumed that the PhC is perfectly crystalline and neglected the spontaneous emission in estimating the lasing threshold. The losses due to the domain cracks, as well as the spontaneous emission, may slightly increase the lasing threshold value without significantly affecting the lasing wavelength.

## 4. Results and discussion

*T*and

*R*were obtained by using 41 reciprocal two-dimensional plane wave vectors, which were expanded in spherical waves with angular momenta

*l*= 1, 2,...,7. The multilayer stack gives a broad stopband shown in Fig. 2 (a), which is seen to be broad enough to cover the stopband of the 3D PhC [see pink curve in Fig. 2(b)]. The group velocity (black curve) and the dispersion relation of the propagating eigenmodes of the 3D PhC calculated using the plane wave expansion method [23

23. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express **8**, 173–190 (2001). [CrossRef] [PubMed]

25. K. Sakoda, *Optical properties of Photonic crystals* (Springer-Verlag, Berlin, 2001) [CrossRef]

*t*= 17.44

_{u}*a*(equal to

*t*with 30 layers) and permittivity of 2.53 (which is the same as that of the 3D PhC).

_{PhC}*ε″*= 0) for the sandwiched 3D PhC with 30 layers. One can observe that the allowed mode is absent in the range of frequencies corresponding to the stopband of the sandwiched 3D PhC (region II). Region I in Fig. 2(d) shows the modes with reduced group velocity of the heterostructure cavity.

*ε″*= −0.0005 for the sandwiched 3D PhC is shown in Fig. 4(a). The transmittance of the defect modes near the band edges is much greater than unity due to the emission. For comparison, Fig. 4(b) shows the transmission spectrum of a similar PhC heterostructure cavity by assuming a purely real permittivity (

*ε″*= 0). It can be clearly seen from Fig. 4 that the enhancement of gain for the cavity modes [shown by arrows in Figs. 4(a) and 4(b)] near the band edges of the 3D PhC is much larger than that for the other modes. This is an expected result due to the large values of DOS.

12. K. Sakoda, K. Ohtaka, and T. Ueta, “Low-threshold laser oscillation due to group-velocity anomaly peculiar to two and three-dimensional photonic crystals,” Opt. Express **4**, 481–489 (1999). [CrossRef] [PubMed]

12. K. Sakoda, K. Ohtaka, and T. Ueta, “Low-threshold laser oscillation due to group-velocity anomaly peculiar to two and three-dimensional photonic crystals,” Opt. Express **4**, 481–489 (1999). [CrossRef] [PubMed]

*ε″*calculated this way may serve as a measure of the population inversion [12

_{th}**4**, 481–489 (1999). [CrossRef] [PubMed]

*ε″*and the normalized frequency in Fig. 5(a). It is clearly seen to diverge at

*ωa*/2

*πc*= 0.6272, with the lasing threshold of

*ε″*

_{th}= −0.00069.

*ε″*

_{th}for the cavity modes decreases drastically due to the reduced group velocity. A decrease of more than two orders of magnitude in

*ε″*

_{th}is observed for the cavity mode near the low-frequency band edge (at

*ωa*/2

*πc*= 0.582), as opposed to a cavity mode far from the band edge (at

*ωa*/2

*πc*= 0.466). Although the cavity confinement effect is present for the mode at the normalized frequency of 0.466, it is far from the stopband and does not have the bandgap effect of the 3D PhC. Thus, the cavity mode at this frequency is equivalent to the cavity mode of the design shown in Fig. 1 (b). A lower value of

*ε″*

_{th}for the mode at the low-frequency edge (at

*ωa*/2

*πc*= 0.582), as compared to the mode at the high-frequency edge (at

*ωa*/2

*πc*= 0.627), is expected [14

14. M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. **38**, 1046–1048 (2013). [CrossRef] [PubMed]

*ε″*

_{th}at the two edges of the stopband for the stand-alone 3D PhC.

*ε″*

_{th}value at the band edges, a significant decrease in the lasing threshold of PhC heterostructure cavity is seen due to the increased feedback provided by the multilayer in comparison to a stand-alone 3D PhC. The

*ε″*

_{th}in active PhCs can be calculated by [12

**4**, 481–489 (1999). [CrossRef] [PubMed]

*f*is the filling factor of the dielectric medium containing gain and

*V*is the group velocity of the mode with frequency

_{g}*ω*.

*ε̄′*is the spatial average of the dielectric function

*ε′*(

*r*), which is the real part of the permittivity of the medium containing gain. It is given by Here

*V*is the volume of unit cell. The values of

_{o}*V*of the stand-alone 3D PhC, shown earlier in Fig. 2(b) are plotted as open squares in Fig. 5(b) for the band edge frequencies. Using these

_{g}*V*values,

_{g}*ε″*can be estimated using Eq. (8) for the 3D PhC. These are found to be in good agreement with the values obtained numerically.

_{th}*V*for the cavity modes of the PhC heterostructure cavity shown in Fig. 1(c) is difficult due to the composite nature of the structure. Hence, using the numerically obtained

_{g}*ε″*of this structure, the

_{th}*V*is estimated using Eq. (8), and shown as open circles in Fig. 5(b). One can note that the group velocity of the cavity modes near the stopband of the 3D PhC is decreased by more than an order of magnitude as compared to the

_{g}*V*in stand-alone 3D PhC. Thus the drastic reduction in the lasing threshold in PhC heterostructure cavity is supported by the lowered group velocity of its modes.

_{g}*γ*) from the relation

26. D. Handapangoda, I. D. Rukhlenko, M. Premaratne, and C. Jagadish, “Optimization of gain-assisted waveguiding in metaldielectric nanowires,” Opt. Lett. **35**, 4190–4192 (2010). [CrossRef] [PubMed]

*k*

_{0}is the free-space propagation constant. The threshold gain cofficient (

*γ*

_{th}) obtained by varying the number of periodic multilayers on either side of the 3D PhC is shown by the black curve in Fig. 6(a). The number of periodic layers in the PhC is chosen to be 25 and

*a*= 367 nm. The threshold gain can be reduced by more than an order of magnitude via increasing the periodic bilayers from two to five in the multilayer stack. With a further increase in the number of bilayers, only a small change in

*γ*

_{th}can be observed. It is interesting to note that five bi-layers periodically stacked on each side of the 3D PhC are sufficient to obtain a significant reduction in

*γ*

_{th}. The reflection calculated for the same mode from a stand-alone multilayer stack with an equivalent number of periodic layers, shown by the blue curve, confirms this conclusion.

*γ*

_{th}on the number N of ordered layers of the sandwiched active 3D PhC, which determines the cavity length, with a five-bilayer periodic stack on either side. The results are shown by the filled circles in Fig. 6(b). The open circles show

*γ*

_{th}for the stand-alone 3D PhC. One can observe a reduction of two orders of magnitude in the gain coefficient of the heterostructure PhC cavity. The change in lasing wavelength, which occurs due to the variation in the number of sandwiched 3D PhC layers, is marked by stars in Fig. 6(b). It implies that one can attain the lasing with reduced threshold values regardless of the number of layers in the sandwiched 3D PhC. Moreover, one can select the lasing mode with a lower threshold from the different cavity modes available, by overlapping that particular mode with the band edge region via a change in the periodicity of the sandwiched 3D PhC.

27. Q. Yan, Z. Zhou, and X. S. Zhao, “Inward-growing self-assembly of colloidal crystal films on horizontal substrates,” Langmuir **21**, 3158–3164 (2005). [CrossRef] [PubMed]

7. J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid onedimensional photonic crystal,” Appl. Phys. Lett. **88**, 091102 (2006). [CrossRef]

5. L.-T. Shi, F. Jin, M.-L. Zheng, X.-Z. Dong, W.-Q. Chen, Z.-S. Zhao, and X.-M. Duan, “Threshold optimization of polymeric opal photonic crystal cavity as organic solid-state dye-doped laser,” Appl. Phys. Lett. **98**, 093304 (2011). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. |

2. | S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. |

3. | R. Herrmann, T. Snner, T. Hein, A. Lffler, M. Kamp, and A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. |

4. | H. Y. Ryu and M. Notomi, “Enhancement of spontaneous emission from the resonant modes of a photonic crystal slab single-defect cavity,” Opt. Lett. |

5. | L.-T. Shi, F. Jin, M.-L. Zheng, X.-Z. Dong, W.-Q. Chen, Z.-S. Zhao, and X.-M. Duan, “Threshold optimization of polymeric opal photonic crystal cavity as organic solid-state dye-doped laser,” Appl. Phys. Lett. |

6. | F. Jin, Y. Song, X.-Z. Dong, W.-Q. Chen, and X.-M. Duan, “Amplified spontaneous emission from dye-doped polymer film sandwiched by two opal photonic crystals,” Appl. Phys. Lett. |

7. | J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid onedimensional photonic crystal,” Appl. Phys. Lett. |

8. | O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. OBrien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science |

9. | N. Susa, “Threshold gain and gain-enhancement due to distributed-feedback in two-dimensional photonic-crystal lasers,” J. Appl. Phys. |

10. | K. Sakoda, “Enhanced light amplification due to group-velocity anomaly peculiar to two- and three-dimensional photonic crystals,” Opt. Express |

11. | 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. |

12. | K. Sakoda, K. Ohtaka, and T. Ueta, “Low-threshold laser oscillation due to group-velocity anomaly peculiar to two and three-dimensional photonic crystals,” Opt. Express |

13. | P.-H. Weng, T.-T. Wu, T.-C. Lu, and S.-C. Wang, “Threshold gain analysis in GaN-based photonic crystal surface emitting lasers,” Opt. Lett. |

14. | M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. |

15. | M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, and M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photonics J. |

16. | M. S. Reddy, R. Vijaya, I. D. Rukhlenko, and M. Premaratne, “Spatial and spectral distributions of emission from dye-doped photonic crystals in reflection and transmission geometries,” J. Nanophotonics |

17. | N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. |

18. | N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. |

19. | M. N. Shkunov, Z. V. Vardeny, M. C. DeLong, R. C. Polson, A. A. Zakhidov, and R. H. Baughman, “Tunable, gap-state lasing in switchable directions for opal photonic crystals,” Adv. Funct. Mat. |

20. | S. Furumi, “Recent advances in polymer colloidal crystal lasers,” Nanosale |

21. | F. Yu. Sychev, I. E. Razdolski, T. V. Murzina, O. A. Aktsipetrov, T. Trifonov, and S. Cheylan, “Vertical hybrid microcavity based on a polymer layer sandwiched between porous silicon photonic crystals,” Appl. Phys. Lett. |

22. | |

23. | S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express |

24. | S. Satpathy, Ze Zhang, and M.R. Salehpour, “Theory of photon bands in three-dimensional periodic dielectric structures,” Phys. Rev. Lett. |

25. | K. Sakoda, |

26. | D. Handapangoda, I. D. Rukhlenko, M. Premaratne, and C. Jagadish, “Optimization of gain-assisted waveguiding in metaldielectric nanowires,” Opt. Lett. |

27. | Q. Yan, Z. Zhou, and X. S. Zhao, “Inward-growing self-assembly of colloidal crystal films on horizontal substrates,” Langmuir |

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(140.3490) Lasers and laser optics : Lasers, distributed-feedback

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: January 17, 2014

Revised Manuscript: February 20, 2014

Manuscript Accepted: February 21, 2014

Published: March 10, 2014

**Citation**

M. Srinivas Reddy, Ramarao Vijaya, Ivan D. Rukhlenko, and Malin Premaratne, "Low-threshold lasing in photonic-crystal heterostructures," Opt. Express **22**, 6229-6238 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6229

Sort: Year | Journal | Reset

### References

- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]
- R. Herrmann, T. Snner, T. Hein, A. Lffler, M. Kamp, A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. 31, 1229–1231 (2006). [CrossRef] [PubMed]
- H. Y. Ryu, M. Notomi, “Enhancement of spontaneous emission from the resonant modes of a photonic crystal slab single-defect cavity,” Opt. Lett. 28, 2390–2392 (2003). [CrossRef] [PubMed]
- L.-T. Shi, F. Jin, M.-L. Zheng, X.-Z. Dong, W.-Q. Chen, Z.-S. Zhao, X.-M. Duan, “Threshold optimization of polymeric opal photonic crystal cavity as organic solid-state dye-doped laser,” Appl. Phys. Lett. 98, 093304 (2011). [CrossRef]
- F. Jin, Y. Song, X.-Z. Dong, W.-Q. Chen, X.-M. Duan, “Amplified spontaneous emission from dye-doped polymer film sandwiched by two opal photonic crystals,” Appl. Phys. Lett. 91, 031109 (2007). [CrossRef]
- J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid onedimensional photonic crystal,” Appl. Phys. Lett. 88, 091102 (2006). [CrossRef]
- O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. OBrien, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]
- N. Susa, “Threshold gain and gain-enhancement due to distributed-feedback in two-dimensional photonic-crystal lasers,” J. Appl. Phys. 89, 815–823 (2001). [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]
- J. P. Dowling, M. Scalora, M. J. Bloemer, C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994). [CrossRef]
- K. Sakoda, K. Ohtaka, T. Ueta, “Low-threshold laser oscillation due to group-velocity anomaly peculiar to two and three-dimensional photonic crystals,” Opt. Express 4, 481–489 (1999). [CrossRef] [PubMed]
- P.-H. Weng, T.-T. Wu, T.-C. Lu, S.-C. Wang, “Threshold gain analysis in GaN-based photonic crystal surface emitting lasers,” Opt. Lett. 36, 1908–1910 (2011). [CrossRef] [PubMed]
- M. S. Reddy, R. Vijaya, I. D. Rukhlenko, M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. 38, 1046–1048 (2013). [CrossRef] [PubMed]
- M. S. Reddy, S. Kedia, R. Vijaya, A. K. Ray, S. Sinha, I. D. Rukhlenko, M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photonics J. 5, 4700409 (2013). [CrossRef]
- M. S. Reddy, R. Vijaya, I. D. Rukhlenko, M. Premaratne, “Spatial and spectral distributions of emission from dye-doped photonic crystals in reflection and transmission geometries,” J. Nanophotonics 6, 063526 (2012). [CrossRef]
- N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: Frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998). [CrossRef]
- N. Stefanou, V. Yannopapas, A. Modinos, “MULTEM 2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132, 189–196 (2000). [CrossRef]
- M. N. Shkunov, Z. V. Vardeny, M. C. DeLong, R. C. Polson, A. A. Zakhidov, R. H. Baughman, “Tunable, gap-state lasing in switchable directions for opal photonic crystals,” Adv. Funct. Mat. 12, 2126, (2002). [CrossRef]
- S. Furumi, “Recent advances in polymer colloidal crystal lasers,” Nanosale 4, 5564–5571 (2012). [CrossRef]
- F. Yu. Sychev, I. E. Razdolski, T. V. Murzina, O. A. Aktsipetrov, T. Trifonov, S. Cheylan, “Vertical hybrid microcavity based on a polymer layer sandwiched between porous silicon photonic crystals,” Appl. Phys. Lett. 95, 163301 (2009). [CrossRef]
- http://refractiveindex.info
- S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane wave basis,” Opt. Express 8, 173–190 (2001). [CrossRef] [PubMed]
- S. Satpathy, Ze Zhang, M.R. Salehpour, “Theory of photon bands in three-dimensional periodic dielectric structures,” Phys. Rev. Lett. 64, 1239–1242 (1990). [CrossRef] [PubMed]
- K. Sakoda, Optical properties of Photonic crystals (Springer-Verlag, Berlin, 2001) [CrossRef]
- D. Handapangoda, I. D. Rukhlenko, M. Premaratne, C. Jagadish, “Optimization of gain-assisted waveguiding in metaldielectric nanowires,” Opt. Lett. 35, 4190–4192 (2010). [CrossRef] [PubMed]
- Q. Yan, Z. Zhou, X. S. Zhao, “Inward-growing self-assembly of colloidal crystal films on horizontal substrates,” Langmuir 21, 3158–3164 (2005). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.