Ordered and Disordered Photonic Band Gap Materials

McPhedran, R. C.; Botten, L. C.; Asatryan, A. A.; Nicorovici, N. A.; Sterke, C. Martijn de; Robinson, P. A.

doi:10.1071/ph98110

Cited by 32 publications

(12 citation statements)

References 7 publications

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“…However, in order to make a direct comparison with the ordered case, we kept the excitation pulse the same as before. The exact cause of the disappearance of the bandgap is being debated in the literature [16,25,26], and is not the subject of this study. In our particular case we found a simple explanation of the threshold behavior in the way the disorder was introduced.…”

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confidence: 99%

“…Random laser modes have the highest Q's and therefore weakly contribute to the transport properties of the system. Among other methods [16,17], finite difference time domain (FDTD) method has been shown to be a convenient tool in studying random laser modes in 1D [10] and 2D [11]. It was recently shown [10,11] that above the threshold, the shape of the lasing modes remain the same as in passive medium.…”

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confidence: 99%

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Highest-quality modes in disordered photonic crystals

Yamilov

Cao

2004

Phys. Rev. A

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We studied lasing modes in a disordered photonic crystal. The scaling of the lasing threshold with the system size depends on the strength of disorder. For sufficiently large size, the minimum of the lasing threshold occurs at some finite value of disorder strength. The highest random cavity quality factor was comparable to that of an intentionally introduced single defect. At the minimum, the lasing threshold showed a super-exponential decrease with the size of the system. We explain it through a migration of the lasing mode frequencies toward the photonic bandgap center, where the localization length takes the minimum value. Random lasers with exponentially low thresholds are predicted.A finite open system of scattering particles can be characterized by a set of quasi-stationary (leaky) optical modes. When gain, sufficient to compensate the leakage in at least one mode, is introduced in such systemrandom laser is formed [1,2,3,4,5,6,7,8,9]. Unconventional feedback mechanism in a random laser leads to properties interesting from both fundamental and practical point of view [1,2,3,4,5,6,7,8,9,10,11,12,13]. While previous studies concentrated mainly on disordered systems, the resent experiments by Shkunov et al [14] demonstrated random lasing peaks associated with the bandgap in partially ordered system. In this letter, we obtain the lasing threshold for a random laser with different degree of ordering. Important information about these states can be extracted from the scaling of the average lasing threshold with the system size [12], L. For increasing values of the disorder parameter we find 5 scaling regimes: (a) photonic band-edge, 1/L 3 , (b) transitional super-exponential, (c) bandgap-related exponential, (d) diffusive, 1/L 2 , and (e) disorder-induced exponential, due to Anderson localized modes, regimes. In this letter we show that by optimizing the disorderness of the sample one can dramatically reduce the threshold of random laser, to the values comparable to those of photonic bandgap defect lasers [15]. This finding can open up a road to practical applications of random lasers.Finding the lasing threshold of a random laser theoretically is a difficult problem. In disordered photonic crystals one cannot take simplifying assumptions such as independent scattering approximation (low density limit), neglect the finite size of the scatterers, or the confined dimensions of the system. Random laser modes have the highest Q's and therefore weakly contribute to the transport properties of the system. Among other methods [16,17], finite difference time domain (FDTD) method has been shown to be a convenient tool in studying random laser modes in 1D [10] and 2D [11]. It was recently shown [10,11] that above the threshold, the shape of the lasing modes remain the same as in passive medium. In this work, we used FDTD method to find the modes with the smallest energy decay rate in an open passive 2D random medium system with different degree of order. These modes determine the value of the lasing threshold in an act...

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Highest-quality modes in disordered photonic crystals

Yamilov

Cao

2004

Phys. Rev. A

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“…Therefore, the (average) transverse wavenumber k ⊥ = (n 2 eff − n 2 fsm ) 1/2 is very small; in fact at V = 0.6, k ⊥ Λ ≈ 7 × 10 −3 . The evaluation of the lattice sums that are used in the FSS method, for the multipole calculation of the grating scattering matrices, now becomes increasingly difficult, as their magnitudes scale as powers of 1/k ⊥ [11].…”

Section: Resultsmentioning

confidence: 99%

Long wavelength behavior of the fundamental mode in microstructured optical fibers

Wilcox¹,

Botten²,

Sterke³

et al. 2005

Opt. Express

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“…where the final term of (7) is the series expansion of E(r) in cylindrical harmonics about the centre of the cylinder l. The field identity (7) shows that the regular part of the field in the vicinity D l of cylinder l (left side), is generated by sources on all the other cylinders, plus contributions from other external sources (right side). In (7) we apply Graf's addition theorem [28] to derive the Rayleigh identity…”

Section: General Frameworkmentioning

confidence: 99%

“…Twersky [6] generalised Ignatowsky's work and developed efficient computational schemes for the lattice sums based on the EulerMacLaurin formula. We have further extended the method [7][8][9] to provide for multiple cylinders in the basis cell, leading to the introduction of both global and relative lattice sums. Other authors [10,11] have used related methods that trace their origin to the well-known Korringa-Kohn-Rostoker method [12] of solid state physics.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh Multipole Methods for Photonic Crystal Calculations

Botten¹,

McPhedran²,

Nicorovici³

et al. 2003

PIER

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Abstract-Multipole methods have evolved to be an important class of theoretical and computational techniques in the study of photonic crystals and related problems. In this chapter, we present a systematic and unified development of the theory, and apply it to a range of scattering problems including finite sets of cylinders, two-dimensional stacks of grating and the calculation of band diagrams from the scattering matrices of grating layers. We also demonstrate its utility in studies of finite systems that involve the computation of the local density of states.

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Ordered and Disordered Photonic Band Gap Materials

Cited by 32 publications

References 7 publications

Highest-quality modes in disordered photonic crystals

Highest-quality modes in disordered photonic crystals

Long wavelength behavior of the fundamental mode in microstructured optical fibers

Rayleigh Multipole Methods for Photonic Crystal Calculations

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