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Large mode splitting and lasing in optimally coupled photonic-crystal microcavities |
Optics Express, Vol. 19, Issue 3, pp. 2619-2625 (2011)
http://dx.doi.org/10.1364/OE.19.002619
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– Abstract
1. Introduction
2. Optimum coupling geometry: 3D FDTD simulation of the coupled system
3. Experimental observation of coupling and very large splitting
4. Coupled-cavity photonic-crystal quantum-wire microlaser
5. Summary
– References and links
– Abstract
1. Introduction
2. Optimum coupling geometry: 3D FDTD simulation of the coupled system
3. Experimental observation of coupling and very large splitting
4. Coupled-cavity photonic-crystal quantum-wire microlaser
5. Summary
– References and links
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Abstract
Coupling of L-type photonic-crystal (PhC) cavities in a geometry that follows inherent cavity field distribution is exploited for demonstrating large mode splitting of up to ~10-20 nm (~15-30 meV) near 1µm wavelength. This is much larger than the disorder-induced cavity detuning for conventional PhC technology, which ensures reproducible coupling. Furthermore, a microlaser based on such optimally coupled PhC cavities and incorporating quantum wire gain medium is demonstrated, with potential applications in fast switching and modulation.
© 2011 OSA
1. Introduction
Tunnel coupling via evanescent waves is a fundamental phenomenon in physics on which the building of complex systems out of more basic components is founded. Optical tunnel coupling is especially practical in nano-photonics, particularly for coupling photonic microcavities [1] into systems interesting for experiments in quantum physics [2, 3] with potential use in the field of quantum information processing [4]. Other particular applications of coupled microcavities include signal transmission [5] and fast semiconductor lasers [6–8]. All these targets require optical modes that can be evenly distributed in intensity between the cavities, which – in view of fabrication-induced disorder and consequent mode localization [9–12] – can be established by sufficiently large coupling. Photonic-crystal (PhC) cavities can yield very tight light confinement within a small volume [1], providing a platform for practical device implementations, in particular for novel microcavity and multiple-cavity lasers [7, 8]. As compared to simple extended photonic systems [9–12], employing coupled structures where the coupling effect is larger than disorder-induced localization may ensure spatial stability of the optical mode thus yielding desired device performance.
K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]
M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2(12), 849–855 (2006). [CrossRef]
D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5(4), 281–284 (2009). [CrossRef]
J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009). [CrossRef]
D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15(3), 1228–1233 (2007). [CrossRef] [PubMed]
L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005). [CrossRef]
S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett. 99(7), 073902 (2007). [CrossRef] [PubMed]
A. Golshani, H. Pier, E. Kapon, and M. Moser, “Photon mode localization in disordered arrays of vertical cavity surface emitting lasers,” J. Appl. Phys. 85(4), 2454–2456 (1999). [CrossRef]
H. Pier and E. Kapon, “Photon localization in lattices of coupled vertical-cavity surface-emitting lasers with dimensionalities between one and two,” Opt. Lett. 22(8), 546–548 (1997). [CrossRef] [PubMed]
K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]
H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2(7), 484–488 (2006). [CrossRef]
S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett. 99(7), 073902 (2007). [CrossRef] [PubMed]
A. Golshani, H. Pier, E. Kapon, and M. Moser, “Photon mode localization in disordered arrays of vertical cavity surface emitting lasers,” J. Appl. Phys. 85(4), 2454–2456 (1999). [CrossRef]
H. Pier and E. Kapon, “Photon localization in lattices of coupled vertical-cavity surface-emitting lasers with dimensionalities between one and two,” Opt. Lett. 22(8), 546–548 (1997). [CrossRef] [PubMed]
In this paper, we present and study a PhC coupled-cavity optical system where, thanks to optimal cavity layout, it is possible to reach very large optical coupling strength. The effects of this large coupling are demonstrated both numerically and experimentally, with structures of PhC membrane cavities in which site-controlled, embedded quantum wires (QWRs) [13] serve as light sources. Furthermore, using the same QWRs as gain medium we achieve lasing action in such a coupled cavity system and discuss its modal features.
G. Biasiol, F. Reinhardt, A. Gustafsson, and E. Kapon, “Self-limiting OMCVD growth of GaAs on V-grooved substrates with application to InGaAs/GaAs quantum wires,” J. Electron. Mater. 26(10), 1194–1198 (1997). [CrossRef]
2. Optimum coupling geometry: 3D FDTD simulation of the coupled system
PhC-cavity coupling has been clearly demonstrated in several configurations [14, 15], with observed mode splitting around 1-2 nm (~1 meV). In PhC line-defect cavities (LN cavities), including the much-investigated L3 cavity, the confined optical field extends spatially following an X-shaped pattern [Fig. 1(a)
]. This gives a clear hint for choosing optimal layout for coupling two or more such cavities, namely, the coupling barrier should be placed along the tails of the decaying field [see arrow in Fig. 1(a)]. Using, first, 3D FDTD simulations we verify this indication, observing that the closest distance between the cavities (“1row” in Fig. 1(b), meaning a 1-row separation along the indicating arrow), results indeed in a very large coupling strength manifested by ~20nm splitting in mode wavelength. If, in addition, the upper cavity is shifted to the right by 1 lattice constant [Fig. 1(b), “1row 1h”], the cavity-cavity distance becomes similar to that studied previously [14] for cavities placed in the same PhC row, yet the wavelength splitting is 6-fold larger. Even if the two cavities are relatively far apart [see Fig. 1(b) “3rows” and “5rows”], sizeable coupling is retained, with splitting of ~4 nm and ~1 nm, respectively. Thus, the preferential coupling path based on the specific evanescent field distribution provides large coupling while maintaining good field confinement within each of the cavities, and the supermodes have cavity components that differ almost only by phase. This is important, e.g., in applications in switchable lasers [8], where switching is done by selecting one of the supermodes via its phase. Preferred or “dedicated” coupling paths were also shown to be useful for charge carrier state hybridization in QD molecules coupled via QWRs without compromising confinement strength [16].
K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008). [CrossRef] [PubMed]
S. Vignolini, F. Intonti, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94(15), 151103 (2009). [CrossRef]
K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008). [CrossRef] [PubMed]
S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett. 99(7), 073902 (2007). [CrossRef] [PubMed]
Q. Zhu, K. F. Karlsson, M. Byszewski, A. Rudra, E. Pelucchi, Z. He, and E. Kapon, “Hybridization of electron and hole states in semiconductor quantum-dot molecules,” Small 5(3), 329–335 (2009). [CrossRef] [PubMed]
Fig. 1 (a) Near field patterns for two GaAs membrane L3 PhCs calculated using 2D finite-difference (FD) method): green arrow follows the field distribution along the intense evanescent field tail. (b) Near field distributions (Ey field component shown, computed with 2D FD) for different barrier size. Separating “rows” are indicated (at left) counting along the arrow in (a). (c) Results of 3D finite difference time domain (FDTD) simulations showing the spectra for all the considered cavity geometries. The spectra are corrected for the infrared dispersion of the GaAs refractive index. Q-factors are obtained by means of Padé-Baker approximation. The definition of the symmetric (MS) and the antisymmetric (MA) supermodes is based on the phase of Ey field component taken at the cavity center; the mode labelling in (c) is ascribed by separate 3D FDTD simulations performed for each supermode ”excited’ with the exact 2D field distribution at the membrane center. Parameters: resolution 0.035a, lattice constant a=198nm, hole radius r/a=0.23, thickness 265nm, software developed in-house.
3. Experimental observation of coupling and very large splitting
We verified experimentally these computations by realizing such optimally-coupled PhC membrane cavities in which site-controlled quantum wires (QWRs) serve as light sources [14]. First, In0.15Ga0.85As site-controlled QWRs were grown by metal-organic vapour-phase epitaxy on V-groove pattern prepared by conventional e-beam lithography and wet etching (Br:HBr:H2O solution) on (100) GaAs substrates. In each V-groove (initially 190-nm deep), we stacked 5 QWRs, each QWR layer being nominally 2.7-nm thick and spaced by GaAs barriers to finally form a fully planarized 265-nm thick GaAs/InGaAs “membrane” placed on top of a 1 μm sacrificial Al0.75Ga0.15As layer. Then, PhC cavities were defined such that each single cavity contained one stack of finite-length QWRs. Each QWR stack has a length equal to that of the cavity and is cut by the cavity terminations during dry etching, implemented by BCl3-based inductively-coupled plasma etching [17]. L3 cavities with shifted terminations [18] were employed [see Fig. 1(a,b)]. The PhC membranes were released by 4% HF acid etching of the AlGaAs layer.
K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008). [CrossRef] [PubMed]
K. A. Atlasov, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Effect of sidewall passivation in BCl3/N2 inductively coupled plasma etching of two-dimensional GaAs photonic crystals,” J. Vac. Sci. Technol. B 27(5), L21–L24 (2009). [CrossRef]
Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]
In such cavity system, the QWRs act as independent internal light sources for each of the cavities. We optically pumped the structures using a micro-photoluminescence (micro-PL) set-up [14]. Scanning the optical pumping spot (diameter ~1 μm) across the coupled cavities [see Fig. 2(b)
] allows observing optical coupling between the pumped cavities [14]. For sufficiently close cavities, we observe the simultaneous excitation of the spectral lines corresponding to the coupled modes, independent of the position of excitation [see Fig. 2(c),(d)]. However, for excessively separated cavities, spectral features representing either cavity are observed, strongly depending on the position of excitation spot [see Fig. 2(e)]. This occurs because the effect of optical disorder in those cases is larger than the coupling strength between the cavities and the modes localize. We observed coupling for several configurations, namely “1row”, “1row 1h” and “3rows”, with mode splitting similar to that predicted by 3D FDTD [see Fig. 2(f)]: Δλ=20.7-21.1 nm, Δλ=12.4-15.2 nm and Δλ=2.7-3.2 nm, respectively. In the case of “5rows” barrier no coupling was seen, which is an indication that the disorder-related detuning (for the e-beam system used here) is larger than ~1 nm wavelength.
K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008). [CrossRef] [PubMed]
K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008). [CrossRef] [PubMed]
Fig. 2 Experimental observation of the optical cavity coupling. (a) SEM top-view image of PhC coupled cavities in “1row 1h” arrangement. (b) Illustration of the scanning micro-PL pumping scheme (displayed on top of an SEM top-view image of one of the “3rows” coupled-cavity geometries). (c-e) Results of the micro-PL scans for different coupled-cavity geometries (as indicated), where each spectrum in a scan is taken at different pump position as sketched by the grey arrow [scan as in (b)]. The PhC-cavity modes are observed on the background of the QWR emission. (f) Summary showing spectra of coupled-cavity supermodes observed for several different coupling-barrier lengths, as indicated.
Interestingly, for some samples with “3rows” and “5rows” barrier geometries it was also observed that the spectrum contained peaks separated by up to 6-9 nm with no coupling effect. These represent extreme cases where astigmatism correction in e-beam writing failed (on the periphery of the writing field) thus producing larger disorder-related detuning. On average, the disorder-related detuning is estimated as less than ~3-4 nm, since coupling was observed in several “3rows” barrier cases for which the coupling strength gives splitting of ~4 nm [Fig. 1(c)]. Remarkably, almost 100% of the geometries with “1row” and “1row 1h” barriers showed coupling. This is indeed expected, as the coupling strength in these cases is much larger than even the “severe” disorder-related detuning. This is significant, since these latter coupling geometries may thus be effectively immune to fabrication-induced disorder, which is important, e.g., for applications in broad-area light emitters [10, 19] where one needs to avoid any localization of the optical field.
L. Mutter, V. Iakovlev, A. Caliman, A. Mereuta, A. Sirbu, and E. Kapon, “1.3 microm-wavelength phase-locked VCSEL arrays incorporating patterned tunnel junction,” Opt. Express 17(10), 8558–8566 (2009). [CrossRef] [PubMed]
A. Surrente, P. Gallo, M. Felici, B. Dwir, A. Rudra, and E. Kapon, “Dense arrays of ordered pyramidal quantum dots with narrow linewidth photoluminescence spectra,” Nanotechnology 20(41), 415205 (2009). [CrossRef] [PubMed]
4. Coupled-cavity photonic-crystal quantum-wire microlaser
Having demonstrated earlier that a ~1µm long QWR stack embedded in a PhC membrane cavity can produce enough gain for lasing [20], we proceeded to study the light output characteristics of the coupled-cavity structures vesrus pump power. In the case of “1row 1h” coupling-barrier configuration [Fig. 3
, Fig. 2(a,f)], where both supermodes overlap well with the QWR emission spectrum, we observe that the lower energy mode MA dominates at low pump power. At higher pump power, the higher energy mode MS takes over in intensity. This is consistent with the expected blue shift in the peak of the QWR optical gain spectrum at increasing pump level. Plotting the integrated intensity (normalized by the CCD acquisition time) of each mode on a log-log scale [Fig. 3(b)], S-shaped curves characteristic of lasing are obtained for both modes. Mode MA, however, gets severely suppressed soon after the onset of mode MS. We analyzed these trends by the following rate-equation model [21] where the third equation was introduced to simulate indirect carrier supply:
K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17(20), 18178–18183 (2009). [CrossRef] [PubMed]
G. Bjork and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27(11), 2386–2396 (1991). [CrossRef]
Fig. 3 Evidence for lasing in coupled-cavity system, “1row 1h” barrier geometry at T=50K. (a) Micro-PL spectra versus pump level. MS/MA modes are ascribed as in Fig. 1(c). (b) Input-output curves in log-log scale (inset: linear scale, near threshold). Fitting is done by time-dependent rate-equation model (see text). (c) Linewidth trends (in inverse normalized values). (d) Peak shift. Pump conditions: Ti:Sapphire laser mode-locked at 700 nm, pulse duration ~3ps, repetition rate 78 MHz.
In this system the optical pump Lin
at angular frequency ωin = 2πc0/λin
(λin
=700nm) provides carrier excitation at level NE
(GaAs) from where the carriers relax, feeding the laser level (QWR) with carrier density N. Note that in this simple model the time constant τE
represents feeding in general and not only carrier relaxation. We used τsp
=300 ps and τnr
=1.25 ns [20] for spontaneous emission and non-radiative recombination times, respectively; Va
=5 × (5 × 5 × 1000) nm3 is the active-medium volume (stack of 5 QWRs) embedded within the cavity; ωcav = 2πc0/λcav
at the output cavity-mode resonance [see Fig. 3(a)]; Q is the quality factor measured as λcav
/Δλcav
below threshold where Δλcav
is the full width at half maximum of the cavity mode; p is the photon number; β is the spontaneous-emission coupling factor; and a linear gain model [21] is used for g with a transparency carrier density of Ntr
=1018 cm−3. Assuming excitation Lin
by a Gaussian pulse of 3 ps width, we solve the rate equations in the time domain at a given pump intensity P. The input-output fit curve is extracted then point by point by integrating each time the intensity of the calculated output pulse. τE
and β are used as fit parameters. The best fits are presented in Fig. 3(b) by solid curves (blue and red). We note that the fitted τE
values match well those measured for similar QWRs (as rise times in time-resolved micro-PL acquired respectively at detuning to shorter or longer wavelength with respect to QWR-emission peak). Fitting the input-output curve for mode MS reasonably reproduces the data points. On the other hand, a regular fit for mode MA diverges approximately at the point where mode MS attains its threshold. At this point mode MA becomes suppressed and its output power declines. Introducing into Eq. (2) a dissipative term with a power-dependent time-constant (which models exponentially growing dissipation due to the lasing onset of the mode MS) does not result in a good fit (not shown). On the other hand, assuming (phenomenologically) a simple dependence of τE
on the input power as τE=150ps+120ps*P produces a rather reasonable fit [displayed in Fig. 3(b)]. This might indicate that, with the onset of lasing of mode MS, the feeding rate for mode MA starts depending on the pump level. It may take place due to competition of the modes on the available cavity gain. On the other hand, the optical gain itself is power-dependent, and due to its spectral shift mode MS becomes favoured. Note that, although our simple model can explain the main findings, more complex analysis using coupled-mode theories [22, 23] should be involved for the exact treatment of the multimode laser field.
K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17(20), 18178–18183 (2009). [CrossRef] [PubMed]
G. Bjork and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27(11), 2386–2396 (1991). [CrossRef]
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76(1), 013813 (2007). [CrossRef]
S. V. Zhukovsky, D. N. Chigrin, and J. Kroha, “Bistability and mode interaction in microlasers,” Phys. Rev. A 79(3), 033803 (2009). [CrossRef]
Suppression of mode MA is also confirmed by the measured linewidth trend [Fig. 3(c)]. Indeed, while mode MS exhibits linewidth narrowing related to the coherence build-up (up to saturation at very high pump intensities), the linewidth for mode MA saturates. On the other hand, the measured peak shift is similar for both MA and MS modes [see Fig. 3(d)] indicating similar mode behaviour due to the variations of the carrier density and hence the refractive index, which affect both modes almost in exactly the same way. This occurs because the modal field distributions apparently differ only by phase and are almost identical in intensity distribution. This feature provides a similar laser threshold for both modes. Note, that this would not be the case for a large-cavity multi-mode structure. However in the present case, the relaxing charge carriers become mostly consumed by the shorter-wavelength mode that dominates thus the output spectrum. Following regular lasing criteria [20], mode MA does not lase, and hence the considered coupled-cavity device operates in a single-mode at high enough pump level, which is of course interesting for applications where single-mode regime is desired. On the other hand, for achieving multimode lasing or bistability, the mode spectral spacing needs to be reduced such that both supermodes spectrally match better the gain.
K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17(20), 18178–18183 (2009). [CrossRef] [PubMed]
5. Summary
In summary, we demonstrated optical coupling in new designs of PhC membrane microcavities favoring strong cavity coupling, where consequently a very large mode splitting (up to ~20 nm, or ~30 meV) was achieved. Such strong tunnel coupling is important for preventing optical mode localization due to optical disorder induced by material and/or fabrication nonuniformities. Lasing in such coupled cavities was demonstrated as well. The results of this paper may find applications in further development of more complex optically coupled systems, multiple-cavity microlasers, lasers exhibiting fast-switching [8], and structures for strongly-coupled light-matter systems based on quantum dots [2–4].
S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett. 99(7), 073902 (2007). [CrossRef] [PubMed]
M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2(12), 849–855 (2006). [CrossRef]
J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009). [CrossRef]
References and links
K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed] | |
M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2(12), 849–855 (2006). [CrossRef] | |
D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5(4), 281–284 (2009). [CrossRef] | |
J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009). [CrossRef] | |
D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15(3), 1228–1233 (2007). [CrossRef] [PubMed] | |
L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005). [CrossRef] | |
H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2(7), 484–488 (2006). [CrossRef] | |
S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett. 99(7), 073902 (2007). [CrossRef] [PubMed] | |
A. Golshani, H. Pier, E. Kapon, and M. Moser, “Photon mode localization in disordered arrays of vertical cavity surface emitting lasers,” J. Appl. Phys. 85(4), 2454–2456 (1999). [CrossRef] | |
L. Mutter, V. Iakovlev, A. Caliman, A. Mereuta, A. Sirbu, and E. Kapon, “1.3 microm-wavelength phase-locked VCSEL arrays incorporating patterned tunnel junction,” Opt. Express 17(10), 8558–8566 (2009). [CrossRef] [PubMed] | |
K. A. Atlasov, M. Felici, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “1D photonic band formation and photon localization in finite-size photonic-crystal waveguides,” Opt. Express 18(1), 117–122 (2010). [CrossRef] [PubMed] | |
H. Pier and E. Kapon, “Photon localization in lattices of coupled vertical-cavity surface-emitting lasers with dimensionalities between one and two,” Opt. Lett. 22(8), 546–548 (1997). [CrossRef] [PubMed] | |
G. Biasiol, F. Reinhardt, A. Gustafsson, and E. Kapon, “Self-limiting OMCVD growth of GaAs on V-grooved substrates with application to InGaAs/GaAs quantum wires,” J. Electron. Mater. 26(10), 1194–1198 (1997). [CrossRef] | |
K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008). [CrossRef] [PubMed] | |
S. Vignolini, F. Intonti, M. Zani, F. Riboli, D. S. Wiersma, L. H. Li, L. Balet, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Near-field imaging of coupled photonic-crystal microcavities,” Appl. Phys. Lett. 94(15), 151103 (2009). [CrossRef] | |
Q. Zhu, K. F. Karlsson, M. Byszewski, A. Rudra, E. Pelucchi, Z. He, and E. Kapon, “Hybridization of electron and hole states in semiconductor quantum-dot molecules,” Small 5(3), 329–335 (2009). [CrossRef] [PubMed] | |
K. A. Atlasov, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Effect of sidewall passivation in BCl3/N2 inductively coupled plasma etching of two-dimensional GaAs photonic crystals,” J. Vac. Sci. Technol. B 27(5), L21–L24 (2009). [CrossRef] | |
Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed] | |
A. Surrente, P. Gallo, M. Felici, B. Dwir, A. Rudra, and E. Kapon, “Dense arrays of ordered pyramidal quantum dots with narrow linewidth photoluminescence spectra,” Nanotechnology 20(41), 415205 (2009). [CrossRef] [PubMed] | |
K. A. Atlasov, M. Calic, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “Photonic-crystal microcavity laser with site-controlled quantum-wire active medium,” Opt. Express 17(20), 18178–18183 (2009). [CrossRef] [PubMed] | |
G. Bjork and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27(11), 2386–2396 (1991). [CrossRef] | |
H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76(1), 013813 (2007). [CrossRef] | |
S. V. Zhukovsky, D. N. Chigrin, and J. Kroha, “Bistability and mode interaction in microlasers,” Phys. Rev. A 79(3), 033803 (2009). [CrossRef] |
OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(140.3945) Lasers and laser optics : Microcavities
(230.4555) Optical devices : Coupled resonators
ToC Category:
Lasers and Laser Optics
History
Original Manuscript: November 18, 2010
Revised Manuscript: December 17, 2010
Manuscript Accepted: December 21, 2010
Published: January 27, 2011
Citation
Kirill A. Atlasov, Alok Rudra, Benjamin Dwir, and Eli Kapon, "Large mode splitting and lasing in optimally coupled photonic-crystal microcavities," Opt. Express 19, 2619-2625 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2619
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References
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