OSA's Digital Library

Optics Express

Optics Express

  • Editor: Martijn de Sterke
  • Vol. 16, Iss. 20 — Sep. 29, 2008
  • pp: 16255–16264
« Show journal navigation

Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities

Kirill A. Atlasov, Karl Fredrik Karlsson, Alok Rudra, Benjamin Dwir, and Eli Kapon  »View Author Affiliations


Optics Express, Vol. 16, Issue 20, pp. 16255-16264 (2008)
http://dx.doi.org/10.1364/OE.16.016255


View Full Text Article

Acrobat PDF (1730 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Coupling between photonic-crystal defect microcavities is observed to result in a splitting not only of the mode wavelength but also of the modal loss. It is discussed that the characteristics of the loss splitting may have an important impact on the optical energy transfer between the coupled resonators. The loss splitting — given by the imaginary part of the coupling strength — is found to arise from the difference in diffractive out-of-plane radiation losses of the symmetric and the antisymmetric modes of the coupled system. An approach to control the splitting via coupling barrier engineering is presented.

© 2008 Optical Society of America

1. Introduction

The direct coupling of optical microcavities has been demonstrated in various cavity systems including microdisks [7

7. S. Ishii, A. Nakagawa, and T. Baba, “Modal characteristics and bistability in twin microdisk photonic molecule lasers,” IEEE J. Sel. Top. Quantum Electron . 12, 71–77 (2006). [CrossRef]

, 12

12. S. V. Boriskina, “Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules,” Opt. Lett. 32, 1557–1559 (2007). [CrossRef] [PubMed]

], distributed Bragg reflector (DBR)-based pillars [13

13. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998). [CrossRef]

, 14

14. M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, “Free-standing porous silicon single and multiple optical cavities,” J. Appl. Phys. 93, 9724–9729 (2003). [CrossRef]

], microspheres [15

15. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999). [CrossRef]

], microrings [16

16. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997). [CrossRef]

] as well as in PhC-based few-cavity photonic molecules [17

17. T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, “Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs,” J. Opt. Soc. Am. B 20, 373–378 (2003). [CrossRef]

21

21. S. Lam, A. R. Chalcraft, D. Szymanski, R. Oulton, B. D. Jones, D. Sanvitto, D. M. Whittaker, M. Fox, M. S. Skolnick, D. O’Brien, T. F. Krauss, H. Liu, P. W. Fry, and M. Hopkinson, “Coupled Resonant Modes of Dual L3-Defect Planar Photonic Crystal Cavities,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper QFG6. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2008-QFG6 [PubMed]

] and large-area arrays [2

2. H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Physics 2, 484–488 (2006). [CrossRef]

, 3

3. D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15, 1228–1233 (2007). [CrossRef] [PubMed]

, 5

5. S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron . 8, 448–456 (2002). [CrossRef]

]. Frequency matching has been the main prerequisite in designing such microphotonics devices. However, loss associated with particular confined cavity modes is also an essential parameter, especially in the case of high-Q structures such as PhC defect cavities. Possible differences in the losses of the coupled supermodes would not only influence the interaction with charge carriers confined in different cavities (altering light-matter interaction e.g. via Purcell effect or influencing coupled-cavity laser performance) but would also affect the efficiency of the photon transfer, as it is shown here.

2. Loss splitting and energy transfer

Consider first a generalized system of two coupled oscillators (e.g. confined photons in our case) of free frequencies ω1 and ω2, and damping (loss) parameters γ 1 and γ 2. In the regime of linear coupling, the complex angular eigen-frequencies (frequencies ΩS,A and linewidths ΓS,A) of the system are given by [22

22. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).

]

Ωs,A+iΓs,A=12[ω1+ω2i(γ1+γ2)]±12[ω1ω2i(γ1γ2)]2+4g2,
(1)

e2Γstei(ΩAΩs)te(ΓAΓs)t±12.
(2)

Fig. 1. Illustration to the loss splitting and the energy transfer. (a) one-dimensional envelope functions (amplitudes) of the supermodes in space. (b) Time evolution of the supermode amplitudes (upper panel; note, AS(t) curve is shifted downwards for clarity) and the intensity in the coupled system within the “cavity 1” (|AS+AA|2) and within the “cavity 2” (|AS-AA|2) in the case of ΓS=ΓA. (c) time evolution in the case of ΓSΓA

3. Observation of wavelength and loss splitting in PhC microcavities

3.1 Sample preparation and integrated quantum-wire system in PhC cavities

To probe the coupling of two optical microcavities, we used a system [23

23. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90, 153107 (2007). [CrossRef]

] consisting of two PhC L3-defect cavities each of which contains a monolithically embedded short, site-controlled quantum wire [24

24. E. Kapon, D. M. Hwang, and R. Bhat, “Stimulated emission in semiconductor quantum wire heterostructures,” Phys. Rev. Lett. 63, 430–433 (1989). [CrossRef] [PubMed]

] (QWR) [Fig. 2(a)]. The PhC-QWR integration technology is based on substrate pre-patterning [23

23. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90, 153107 (2007). [CrossRef]

], which allows for a predefined nucleation site for the QWR. The lateral confinement in the QWRs ensures an efficient trapping of the excited carriers near the peaks of the optical field of the microcavity, thus yielding an efficient exciton-photon interaction. The micro-photoluminescence (micro-PL) spectrum of a “bare” InGaAs/GaAs QWR heterostructure, located outside the optical cavity, consists of two peaks [Fig. 2(b)]: one is due to recombination in the QWR (at ~923nm), the other (at ~886nm) — due to the quantum wells (QWs) located on both sides of the wire [see Fig. 2(a)]. The fabrication [23

23. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90, 153107 (2007). [CrossRef]

] starts by growing a ~1-µm Al0.7Ga0.3As layer and a 200-nm GaAs membrane layer on a (100) GaAs substrate using low-pressure metal-organic vapor phase epitaxy (MOVPE). A 1-µm pitch, ~170-nm deep V-groove grating (lined along the [01

1. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef] [PubMed]

1

1. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef] [PubMed]

] direction is then fabricated using electron beam lithography (implemented on a JEOL JSM 6400 scanning electron microscope) and wet etching. Next, the patterned substrate is MOVPE-regrown with a 5-nm In0.15Ga0.85As layer sandwiched between thin GaAs barriers such that a ~10-nm thick, crescent-shaped InGaAs QWR is formed at the bottom of each groove, near the center of the 265-nm (once regrown) GaAs membrane layer. After the regrowth, the QWRs are characterized using the micro-PL spectroscopy, and PhC structures are accordingly designed to resonantly match the QWR low-temperature (10K) PL peak [Fig. 2(b)]. The PhC design implements intercavity photonic tunnel barriers consisting of one or more missing holes in a longitudinal configuration [Figs. 2(c), 2(d)]. In the experiment discussed here, the PhC lattice constant was a≈210 nm and the radius of the holes corresponds to r/a≈0.255, in order to match the QWR ground-subband emission to the L3-cavity fundamental mode at the frequency within the TE0 PhC bandgap. The spatial alignment was implemented by the electron-beam lithography using conventional alignment marks, positioning the QWR coaxially with the cavities and centering it with the accuracy of ~40 nm [23

23. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90, 153107 (2007). [CrossRef]

]. The PhC holes were drilled using Cl2/SiCl4 reactive ion etching. Finally, the membrane was released by selectively undercutting the Al0.7Ga0.3As layer in HF solution.

Fig. 2. Experimental arrangement. (a) Schematics of the fabricated structure: free-standing membrane with V-groove QWRs integrated into two coupled PhC L3 cavities, (b) Low-temperature (T=10K) micro-PL spectrum of a “bare” QWR located outside the membrane, (c,d) SEM top-views of the measured samples, (e) schematics of the selective pumping configuration.

3.2 Optical characterization method

The optical characterization was done by the low-temperature (10K) micro-PL. The excitation was performed non-resonantly using a 532-nm frequency-doubled Nd:YAG laser beam focussed by a 50x objective lens with NA=0.55. The signal was collected by the same objective lens, dispersed by a 450-mm single-grating spectrometer (resolution around 0.06 nm) and acquired by a N2-cooled CCD array.

3.3 Discussion

Serving as internal light sources, the QWRs integrated into each cavity can be pumped optically independently using the micro-PL set-up that provides a ~1-µm spot size. Such a photoexcitation of the system allows for the selective cavity excitation [Fig. 2(e)]. This feature makes it possible to probe the extent of localization of the cavity modes, as further discussed below, and remove ambiguities in the conclusions on the presence or absence of the cavity coupling in experimental observations. Indeed, if the coupled-cavity structure is instead pumped uniformly, the measured spectrum can contain two peaks that may be referred as to the coupled states, while the modes actually originate from the decoupled (detuned) cavities.

Figures 3(a), 3(d) displays the measured micro-PL spectra for the single- and triple-hole barrier, coupled-cavity structures, each obtained using several locations of the pumping beam. In both cases, two cavity modes can be excited near 910 or 920nm. However, whereas these two modes have the same relative intensity in the case of the single-hole barrier, they exhibit strong dependency on the pumping location for the triple-barrier structure. In particular, for the triple-barrier structure, pumping near the left- or right-cavity yields excitation of predominantly either one of the spectral lines M1 or M2 [Fig. 3(d)].

Fig. 3. Evidence for direct coupling of PhC L3 microcavities. (a) Micro-PL spectrum acquired for different pump locations as shown in Fig. 2(e) for a single- hole barrier structure [Fig. 2(c)]. (b) 3D FDTD simulation of the cavity spectrum using the imported SEM top view of Fig. 2(c). (c) Near-field patterns of the symmetric (MS) and the antisymmetric (MA) supermodes inferred from computed stationary mode distributions (Ey components) for the single-hole barrier structure. (d) Position-dependent micro-PL spectra for the three-hole barrier structure [Fig. 2(d)]. (e) near-field patterns for the three-hole structure showing virtually complete localization (Ey components).

This behavior is explained with the aid of a three dimensional (3D) finite-difference time-domain (FDTD) simulation of the coupled-cavity structures. The 3D FDTD numerical modelling is based on the standard Yee algorithm [25

25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

]; and the Padé-Baker approximation is used for the Fourier transforms of the signals [26

26. W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microwave Wirel. Compon. Lett. 11, 223–225 (2001). [CrossRef]

, 27

27. M. Qiu, “Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately,” Microwave Opt. Technol. Lett. 45, 381–385 (2005). [CrossRef]

], which yields high spectral resolution for a moderate number of iterations. The simulations implement the actual patterns of the PhC structures extracted from scanning electron microscope (SEM) images, hence accounting for the fabrication-induced disorder in hole size, shape and position. The simulated spectrum of the single-hole barrier system [Fig. 3(b)] clearly shows a pair of modes, separated by 2.75 nm (6138 GHz), in a good agreement with the observed splitting (1.7 nm, 3803 GHz). The corresponding near-field patterns [Fig. 3(e)], confirm that these modes are indeed the “symmetric” (MS) and the “antisymmetric” (MA) coupled modes of the system. The field distributions show virtually no localization at either of the coupled cavities, indicating that the coupling in this case is strong enough to overcome the disorder-induced detuning. The delocalization is consistent with the observation in the PL spectra of only small changes in the relative intensity of the doublet’s peaks at different locations of the pump.

By contrast, the near-field distributions of the two modes confined by the structure with a triple-hole barrier show pronounced localization at either cavity [Fig. 3(e)]. Here, the intercavity coupling is significantly lower than for the single-hole case, and thus the same degree of disorder leads to mode localization. As a result, pumping with the optical beam positioned over either cavity yields excitation of the mode localized at that region.

A distinct feature apparent in the calculated and measured spectra of Fig. 3 is that the coupled-cavity modes are split not only in the resonant wavelength, but also in their losses. For the single-hole barriers, the loss splitting is manifested by measured Q-factors of 3200 and 1150 for the antisymmetric and the symmetric modes, respectively. On the other hand, the virtually uncoupled M1 or M2 modes of the three-hole barrier structures exhibit similar Q-factors of 1400 and 1520. Since —for the single-hole barrier— the fields of the eigenmodes are completely delocalized [Fig. 3(c)], the coupling term g in this case is much larger than the detuning. Therefore, the measured splitting can provide a good estimation of g, yielding Re(g)=1901 GHz and Im(g)=571 GHz. Using these values, frequency and loss detuning curves can be calculated from Eq. (1), which is shown in Fig. 4. Note that Eq. (1) necessitates the asymmetric splitting in Q-values, fully consistent with the experiment. Note also that the cavity loss parameter approaches Q=1700 for very large detuning, consistent with the measured values for the (virtually uncoupled) modes of the three-hole barrier structure. The fact that the Q-values in the latter case are lower (1400 and 1520) is explained by the frequency overdamping in the weak-coupling regime [28

28. J. M. Raimond and S. Haroche, “Atoms in Cavities,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein and C. Weisbuch, eds. (Plenum Press, New York, 1995). [CrossRef]

] implying that each cavity should have Q lower than that for the unperturbed case. The presence of such very weak coupling in the triple-hole barrier can be noticed in the field distributions [Fig. 3(e)].

Fig. 4. Calculated complex-frequency splitting vs detuning. The Splitting curves are computed from Eq. (1) where the coupling strength g is estimated from the Fig. 3(a).

In order to further verify the experimental observations, we performed 3D FDTD simulations for intentionally detuned cavities with ω2=ω1+Δ. In this case in order to produce comparable intensities, the modes were excited resonantly by the corresponding field distributions in the central plane of the membrane. These field distributions were obtained from the 2D finite-difference computation. The finite detuning Δ was achieved in the simulations by a slight modification of the PhC holes surrounding one of the cavities (note the cavity at right position in Fig. 5). Figure 5 displays the calculated spectra and near-field patterns for Δ≈1854 GHz (0.8 nm); the results reproduce the features observed in the PL spectra and the simulations based on the actual structures, further confirming the interpretation of the coupling behaviour. Note that for a larger cavity detuning of Δ≈2 nm, the simulations yield localized modes even for the single-barrier structure, providing estimation for the maximum detuning tolerated in this geometrical configuration.

Fig. 5. 3D-FDTD simulated spectral response and Ey field distributions of the intentionally detuned L3 cavities (at fixed detuning). Note that the coupling strength is greatly reduced already for the triple-hole barrier, and the mode separation is marginally larger than for an infinite barrier (cavities computed separately). The Ey-field distributions in the case of the 3-hole barrier show slight mode delocalization, which indicates a very weak, but finite, coupling.

4. Diffractive losses of the supermodes in the PhC-microcavity coupled system

Insight into the physical mechanisms responsible for the loss splitting can be gained by recalling that the cavity losses of the PhCs discussed here are governed by the out-of-plane diffraction. It strongly depends on the PhC geometry and is described by the light cone of the cladding region [29

29. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

, 30

30. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

]. This is different than in the case of other cavity types, e.g., microdisks for which Q difference of coupled modes ascribed to scattering at imperfections was observed [7

7. S. Ishii, A. Nakagawa, and T. Baba, “Modal characteristics and bistability in twin microdisk photonic molecule lasers,” IEEE J. Sel. Top. Quantum Electron . 12, 71–77 (2006). [CrossRef]

]. The relation of the loss splitting to the PhC diffractive losses can be visualized by inspecting the Fourier transform (FT) of a near-field pattern within a reference plane located just above the PhC membrane. Figure 6(a) shows the distributions in the reciprocal (kx,ky) space computed for ideal (disorder-free) PhC coupled-cavity structures with parameters similar to those used in the experiments. For clarity, the cases of single- and five-hole barriers are compared, the latter being an example of a “long” barrier; a single cavity is also shown, for reference. To aid visualization, Fig. 6(b) illustrates directly the out-of-plane radiation patterns in the real space. Quantitatively, the diffractive losses of each mode were estimated by the ratio of the integral intensity within the light cone to the integral intensity within the entire reference-plane:

ηdiff=k2πλFT(E)2dkxdkykFT(E)2dkxdky100%,
FT(E)2=FT(Ex)2+FT(Ey)2+FT(Ez)2
(3)

(Only the electric component (E) of the field is considered here, since time-averaged electromagnetic energy is distributed equally between E and H). Compared to the corresponding Q-values of the modes extracted directly from the 3D FDTD temporal response [insets in Fig. 6(b)], the results of the light-cone analysis confirm much higher radiation losses for the symmetric supermode in the “short”-barrier case. The radiation-loss difference for the “long” barrier is much less pronounced resulting in much smaller loss splitting. Note, that due to formation of the supermode amplitudes, the symmetric mode will always have larger amplitude in the barrier region. However, for sufficiently long barriers, due to tight confinement provided by the PhC, both supermodes do not overlap significantly with the barrier, which equalizes their losses (see Fig. 6(b), 5-hole barrier), and the Q-factors and the radiation patterns then resemble those of an individual L3 cavity.

Fig. 6. Diffractive losses of the coupled-cavity system (3D FDTD analysis applied to disorder-free PhC structures). (a) E-fields of the symmetric (MS) and the antisymmetric (MA) modes in the reciprocal k-space (Fourier transforms at the reference plane above the membrane), for two coupled-cavity structures with different (one-hole, five-hole) barriers schematically illustrated on the right. The corresponding field pattern for the single L3 cavity is also shown, at the bottom. Leaky field components are situated within the air light cone (encircled area). Calculated from Eq. (3), the percentage of the integrated field intensity with k-vectors located inside the light cone is shown in the insets. (b) Real-space E-field patterns (absolute value) in the plane perpendicular to the membrane and along the symmetry axis (X) of the cavities for the structures of part (a), visualizing the radiation responsible for loss. The Q-factors, shown in the insets, were extracted directly from the 3D FDTD temporal response.

5. Coupling barrier engineering and the time-evolving photon transfer

Geometrical adjustments of PhC cavity terminations affect dramatically the mode diffraction within the light-cone [30

30. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

]. Therefore barrier engineering in between the two coupled cavities —affecting strongly the loss in the coupled system— should be possible. Having direct implications on the photon transfer, the loss splitting and coupling performance can therefore be designed. To this end, we performed numerical modelling based on disorder-free cavities, first varying discretely the barrier length by adding an integer number of holes [Fig. 7(a)], and secondly, changing adiabatically the single-hole barrier [Fig. 7(b)]. In the first case, in addition to the expected rapid decrease of the coupling strength manifested by reduced spectral splitting, we observe a pronounced splitting of losses for short barriers and a periodic flipping [31

31. The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (ΩAS) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of twohole barrier.

] in the spectral positions of the coupled-system states. If the barrier is removed, the coupled modes degenerate into the fundamental and the first higher-order states of the L7 cavity. Most importantly, one can notice from the spectra [Fig. 7(a)] that the loss splitting may assume different “sign” (e.g., compare the Qs of the L7 cavity and the single-hole structure). Thus, at some intermediate geometry between the two the reversal of the loss splitting sign and an equalization of the supermode loss is expected. This is indeed confirmed by adiabatically increasing the single-hole barrier [see Fig. 7(b)].

Fig. 7. Coupling and energy transfer design by PhC barrier engineering (3D FDTD analysis on disorder-free PhC structures). (a) Spectral response of the two coupled L3 cavities with increasing barrier length by adding holes. Geometry: the (normalized) radius of PhC holes is r/a=0.255, the lattice constant is a=210 nm. The field distributions (Ey) of the symmetric (MS, red) and the antisymmetric (MA, blue) modes are fully delocalized being essentially similar to the ones shown e.g. in the Fig. 3(c). (b) Adiabatic modification of the single-hole barrier by varying the radius of the separating hole from r/a=0 to 0.4. The trends are shown for both the mode frequencies (MA and MS solid curves, left axis) and their Q-factors (dashed curves, right axis). Crossing point ΓSA is indicated. The horizontal straight lines indicate the wavelength (solid) and the Q-factor (dashed) of an unperturbed L3 cavity. Vertical straight line indicates the close-to “experimental” case [i.e. compared to Fig. 3(a)]. (c) Calculated from Eq. (2), the time evolution of the field intensities in each cavity showing the energy transfer in the coupled system. The “experimental” case with loss splitting (upper panel) is compared to an optimized case (lower panel) where the losses can equalize (ΓSA). (d) 3D FDTD simulation of the PhC system that shows ΓSA : (left) time evolution of the probed field intensities (Hz component extracted from the two probes at the membrane center laterally positioned as shown on the sketch to the right); (right, bottom) cut by mirror symmetry, the in-plane near-field distributions (recorded in lg(1+|He|2) scale) corresponding to different moments in time (Media 1).

6. Summary

In summary, we demonstrated the photonic coupling of two closely spaced PhC membrane defect cavities and showed that the coupled modes split not only in wavelength but also in cavity loss. Such loss splitting is given by the imaginary part of the coupling strength and explained as arising from the difference in radiative losses of the symmetric and the antisymmetric modes of the system determined by the PhC out-of-plane diffraction. Since these modes beat together to transfer the photons back and forth between the cavities by coherent superposition, such loss difference may prohibit the complete transfer. Therefore the loss splitting needs to be taken into account in structures which rely on the photon transfer processes, e.g. few laterally cavity-mode coupled QDs, coupled QD polaritons [11

11. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Physics 2, 856–861 (2006). [CrossRef]

] or transfer of single photons into coupled waveguides [32

32. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vučković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15, 5550–5558 (2007). [CrossRef] [PubMed]

]. Means for photonic barrier engineering were introduced and shown to be effective in controlling the loss splitting, and hence the photon transfer, that may apply to such systems.

References and links

1.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef] [PubMed]

2.

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Physics 2, 484–488 (2006). [CrossRef]

3.

D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15, 1228–1233 (2007). [CrossRef] [PubMed]

4.

E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures,” IEEE J. Quantum Electron. 38, 837–843 (2002). [CrossRef]

5.

S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron . 8, 448–456 (2002). [CrossRef]

6.

S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, “Switchable lasing in multimode microcavities,” Phys. Rev. Lett. 99, 073902 (2007). [CrossRef] [PubMed]

7.

S. Ishii, A. Nakagawa, and T. Baba, “Modal characteristics and bistability in twin microdisk photonic molecule lasers,” IEEE J. Sel. Top. Quantum Electron . 12, 71–77 (2006). [CrossRef]

8.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004). [CrossRef] [PubMed]

9.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum Information Processing Using Quantum Dot Spins and Cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999). [CrossRef]

10.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007). [CrossRef] [PubMed]

11.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Physics 2, 856–861 (2006). [CrossRef]

12.

S. V. Boriskina, “Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules,” Opt. Lett. 32, 1557–1559 (2007). [CrossRef] [PubMed]

13.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998). [CrossRef]

14.

M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, “Free-standing porous silicon single and multiple optical cavities,” J. Appl. Phys. 93, 9724–9729 (2003). [CrossRef]

15.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999). [CrossRef]

16.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997). [CrossRef]

17.

T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, “Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs,” J. Opt. Soc. Am. B 20, 373–378 (2003). [CrossRef]

18.

S. Ishii, K. Nozaki, and T. Baba, “Photonic molecules in photonic crystals,” Jpn. J. Appl. Phys. 45, 6108–6111 (2006). [CrossRef]

19.

D. P. Fussell and M. M. Dignam, “Engineering the quality factors of coupled-cavity modes in photonic crystal slabs,” Appl. Phys. Lett. 90, 183121 (2007). [CrossRef]

20.

E. Centeno and D. Felbacq, “Rabi oscillations in bidimensional photonic crystals,” Phys. Rev. B 62, 10101–10108 (2000). [CrossRef]

21.

S. Lam, A. R. Chalcraft, D. Szymanski, R. Oulton, B. D. Jones, D. Sanvitto, D. M. Whittaker, M. Fox, M. S. Skolnick, D. O’Brien, T. F. Krauss, H. Liu, P. W. Fry, and M. Hopkinson, “Coupled Resonant Modes of Dual L3-Defect Planar Photonic Crystal Cavities,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper QFG6. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2008-QFG6 [PubMed]

22.

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).

23.

K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90, 153107 (2007). [CrossRef]

24.

E. Kapon, D. M. Hwang, and R. Bhat, “Stimulated emission in semiconductor quantum wire heterostructures,” Phys. Rev. Lett. 63, 430–433 (1989). [CrossRef] [PubMed]

25.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).

26.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microwave Wirel. Compon. Lett. 11, 223–225 (2001). [CrossRef]

27.

M. Qiu, “Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately,” Microwave Opt. Technol. Lett. 45, 381–385 (2005). [CrossRef]

28.

J. M. Raimond and S. Haroche, “Atoms in Cavities,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein and C. Weisbuch, eds. (Plenum Press, New York, 1995). [CrossRef]

29.

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

30.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

31.

The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (ΩAS) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of twohole barrier.

32.

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vučković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15, 5550–5558 (2007). [CrossRef] [PubMed]

OCIS Codes
(260.2160) Physical optics : Energy transfer
(140.3945) Lasers and laser optics : Microcavities
(230.4555) Optical devices : Coupled resonators
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: August 19, 2008
Revised Manuscript: September 19, 2008
Manuscript Accepted: September 23, 2008
Published: September 26, 2008

Citation
Kirill A. Atlasov, Karl F. Karlsson, Alok Rudra, Benjamin Dwir, and Eli Kapon, "Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities," Opt. Express 16, 16255-16264 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-16255


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003). [CrossRef] [PubMed]
  2. H. Altug, D. Englund, and J. Vuckovic, "Ultrafast photonic crystal nanocavity laser," Nat. Physics 2, 484-488 (2006). [CrossRef]
  3. D. O'Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, "Coupled photonic crystal heterostructure nanocavities," Opt. Express 15, 1228-1233 (2007). [CrossRef] [PubMed]
  4. E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, "Investigation of localized coupled-cavity modes in two-dimensional photonic bandgap structures," IEEE J. Quantum Electron. 38, 837-843 (2002). [CrossRef]
  5. S. Mookherjea, and A. Yariv, "Coupled resonator optical waveguides," IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002). [CrossRef]
  6. S. V. Zhukovsky, D. N. Chigrin, A. V. Lavrinenko, and J. Kroha, "Switchable lasing in multimode microcavities," Phys. Rev. Lett. 99, 073902 (2007). [CrossRef] [PubMed]
  7. S. Ishii, A. Nakagawa, and T. Baba, "Modal characteristics and bistability in twin microdisk photonic molecule lasers," IEEE J. Sel. Top. Quantum Electron. 12, 71-77 (2006). [CrossRef]
  8. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oel, H. Binsma, G. D. Khoe, and M. K. Smit, "A fast low-power optical memory based on coupled micro-ring lasers," Nature 432, 206-209 (2004). [CrossRef] [PubMed]
  9. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999). [CrossRef]
  10. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896-899 (2007). [CrossRef] [PubMed]
  11. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Physics 2, 856-861 (2006). [CrossRef]
  12. S. V. Boriskina, "Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules," Opt. Lett. 32, 1557-1559 (2007). [CrossRef] [PubMed]
  13. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, "Optical modes in photonic molecules," Phys. Rev. Lett. 81, 2582-2585 (1998). [CrossRef]
  14. M. Ghulinyan, C. J. Oton, G. Bonetti, Z. Gaburro, and L. Pavesi, "Free-standing porous silicon single and multiple optical cavities," J. Appl. Phys. 93, 9724-9729 (2003). [CrossRef]
  15. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623-4626 (1999). [CrossRef]
  16. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997). [CrossRef]
  17. T. D. Happ, M. Kamp, A. Forchel, A. V. Bazhenov, I. I. Tartakovskii, A. Gorbunov, and V. D. Kulakovskii, "Coupling of point-defect microcavities in two-dimensional photonic-crystal slabs," J. Opt. Soc. Am. B 20, 373-378 (2003). [CrossRef]
  18. S. Ishii, K. Nozaki, and T. Baba, "Photonic molecules in photonic crystals," Jpn. J. Appl. Phys. 45, 6108-6111 (2006). [CrossRef]
  19. D. P. Fussell and M. M. Dignam, "Engineering the quality factors of coupled-cavity modes in photonic crystal slabs," Appl. Phys. Lett. 90, 183121 (2007). [CrossRef]
  20. E. Centeno and D. Felbacq, "Rabi oscillations in bidimensional photonic crystals," Phys. Rev. B 62, 10101-10108 (2000). [CrossRef]
  21. S. Lam, A. R. Chalcraft, D. Szymanski, R. Oulton, B. D. Jones, D. Sanvitto, D. M. Whittaker, M. Fox, M. S. Skolnick, D. O'Brien, T. F. Krauss, H. Liu, P. W. Fry, and M. Hopkinson, "Coupled Resonant Modes of Dual L3-Defect Planar Photonic Crystal Cavities," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper QFG6. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2008-QFG6 [PubMed]
  22. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).
  23. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, "Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity," Appl. Phys. Lett. 90, 153107 (2007). [CrossRef]
  24. E. Kapon, D. M. Hwang, and R. Bhat, "Stimulated emission in semiconductor quantum wire heterostructures," Phys. Rev. Lett. 63, 430-433 (1989). [CrossRef] [PubMed]
  25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2005).
  26. W. H. Guo, W. J. Li, and Y. Z. Huang, "Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation," IEEE Microwave Wirel. Compon. Lett. 11, 223-225 (2001). [CrossRef]
  27. M. Qiu, "Micro-cavities in silicon-on-insulator photonic crystal slabs: Determining resonant frequencies and quality factors accurately," Microwave Opt. Technol. Lett. 45, 381-385 (2005). [CrossRef]
  28. J. M. Raimond and S. Haroche, "Atoms in Cavities," in Confined Electrons and Photons: New Physics and Applications, E. Burstein, and C. Weisbuch, eds. (Plenum Press, New York, 1995). [CrossRef]
  29. K. Srinivasan, and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002). [PubMed]
  30. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003). [CrossRef] [PubMed]
  31. The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (?A = ?S) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of two-hole barrier.
  32. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vuckovic, "Generation and transfer of single photons on a photonic crystal chip," Opt. Express 15, 5550-5558 (2007). [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.

Supplementary Material


» Media 1: MOV (4034 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited