OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8136–8142
« Show journal navigation

Bright single photon source based on self-aligned quantum dot–cavity systems

Sebastian Maier, Peter Gold, Alfred Forchel, Niels Gregersen, Jesper Mørk, Sven Höfling, Christian Schneider, and Martin Kamp  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8136-8142 (2014)
http://dx.doi.org/10.1364/OE.22.008136


View Full Text Article

Acrobat PDF (2481 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-aligned manner. We investigate the morphology of these defects and characterize the photonic operation mechanism. Our results show that these naturally arising coupled quantum dot-defects provide a new avenue for efficient (up to 42% demonstrated) and pure (g2(0) value of 0.023) single-photon emission.

© 2014 Optical Society of America

Bright sources of single and indistinguishable photons are of great interest in the field of quantum key distribution [1

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

], quantum optics [2

2. S. Strauf, “Quantum optics: Towards efficient quantum sources,” Nat. Photonics 4(3), 132–134 (2010). [CrossRef]

], and linear optical quantum computing [3

3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]

]. Single semiconductor quantum dots (QDs) are promising candidates for this purpose, as they behave like artificial atoms [4

4. M. Bayer, O. Stern, P. Hawrylak, S. Fafard, and A. Forchel, “Hidden symmetries in the energy levels of excitonic ‘artificial atoms’,” Nature 405(6789), 923–926 (2000). [CrossRef] [PubMed]

]. However, efficient light outcoupling is critical and many sample designs [5

5. N. Gregersen, P. Kaer, and J. Mørk, “Modeling and design of high-efficiency single-photon sources,” IEEE J. Sel. Top. Quantum Electron. 19(5), 9000516 (2013). [CrossRef]

] have been explored to maximize extraction efficiencies, such as micropillar cavities [6

6. T. Heindel, C. Schneider, M. Lermer, S. H. Kwon, T. Braun, S. Reitzenstein, S. Höfling, M. Kamp, and A. Forchel, “Electrically driven quantum dot-micropillar single photon source with 34% overall efficiency,” Appl. Phys. Lett. 96(1), 011107 (2010). [CrossRef]

8

8. O. Gazzano, S. Michaelis de Vasconcellos, C. Arnold, A. Nowak, E. Galopin, I. Sagnes, L. Lanco, A. Lemaître, and P. Senellart, “Bright solid-state sources of indistinguishable single photons,” Nat. Commun. 4, 1425 (2013). [CrossRef] [PubMed]

], photonic nanowires [9

9. J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010). [CrossRef]

,10

10. M. E. Reimer, G. Bulgarini, N. Akopian, M. Hocevar, M. B. Bavinck, M. A. Verheijen, E. P. A. M. Bakkers, L. P. Kouwenhoven, and V. Zwiller, “Bright single-photon sources in bottom-up tailored nanowires,” Nat. Commun. 3, 737 (2012). [CrossRef] [PubMed]

] and planar dielectric antennas [11

11. X.-W. Chen, S. Götzinger, and V. Sandoghdar, “99% efficiency in collecting photons from a single emitter,” Opt. Lett. 36(18), 3545–3547 (2011). [CrossRef] [PubMed]

]. Planar single-photon sources are of particular interest for spin manipulation experiments in order to avoid etched surfaces [12

12. D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4(6), 367–370 (2010). [CrossRef]

], which lead to spin dephasing. Furthermore a two-dimensional planar QD array can serve as basis for the realization of an optically controlled 2-qubit scheme [13

13. K. De Greve, D. Press, P. L. McMahon, and Y. Yamamoto, “Ultrafast optical control of individual quantum dot spin qubits,” Rep. Prog. Phys. 76(9), 092501 (2013). [CrossRef] [PubMed]

].

Here we demonstrate a quantum-dot-based single-photon source based on a simple planar low quality factor cavity with an experimentally determined extraction efficiency of 42% ± 5%. The high efficiency is caused by the self-aligned formation of oval nanohill defects on top of the QDs. It significantly exceeds the maximum for the extraction efficiency from planar bulk GaAs semiconductor structures (~2%) and planar DBR microcavities without lateral optical confinement (~30%) [14

14. P. Royo, R. P. Stanley, and M. Ilegems, “Planar dielectric microcavity light-emitting diodes: Analytical analysis of the extraction efficiency,” J. Appl. Phys. 90(1), 283–293 (2001). [CrossRef]

]. Our sample was fabricated via molecular beam epitaxy (MBE) and contains a λ-thick cavity, which is sandwiched between two distributed Bragg reflector (DBRs), consisting of 18 (5) bottom (top) layers of AlAs/GaAs mirror pairs (MPs). The asymmetric design with a planar Q factor of about 200 is optimized for enhanced light outcoupling. The modulation doped low density In(Ga)As QDs are centered in the GaAs cavity and are spectrally shifted to the 900 nm range by using the Indium flush technique [15

15. J. M. García, T. Mankad, P. O. Holtz, P. J. Wellman, and P. M. Petroff, “Electronic states tuning of InAs self-assembled quantum dots,” Appl. Phys. Lett. 72(24), 3172–3174 (1998). [CrossRef]

]. The microcavity layers were designed to accomplish spectral matching between the QD emission band and the optical resonance.

To investigate the surface of the areas on the sample where the bright QD emission is measured, atomic force microscopy (AFM) was performed. The AFM image in Fig. 2(a) shows the sample surface above such a QD cluster which indicates the presence of an incidentally formed crystal defect which evolved during MBE growth.
Fig. 2 (a), (b) Atomic force microscopy measurements reveal oval defects. (c) Cross sectional height distribution of the oval defects.
Detailed analysis of the measurement in Figs. 2(b) and 2(c) reveals an oval structure which is oriented along the (0-11) direction. Its dimensions amount to approximately 3.5 µm length, 800 nm width and 14 nm in height. The formation of lateral optical confinement via oval defect structures in quasi-planar microcavities has already been observed [16

16. J. M. Zajac and W. Langbein, “Structure and zero-dimensional polariton spectrum of natural defects in GaAs/AlAs microcavities,” Phys. Rev. B 86(19), 195401 (2012). [CrossRef]

] and it is known that oval defects occur when Ga droplets are formed during MBE growth.

Figure 3(a) shows a photoluminescence spectrum of a spectrally well isolated QD exciton in a natural trap structure under pulsed p-shell excitation.
Fig. 3 (a) µPL spectrum (measured at 6 K) of a single QD in a natural trap. (b) Second order auto-correlation function measured in a Hanbury Brown and Twiss setup under pulsed excitation.
The single-photon emission characteristics were investigated by measuring the second order auto-correlation function in a standard Hanbury Brown and Twiss (HBT) setup. The QD was excited into the p-shell by a ps-pulsed Ti:sapphire Laser with a pulse separation of 12.2 ns at a wavelength of 911 nm. We calculate a g2(0) value of 0.023 from the raw data, which is depicted in Fig. 3(b) without any background corrections by dividing the number of counts in the range of ± 6.1 ns around zero delay time by the average number of counts of the peaks. These measurements demonstrate the high purity of the single-photon source and the excellent quality of the quantum emitter.

The extraction efficiency of the single photon source is measured at saturation of the QD-exciton: The QD emission is coupled to an avalanche photo diode (APD) using a microscope objective with a numerical aperture of NA = 0.7. We compare the photon counts per second on the single photon detectors (relative error 4%) with the laser repetition frequency of 82 MHz under consideration of the optical losses in the beam path due to an imperfect setup efficiency. The overall setup efficiency is assessed by using pulsed laser light of known power, which is tuned to the wavelength of the exciton (930 nm) and reflected from a gold mirror inside the cryostat. The photon counts per second on the single photon detectors are measured under the same setup conditions that we use for the single photon source, except for an additional density filter. We calculate the overall setup efficiency by comparing the laser photon flux, reflected on the gold mirror, with the maximum count rates on the APD, considering the transmission of the additional density filters. We find an overall detection efficiency of (0.35 ± 0.04)∙10−3. Furthermore, all optical elements on the detection path have been calibrated with a continuous wave laser at the same wavelength. Table 1 shows a compilation of the transmission of these optical elements with relative errors.

Table 1. Transmission of the optical elements in the detection path with relative errors.

table-icon
View This Table
Considering the finite g2(0) value the efficiency of the single photon source amounts to 42% ± 5%.

This bright single-photon source was used to measure two photon interference in a Hong-Ou-Mandel (HOM) setup as shown schematically in Fig. 4(a).
Fig. 4 Hong-Ou-Mandel experiment: (a) Schematic drawing of the interference setup. (b) Correlation histogram for two photon interference of consecutively emitted photons from the same QD.
The laser is tuned to a wavelength of 911 nm and the QD is driven via pulsed p-shell excitation. After spectral filtering with a monochromator, the QD emission is coupled into the first 50/50 fiber beamsplitter of the HOM interferometer. In order to facilitate the interference of consecutively emitted photons on the second 50/50 fiber beamsplitter, we include a variable optical fiber delay in one of the two arms of the interferometer, which is adapted to the pulse separation and additionally allows us to fine adjust the time difference Δt between two photons. Figure 4(b) shows the two photon interference correlation histogram at an interferometer path length difference of Δt0. From the raw data we calculate a g2indist(0) value of 0.17<0.50, which clearly shows indistinguishability of two consecutively emitted photons from the same QD [20

20. C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002). [CrossRef] [PubMed]

] with a visibility of 66%. The exciton lifetime (T1) and coherence time (T2) of this QD amount to 670 ps and 330 ps, as extracted from time resolved measurements and Michelson interferometry. Despite being far away from the fourier limit, the rather high interference visibilities extracted from the two photon interference measurements lead us to the conclusion, that the spectral broadening mechanisms leading to a reduction of the coherence time assessed in the interferometric experiment occurs on a timescale larger than 12.2 ns, i.e the repetition rate of our pump laser. A detailed discussion of the effects of spectral broadening on the interference properties of single photons emitted from such QDs can be found in [21

21. P. Gold, A. Thoma, S. Maier, S. Reitzenstein, C. Schneider, S. Höfling, and M. Kamp, “Two-photon interference from remote quantum dots with inhomogeneously broadened linewidths,” Phys. Rev. B 89(3), 035313 (2014). [CrossRef]

].

In conclusion we demonstrated a quasi-planar single-photon source with a very high extraction efficiency of 42% ± 5%, in good agreement with theoretical values. The cavity is based on naturally occurring nanohills on planar microcavities, which are self aligned to the implemented QD emitters. Similar high photon outcoupling efficiencies in QD-microcavity systems have previously required complicated photonic resonator geometries, highly advanced lithography and perfect spatial alignment. The high extraction efficiency in our experiment can be attributed to an efficient guiding of the light into a collection objective provided by the defect structure. Due to the absence of any etched and exposed lateral semiconductor-air interfaces, such cavities have great potential for experiments and applications relying on extended spin-coherence times, or large scale coupling of neighboring QDs.

Acknowledgments

The authors gratefully thank M. Emmerling and T. Steinl for expert sample preparation. This work was financially supported by the German Ministry of Education and Research (BMBF) via the project QuaHL-Rep and by the State of Bavaria.

References and links

1.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

2.

S. Strauf, “Quantum optics: Towards efficient quantum sources,” Nat. Photonics 4(3), 132–134 (2010). [CrossRef]

3.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]

4.

M. Bayer, O. Stern, P. Hawrylak, S. Fafard, and A. Forchel, “Hidden symmetries in the energy levels of excitonic ‘artificial atoms’,” Nature 405(6789), 923–926 (2000). [CrossRef] [PubMed]

5.

N. Gregersen, P. Kaer, and J. Mørk, “Modeling and design of high-efficiency single-photon sources,” IEEE J. Sel. Top. Quantum Electron. 19(5), 9000516 (2013). [CrossRef]

6.

T. Heindel, C. Schneider, M. Lermer, S. H. Kwon, T. Braun, S. Reitzenstein, S. Höfling, M. Kamp, and A. Forchel, “Electrically driven quantum dot-micropillar single photon source with 34% overall efficiency,” Appl. Phys. Lett. 96(1), 011107 (2010). [CrossRef]

7.

M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002). [CrossRef] [PubMed]

8.

O. Gazzano, S. Michaelis de Vasconcellos, C. Arnold, A. Nowak, E. Galopin, I. Sagnes, L. Lanco, A. Lemaître, and P. Senellart, “Bright solid-state sources of indistinguishable single photons,” Nat. Commun. 4, 1425 (2013). [CrossRef] [PubMed]

9.

J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010). [CrossRef]

10.

M. E. Reimer, G. Bulgarini, N. Akopian, M. Hocevar, M. B. Bavinck, M. A. Verheijen, E. P. A. M. Bakkers, L. P. Kouwenhoven, and V. Zwiller, “Bright single-photon sources in bottom-up tailored nanowires,” Nat. Commun. 3, 737 (2012). [CrossRef] [PubMed]

11.

X.-W. Chen, S. Götzinger, and V. Sandoghdar, “99% efficiency in collecting photons from a single emitter,” Opt. Lett. 36(18), 3545–3547 (2011). [CrossRef] [PubMed]

12.

D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4(6), 367–370 (2010). [CrossRef]

13.

K. De Greve, D. Press, P. L. McMahon, and Y. Yamamoto, “Ultrafast optical control of individual quantum dot spin qubits,” Rep. Prog. Phys. 76(9), 092501 (2013). [CrossRef] [PubMed]

14.

P. Royo, R. P. Stanley, and M. Ilegems, “Planar dielectric microcavity light-emitting diodes: Analytical analysis of the extraction efficiency,” J. Appl. Phys. 90(1), 283–293 (2001). [CrossRef]

15.

J. M. García, T. Mankad, P. O. Holtz, P. J. Wellman, and P. M. Petroff, “Electronic states tuning of InAs self-assembled quantum dots,” Appl. Phys. Lett. 72(24), 3172–3174 (1998). [CrossRef]

16.

J. M. Zajac and W. Langbein, “Structure and zero-dimensional polariton spectrum of natural defects in GaAs/AlAs microcavities,” Phys. Rev. B 86(19), 195401 (2012). [CrossRef]

17.

F. Ding, T. Stöferle, L. Mai, A. Knoll, and R. F. Mahrt, “Vertical microcavities with high Q and strong lateral mode confinement,” Phys. Rev. B 87(16), 161116 (2013). [CrossRef]

18.

L. Mai, F. Ding, T. Stöferle, A. Knoll, B. J. Offrein, and R. F. Mahrt, “Integrated vertical microcavity using a nano-scale deformation for strong lateral confinement,” Appl. Phys. Lett. 103(24), 243305 (2013). [CrossRef]

19.

O. El Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. Idrissi Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006). [CrossRef]

20.

C. Santori, D. Fattal, J. Vucković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002). [CrossRef] [PubMed]

21.

P. Gold, A. Thoma, S. Maier, S. Reitzenstein, C. Schneider, S. Höfling, and M. Kamp, “Two-photon interference from remote quantum dots with inhomogeneously broadened linewidths,” Phys. Rev. B 89(3), 035313 (2014). [CrossRef]

22.

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33(4–5), 327–341 (2001). [CrossRef]

OCIS Codes
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(230.5750) Optical devices : Resonators
(270.5290) Quantum optics : Photon statistics
(270.5565) Quantum optics : Quantum communications

ToC Category:
Optoelectronics

History
Original Manuscript: February 4, 2014
Revised Manuscript: March 13, 2014
Manuscript Accepted: March 14, 2014
Published: March 31, 2014

Citation
Sebastian Maier, Peter Gold, Alfred Forchel, Niels Gregersen, Jesper Mørk, Sven Höfling, Christian Schneider, and Martin Kamp, "Bright single photon source based on self-aligned quantum dot–cavity systems," Opt. Express 22, 8136-8142 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8136


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  2. S. Strauf, “Quantum optics: Towards efficient quantum sources,” Nat. Photonics 4(3), 132–134 (2010). [CrossRef]
  3. E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]
  4. M. Bayer, O. Stern, P. Hawrylak, S. Fafard, A. Forchel, “Hidden symmetries in the energy levels of excitonic ‘artificial atoms’,” Nature 405(6789), 923–926 (2000). [CrossRef] [PubMed]
  5. N. Gregersen, P. Kaer, J. Mørk, “Modeling and design of high-efficiency single-photon sources,” IEEE J. Sel. Top. Quantum Electron. 19(5), 9000516 (2013). [CrossRef]
  6. T. Heindel, C. Schneider, M. Lermer, S. H. Kwon, T. Braun, S. Reitzenstein, S. Höfling, M. Kamp, A. Forchel, “Electrically driven quantum dot-micropillar single photon source with 34% overall efficiency,” Appl. Phys. Lett. 96(1), 011107 (2010). [CrossRef]
  7. M. Pelton, C. Santori, J. Vucković, B. Zhang, G. S. Solomon, J. Plant, Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89(23), 233602 (2002). [CrossRef] [PubMed]
  8. O. Gazzano, S. Michaelis de Vasconcellos, C. Arnold, A. Nowak, E. Galopin, I. Sagnes, L. Lanco, A. Lemaître, P. Senellart, “Bright solid-state sources of indistinguishable single photons,” Nat. Commun. 4, 1425 (2013). [CrossRef] [PubMed]
  9. J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, J.-M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photonics 4(3), 174–177 (2010). [CrossRef]
  10. M. E. Reimer, G. Bulgarini, N. Akopian, M. Hocevar, M. B. Bavinck, M. A. Verheijen, E. P. A. M. Bakkers, L. P. Kouwenhoven, V. Zwiller, “Bright single-photon sources in bottom-up tailored nanowires,” Nat. Commun. 3, 737 (2012). [CrossRef] [PubMed]
  11. X.-W. Chen, S. Götzinger, V. Sandoghdar, “99% efficiency in collecting photons from a single emitter,” Opt. Lett. 36(18), 3545–3547 (2011). [CrossRef] [PubMed]
  12. D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nat. Photonics 4(6), 367–370 (2010). [CrossRef]
  13. K. De Greve, D. Press, P. L. McMahon, Y. Yamamoto, “Ultrafast optical control of individual quantum dot spin qubits,” Rep. Prog. Phys. 76(9), 092501 (2013). [CrossRef] [PubMed]
  14. P. Royo, R. P. Stanley, M. Ilegems, “Planar dielectric microcavity light-emitting diodes: Analytical analysis of the extraction efficiency,” J. Appl. Phys. 90(1), 283–293 (2001). [CrossRef]
  15. J. M. García, T. Mankad, P. O. Holtz, P. J. Wellman, P. M. Petroff, “Electronic states tuning of InAs self-assembled quantum dots,” Appl. Phys. Lett. 72(24), 3172–3174 (1998). [CrossRef]
  16. J. M. Zajac, W. Langbein, “Structure and zero-dimensional polariton spectrum of natural defects in GaAs/AlAs microcavities,” Phys. Rev. B 86(19), 195401 (2012). [CrossRef]
  17. F. Ding, T. Stöferle, L. Mai, A. Knoll, R. F. Mahrt, “Vertical microcavities with high Q and strong lateral mode confinement,” Phys. Rev. B 87(16), 161116 (2013). [CrossRef]
  18. L. Mai, F. Ding, T. Stöferle, A. Knoll, B. J. Offrein, R. F. Mahrt, “Integrated vertical microcavity using a nano-scale deformation for strong lateral confinement,” Appl. Phys. Lett. 103(24), 243305 (2013). [CrossRef]
  19. O. El Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. Idrissi Kaitouni, J. L. Staehli, F. Morier-Genoud, B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006). [CrossRef]
  20. C. Santori, D. Fattal, J. Vucković, G. S. Solomon, Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419(6907), 594–597 (2002). [CrossRef] [PubMed]
  21. P. Gold, A. Thoma, S. Maier, S. Reitzenstein, C. Schneider, S. Höfling, M. Kamp, “Two-photon interference from remote quantum dots with inhomogeneously broadened linewidths,” Phys. Rev. B 89(3), 035313 (2014). [CrossRef]
  22. P. Bienstman, R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33(4–5), 327–341 (2001). [CrossRef]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited