Theory of high-speed nanolasers and nanoLEDs

doi:10.1364/OE.20.016450

Theory of high-speed nanolasers and nanoLEDs

Chi-Yu Adrian Ni and Shun Lien Chuang »View Author Affiliations

Optics Express, Vol. 20, Issue 15, pp. 16450-16470 (2012)
http://dx.doi.org/10.1364/OE.20.016450

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Abstract

We investigate the intrinsic high speed modulation responses of nanolasers and nanoLEDs using bulk, quantum wells (QWs), and quantum dots (QDs) based on a rigorous rate-equation model, which incorporates the optical energy confinement factor to properly account for the negative permittivity and dispersive metal plasma property. We then investigate the dependence of the bandwidth and the energy per bit on the quality factor and the normalized optical volume. We find out that the conditions for the energy per bit less than 50 fJ/bit and 10 fJ/bit are the normalized optical modal volume less than 20 and 5, respectively. In addition, with a uniform quantum dot size in a nanocavity, quantum-dot metal-cavity nanolasers exhibit the largest bandwidth among three types of active materials, and a low energy per bit. With their insensitivity to temperature, quantum-dot metal-cavity nanolasers are favorable for future high speed light sources.

OCIS Codes
(060.4080) Fiber optics and optical communications : Modulation
(140.3410) Lasers and laser optics : Laser resonators
(230.5590) Optical devices : Quantum-well, -wire and -dot devices
(250.5403) Optoelectronics : Plasmonics
(250.5960) Optoelectronics : Semiconductor lasers

ToC Category:
Optoelectronics

History
Original Manuscript: May 3, 2012
Revised Manuscript: June 14, 2012
Manuscript Accepted: June 14, 2012
Published: July 5, 2012

Citation
Chi-Yu Adrian Ni and Shun Lien Chuang, "Theory of high-speed nanolasers and nanoLEDs," Opt. Express 20, 16450-16470 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16450

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References

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE97, 1166–1185 (2009). [CrossRef]
S. Matsuo, A. Shinya, C.-H. Chen, K. Nozaki, T. Sato, Y. Kawaguchi, H. Taniyama, and M. Notomi, “20-Gbit/s directly modulated photonic crystal nanocavity laser with ultra-low power consumption,” Opt. Express19, 2242–2250 (2011). [CrossRef] [PubMed]
S. Matsuo, K. Takeda, T. Sato, M. Notomi, A. Shinya, K. Nozaki, H. Taniyama, K. Hasebe, and T. Kakitsuka, “Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser,” Opt. Express20, 3773–3780 (2012). [CrossRef] [PubMed]
E. M. Purcell, “Spontaneous emission probabilities at radio frequency,” Phys. Rev.69, 681 (1946).
H. Yokoyama and S. D. Brorson, “Rate equations analysis of microcavity lasers,” J. Appl. Phys.66, 4801–4805 (1989). [CrossRef]
G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron.27, 2386–2396 (1991). [CrossRef]
E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express17, 7790–7799 (2009). [CrossRef] [PubMed]
K. A. Shore, “Modulation bandwidth of metal-clad semiconductor nanolasers with cavity-enhanced spontaneous emission,” Electron. Lett.46, 1688–1689 (2010). [CrossRef]
T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoLEDs and nanolasers exploiting Purcell enhanced spontaneous emission,” Opt. Express18, 11230–11240 (2010). [CrossRef] [PubMed]
T. Suhr, N. Gregersen, M. Lorke, and J. Mørk, “Modulation response of quantum dot nanolight-emitting-diodes exploiting purcell-enhanced spontaneous emission,” Appl. Phys. Lett.98, 211109-1–211109-3 (2011). [CrossRef]
S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron.39, 1014–1023 (2009). [CrossRef]
M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. deVries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkenmans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1, 589–594 (2009). [CrossRef]
M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express17, 11107–11112 (2009). [CrossRef] [PubMed]
J. H. Lee, M. Khajavikhan, A. Simic, Q. Gu, O. Bondarenko, B. Slutsky, M. P. Nezhad, and Y. Fainman, “Electrically pumped sub-wavelength metallo-dielectric pedestal pillar lasers,” Opt. Express19, 21524–21531 (2011). [CrossRef] [PubMed]
K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. Veldhoven, R. Nötzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108-1–231108-3 (2011). [CrossRef]
C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett.96, 251101-1–251101-3 (2010). [CrossRef]
C. Y. Lu, S. L. Chuang, A. Mutig, and D. Bimberg, “Metal-cavity surface-emitting microlaser with hybrid metal-DBR reflectors,” Opt. Lett.36, 2447–2449 (2011). [CrossRef] [PubMed]
S. L Chuang, C. Y. Ni, C. Y. Lu, and A. Matsudaira, “Metal-cavity nanolasers and nanoLEDs,” IEICE Trans Electron. to be published (2012).
C. Y. Lu and S. L. Chuang, “A surface-emitting 3D metal-nanocavity laser: proposal and theory,” Opt. Express19, 13225–13244 (2011). [CrossRef] [PubMed]
S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express16, 10580–10595 (2008). [CrossRef] [PubMed]
S. L. Chuang, Physics of Photnic Devices, 2nd ed. (Wiley, Hoboken, NJ, 2009), Chap. 12.
L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits (Wiley, New York, NY, 1995), Chap. 4.
Y. Matsui, H. Murai, S. Arahira, Y. Ogawa, and A. Suzuki, “Enhanced modulation bandwidth for strain-compensated InGaAlAs-InGaAsP MQW lasers,” IEEE J. Quantum Electron.34, 1970–1978 (1998). [CrossRef]
N. N. Ledentsov, D. Bimberg, F. Hopfer, A. Mutig, V. A. Shchukin, A. V. Savel’ev, G. Fiol, E. Stock, H. Eisele, M. Dähane, D. Gerthsen, U. Fischer, D. Litvinov, A. Rosenauer, S. S. Mikhrin, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Submonolayer quantum dots for high speed surface emitting lasers,” Nanoscale Res. Lett.2, 417–429 (2007). [CrossRef] [PubMed]
A. Lenz, H. Eisele, J. Becker, J. Schulze, T. Germann, F. Luckert, K. Pötschke, E. Lenz, L. Ivanova, A. Strittmatter, D. Bimberg, U. W. Pohl, and M. Dähne, “Atomic structure and optical properties of InAs submonolayer depositions in GaAs,” J. Vac. Sci. Technol. B29, 04D104 (2011). [CrossRef]
N. Ledentsov, J. Lotta, V. Shchukin, H. Quast, F. Hopfer, G. Fiol, A. Mutig, P. Moser, T. Germann, A. Strittmatter, L. Y. Karachinsky, S. A. Blokhin, I. I. Novikov, A. M. Nadtochi, N. D. Zakharov, P. Werner, and D. Bimberg, “Quantum dot insertions in VCSELs from 840 to 1300 nm: growth, characterization, and device performance,” in Proc. SPIE, Photonics West 2009, San Jose, CA, 7224, 72240P-1–72240P-12 (2009).
J. Kim and S. L. Chuang, “Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers,” IEEE J. Quantum Electron.42, 942–952 (2006). [CrossRef]
Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A61, 033808-1–033808-10 (2000). [CrossRef]
A. Fiore and A. Markus, “Differential gain and gain compression in quantum dot lasers,” IEEE J. Quantum Electron.43, 287–294 (2007). [CrossRef]

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[1] D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE97, 1166–1185 (2009). [CrossRef]

[2] S. Matsuo, A. Shinya, C.-H. Chen, K. Nozaki, T. Sato, Y. Kawaguchi, H. Taniyama, and M. Notomi, “20-Gbit/s directly modulated photonic crystal nanocavity laser with ultra-low power consumption,” Opt. Express19, 2242–2250 (2011). [CrossRef] [PubMed]

[3] S. Matsuo, K. Takeda, T. Sato, M. Notomi, A. Shinya, K. Nozaki, H. Taniyama, K. Hasebe, and T. Kakitsuka, “Room-temperature continuous-wave operation of lateral current injection wavelength-scale embedded active-region photonic-crystal laser,” Opt. Express20, 3773–3780 (2012). [CrossRef] [PubMed]

[4] E. M. Purcell, “Spontaneous emission probabilities at radio frequency,” Phys. Rev.69, 681 (1946).

[5] H. Yokoyama and S. D. Brorson, “Rate equations analysis of microcavity lasers,” J. Appl. Phys.66, 4801–4805 (1989). [CrossRef]

[6] G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron.27, 2386–2396 (1991). [CrossRef]

[7] E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express17, 7790–7799 (2009). [CrossRef] [PubMed]

[8] K. A. Shore, “Modulation bandwidth of metal-clad semiconductor nanolasers with cavity-enhanced spontaneous emission,” Electron. Lett.46, 1688–1689 (2010). [CrossRef]

[9] T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoLEDs and nanolasers exploiting Purcell enhanced spontaneous emission,” Opt. Express18, 11230–11240 (2010). [CrossRef] [PubMed]

[10] T. Suhr, N. Gregersen, M. Lorke, and J. Mørk, “Modulation response of quantum dot nanolight-emitting-diodes exploiting purcell-enhanced spontaneous emission,” Appl. Phys. Lett.98, 211109-1–211109-3 (2011). [CrossRef]

[11] S. W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron.39, 1014–1023 (2009). [CrossRef]

[12] M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. deVries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkenmans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1, 589–594 (2009). [CrossRef]

[13] M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. Oei, R. Notzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express17, 11107–11112 (2009). [CrossRef] [PubMed]

[14] J. H. Lee, M. Khajavikhan, A. Simic, Q. Gu, O. Bondarenko, B. Slutsky, M. P. Nezhad, and Y. Fainman, “Electrically pumped sub-wavelength metallo-dielectric pedestal pillar lasers,” Opt. Express19, 21524–21531 (2011). [CrossRef] [PubMed]

[15] K. Ding, Z. Liu, L. Yin, H. Wang, R. Liu, M. T. Hill, M. J. H. Marell, P. J. Veldhoven, R. Nötzel, and C. Z. Ning, “Electrical injection, continuous wave operation of subwavelength-metallic-cavity lasers at 260 K,” Appl. Phys. Lett.98, 231108-1–231108-3 (2011). [CrossRef]

[16] C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett.96, 251101-1–251101-3 (2010). [CrossRef]

[17] C. Y. Lu, S. L. Chuang, A. Mutig, and D. Bimberg, “Metal-cavity surface-emitting microlaser with hybrid metal-DBR reflectors,” Opt. Lett.36, 2447–2449 (2011). [CrossRef] [PubMed]

[18] S. L Chuang, C. Y. Ni, C. Y. Lu, and A. Matsudaira, “Metal-cavity nanolasers and nanoLEDs,” IEICE Trans Electron. to be published (2012).

[19] C. Y. Lu and S. L. Chuang, “A surface-emitting 3D metal-nanocavity laser: proposal and theory,” Opt. Express19, 13225–13244 (2011). [CrossRef] [PubMed]

[20] S. W. Chang, C. Y. A. Ni, and S. L. Chuang, “Theory for bowtie plasmonic nanolasers,” Opt. Express16, 10580–10595 (2008). [CrossRef] [PubMed]

[21] S. L. Chuang, Physics of Photnic Devices, 2nd ed. (Wiley, Hoboken, NJ, 2009), Chap. 12.

[22] L. A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits (Wiley, New York, NY, 1995), Chap. 4.

[23] Y. Matsui, H. Murai, S. Arahira, Y. Ogawa, and A. Suzuki, “Enhanced modulation bandwidth for strain-compensated InGaAlAs-InGaAsP MQW lasers,” IEEE J. Quantum Electron.34, 1970–1978 (1998). [CrossRef]

[24] N. N. Ledentsov, D. Bimberg, F. Hopfer, A. Mutig, V. A. Shchukin, A. V. Savel’ev, G. Fiol, E. Stock, H. Eisele, M. Dähane, D. Gerthsen, U. Fischer, D. Litvinov, A. Rosenauer, S. S. Mikhrin, A. R. Kovsh, N. D. Zakharov, and P. Werner, “Submonolayer quantum dots for high speed surface emitting lasers,” Nanoscale Res. Lett.2, 417–429 (2007). [CrossRef] [PubMed]

[25] A. Lenz, H. Eisele, J. Becker, J. Schulze, T. Germann, F. Luckert, K. Pötschke, E. Lenz, L. Ivanova, A. Strittmatter, D. Bimberg, U. W. Pohl, and M. Dähne, “Atomic structure and optical properties of InAs submonolayer depositions in GaAs,” J. Vac. Sci. Technol. B29, 04D104 (2011). [CrossRef]

[26] N. Ledentsov, J. Lotta, V. Shchukin, H. Quast, F. Hopfer, G. Fiol, A. Mutig, P. Moser, T. Germann, A. Strittmatter, L. Y. Karachinsky, S. A. Blokhin, I. I. Novikov, A. M. Nadtochi, N. D. Zakharov, P. Werner, and D. Bimberg, “Quantum dot insertions in VCSELs from 840 to 1300 nm: growth, characterization, and device performance,” in Proc. SPIE, Photonics West 2009, San Jose, CA, 7224, 72240P-1–72240P-12 (2009).

[27] J. Kim and S. L. Chuang, “Theoretical and experimental study of optical gain, refractive index change, and linewidth enhancement factor of p-doped quantum-dot lasers,” IEEE J. Quantum Electron.42, 942–952 (2006). [CrossRef]

[28] Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A61, 033808-1–033808-10 (2000). [CrossRef]

[29] A. Fiore and A. Markus, “Differential gain and gain compression in quantum dot lasers,” IEEE J. Quantum Electron.43, 287–294 (2007). [CrossRef]

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Theory of high-speed nanolasers and nanoLEDs