OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20274–20279
« Show journal navigation

Ultrafast all-optical modulation in a silicon nanoplasmonic resonator

M. P. Nielsen and A. Y. Elezzabi  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20274-20279 (2013)
http://dx.doi.org/10.1364/OE.21.020274


View Full Text Article

Acrobat PDF (1084 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Ultrafast all-optical modulation in silicon-based metal-insulator-semiconductor-insulator-metal nanoring resonators through photogeneration of free-carriers using two-photon absorption is presented 3-D through finite difference time domain simulations. In a compact device footprint of only 1.4µm2, a 13.1dB modulation amplitude was obtained with a switching time of only 2ps using a modest pump pulse energy of 16.0pJ. The larger bandwidth associated with more compact nanorings is shown to result in increased modulation amplitude.

© 2013 OSA

1. Introduction

In this investigation, we explore the viability of ultrafast all-optical modulation in a silicon MISIM nanoring resonator using TPA. Carriers generated by degenerate TPA from a pump pulse at 1.35-1.44µm modify the complex refractive index of the nanoring resonator, modulating the resonant characteristics of the nanoring and modulating the transmission of a probe pulse at 1.53-1.58µm. Three separate devices are explored to examine how the thickness of the insulator layers and the nanoring dimensions influence the light modulation characteristics. Signal modulation of up to 13.1dB was obtained with an off-on switching time of 2ps using a modest pump pulse energy of 16.0pJ in a compact 1.4µm2 device footprint.

2. Devices

The nanoring resonator devices and associated coupling waveguides presented are formed of Ag/HfO2/Si/HfO2/Ag MISIM nanoplasmonic waveguides. Such devices would be fabricated by first lithographically defining a mask on an oxygen implanted SOI wafer, and dry etching through the device layer to define the silicon elements. Following this, the HfO2 dielectric spacer can be deposited conformally through atomic layer deposition (ALD). Finally, a second lithography step can be used to deposit silver around the structure though sputtering and lift-off processes. Although the indirect bandgap nature of silicon normally limits the carrier recombination time to timescales of nanoseconds, it has been shown that through ion implantation of oxygen into silicon, the introduction of carrier recombination centers reduces the carrier recombination lifetime to 600fs [13

13. F. E. Doany, D. Grischkowsky, and C. C. Chi, “Carrier lifetime versus ion-implantation dose in silicon on sapphire,” Appl. Phys. Lett. 50(8), 460–462 (1987). [CrossRef]

]. The silicon core in the MISIM nanoplasmonic waveguides is taken as oxygen doped silicon with a carrier recombination time of τr = 1ps to enable terahertz modulation bandwidth.

Schematics of the three presented devices, hereafter denoted as Device A, Device B and Device C, are depicted in Figs. 1(a)
Fig. 1 Schematic diagrams and broadband spectral response with pump and probe pulse resonances for (a) Device A, (b) Device B, and (c) Device C. Electric field intensity distribution for the fundamental TE modes of the MISIM waveguides for (a) Device A and (b) Devices B and C.
-1(c) along with their broadband spectral responses calculated within the 1.3-1.6µm wavelength range. Figures 1(d) and 1(e) depict the input modes for the input bus waveguides of the devices. All three devices are formed of 100nm wide by 340nm tall Si waveguides surrounded by hafnium oxide (HfO2) dielectric spacers and silver sidewalls. By varying the HfO2 dielectric spacer layer from 10nm in Device A to 20nm in Device B and Device C, it is possible to discern the influence of the spacer layer on device performance. Similarly, by varying the outer radii of the nanorings from 540nm in Device A and Device B to 1µm in Device C, the influence of the nanoring radii can be determined. These radii allow for compact device footprints as small as 1.4µm2. The MISIM nanoplasmonic waveguides are aperture coupled to the nanorings via a 200nm wide and 50nm deep silicon opening. To characterize the modulation properties of the devices, 400fs FWHM probe pulses, comparable to the lifetime of the nanoring resonances, are injected at the input port with a pulse energy of 6.4fJ and centered at resonances (depicted in Fig. 1) at 1.53µm, 1.58µm, and 1.55µm for Device A, Device B and Device C, respectively. To modulate the probe pulses, 400fs FWHM pump pulses are injected at the input port with various pulse energies ranging from 6.4fJ to 64pJ and centered at resonances (depicted in Fig. 1) at 1.35µm, 1.37µm, and 1.44µm for Device A, Device B and Device C, respectively.

3. FDTD formulation

To assess the proposed nanoring resonators as all-optical switch devices, self-consistent 2-D finite difference time domain (FDTD) simulations incorporating the nonlinear two-photon absorption (TPA) process, free-carrier absorption (FCA), and plasma dispersion effects (PDE) in silicon were conducted. In the standard Yee algorithm for the FDTD method used here, the electric displacement field D is calculated from Ampère’s equation, and the electric field E is calculated from both D and the polarization P by D=ε0E+P. For Ag and HfO2, the polarization is calculated through auxiliary differential equations using a multi-pole Lorentzian fit to the refractive index values from [14

14. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] and [15

15. J. D. Traylor Kruschwitz and W. T. Pawlewicz, “Optical and durability properties of infrared transmitting thin films,” Appl. Opt. 36(10), 2157–2159 (1997). [CrossRef] [PubMed]

], respectively. The polarization for silicon, on the other hand, is divided into linear and nonlinear components, P=Plinear+PTPA+PFCA+Pplasma, where the linear component is calculated through an auxiliary differential equation using a multi-pole Lorentzian fit to the refractive index values from [16

16. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1998).

] and the nonlinear components are calculated using the method derived in [17

17. N. Suzukim, “FDTD analysis of two-photon absorption and free-carrier absorption in Si high-index-contrast waveguides,” J. Lightwave Technol. 25(9), 2495–2501 (2007). [CrossRef]

] as follows. Silicon’s Kerr and Raman nonlinearities are neglected for this investigation as they are much weaker than the TPA and carrier effects for the time duration, length scales, and pulse energies under consideration [18

18. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

,19

19. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express 19(1), 206–217 (2011). [CrossRef] [PubMed]

]. With the change in optical intensity, I, due to TPA, dI/dL=βTPAI2, where βTPA = 0.8cm/GW [20

20. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

] is the TPA coefficient and L is the interaction length, the nonlinear polarization due to TPA, PTPA=ε0χTPAE, can be calculated from:
χTPA=ic0n0βTPAωI=c02ε0n02βTPAiω|E|2,
(1)
which can be discretized through the use of the substitution – by ∂/∂t into:
χTPAn+1=χTPAnc02ε0n02βTPAΔt2|En+1/2|2χTPAnc02ε0n02βTPAΔt4[|En+1|2+|En|2],
(2)
where χTPA is the nonlinear susceptibility due to TPA, c0 is the speed of light, n0 = 3.48 is the refractive index of silicon at 1.55µm, ε0 is the permittivity of free space, ω is the angular frequency, n is the discretized step index, and Δt is the time step. The dependence of χTPAn+1 on En + 1 requires iteration for self-consistency. The free-carrier concentration, Nf, equivalent to both the electron, Ne, and the hole, Nh, concentrations, is calculated through the rate equation:
dNfdt=12ω(dIdz)Nfτr=c02ε02n02βTPA8ω|E|4Nfτr,
(3)
which can be discretized into:
Nfn+1/2=2τrΔt2τr+ΔtNfn1/2+τrΔt2τr+Δtc02ε02n02βTPA4ω|En|4,
(4)
where τr = 1ps is the free-carrier recombination time in oxygen doped silicon. The generated free-carriers then lead to FCA and plasma dispersion effects. The change in optical intensity due to FCA is dI/dL=σFCANfI leads to the polarization due to FCA of:
PFCA=iε0εiFCAE=c0ε0n0σFCANfiωE,
(5)
where σFCA=3.6×1021[m2](λ[μm]/1.55)2 [21

21. R. D. Kekatpure and M. L. Brongersma, “Near-infrared free-carrier absorption in silicon nanocrystals,” Opt. Lett. 34(21), 3397–3399 (2009). [CrossRef] [PubMed]

] is the free-carrier absorption cross-section. The plasma dispersion polarization arising from the free-carrier refractive index change is:
Pplasma=ε0εrPlasmaE=ε02n0ΔnplasmaE,
(6)
where ΔnPlasma=[8.8×1022Ne8.5×1018Nh0.8](λ[μm]/1.55)2 [22

22. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

].

This allows the relationship between D and E for silicon to be rewritten as:
D˜=DPLinear=ε0E[2n0Δnplasmac0n0σFCANfiωc02ε0n02βTPA2iω|E|2],
(7)
Discretizing through the substitution of – by ∂/∂t and rearranging to solve for En + 1 yields:
En+1=g(En+1)g+(En+1)En+D˜n+1D˜nε0g+(En+1),
(8)
where,

g±(En+1)=2n0Δnplasma(En+1)±c0n0σFCANfn+1/2Δt2±c02ε0n02βTPAΔt[|En+1|2+|En|2]8.
(9)

As with Eq. (3), Eq. (8) must be solved with iteration. In this case, the maximum number of iterations was set to six to ensure accuracy without compromising simulation performance.

4. Results

To characterize the three devices, a 400fs FWHM pump pulse was injected at the input port at various pulse energies and the device was probed with the 400fs FWHM 6.4fJ probe pulse. Figure 2(a)
Fig. 2 Intensity plots for Device A with the 400fs FWHM probe pulse centered at 1.53µm (a) ‘on’ resonance and (b) after the pump pulse has turned it ‘off’ resonance at 16.0pJ. (c) Average carrier concentration in the nanoring for Device A at pump pulse energies of 31.3pJ (green solid line), 16.0pJ (red dashed line), and 5.8pJ (blued dotted line).
depicts Device A at the probe resonance at 1.53µm, without injection of the pump pulse. When the 16.0pJ pump pulse at 1.35µm generates free-carriers inside the nanoring, it causes a shift of the nanoring’s resonant characteristics, thus, moving the probe pulse ‘off’ resonance and away from the minimum transmission. Figure 2(b) shows Device A after the pump pulse has shifted the probe resonance away from the probe 1.53µm resonant wavelength. The time dynamics for the average carrier concentration generated in the nanoring for Device A at several pump pulse energies are depicted in Fig. 2(c). The carrier density increases within the first 400fs and decays within 1ps. During this time, it is expected that the nanoring resonance will shift and revert back to its original state. Figure 3
Fig. 3 Ultrafast response of the devices as a function of the signal delay between pump and probe pulses for (a) Device A, (b) Device B, and (c) Device C at pump pulse energies of 31.3pJ (green solid line), 16.0pJ (red dashed line), and 5.8pJ (blued dotted line).
depicts the ultrafast response of the devices under various pump energy excitations. Maximum transmission is obtained for a 400fs delay between pump and probe pulses, as this corresponds to the free-carrier concentration reaching its maximum value. The broader resonances associated with the smaller nanorings in Device A and Device B (pump at 1.37µm, probe at 1.58µm) result in more of the spectral contents of the probe pulse to fall within the nanoring resonator’s bandwidth, thus leading to transmission minimum on the order of a few percent for the ‘off’ state. Figure 4(a)
Fig. 4 Effect of increased pump pulse energies up to 64pJ for Device A (blue diamonds and solid line), Device B (red squares and dashed line), and Device C (green triangles and dotted line) on (a) modulation amplitude, (b) maximum carrier concentration in the nanoring, (c) maximum resonance shift, and (d) switching time for the respective probe pulses.
shows how the lower transmission minimum leads to a greater on-off modulation amplitude for Device A and Device B compared to Device C (pump at 1.44µm, probe at 1.55µm) which has a 51% narrower resonance as shown in Fig. 1(f). The thinner (10nm) HfO2 spacer layers in Device A confine more of the pump energy to the silicon core, leading to greater modulation of up to 13.1dB at lower pump pulse energies. As the pump pulse energy is increased above 31.3pJ, the modulation amplitude plateaus and decreases due to increased FCA and non-degenerate TPA between the pump and probe pulses. At higher pump energies, the pump begins to experience increased FCA from its leading edge, hence the maximum nanoring carrier concentration [Fig. 4(b)] increases slowly with pump energy. Another cause of the plateau behaviour of the signal response is that, similarly to the probe pulse, the leading edge of the pump pulse shifts the pump resonance before the trailing edge reaches the device. The plateau behaviour at higher pump energies is also illustrated in Fig. 4(c) for the maximum resonance shift of the nanorings. An important characteristic of any signal modulating device is its switching time. Here, the devices’ switching time is defined as the time over which the signal reaches 3dB over its initial value. As depicted in Fig. 4(d), this value is very dependent on the ring geometry with smaller rings having longer switching times due to their lower ‘off’ state transmission. It can be seen that using smaller nanorings with thinner dielectric spacer layers enables more efficient and stronger modulation capabilities. Using a modest pump pulse energy of 16.0pJ, Device A achieved 13.1dB modulation amplitude with an ultrafast switching time of only 2ps. The required energy formodulation could be further reduced by utilizing shorter pump pulses in smaller nanorings with thinner dielectric spacer layers.

5. Conclusion

Self-consistent FDTD simulations incorporating TPA, FCA, and plasma dispersion are utilized to examine ultrafast all-optical modulation in silicon-based MISIM nanoring resonators. With a modest pump pulse energy of 16.0pJ, a 13.1dB modulation amplitude was obtained with a switching time of only 2ps with a compact 1.4µm2 device footprint. It is shown that the modulation amplitude is maximized for smaller nanorings and thinner dielectric spacer layers due to the broader device bandwidth.

References and links

1.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

2.

P. Berini, R. Charbonneau, S. Jettè-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007). [CrossRef]

3.

J. Grandidier, S. Massenot, G. Colas des Francs, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B 78(24), 245419 (2008). [CrossRef]

4.

S. Sederberg, V. Van, and A. Y. Elezzabi, “Monolithic integration of plasmonic waveguides into a complimentary metal-oxide-semiconductor- and photonic-compatible platform,” Appl. Phys. Lett. 96(12), 121101 (2010). [CrossRef]

5.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics 3(5), 283–286 (2009). [CrossRef]

6.

S. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express 19(9), 8888–8902 (2011). [CrossRef] [PubMed]

7.

S. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express 21(7), 8320–8330 (2013). [CrossRef] [PubMed]

8.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009). [CrossRef] [PubMed]

9.

A. Y. Elezzabi, Z. Han, S. Sederberg, and V. Van, “Ultrafast all-optical modulation in silicon-based nanoplasmonic devices,” Opt. Express 17(13), 11045–11056 (2009). [CrossRef] [PubMed]

10.

J. N. Caspers, N. Rotenberg, and H. M. van Driel, “Ultrafast silicon-based active plasmonics at telecom wavelengths,” Opt. Express 18(19), 19761–19769 (2010). [CrossRef] [PubMed]

11.

S. Sederberg, D. Driedger, M. Nielsen, and A. Y. Elezzabi, “Ultrafast all-optical switching in a silicon-based plasmonic nanoring resonator,” Opt. Express 19(23), 23494–23503 (2011). [CrossRef] [PubMed]

12.

K. F. MacDonald, Z. L. Sámson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]

13.

F. E. Doany, D. Grischkowsky, and C. C. Chi, “Carrier lifetime versus ion-implantation dose in silicon on sapphire,” Appl. Phys. Lett. 50(8), 460–462 (1987). [CrossRef]

14.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

15.

J. D. Traylor Kruschwitz and W. T. Pawlewicz, “Optical and durability properties of infrared transmitting thin films,” Appl. Opt. 36(10), 2157–2159 (1997). [CrossRef] [PubMed]

16.

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1998).

17.

N. Suzukim, “FDTD analysis of two-photon absorption and free-carrier absorption in Si high-index-contrast waveguides,” J. Lightwave Technol. 25(9), 2495–2501 (2007). [CrossRef]

18.

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

19.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express 19(1), 206–217 (2011). [CrossRef] [PubMed]

20.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

21.

R. D. Kekatpure and M. L. Brongersma, “Near-infrared free-carrier absorption in silicon nanocrystals,” Opt. Lett. 34(21), 3397–3399 (2009). [CrossRef] [PubMed]

22.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(230.4320) Optical devices : Nonlinear optical devices
(230.5750) Optical devices : Resonators
(240.6680) Optics at surfaces : Surface plasmons
(200.6715) Optics in computing : Switching

ToC Category:
Integrated Optics

History
Original Manuscript: May 14, 2013
Revised Manuscript: June 28, 2013
Manuscript Accepted: August 12, 2013
Published: August 22, 2013

Citation
M. P. Nielsen and A. Y. Elezzabi, "Ultrafast all-optical modulation in a silicon nanoplasmonic resonator," Opt. Express 21, 20274-20279 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20274


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
  2. P. Berini, R. Charbonneau, S. Jettè-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys.101(11), 113114 (2007). [CrossRef]
  3. J. Grandidier, S. Massenot, G. Colas des Francs, A. Bouhelier, J.-C. Weeber, L. Markey, and A. Dereux, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B78(24), 245419 (2008). [CrossRef]
  4. S. Sederberg, V. Van, and A. Y. Elezzabi, “Monolithic integration of plasmonic waveguides into a complimentary metal-oxide-semiconductor- and photonic-compatible platform,” Appl. Phys. Lett.96(12), 121101 (2010). [CrossRef]
  5. P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal-insulator-metal waveguides,” Nat. Photonics3(5), 283–286 (2009). [CrossRef]
  6. S. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, “Silicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,” Opt. Express19(9), 8888–8902 (2011). [CrossRef] [PubMed]
  7. S. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express21(7), 8320–8330 (2013). [CrossRef] [PubMed]
  8. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009). [CrossRef] [PubMed]
  9. A. Y. Elezzabi, Z. Han, S. Sederberg, and V. Van, “Ultrafast all-optical modulation in silicon-based nanoplasmonic devices,” Opt. Express17(13), 11045–11056 (2009). [CrossRef] [PubMed]
  10. J. N. Caspers, N. Rotenberg, and H. M. van Driel, “Ultrafast silicon-based active plasmonics at telecom wavelengths,” Opt. Express18(19), 19761–19769 (2010). [CrossRef] [PubMed]
  11. S. Sederberg, D. Driedger, M. Nielsen, and A. Y. Elezzabi, “Ultrafast all-optical switching in a silicon-based plasmonic nanoring resonator,” Opt. Express19(23), 23494–23503 (2011). [CrossRef] [PubMed]
  12. K. F. MacDonald, Z. L. Sámson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3(1), 55–58 (2009). [CrossRef]
  13. F. E. Doany, D. Grischkowsky, and C. C. Chi, “Carrier lifetime versus ion-implantation dose in silicon on sapphire,” Appl. Phys. Lett.50(8), 460–462 (1987). [CrossRef]
  14. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  15. J. D. Traylor Kruschwitz and W. T. Pawlewicz, “Optical and durability properties of infrared transmitting thin films,” Appl. Opt.36(10), 2157–2159 (1997). [CrossRef] [PubMed]
  16. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, 1998).
  17. N. Suzukim, “FDTD analysis of two-photon absorption and free-carrier absorption in Si high-index-contrast waveguides,” J. Lightwave Technol.25(9), 2495–2501 (2007). [CrossRef]
  18. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express15(25), 16604–16644 (2007). [CrossRef] [PubMed]
  19. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear propagation in silicon-based plasmonic waveguides from the standpoint of applications,” Opt. Express19(1), 206–217 (2011). [CrossRef] [PubMed]
  20. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003). [CrossRef]
  21. R. D. Kekatpure and M. L. Brongersma, “Near-infrared free-carrier absorption in silicon nanocrystals,” Opt. Lett.34(21), 3397–3399 (2009). [CrossRef] [PubMed]
  22. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited