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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20210–20219
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The metal grating design of plasmonic hybrid III-V/Si evanescent lasers

Min-Hsiang Hsu, Chien-Chung Lin, and Hao-Chung Kuo  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20210-20219 (2013)
http://dx.doi.org/10.1364/OE.21.020210


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Abstract

A hybrid III-V/silicon laser design with a metal grating layer inserted in between is proposed and numerically studied. The metal grating layer is buried in a silicon ridge waveguide surrounded by silicon dioxide, and its structural parameters such as periodicity, width and depth can be varied for optimization purpose. The plasmonic effect originated from the grating layer can manage optical fields between III-V and silicon layers in hopes of dimension reduction. The substrate is planarized to minimize the bonding failure. A numerical algorithm with various combinations of metal grating and waveguide structural parameters was created and the optimal design with 730 nm grating period and 600 nm of buried waveguide ridge height was obtained by minimizing the corresponding laser threshold. With top AlInGaAs quantum wells and optimized design of hybrid metal/silicon waveguide, a 0.6 μm−1 threshold gain can be achieved.

© 2013 OSA

1. Introduction

2. Proposed process flow

3. Simulation methodology

To evaluate different design parameters such as grating period and waveguide height, we proceed a three-dimensional (3-D) eigenmode calculation at wavelength 1.55 μm by the finite-element method in COMSOL® differential equation solver. Both the cross-section and side views of the hybrid device are shown in Fig. 3
Fig. 3 The schematic of simulation models viewed from (a) the cross-section and (b) the side of the device.
. The coordinate system is also defined in the figure. The solver neglects the reflection from the boundaries in x and z directions, which are sometimes called scattering boundary condition [16

16. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

]. In y direction, we choose the unit cell, as indicated by red dot lines in the Fig. 3(b), to be the calculation domain, and assume the periodic boundary condition in y-direction. Besides, the stability of the numerical results can be guaranteed by the convergence tests and be independent from mesh sizes and boundaries. The III-V structure, as shown in Fig. 3, consists of 1-μm InP substrate, 0.25-μm Al0.131In0.528Ga0.34As separated confinement hetero-structure (SCH), 0.125-μm Al0.055In0.653Ga0.292As quantum well (QW) and 0.12-μm InP contact layer. The height of the embedded silicon waveguide, H, can be treated as one of the variables, and the width of the waveguide is fixed at 300 nm; the thickness of Al layer located at bottom of the silicon ridge waveguide is 0.05 μm. The dimensions of metal gratings are h in depth, w in width and 0.1 μm in length and the periodicity is p (h, w, and p will be used as design variables in the following contents.). The refractive indices of materials used in the simulations are described in the Table 1

Table 1. The Refractive Index of Materials in Simulation Models

table-icon
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. Other than the refractive index of Al, we only consider the real part of refractive index to observe the fundamental optical behaviors of the proposed device.

The optimization criterion is governed by the laser threshold gain of the device which is evaluated by [17

17. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, “Modal gain, modal loss, and confinement factors,” in Diode Lasers and Photonic Integrated Circuits, K. Chang, ed. (John Wiley & Sons, 2012).

]:
gth=1ΓQW×(neff(r)nQW)×[4πneff(i)λ+ln(1R2)2]
(1)
where gth is threshold gain, neff(r) and neff(i) is real part and imaginary part of effective index, respectively, λ is the target wavelength of 1.55 μm, R is the reflectivity, ΓQW is the power confinement factor in quantum wells and nQW is the refractive index equal to 3.6594. The cavity length in the y-direction, l, is deliberately set to be 30 μm in total. This reduced length, compared to 300 μm in most designs, is due to the everlasting request of scaling-down in the silicon IC industries, and also can be served as a testament for the potential of this hybrid platform. Note that we also assume the mirror loss is resulted from dielectric-air Fresnel reflection instead of from mirrors or any other reflectors, so R is [(neff-1)/(neff + 1)]2. The nature of this design brings us a large number of variables to deal with, including metal grating depth, width, and periods, silicon waveguide height etc. If all parameters are varying at the same time, the sheer quantity of calculation becomes impractical. So we assume that a global optimal gth exists and no other significant saddle points for this solution. Under this assumption, we can focus on two or three variables at one time and optimize our design step by step with the gth value winding down as the optimization procedure proceeds. We firstly determine the waveguide height (H) to have a well confined optical mode; then, the metal grating depth (h), width (w) and period (p) can be optimized subsequently. Low threshold gain (gth) is usually preferred in a generic laser operation, however, we believe the transverse and longitudinal energy distribution patterns are also important for a good laser operation, and, thus, need to be considered.

4. Structural optimization of plasmonic III-V/silicon hybrid lasers

4.1 Mode behaviors with ridge height (H) and grating depth (h)

First the embedded ridge height (H) and Al grating depth (h) are set as variables to test their influences on the transverse energy distribution, and grating width (w) and period (p) are fixed at 0.1 and 0.3 μm. The Fig. 4(a)
Fig. 4 (a) The real part and (b) imaginary part of effective refractive index of the device with different ridge height and Al grating depth. The inset shown in the (a) describes the definition of simulation parameters.
and 4(b) show the real part and imaginary part of effective index with different ridge heights of 50 nm-, 100 nm- and 200 nm-deep Al gratings, respectively. From the simulation, the high real part is accompanied with the high imaginary part of the effective refractive index. Besides, with increasing ridge height, the real part and imaginary part of effective indices reach stable values; the deeper the grating is, the lower asymptotical effective indices the devices get. Similar behaviors can be explained by the metal-insulator-metal model discussed previously [22

22. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef] [PubMed]

24

24. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005). [CrossRef] [PubMed]

]. Short distance between Al gratings and Al bottom layer results in stronger mutual coupling and high refractive index. However, as the distance between metal gratings and layer is gradually increased beyond a critical distance, the model shifts from metal-insulator-metal relation to the metal-insulator condition. In the meantime, the effective refractive index becomes constant and no longer correlates to the distance between top and bottom Al layer. Because this critical distance is a constant in our simulation, it is natural that the elbows of the refractive indices shifts like the red arrows in the Fig. 4 when Al grating depth is considered.

Figure 5(a)
Fig. 5 (a) The silicon waveguide (WG) and (b) the quantum well (QW) power confinement with various ridge heights and Al grating depths. (c) the calculated threshold gain of the device. (d) the corresponding structure schematic to the simulated normalized energy density distribution results with (e) 0.3 μm-, (f) 0.6 μm- and (g) 0.9 μm-high ridge.
and 5(b) show the energy confinement factors of embedded ridge waveguide (ΓWG) and quantum well structures (ΓQW) with various ridge heights and grating depths, calculated by the equation:
ΓQW/WG=QW/WG|E|2dxdydz/Total|E|2dxdydz
(2)
where E is electric field in the structure. In Fig. 5(a) and 5(b), the ΓWG and ΓQW oscillate periodically with the increasing ridge height. As shown in the inset of Fig. 5(b), the ΓWG and ΓQW are complementary to each other under the same Al grating depth. When Al grating depth increases, the waveguide confinement (ΓWG) tends to increase while the ΓQW goes down as shown in Fig. 5(a) and 5(b). This tendency indicates that as the top Al layer grows thicker, the optical energy resides more easily in the waveguide part, not the upper quantum well region. Besides, the calculated threshold gain is shown in the Fig. 5(c). Even though most points of threshold gains are located around 20 μm−1, not every condition is suitable for our device. In fact, with increasing ridge height, more propagating modes can exist along the waveguide. However, multi-modes are unfavorable to the laser device most of time. Hence, we can’t determine the parameters only through the threshold data, but also take the energy distribution into consideration. Figure 5(d) is the cross-section view of our structure, and from Fig. 5(e) to 5(g), the normalized energy density distributions of different ridge heights (Fig. 5(e): 0.3 μm, Fig. 5(f): 0.6 μm, Fig. 5(g): 0.9 μm) are shown. The energy density is calculated by (1/2) × Re[E × H*] and normalized to its maximum value in each case. Figure 5(e)-5(g) describe how the energy density distribution evolves when the ridge height changes. As the height of buried silicon waveguide is increased from 0.3 to 0.9 μm, transformation in energy distribution is expected. With small waveguide height, only the surface plasmonic polariton (SPP) mode on the bottom Al layer is possible (like in 0.3 μm case of Fig. 5(e)). However, if the ridge is too high, as in Fig. 5(g), multiple transverse hybrid SPP modes can be seen in the waveguide. We believe if the design falls in the middle of these two situations, it will be the best for the lasers device (as in Fig. 5(f)).

4.2 Mode behaviors with grating depth (h) and grating width (w)

The threshold gain is also calculated to determine suitable parameters of metal grating depth (h) and width (w) in our design, as shown in the Fig. 6(c). Between 0.3 μm- and 0.5 μm-deep metal gratings, because of very few confined energy in the QW, the calculated threshold soars high; conversely, the extremely low threshold occurs at the grating width 0.3 μm and depth in the range from 0.05 μm to 0.25 μm.

4.3 Mode behaviors with gGrating period (p)

In the past, a nano-scale laser can usually yield ultra-low threshold gain (from tens to several hundreds of cm−1 [26

26. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008). [CrossRef] [PubMed]

28

28. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

],) during operation. Our design, on the other hand, is the traditional quantum well with micron-scale length of the active region. While the theoretical calculation and the past data [17

17. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, “Modal gain, modal loss, and confinement factors,” in Diode Lasers and Photonic Integrated Circuits, K. Chang, ed. (John Wiley & Sons, 2012).

] predict the proposed structure is possible for a electrically pumped laser, it has to be pointed out that this design sacrifices the performance due to a smaller active region and extra loss from metal gratings in order to achieve the higher yield in metal bonding process [29

29. J. B. Laskey, C. L. Shieh, X. Huang, G. Liu, M. V. R. Murty, C. C. Lin, and D. X. Xu, “Wafer bonding for silicon-on-insulator technologies,” Appl. Phys. Lett. 48(1), 78–80 (1986). [CrossRef]

, 30

30. C. C. Lee and G. S. Matijasevic, “Highly reliable die attachment on polished GaAs surfaces using gold-tin eutectic alloy,” IEEE T. Compon. Hybr. 12(3), 406–409 (2005). [CrossRef]

] and better optical mode coupling into silicon waveguide. The final optimized structure parameters are listed in Table 2

Table 2. Optimized Structural Parameters of a Nano-scale Plasmonic Hybrid Laser

table-icon
View This Table
| View All Tables
.

All units are in nm, the QW power confinement factor is 16.3%, and threshold gain is 0.616 μm−1.

5. Conclusion

In conclusion, we propose an alternative method to fabricate a small-sized hybrid III-V/Silicon laser device, whose device length is dramatically reduced from 300 μm to 30 μm with integrated metal grating layers. The simulation software also assists us to determine the favorable fabrication parameters including ridge height for 0.6 μm, Al grating width and depth at 0.3 μm and 0.1 μm, respectively. The grating period can be as small as 730 nm although 2 to 3 μm would be better in terms of process tolerance. Most of all, the calculated gain threshold, around 0.6 μm−1, shows great potential to realize this design in practice.

Acknowledgments

References and links

1.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006). [CrossRef] [PubMed]

2.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007). [CrossRef] [PubMed]

3.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]

4.

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004). [CrossRef] [PubMed]

5.

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006). [CrossRef]

6.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408(6811), 440–444 (2000). [CrossRef] [PubMed]

7.

R. Chen, T. T. D. Tran, K. W. Ng, W. S. Ko, L. C. Chuang, F. G. Sedgwick, and C. Chang-Hasnain, “Nanolasers grown on silicon,” Nat. Photonics 5(3), 170–175 (2011). [CrossRef]

8.

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]

9.

A. J. Zilkie, P. Seddighian, B. J. Bijlani, W. Qian, D. C. Lee, S. Fathololoumi, J. Fong, R. Shafiiha, D. Feng, B. J. Luff, X. Zheng, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Power-efficient III-V/Silicon external cavity DBR lasers,” Opt. Express 20(21), 23456–23462 (2012). [CrossRef] [PubMed]

10.

A. W. Fang, E. Lively, Y. H. Kuo, D. Liang, and J. E. Bowers, “A distributed feedback silicon evanescent laser,” Opt. Express 16(7), 4413–4419 (2008). [CrossRef] [PubMed]

11.

X. Sun, A. Zadok, M. J. Shearn, K. A. Diest, A. Ghaffari, H. A. Atwater, A. Scherer, and A. Yariv, “Electrically pumped hybrid evanescent Si/InGaAsP lasers,” Opt. Lett. 34(9), 1345–1347 (2009). [CrossRef] [PubMed]

12.

D. Liang, G. Roelkens, R. Baets, and J. E. Bowers, “Hybrid Integrated Platforms for Silicon Photonics,” Materials 3(3), 1782–1802 (2010). [CrossRef]

13.

J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, “Ge-on-Si laser operating at room temperature,” Opt. Lett. 35(5), 679–681 (2010). [CrossRef] [PubMed]

14.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

15.

D. Pasquariello and K. Hjort, “Plasma-assisted InP-to-Si low temperature wafer bonding,” IEEE J. Sel. Top. Quant. 8(1), 118–131 (2002). [CrossRef]

16.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

17.

L. A. Coldren, S. W. Corzine, and M. L. Masanovic, “Modal gain, modal loss, and confinement factors,” in Diode Lasers and Photonic Integrated Circuits, K. Chang, ed. (John Wiley & Sons, 2012).

18.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, “Optical properties of materials, nonlinear optics, quatum optics” in Handbook of Optics third edition, (McGraw-Hill Professional, New York, 2009).

19.

H. Dejun, “Refractive index of AlInGaAs layers in the transparent wavelength region,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (1994), vol. 2 pp. 349–350.

20.

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999). [CrossRef]

21.

A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34(22), 4755–4767 (1995). [CrossRef] [PubMed]

22.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef] [PubMed]

23.

G. Veronic and S. Fan, “Modes of Subwavelength Plasmonic Slot Waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007). [CrossRef]

24.

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005). [CrossRef] [PubMed]

25.

A. Polyakov, M. Zolotorev, P. J. Schuck, and H. A. Padmore, “Collective behavior of impedance matched plasmonic nanocavities,” Opt. Express 20(7), 7685–7693 (2012). [CrossRef] [PubMed]

26.

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008). [CrossRef] [PubMed]

27.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010). [CrossRef]

28.

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

29.

J. B. Laskey, C. L. Shieh, X. Huang, G. Liu, M. V. R. Murty, C. C. Lin, and D. X. Xu, “Wafer bonding for silicon-on-insulator technologies,” Appl. Phys. Lett. 48(1), 78–80 (1986). [CrossRef]

30.

C. C. Lee and G. S. Matijasevic, “Highly reliable die attachment on polished GaAs surfaces using gold-tin eutectic alloy,” IEEE T. Compon. Hybr. 12(3), 406–409 (2005). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(230.7370) Optical devices : Waveguides
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 9, 2013
Revised Manuscript: July 11, 2013
Manuscript Accepted: July 25, 2013
Published: August 21, 2013

Citation
Min-Hsiang Hsu, Chien-Chung Lin, and Hao-Chung Kuo, "The metal grating design of plasmonic hybrid III-V/Si evanescent lasers," Opt. Express 21, 20210-20219 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20210


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References

  1. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature441(7090), 199–202 (2006). [CrossRef] [PubMed]
  2. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007). [CrossRef] [PubMed]
  3. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeration using low-power four-wave mixing on silicon chip,” Nat. Photonics2(1), 35–38 (2008). [CrossRef]
  4. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express12(21), 5269–5273 (2004). [CrossRef] [PubMed]
  5. T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A74(5), 051802 (2006). [CrossRef]
  6. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature408(6811), 440–444 (2000). [CrossRef] [PubMed]
  7. R. Chen, T. T. D. Tran, K. W. Ng, W. S. Ko, L. C. Chuang, F. G. Sedgwick, and C. Chang-Hasnain, “Nanolasers grown on silicon,” Nat. Photonics5(3), 170–175 (2011). [CrossRef]
  8. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express14(20), 9203–9210 (2006). [CrossRef] [PubMed]
  9. A. J. Zilkie, P. Seddighian, B. J. Bijlani, W. Qian, D. C. Lee, S. Fathololoumi, J. Fong, R. Shafiiha, D. Feng, B. J. Luff, X. Zheng, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Power-efficient III-V/Silicon external cavity DBR lasers,” Opt. Express20(21), 23456–23462 (2012). [CrossRef] [PubMed]
  10. A. W. Fang, E. Lively, Y. H. Kuo, D. Liang, and J. E. Bowers, “A distributed feedback silicon evanescent laser,” Opt. Express16(7), 4413–4419 (2008). [CrossRef] [PubMed]
  11. X. Sun, A. Zadok, M. J. Shearn, K. A. Diest, A. Ghaffari, H. A. Atwater, A. Scherer, and A. Yariv, “Electrically pumped hybrid evanescent Si/InGaAsP lasers,” Opt. Lett.34(9), 1345–1347 (2009). [CrossRef] [PubMed]
  12. D. Liang, G. Roelkens, R. Baets, and J. E. Bowers, “Hybrid Integrated Platforms for Silicon Photonics,” Materials3(3), 1782–1802 (2010). [CrossRef]
  13. J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, “Ge-on-Si laser operating at room temperature,” Opt. Lett.35(5), 679–681 (2010). [CrossRef] [PubMed]
  14. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  15. D. Pasquariello and K. Hjort, “Plasma-assisted InP-to-Si low temperature wafer bonding,” IEEE J. Sel. Top. Quant.8(1), 118–131 (2002). [CrossRef]
  16. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008). [CrossRef]
  17. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, “Modal gain, modal loss, and confinement factors,” in Diode Lasers and Photonic Integrated Circuits, K. Chang, ed. (John Wiley & Sons, 2012).
  18. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, “Optical properties of materials, nonlinear optics, quatum optics” in Handbook of Optics third edition, (McGraw-Hill Professional, New York, 2009).
  19. H. Dejun, “Refractive index of AlInGaAs layers in the transparent wavelength region,” in Proceedings of IEEE Lasers and Electro-Optics Society Annual Meeting (1994), vol. 2 pp. 349–350.
  20. G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun.163(1-3), 95–102 (1999). [CrossRef]
  21. A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt.34(22), 4755–4767 (1995). [CrossRef] [PubMed]
  22. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A21(12), 2442–2446 (2004). [CrossRef] [PubMed]
  23. G. Veronic and S. Fan, “Modes of Subwavelength Plasmonic Slot Waveguides,” J. Lightwave Technol.25(9), 2511–2521 (2007). [CrossRef]
  24. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett.30(24), 3359–3361 (2005). [CrossRef] [PubMed]
  25. A. Polyakov, M. Zolotorev, P. J. Schuck, and H. A. Padmore, “Collective behavior of impedance matched plasmonic nanocavities,” Opt. Express20(7), 7685–7693 (2012). [CrossRef] [PubMed]
  26. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett.33(11), 1261–1263 (2008). [CrossRef] [PubMed]
  27. M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4(6), 395–399 (2010). [CrossRef]
  28. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18(9), 8790–8799 (2010). [CrossRef] [PubMed]
  29. J. B. Laskey, C. L. Shieh, X. Huang, G. Liu, M. V. R. Murty, C. C. Lin, and D. X. Xu, “Wafer bonding for silicon-on-insulator technologies,” Appl. Phys. Lett.48(1), 78–80 (1986). [CrossRef]
  30. C. C. Lee and G. S. Matijasevic, “Highly reliable die attachment on polished GaAs surfaces using gold-tin eutectic alloy,” IEEE T. Compon. Hybr.12(3), 406–409 (2005). [CrossRef]

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