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Enhancement of second-harmonic generation from silicon nitride with gold gratings

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Abstract

We report strong enhancement of second-harmonic generation in a hybrid nanostructure with gold gratings embedded in a silicon nitride film. Compared to a flat silicon nitride film, the enhancement factor can be as large as 102 to 103 for transverse magnetic and electric polarizations, respectively in good agreement with numerical results calculated using finite element method. For both polarizations, the enhancement arises from a resonance between the waveguide modes and grating.

© 2015 Optical Society of America

1. Introduction

Nonlinear photonic chips based on non-silicon platforms for all-optical signal generation and processing have attracted increasing attention in recent years [1]. In particular, silicon nitride (SiN) is a promising candidate for on-chip nonlinear optics, not only because it is a complementary metal-oxide-semiconductor (CMOS) compatible material, but also because recent studies have reported large second- and third-order optical nonlinearities in this material [2–8]. Significantly, SiN also possesses superior linear optical properties compared to the traditional silicon platform, with a wider band-gap down to visible wavelengths, which can be tuned by adjusting the material composition [1,9]. Taking advantage of the large nonlinearity of SiN, integrated on-chip nonlinear functionalities have been demonstrated including wavelength conversion [2], optical parametric oscillation [10,11], and supercontinuum generation [12]. Depending on the composition, the second-order nonlinear susceptibility of SiN can reach 5.9 pm/V [4] or even higher [5]. In addition, values on the order of 10−13 m2/W have been reported for the nonlinear refractive index [8]. However, larger nonlinear responses would greatly benefit applications, with operation at even lower power.

The nonlinear responses can be enhanced by the strong local fields in resonant structures such as metallic nanostructures with surface plasmon resonances (SPR) [13], resonant cavities induced by defect modes in photonic crystals [14], resonant microspheres [15], resonant waveguide gratings [16,17], waveguides [18], or hybrid plasmonic-dielectric systems [19].

Here, we demonstrate enhanced second-harmonic generation (SHG) in a hybrid nanostructure consisting of a gold (Au) grating embedded in a SiN waveguide layer. The structure properties (linear transmission, local field distributions) are modeled as a function of the angle of incidence using the finite element method. Experimental characterization of the fabricated structure is then performed, showing significant enhancement of the SHG due to a resonance between the waveguide modes and the grating. Compared to a flat SiN film of the same thickness, the SHG efficiency is found to be enhanced by factors as much as 102 and 103 for the TM-in/TM-out and TE-in/TM-out polarization combinations, respectively.

2. Sample fabrication

A schematic of the hybrid structure designed using the finite element method is shown in Fig. 1(a). It consists of an Au grating with 575 nm period, fill factor of 0.24, and height of 30 nm, embedded in a SiN waveguide layer with a thickness of 450 nm. We first manufactured the Au grating on top of a fused silica substrate using nanoimprint lithography and lift-off technique. A scanning electron microscope (SEM) image of the grating is shown in Fig. 1(b). The SiN film was then deposited on the Au grating by plasma enhanced chemical vapor deposition (PECVD) under similar preparation conditions as in our recent demonstration of a strong second-order response in PECVD-grown SiN films [3].

 figure: Fig. 1

Fig. 1 (a) Schematic image of the cross-section of the hybrid structure. The design parameters are: period = 575 nm, HAu = 30 nm, WAu = 137 nm, and HSiN = 450 nm. (b) SEM image of the Au grating.

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3. Numerical modelling

In the undepleted pump approximation, the spatial dependence of the fundamental and SH time-harmonic fields can be modeled as [20]

××E(ω)k12E(ω)=μ0ω2P(1)(ω),
××E(2ω)k22E(2ω)=μ0ω2[P(1)(2ω)+P(2)(2ω)],
where E(ω) and E(2ω) are the fundamental and SHG electric fields, respectively. Here k1 = ω /c and k2 = 2ω /c are the wavevectors associated with the fundamental and SH beams, respectively, with c the light velocity in vacuum. P(1) = ε0χ(1)(ω)E(ω) and P(1)(2ω) = ε0χ(1)(2ω)E(2ω) represent the linear polarizations at fundamental and SH frequencies, respectively, with corresponding linear susceptibilities of the material χ(1)(ω) and χ(1)(2ω). P(2) = ε0χ(2)(2ω):E(ω)E(ω) is the second-order polarization. The second-order susceptibility χ(2)(2ω) is a third-rank tensor with the values as reported [3]. The constants ε0 and μ0 are the vacuum permittivity and permeability, respectively. The coupled equations above can be solved numerically to obtain the linear optical transmission/reflection and SHG emission from the nanostructure.

We first calculated the extinction spectrum of our structure as a function of the angle of incidence [21,22]. At the wavelength of 1064 nm (corresponding to that of our experiments), the resonance angle is found to be around 6° and 6.5° for incident TM- and TE-polarized fundamental light, respectively. In order to clarify the origin of the resonance modes at these particular angles, we plot the local electric and magnetic fields in Figs. 2(a) and 2(b) for TM-polarized light and in Figs. 2(c) and 2(d) for TE-polarized light.

 figure: Fig. 2

Fig. 2 Local-field distribution of fundamental light (|Eω/Eo|) (a) and (c) and corresponding transverse field at their resonance angles (b) and (d) for TM-in and TE-in. An input intensity of 1.74 × 106 W/m2 at the fundamental wavelength was used in the modeling.

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The symmetric first-order TM (TM0) and anti-symmetric first-order TE (TE0) waveguide modes can be clearly identified from the profile of the transverse magnetic and electric field [Figs. 2(b) and 2(d)]. We can then expect SHG enhancement due to the tight field confinement at these particular resonances as shown in Figs. 2(a) and 2(c). We also note that the electric field for TM-polarized light exhibits additional localization around the corners of the Au nanowires, although the structure is not excited under plasmon resonance conditions. This may be due to the lightning-rod type effect of the metal tip. We also point out that other types of resonance can be seen but for wavelengths below 1064 nm and therefore they do not play a role here.

Our numerical model for SHG was validated by comparing the SHG response calculated for a flat 450 nm SiN film vs. angle of incidence with that experimentally measured. The result is shown in Figs. 3(a) and 3(b) for TM-in/TM-out and TE-in/TM-out configurations, respectively. Note that there is no SHG for TM-in/TE-out and TE-in/TE-out due to symmetry rules associated with the in-plane isotropy of SiN [2]. We subsequently simulated the SHG response of our structure for different polarization combinations and the transmitted SHG signal [see Figs. 3(c) and 3(d)]. Both SiN and gold are considered as nonlinear materials for SHG emission but the maximum SHG from the gold grating alone is about three orders of magnitude weaker than that from the SiN waveguide at the same resonance angle and can therefore be neglected. The SHG is thus dominated by the SiN layer. The linear transmission of fundamental light is also shown with the SHG response for comparison of the resonance behavior. It is clear that the enhancement of the SHG signal can only occur within a narrow range of incident angles around the resonant angle for TM-in/TM-out and TE-in/TM-out polarization configurations. The theoretical SHG enhancement factor achieved in the hybrid structure is obtained by comparing the maximum SHG intensity from the hybrid structure to that from a flat SiN film with thickness identical to the waveguide layer [see Figs. 3(a) and 3(b)]. We emphasize that the two types of structures lead to maximum SHG efficiency at very different angles of incidence, so that we are comparing the two true maxima. With our design, the theoretically predicted enhancement factor is about 150 for the TM-in/TM-out configuration and up to 20,000 for the TE-in/TM-out configuration.

 figure: Fig. 3

Fig. 3 Numerically calculated SHG emission vs. angle of incidence in a SiN film under TM-in/TM-out configuration (a) and TE-in/TM-out configuration (b). (c-d) Same in hybrid structure. The linear transmittance is also shown. An input intensity of 1.74 × 106 W/m2 at the fundamental wavelength was used in the modeling.

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4. Experimental results and discussion

The linear and SHG responses were characterized with a setup similar to that described in [3,16]. Specifically, we used a mode-locked Nd:YAG laser as the source of fundamental light at 1064 nm, emitting pulses of 70 ps duration. The laser beam was collimated to a 1 mm diameter at the samples. The polarization state of the fundamental and SHG beams were controlled by calcite Glan polarizers and wave plates. The transmitted fundamental light and the generated SHG signal were detected with a photodiode and a photomultiplier tube (PMT), respectively. A long-pass filter was used before the sample to remove any possible second-harmonic light from the various optical components. In addition, a short-pass filter and an interference filter (with central wavelength at 532 nm) were used after the sample to ensure that only SHG light was detected. The sample was mounted on a high-precision rotation stage to control the angle of incidence during the measurements. We first measured the resonance angle of our sample under TM-in/TM-out configuration [Fig. 4(a)]. The resonant angle was found to be around 8°, which is shifted by 2° compared to the theoretical value from the modeling. This can be attributed to imperfections and deviations from the design parameters of the fabricated nanostructure. The strong oscillations seen in the transmission spectrum arises from the interference of reflected light inside the 1 mm-thick silica substrate [17].

 figure: Fig. 4

Fig. 4 Measured (a) linear transmittance and (b) SHG intensities from the hybrid structure measured for TM-in/TM-out configuration vs. angle of incidence. (c) SHG intensity from a 450-nm planar SiN film for the same configuration. (d) Comparison of SHG intensity from the hybrid structure and planar SiN film.

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The SHG signal measured as a function of the angle of incidence is shown in Fig. 4(b). One can clearly observe the resonantly enhanced SHG signal, emitted only for angles of incidence within the transmission resonance (note the logarithmic scale in intensity). We next verified the quadratic dependence of the SHG signal on the fundamental intensity as shown in Fig. 4(d). In order to confirm that the hybrid structure indeed leads to large SHG enhancement, we compared the SHG signal to that generated from a planar reference SiN film with the same 450 nm thickness as the waveguide layer. The SHG signal from the reference was also measured vs. the angle of incidence for TM-in/TM-out. The results in Fig. 4(c) show that the SHG is maximum at a 60° angle, and it is the SHG intensity at this particular angle that we use as the reference for the enhancement factor. The SHG power from the hybrid structure is compared to that from the reference SiN layer in Fig. 4(d) where one can see that the hybrid resonant structure allows for enhancement by as much as a factor of 130.

We then conducted similar measurements for the TE-in/TM-out configuration (see Fig. 5). In this case, the grating enhances the SHG signal by a factor of 1000 compared to the maximum TE-in/TM-out reference signal at about 50° angle of incidence. Note however, that the reference signal for this configuration is substantially lower (factor of ~25) than that for the TM-in/TM-out configuration. The strongest SHG signal produced is thus that from the hybrid structure with TM-in/TM-out polarization combination. This is because this particular configuration corresponds to the best coupling to the nonlinear tensor of the SiN film. Interestingly, the enhancement factor observed for the TM-in/TM-out configuration is very close to the one predicted numerically. The factor for the TE-in/TM-out configuration, however, is about a factor of 20 weaker than predicted. Yet, the SHG signal scales with the fourth power of the fundamental field amplitude and the discrepancy in the amplitude is therefore only about a factor of two, which can easily arise from imperfections in the fabricated nanostructure. This was confirmed by additional numerical simulations on deviations from design parameters, such as the period of the Au grating, the width of the Au nanowires, the thickness of the SiN layer, and the Au cross-section shape. The resonance angle of the structure is mainly affected by the period of the grating, whilst the SHG signal is mainly influenced by the imperfections of the Au-nanowire cross-section. Such imperfections will affect local distribution of TM-in fundamental field and generated SH field, and lead to the different SHG emission efficiency accordingly. However, it is difficult to find one specific type of imperfection that can explain the deviation between the model and the experiment.

 figure: Fig. 5

Fig. 5 Measured (a) linear transmittance and (b) SHG intensities from the hybrid structure for TE-in/TM-out configuration vs. angle of incidence. (c) SHG intensity from a 450-nm planar SiN film for the same configuration. (d) Comparison of SHG intensity from the hybrid structure and planar SiN film.

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5. Conclusions

In conclusion, we have demonstrated that SHG from SiN can be significantly enhanced by Au gratings. Depending on the polarization configuration, the SHG efficiency can be enhanced by up to three orders of magnitude. We also found that the enhancement mechanism is associated with the excitation of a guided-mode resonance with additional contribution from local field enhancement for TM polarization. The imperfections influence the enhancement greatly especially for the TE incidence. We therefore believe that even higher enhancement factors can be achieved in future structures with improved quality.

Acknowledgments

We acknowledge the financial support from the TUT Optics and Photonics Strategy funding and Academy of Finland (Grant 134980).

References and links

1. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013). [CrossRef]  

2. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011). [CrossRef]   [PubMed]  

3. T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012). [CrossRef]  

4. A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014). [CrossRef]  

5. E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013). [CrossRef]  

6. K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express 16(17), 12987–12994 (2008). [CrossRef]   [PubMed]  

7. T. Ning, O. Hyvärinen, H. Pietarinen, T. Kaplas, M. Kauranen, and G. Genty, “Third-harmonic UV generation in silicon nitride nanostructures,” Opt. Express 21(2), 2012–2017 (2013). [CrossRef]   [PubMed]  

8. S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012). [CrossRef]  

9. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010). [CrossRef]  

10. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]  

11. S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22(22), 26517–26525 (2014). [CrossRef]   [PubMed]  

12. R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, “Ultrabroadband supercontinuum generation in a CMOS-compatible platform,” Opt. Lett. 37(10), 1685–1687 (2012). [CrossRef]   [PubMed]  

13. Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011). [CrossRef]   [PubMed]  

14. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009). [CrossRef]  

15. J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011). [CrossRef]   [PubMed]  

16. M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007). [CrossRef]  

17. T. Ning, H. Pietarinen, O. Hyvärinen, R. Kumar, T. Kaplas, M. Kauranen, and G. Genty, “Efficient second-harmonic generation in silicon nitride resonant waveguide gratings,” Opt. Lett. 37(20), 4269–4271 (2012). [CrossRef]   [PubMed]  

18. D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013). [CrossRef]  

19. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011). [CrossRef]   [PubMed]  

20. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 2003).

21. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]  

22. C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012). [CrossRef]  

References

  • View by:

  1. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013).
    [Crossref]
  2. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
    [Crossref] [PubMed]
  3. T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
    [Crossref]
  4. A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
    [Crossref]
  5. E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
    [Crossref]
  6. K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express 16(17), 12987–12994 (2008).
    [Crossref] [PubMed]
  7. T. Ning, O. Hyvärinen, H. Pietarinen, T. Kaplas, M. Kauranen, and G. Genty, “Third-harmonic UV generation in silicon nitride nanostructures,” Opt. Express 21(2), 2012–2017 (2013).
    [Crossref] [PubMed]
  8. S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012).
    [Crossref]
  9. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
    [Crossref]
  10. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
    [Crossref]
  11. S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22(22), 26517–26525 (2014).
    [Crossref] [PubMed]
  12. R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, “Ultrabroadband supercontinuum generation in a CMOS-compatible platform,” Opt. Lett. 37(10), 1685–1687 (2012).
    [Crossref] [PubMed]
  13. Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
    [Crossref] [PubMed]
  14. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
    [Crossref]
  15. J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
    [Crossref] [PubMed]
  16. M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
    [Crossref]
  17. T. Ning, H. Pietarinen, O. Hyvärinen, R. Kumar, T. Kaplas, M. Kauranen, and G. Genty, “Efficient second-harmonic generation in silicon nitride resonant waveguide gratings,” Opt. Lett. 37(20), 4269–4271 (2012).
    [Crossref] [PubMed]
  18. D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
    [Crossref]
  19. T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
    [Crossref] [PubMed]
  20. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 2003).
  21. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
    [Crossref]
  22. C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012).
    [Crossref]

2014 (2)

A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
[Crossref]

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22(22), 26517–26525 (2014).
[Crossref] [PubMed]

2013 (4)

E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
[Crossref]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013).
[Crossref]

T. Ning, O. Hyvärinen, H. Pietarinen, T. Kaplas, M. Kauranen, and G. Genty, “Third-harmonic UV generation in silicon nitride nanostructures,” Opt. Express 21(2), 2012–2017 (2013).
[Crossref] [PubMed]

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

2012 (5)

C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012).
[Crossref]

S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012).
[Crossref]

R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, and A. L. Gaeta, “Ultrabroadband supercontinuum generation in a CMOS-compatible platform,” Opt. Lett. 37(10), 1685–1687 (2012).
[Crossref] [PubMed]

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

T. Ning, H. Pietarinen, O. Hyvärinen, R. Kumar, T. Kaplas, M. Kauranen, and G. Genty, “Efficient second-harmonic generation in silicon nitride resonant waveguide gratings,” Opt. Lett. 37(20), 4269–4271 (2012).
[Crossref] [PubMed]

2011 (4)

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref] [PubMed]

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[Crossref] [PubMed]

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

2010 (2)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[Crossref]

2009 (2)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

2008 (1)

2007 (1)

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Abolghasem, P.

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

Alamin Dow, A. B.

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

Alic, N.

Ayala-Orozco, C.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Capretti, A.

E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
[Crossref]

Cardenas, J.

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Dal Negro, L.

E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
[Crossref]

S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012).
[Crossref]

Dominguez-Juarez, J. L.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref] [PubMed]

Eggleton, B. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Fainman, Y.

Foster, M. A.

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

Fuji, M.

A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
[Crossref]

Gaeta, A. L.

Genty, G.

Giessen, H.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[Crossref]

Grady, N. K.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Grillet, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Halas, N. J.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Halir, R.

Helmy, A. S.

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

Hyvärinen, O.

Ikeda, K.

Imakita, K.

A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
[Crossref]

Kaplas, T.

Karvinen, P.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Kauranen, M.

T. Ning, O. Hyvärinen, H. Pietarinen, T. Kaplas, M. Kauranen, and G. Genty, “Third-harmonic UV generation in silicon nitride nanostructures,” Opt. Express 21(2), 2012–2017 (2013).
[Crossref] [PubMed]

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

T. Ning, H. Pietarinen, O. Hyvärinen, R. Kumar, T. Kaplas, M. Kauranen, and G. Genty, “Efficient second-harmonic generation in silicon nitride resonant waveguide gratings,” Opt. Lett. 37(20), 4269–4271 (2012).
[Crossref] [PubMed]

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Kawamura, I.

A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
[Crossref]

Kherani, N. P.

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

Kitao, A.

A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
[Crossref]

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

Kozyreff, G.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref] [PubMed]

Krauss, T. F.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Kuittinen, M.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Kumar, R.

Lederer, F.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Leivo, S.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

Levy, J. S.

Lippitz, M.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Lipson, M.

Logan, D. F.

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

Luke, K.

Martorell, J.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref] [PubMed]

Miano, G.

E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
[Crossref]

Miller, S.

Minissale, S.

S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012).
[Crossref]

Monat, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Morandotti, R.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013).
[Crossref]

Moss, D. J.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Niemi, T.

C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012).
[Crossref]

Ning, T.

O’Faolain, L.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Okawachi, Y.

Oulton, R. F.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Paul, T.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Pecora, E. F.

E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
[Crossref]

Pietarinen, H.

Rockstuhl, C.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Saperstein, R. E.

Siltanen, M.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Simonen, J.

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012).
[Crossref]

Stepanov, D.

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

Tan, C.

C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012).
[Crossref]

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[Crossref]

Utikal, T.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Vahimaa, P.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

Voima, P.

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

White, T. P.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

Yerci, S.

S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012).
[Crossref]

Zentgraf, T.

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Zhang, S.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Zhang, X.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Zhang, Y.

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (5)

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

S. Minissale, S. Yerci, and L. Dal Negro, “Nonlinear optical properties of low temperature annealed silicon-rich oxide and silicon-rich nitride materials for silicon photonics,” Appl. Phys. Lett. 100(2), 021109 (2012).
[Crossref]

E. F. Pecora, A. Capretti, G. Miano, and L. Dal Negro, “Generation of second harmonic radiation from sub-stoichiometric silicon nitride thin films,” Appl. Phys. Lett. 102(14), 141114 (2013).
[Crossref]

M. Siltanen, S. Leivo, P. Voima, M. Kauranen, P. Karvinen, P. Vahimaa, and M. Kuittinen, “Strong enhancement of second-harmonic generation in all-dielectric resonant waveguide grating,” Appl. Phys. Lett. 91(11), 111109 (2007).
[Crossref]

D. F. Logan, A. B. Alamin Dow, D. Stepanov, P. Abolghasem, N. P. Kherani, and A. S. Helmy, “Harnessing second-order optical nonlinearities at interfaces in multilayer silicon-oxy-nitride waveguides,” Appl. Phys. Lett. 102(6), 061106 (2013).
[Crossref]

J. Phys. D (1)

A. Kitao, K. Imakita, I. Kawamura, and M. Fuji, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47(21), 215101 (2014).
[Crossref]

Nano Lett. (1)

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011).
[Crossref] [PubMed]

Nat. Commun. (1)

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[Crossref] [PubMed]

Nat. Photonics (4)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[Crossref]

Opt. Commun. (1)

C. Tan, J. Simonen, and T. Niemi, “Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating,” Opt. Commun. 285(21-22), 4381–4386 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (1)

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Phys. Rev. Lett. (1)

T. Utikal, T. Zentgraf, T. Paul, C. Rockstuhl, F. Lederer, M. Lippitz, and H. Giessen, “Towards the origin of the nonlinear response in hybrid plasmonic systems,” Phys. Rev. Lett. 106(13), 133901 (2011).
[Crossref] [PubMed]

Other (1)

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 2003).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic image of the cross-section of the hybrid structure. The design parameters are: period = 575 nm, HAu = 30 nm, WAu = 137 nm, and HSiN = 450 nm. (b) SEM image of the Au grating.
Fig. 2
Fig. 2 Local-field distribution of fundamental light (|Eω/Eo|) (a) and (c) and corresponding transverse field at their resonance angles (b) and (d) for TM-in and TE-in. An input intensity of 1.74 × 106 W/m2 at the fundamental wavelength was used in the modeling.
Fig. 3
Fig. 3 Numerically calculated SHG emission vs. angle of incidence in a SiN film under TM-in/TM-out configuration (a) and TE-in/TM-out configuration (b). (c-d) Same in hybrid structure. The linear transmittance is also shown. An input intensity of 1.74 × 106 W/m2 at the fundamental wavelength was used in the modeling.
Fig. 4
Fig. 4 Measured (a) linear transmittance and (b) SHG intensities from the hybrid structure measured for TM-in/TM-out configuration vs. angle of incidence. (c) SHG intensity from a 450-nm planar SiN film for the same configuration. (d) Comparison of SHG intensity from the hybrid structure and planar SiN film.
Fig. 5
Fig. 5 Measured (a) linear transmittance and (b) SHG intensities from the hybrid structure for TE-in/TM-out configuration vs. angle of incidence. (c) SHG intensity from a 450-nm planar SiN film for the same configuration. (d) Comparison of SHG intensity from the hybrid structure and planar SiN film.

Equations (2)

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××E(ω) k 1 2 E(ω)= μ 0 ω 2 P (1) (ω),
××E(2ω) k 2 2 E(2ω)= μ 0 ω 2 [ P (1) (2ω)+ P (2) (2ω) ],

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