Abstract

CMOS platforms with a high nonlinear figure of merit are highly sought after for high photonic quantum efficiencies, enabling functionalities not possible from purely linear effects and ease of integration with CMOS electronics. Silicon-based platforms have been prolific amongst the suite of advanced nonlinear optical signal processes demonstrated to date. These include crystalline silicon, amorphous silicon, Hydex glass, and stoichiometric silicon nitride. Residing between stoichiometric silicon nitride and amorphous silicon in composition, silicon-rich nitride films of various formulations have emerged recently as promising nonlinear platforms for high nonlinear figure of merit nonlinear optics. Silicon-rich nitride films are compositionally engineered to create bandgaps that are sufficiently large to eliminate two-photon absorption at telecommunications wavelengths while enabling much larger nonlinear waveguide parameters (5x–500x) than those in stoichiometric silicon nitride. This paper reviews recent developments in the field of nonlinear optics using silicon-rich nitride platforms, as well as the outlook and future opportunities in this burgeoning field.

© 2018 Chinese Laser Press

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2017 (11)

X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
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2015 (9)

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S. W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D. L. Kwong, L. Maleki, and C. W. Wong, “A broadband chip-scale optical frequency synthesizer at 2.7 × 10−16 relative uncertainty,” Phys. Rev. Lett. 114, 053901 (2015).
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2013 (4)

T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21, 32192–32198 (2013).
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D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96, 061101 (2010).
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I. Goykhman, B. Desiatov, and U. Levy, “Ultrathin silicon nitride microring resonator for bio-photonic applications at 970  nm wavelength,” Appl. Phys. Lett. 97, 081108 (2010).
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E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14, 5524–5534 (2006).
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K. J. A. Ooi, D. K. T. Ng, T. Wang, A. K. L. Chee, L. K. Ang, Q. Wang, and D. T. H. Tan, “Ultralow power, broadband continuous wave four wave mixing in silicon rich nitride waveguides,” in Nonlinear Optics, OSA Technical Digest Series (Optical Society of America, 2015), paper NTh3A.9.

A. Mekis, S. Abdalla, D. Foltz, S. Gloeckner, S. Hovey, S. Jackson, Y. Liang, M. Mack, G. Masini, M. Peterson, T. Pinguet, S. Sahni, M. Sharp, P. Sun, D. Tan, L. Verslegers, B. P. Welch, K. Yokoyama, S. Yu, and P. M. de Dobbelaere, “A CMOS photonics platform for high-speed optical interconnects,” in IEEE Photonics Conference (IEEE, 2012), pp. 356–357.

M. Mitrovic, X. Guan, H. Ji, L. K. Oxenløwe, and L. H. Frandsen, “Four-wave mixing in silicon-rich nitride waveguides,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2015), paper FM1D.6.

H. Mertens, K. N. Andersen, and W. E. Svendsen, “Optical loss analysis of silicon rich nitride waveguides,” in European Conference on Optical Communications (IEEE, 2002), paper p1.38.

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

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Figures (15)

Fig. 1.
Fig. 1. Tailoring of the refractive index of silicon-rich nitride films grown using low-temperature (250°C) inductively coupled chemical vapor deposition. (a) It is observed that the measured refractive index of films increases as the SiH4N2 ratio increases from 0.85 to 1.36 to 2.27. (b) The measured extinction coefficient is small beyond 700 nm. At shorter wavelengths, the extinction coefficient becomes larger for higher silicon content. (c) The measured refractive index at 1550 nm as a function of SiH4N2 process ratio. Varying the SiH4N2 ratio from the smallest to largest value results in a variation of the refractive index from 2.2 to 3.1. (d) The inverse relation between band gap energy and film refractive index. From Refs. [16,17].
Fig. 2.
Fig. 2. Refractive index tailoring in plasma-enhanced chemical vapor deposited silicon-rich nitride films. (a) Larger ratios of flow rate between SiH4NH3 precursor gases result in larger refractive indices. (b) Redshifting of the linear absorption band edge as a function of SiH4NH3 flow rate ratio. From Ref. [21].
Fig. 3.
Fig. 3. Refractive index of PECVD-grown silicon-rich nitride films as the N:Si ratio is varied. Films with higher silicon content result in larger refractive indices. From Ref. [28].
Fig. 4.
Fig. 4. (a) Calculated second-order (β2) and fourth-order (β4) dispersion of ICP-CVD-grown USRN waveguides for different waveguide widths (W) for a fixed height of 300 nm. (b) Calculated nonlinear parameter of the USRN waveguides as a function of wavelength for various waveguide widths (W) and fixed height of 300 nm.
Fig. 5.
Fig. 5. (a) Amorphous CMOS materials as a function of linear refractive index. Films with larger linear refractive indices possess larger nonlinear refractive indices and smaller bandgaps [6,11,1621,25,4852,62,67].The relationship between bandgap and refractive index is fitted empirically with reported values. From Ref. [25]. (b) Calculated waveguide mode effective areas for various SiO2-cladded CMOS waveguides with their geometry optimized for high modal confinement.
Fig. 6.
Fig. 6. (a) Generated four-wave-mixing spectra as the signal wavelength is tuned from 1560 to 1610 nm using a pump located at 1555 nm. Brown, red, cyan, green, blue, yellow, orange, purple, and black lines denote the four-wave-mixing spectra for a signal located at 1560, 1565, 1570, 1575, 1580, 1585, 1590, 1595, and 1600 nm, respectively. (b) Four-wave-mixing using a pump at 1535 nm and signal at 1620 nm, representing conversion over 170 nm. Red, yellow, and blue lines denote the four-wave-mixing spectra for a signal located at 1600, 1610, and 1620 nm, respectively. Inset shows the calculated (purple line) and measured (black diamonds) conversion efficiency as a function of wavelength. (c) Measured conversion efficiency as a function of the pump power. Blue solid and yellow dashed lines represent the calculated conversion efficiency as a function of the pump power for a pump wavelength of 1555 nm and 1560 nm, respectively. (d) Four-wave-mixing experiments using a pump at 1560 nm and a signal at 1555 nm. From Refs. [17,25].
Fig. 7.
Fig. 7. (a) Four-wave mixing spectra using an LPCVD-grown silicon rich nitride waveguide. The inset shows the scanning electron micrograph of the fabricated waveguide. Conversion efficiency as a function of (b) peak pump power and (c) SRN waveguide length. A peak pump power of 40.5 dBm generates a conversion efficiency of 13.6 dB in a 1.8 cm SRN waveguide. From Ref. [23].
Fig. 8.
Fig. 8. (a) Four-wave mixing spectra as a function of wavelength for a peak pump power of 14 W using USRN waveguides. Cascaded four-wave-mixing is observed, including second and third idlers, which extend the spectrum to 1300 nm. Black, green, cyan, yellow, blue, and red lines represent measured spectra with the signal wavelength at 1620, 1622, 1624, 1626, 1628, and 1630 nm, respectively. The grey dashed curve represents the pump spectrum offset by 25  dB, with the signal off. (b) Measured parametric gain in the signal (blue squares), first (red circles), second (dark blue stars), and third idlers (green diamonds). (c) Transmission spectrum as a function of wavelength for a peak pump power of 10 W. Blue, orange, green, yellow, cyan, and red lines denote measured spectra with the signal wavelength at 1620, 1622, 1624, 1626, 1628, and 1630 nm, respectively. Grey dashed curve denotes the pump spectrum offset by 25  dB, with the signal off. (d) Measured signal (blue squares) and idler gain (red circles) as a function of signal wavelength. From Ref. [25].
Fig. 9.
Fig. 9. (a) Output spectra of 1.2 mm (red solid line) and 1.6 mm (black solid line) USRN waveguides compared with femtosecond laser spectrum (blue dashed line). Seed pulses are 500 fs wide with a peak power of 66 W. (b) Measured value of Ppeak/Pout versus Ppeak. That the flat profile obtained for Ppeak/Pout as Ppeak is varied implies negligible nonlinear losses. (c) Spectral bandwidth at the 30  dB level as a function of waveguide length. (d) Simulated evolution of the 500 fs pulses as a function of the input peak power. From Ref. [22].
Fig. 10.
Fig. 10. Characterization of supercontinuum from the SRN waveguide. (a) Spectral output as a function of input peak power. The location of the dispersive wave varies as a function of input peak power. (b) Dispersion slope calculated from the waveguide’s second-order dispersion. (c) Theoretical location of the generated dispersive wave as a function of third-order dispersion and input peak power. The color bar represents the wavelength of the dispersive wave corresponding to each color in the plot. The value of β3=35  ps3/km provides the best agreement with the locations of the dispersive waves generated in the experiment. From Ref. [18].
Fig. 11.
Fig. 11. (a) Calculated group velocity dispersion of an LPCVD-grown silicon-rich nitride waveguide with two zero-dispersion wavelengths (ZDWs). (b) Experimental and (c) calculated supercontinuum spectra using pulses with a temporal width of 130 fs. The power spectral density at the waveguide’s output is averaged over 50 noise realizations. From Ref. [23].
Fig. 12.
Fig. 12. (a) Top row shows the 12 Gbit/s pulsed RZ-OOK data encoded within the pump and injected into three Si-rich SiNx microring resonators with varying Si content. R=0.9 represents the Si-rich SiNx microring resonator with the highest Si content. The middle row shows the probe signal that has been modulated with the data from the pump after experiencing the Kerr nonlinearity in the Si-rich SiNx microring resonators. The lower row shows the probe signal that has been modulated with inverted data from the pump. Modulation contrast is greatest for R=0.9. (b) Measured eye diagrams for the three ring resonators. The Si-rich SiNx microring resonator with the largest Si content (R=0.9) has the highest modulation contrast and most open eye. From Ref. [20].
Fig. 13.
Fig. 13. (a) Wavelength conversion of 10 Gb/s signals for various probe wavelengths using LPCVD-grown silicon-rich nitride waveguides. (b) Measured bit error rate (BER) as a function of received power. Inset shows the electrical eye diagrams for the data signal (back-to-back) as well as the wavelength converted signal at 1562 nm for error-free operation (50 ps/div). (c) XPM-based spectral broadening of a probe at 1310 nm using a pump located at 1550 nm. (d) Close up of the XPM-broadened probe at 1310 nm. From Ref. [29].
Fig. 14.
Fig. 14. Ultra-silicon-rich nitride photonic crystal waveguide (PhCWs). (a) Scanning electron micrograph of a USRN photonic crystal waveguide. s1 and s2 denote the direction of hole shifts to engineer a region of flat group index near the band edge; r denotes the radius of the PhCW holes. (b) Calculated and diagram for PhCW with r=135  nm, s1=30  nm, and s2=0, insets show the mode profiles from the propagation direction and the top of PhCW, red dashed graph corresponds to the band of interest. Light line for SiO2 cladding is shown in yellow. (c) Measured transmission (red solid line) and group index (black squares) of a flat-band dispersion-engineered USRN PhCW. (d) Measured transmission (red dashed line) and group index (black squares) of a non-flat-band dispersion-engineered USRN PhCW. (e) Measured source spectrum (blue solid line) and output spectrum of a 96.6 μm PhCW (red dashed line) at a peak power of 2.5 W. A 1.5π nonlinear phase shift is acquired by the input pulse. From Ref. [27].
Fig. 15.
Fig. 15. (a) Gray and black curves show the measured transmission spectrum of a W1 photonic crystal waveguide with a length of 200 μm and a lattice period of 580 nm. The transmission region is about 20 nm and highlighted by the dashed lines. (b) Calculated (black solid line) and estimated (green squares) group index values of the fabricated showing the highest estimated group index of 110. The waveguide propagation loss is denoted by red dots, and the lowest propagation loss measured was 53 dB/cm for a group index of 37. (c) Gray and black curves show the measured transmission spectrum with a transmission bandwidth of over 70 nm for a W0.7 photonic crystal waveguide with a length of 200 μm and a lattice period of 580 nm. (d) Calculated (black solid line) and estimated (green squares) group index values of the fabricated. The highest estimated group index is 34. The waveguide propagation loss is denoted by red dots, and the lowest measured propagation loss was 4.6 dB/cm for a group index of 7.4. From Ref. [47].

Tables (2)

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Table 1. List of Nonlinear Optics Applications

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Table 2. Nonlinear Optical Properties for Various CMOS Platformsa

Equations (4)

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γ=2πn2λAeff.
Ppeak=1Rp.TS(λ)dλ,
S2=(ngn0)2.
βTPA,eff=βTPA,bulkAeffS2.

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