Abstract

Actively-controlled second harmonic generation in a silicon nitride ring resonator is proposed and simulated. The ring was designed to resonate at both pump and second harmonic wavelengths and quasi-phase-matched frequency conversion is induced by a periodic static electric field generated by voltage applied to electrodes arranged along the ring. Nonlinear propagation simulations were undertaken and an efficiency of −21.67 dB was calculated for 60 mW of pump power at 1550 nm and for a 30V applied voltage, which compares favorably with demonstrated all-optical second harmonic generation in integrated microresonators. Transient effects were also evaluated. The proposed design can be exploited for the construction of electro-optical devices based on nonlinear effects in CMOS compatible circuits.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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2013 (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. Photonics7(8), 597–607 (2013).
[CrossRef]

2012 (1)

2011 (2)

2010 (4)

J. L. O’Brien, “Exploiting entanglement,” Science330(6004), 588–589 (2010).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron.16(1), 216–225 (2010).
[CrossRef]

2009 (1)

M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: Geometry and absolute brightness,” Phys. Rev. A79(4), 043835 (2009).
[CrossRef]

2008 (2)

2007 (1)

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics1(5), 293–296 (2007).
[CrossRef]

2006 (3)

M. Lipson, “Compact electro-optic modulators on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.12(6), 1520–1526 (2006).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett.96, 63601 (2006).

2005 (2)

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol.23(12), 4222–4238 (2005).
[CrossRef]

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys.77(2), 513–577 (2005).
[CrossRef]

2004 (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

2000 (1)

D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron.6(6), 1312–1317 (2000).
[CrossRef]

1994 (1)

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A38(9), 4931–4934 (1988).
[CrossRef] [PubMed]

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

1973 (1)

H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc.120(2), 295–300 (1973).
[CrossRef]

Alic, N.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

Andersen, U. L.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

Bachor, H. A.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

Bergman, K.

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

Bowen, W. P.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett.96, 63601 (2006).

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys.77(2), 513–577 (2005).
[CrossRef]

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron.16(1), 216–225 (2010).
[CrossRef]

Chan, J.

Chen, L.

Collett, M.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

Elser, D.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

Fainman, Y.

Fiedler, K.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

Fong, K. Y.

Foster, M. A.

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Fürst, J. U.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

Gaeta, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

Gaeta, A. L.

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. Photonics7(8), 597–607 (2013).
[CrossRef]

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

Grosse, N. B.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett.96, 63601 (2006).

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A38(9), 4931–4934 (1988).
[CrossRef] [PubMed]

Ikeda, K.

Kashyap, R.

Kimble, H. J.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A38(9), 4931–4934 (1988).
[CrossRef] [PubMed]

Krause, M.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron.16(1), 216–225 (2010).
[CrossRef]

Kürz, P.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

Lam, P. K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett.96, 63601 (2006).

Lassen, M.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

Leuchs, G.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

Levy, J. S.

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

Lipson, M.

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. Photonics7(8), 597–607 (2013).
[CrossRef]

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express20(27), 27999–28008 (2012).
[CrossRef] [PubMed]

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics1(5), 293–296 (2007).
[CrossRef]

M. Lipson, “Compact electro-optic modulators on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.12(6), 1520–1526 (2006).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol.23(12), 4222–4238 (2005).
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

Marquardt, C.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

McKenzie, K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett.96, 63601 (2006).

Miller, D. A. B.

D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron.6(6), 1312–1317 (2000).
[CrossRef]

Mitchell, M. W.

M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: Geometry and absolute brightness,” Phys. Rev. A79(4), 043835 (2009).
[CrossRef]

Mlynek, J.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

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. Photonics7(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. Photonics7(8), 597–607 (2013).
[CrossRef]

O’Brien, J. L.

J. L. O’Brien, “Exploiting entanglement,” Science330(6004), 588–589 (2010).
[CrossRef]

Padmaraju, K.

Palacios, T.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

Paschotta, R.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994).
[CrossRef] [PubMed]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A38(9), 4931–4934 (1988).
[CrossRef] [PubMed]

Pernice, W.

Philipp, H. R.

H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc.120(2), 295–300 (1973).
[CrossRef]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics1(5), 293–296 (2007).
[CrossRef]

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron.16(1), 216–225 (2010).
[CrossRef]

Ryu, K. K.

Saperstein, R. E.

Schmidt, B. S.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Schuck, C.

Sharping, J. E.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

Strekalov, D. V.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010).
[CrossRef] [PubMed]

Tang, H. X.

Turner, A. C.

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010).
[CrossRef]

van Loock, P.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys.77(2), 513–577 (2005).
[CrossRef]

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A38(9), 4931–4934 (1988).
[CrossRef] [PubMed]

Xiong, C.

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Figures (6)

Fig. 1
Fig. 1

Ring resonator scheme. Light launched into the bus waveguide couples to the ring where resonating wavelengths experience an intensity build up.

Fig. 2
Fig. 2

Intensity distribution in the ring waveguide cross section of the transverse component of the optical electric field for the quasi-TE mode. The red arrows indicate the optical electric field direction.

Fig. 3
Fig. 3

Normalized B factor spectra for pump and second harmonic resonances. The arrows indicate the resonance shifts for second harmonic generation with 60 mW of pump power and 10 V applied voltage.

Fig. 4
Fig. 4

Ring resonator design with inner electrodes subjected to ground (GND) and V voltage. Inset: Radial static electric field along the ring resonator for V = 10V.

Fig. 5
Fig. 5

(a) SHG power evolution for different applied voltages. (b) Output power and conversion efficiency as an applied voltage function.

Fig. 6
Fig. 6

SHG transient response when 10V is turned on and off.

Equations (12)

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( E t1 E t2 )=( t jκ jκ t )( E i1 E i2 ),
θ= n eff 4 π 2 λ R=2πm,
B= | E i2 E i1 | 2 = (κ) 2 1+ (t) 2 2tcos(θ) .
m 0 =2 m 1 m 2 = N 2 ,
E(r,φ,z)=A(φ)Ψ(r,z),
P= |F | 2 ε 0 c n eff 2 ,
|F | 2 =|A | 2 Ψ 2 drdz .
F 1 Rφ = i3 χ rrrr (3) ω 1 8 n eff1 c {[(| F 1 | 2 f 1111 +2| F 2 | 2 f 1122 +(2| F 0 | 2 +2 F 0 2 cos(2 k 0 Rφ)) f 1100 ] F 1 +2[ e i( k 2 2 k 1 + k 0 )Rφ + e i( k 2 2 k 1 k 0 )Rφ ] F 1 * F 2 F 0 f 1120 }
F 2 Rφ = i3 χ rrrr (3) ω 2 8 n eff2 c {[2| F 1 | 2 f 2211 +| F 2 | 2 f 2222 +(2| F 0 | 2 +2 F 0 2 cos(2 k 0 Rφ)) f 2200 ] F 2 +[ e i(2 k 1 k 2 + k 0 )Rφ + e i(2 k 1 k 2 k 0 )Rφ ] F 1 2 F 0 f 2110 },
f abcd = Ψ a Ψ b Ψ c Ψ d drdz Ψ a 2 drdz Ψ b 2 drdz Ψ c 2 drdz Ψ d 2 drdz ,
Δλ=λ ϕ NL 2πm+ ϕ NL .
W= Γ eff P 775 Q SHG ,

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