Abstract

A polymer-infiltrated P-S-N diode capacitor configuration is proposed and a high speed electro-optic phase shifter based on a silicon organic hybrid platform is designed and modeled. The structure enables fast carrier depletion in addition to the second order nonlinearity so that a large electro-optic overlapped volume is achievable. Moreover, the device speed can be significantly improved with the introduction of free carriers due to a reduced experienced transient capacitance. The advantages of the diode capacitor structure are highly suitable for application to a class of low aspect ratio slot waveguides where the RC limitation of the radio frequency response is minimized. According to our numerical results, by optimizing both the waveguide geometry and polarization mode, at least 269 GHz 3-dB bandwidth with high efficiency of 5.5 V-cm is achievable. More importantly, the device does not rely on strong optical confinement within the nano-slot, a feature that gives considerable tolerance in the use of nano-fabrication techniques. Finally, the high overlap and energy efficiency of the device can be applied to slow light or optical resonance media for realizing photonic integrated circuits-based green photonics.

© 2011 OSA

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2011 (2)

2010 (3)

2009 (6)

K. Preston and M. Lipson, “Slot waveguides with polycrystalline silicon for electrical injection,” Opt. Express 17(3), 1527–1534 (2009).
[CrossRef] [PubMed]

B. Jalali, S. Fathpour, and K. Tsia, “Green silicon photonics,” Opt. Photon. News 20(6), 18–23 (2009).
[CrossRef]

F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fedeli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009).
[CrossRef] [PubMed]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17(11), 9282–9287 (2009).
[CrossRef] [PubMed]

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

2008 (5)

C. E. Png, G. H. Park, S. T. Lim, E. P. Li, A. J. Danner, K. Ogawa, and Y. T. Tan, “Electrically controlled silicon-based photonic crystal chromatic dispersion compensator with ultralow power consumption,” Appl. Phys. Lett. 93(6), 061111 (2008).
[CrossRef]

J.-M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008).
[CrossRef] [PubMed]

T. Gorman, S. Haxha, H. Ademgil, and J. J. Ju, “Ultra-high-speed deeply etched electrooptic polymer modulator,” IEEE J. Quantum Electron. 44(12), 1180–1187 (2008).
[CrossRef]

T. B. Jones, B. Penkov, J. Huang, P. Sullivan, J. Davis, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16(21), 16659–16669 (2008).
[CrossRef] [PubMed]

2007 (4)

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007).
[CrossRef] [PubMed]

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, H. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybird polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

T. D. Kim, J. W. Kang, J. Luo, S. H. Jang, J. W. Ka, N. Tucker, J. B. Benedict, L. R. Dalton, T. Gray, R. M. Overney, D. H. Park, W. N. Herman, and A. K. Jen, “Ultralarge and thermally stable electro-optic activities from supramolecular self-assembled molecular glasses,” J. Am. Chem. Soc. 129(3), 488–489 (2007).
[CrossRef] [PubMed]

H. S. Lee, T. D. Kang, H. Lee, S. K. Lee, J. H. Kim, and D. H. Choi, “Ellipsometric study of the poling effect on nonlinear-optical side-chain polymers containing disperse red 1,” J. Appl. Phys. 102(1), 013514 (2007).
[CrossRef]

2006 (1)

M. Hochberg, T. Baehr-Jones, G. X. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (2)

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[CrossRef] [PubMed]

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

2002 (1)

1994 (1)

A. G. Rickman, G. T. Reed, and F. Namavar, “Silicon-on-insulator optical rib waveguide loss and mode characteristics,” J. Lightwave Technol. 12(10), 1771–1776 (1994).
[CrossRef]

1993 (1)

1987 (1)

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

Ademgil, H.

T. Gorman, S. Haxha, H. Ademgil, and J. J. Ju, “Ultra-high-speed deeply etched electrooptic polymer modulator,” IEEE J. Quantum Electron. 44(12), 1180–1187 (2008).
[CrossRef]

Almeida, V. R.

Andreani, L. C.

Asghari, M.

Baehr-Jones, T.

Baets, R.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Barrios, C. A.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[CrossRef] [PubMed]

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

Benedict, J. B.

T. D. Kim, J. W. Kang, J. Luo, S. H. Jang, J. W. Ka, N. Tucker, J. B. Benedict, L. R. Dalton, T. Gray, R. M. Overney, D. H. Park, W. N. Herman, and A. K. Jen, “Ultralarge and thermally stable electro-optic activities from supramolecular self-assembled molecular glasses,” J. Am. Chem. Soc. 129(3), 488–489 (2007).
[CrossRef] [PubMed]

Benight, S.

Bennett, B. R.

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

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Bojko, R.

Brimont, A.

Brosi, J.-M.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

J.-M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008).
[CrossRef] [PubMed]

Cao, H.

Chen, B.

M. Hochberg, T. Baehr-Jones, G. X. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Choi, D. H.

H. S. Lee, T. D. Kang, H. Lee, S. K. Lee, J. H. Kim, and D. H. Choi, “Ellipsometric study of the poling effect on nonlinear-optical side-chain polymers containing disperse red 1,” J. Appl. Phys. 102(1), 013514 (2007).
[CrossRef]

Cunningham, J. E.

Dalton, L.

R. Ding, T. Baehr-Jones, Y. Liu, R. Bojko, J. Witzens, S. Huang, J. Luo, S. Benight, P. Sullivan, J. M. Fedeli, M. Fournier, L. Dalton, A. Jen, and M. Hochberg, “Demonstration of a low V π L modulator with GHz bandwidth based on electro-optic polymer-clad silicon slot waveguides,” Opt. Express 18(15), 15618–15623 (2010).
[CrossRef] [PubMed]

T. B. Jones, B. Penkov, J. Huang, P. Sullivan, J. Davis, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

M. Hochberg, T. Baehr-Jones, G. X. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Dalton, L. R.

T. D. Kim, J. W. Kang, J. Luo, S. H. Jang, J. W. Ka, N. Tucker, J. B. Benedict, L. R. Dalton, T. Gray, R. M. Overney, D. H. Park, W. N. Herman, and A. K. Jen, “Ultralarge and thermally stable electro-optic activities from supramolecular self-assembled molecular glasses,” J. Am. Chem. Soc. 129(3), 488–489 (2007).
[CrossRef] [PubMed]

Danner, A. J.

M. Xin, C. E. Png, and A. J. Danner, “Breakdown delay-based depletion mode silicon modulator with photonic hybrid-lattice resonator,” Opt. Express 19(6), 5063–5076 (2011).
[CrossRef] [PubMed]

C. E. Png, G. H. Park, S. T. Lim, E. P. Li, A. J. Danner, K. Ogawa, and Y. T. Tan, “Electrically controlled silicon-based photonic crystal chromatic dispersion compensator with ultralow power consumption,” Appl. Phys. Lett. 93(6), 061111 (2008).
[CrossRef]

Davis, J.

T. B. Jones, B. Penkov, J. Huang, P. Sullivan, J. Davis, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Derose, C. T.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, H. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybird polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Ding, R.

Dong, F.

Dong, P.

Dumon, P.

F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fedeli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009).
[CrossRef] [PubMed]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Emerson, N. G.

Enami, Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, H. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybird polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Fathpour, S.

B. Jalali, S. Fathpour, and K. Tsia, “Green silicon photonics,” Opt. Photon. News 20(6), 18–23 (2009).
[CrossRef]

Fedeli, J. M.

Feng, D.

Feng, N.-N.

Fournier, M.

Frank, B.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Freude, W.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-a platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(a) 2D schematic cross section of the device showing the lateral polymer infiltrated P-S-N diode capacitor configuration. (b) The small signal equivalent circuit corresponding to (a) showing the RC limitation of the phase shifter.

Fig. 2
Fig. 2

The fundamental mode profile cross section of the RM SWG: (a) TE-like polarization and (b) TM-like polarization. (c) E-field intensity cutlines of the TE-like and TM-like mode profiles in the x direction across the waveguide center, which show a large portion of the total intensity located within the silicon ridges.

Fig. 3
Fig. 3

(a) E-field (x component) profile within the nonlinear slot when the diode capacitor is reverse biased. (b) Free carrier (hole) concentration profile within the silicon ridges under the same bias. (c) Localized index perturbation corresponding to (a) via Pockels effect. (d) Localized index perturbation corresponding to a combined effort of hole and electron depletion via free carrier effect (values below the lower end of the color scale are shown in black).

Fig. 4
Fig. 4

(a) ∆neff and ∆neff,poly changes when Wslot is varied for both TE- and TM-like polarizations. (b) Change of the intensity fraction within the slot for both polarizations when Wslot is swept over the same range.

Fig. 5
Fig. 5

The carrier concentration evolution with time indicating a reduced device response time with an increase in Wslot.

Fig. 6
Fig. 6

(a) ∆neff decreases as propagation loss increases with an increase of hslab. (b) The device response time is further reduced with an increase of hslab.

Fig. 7
Fig. 7

(a) Faster response is found for free carriers than E-field due to the reduced transient capacitance. (b) A carrier cutline along the x direction indicating the depletion width shift under reverse bias.

Fig. 8
Fig. 8

(a) The tradeoff relationship between bias voltage and phase shift. (b) The RF driving signal with Vpp=10 V and period of 2.4 ps. (c) The modulated phase shift in response to (b). (d) The transient current flow within the P-S-N diode capacitor in response to (b).

Fig. 9
Fig. 9

Equivalent circuit of the TL loaded with the P-S-N diode capacitor.

Fig. 10
Fig. 10

The walk-off bandwidth (ON and OFF states) reduces with an increase of the polymer index shift due to the poling effect.

Tables (1)

Tables Icon

Table 1 List of the major design parameters in the RM device.

Equations (13)

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Δ n eff = Γ S Δ n poly = n g n S S ε | E | 2 d x d y ε | E | 2 d x d y Δ n poly
Δ n poly = n poly 3 r 33 E bias / 2 n poly 3 r 33 V b i a s / 2 W s l o t
Δ n eff Δ n eff,poly + Δ n eff,si = n g n S S ε | E | 2 Δ n poly d x d y ε | E | 2 d x d y + n g n R R ε | E | 2 Δ n si d x d y ε | E | 2 d x d y
Δ n si = 8.8 × 10 22 Δ n e 8.5 × 10 18 ( Δ n h ) 0.8
f U L = 1 2 π τ R C = 1 2 π i = 1 3 ( R i p + R i n ) C 1 W s l o t h s l a b 2 π ε poly ( ρ p + L p + + ρ n + L n + ) h W G
Δ α si = 8.5 × 10 18 Δ n e + 6.0 × 10 18 Δ n h .
C s l o t = ε poly h W G W s l o t 1 / C D = 1 / C s l o t + 1 / C D p + 1 / C D n = W s l o t ε poly h W G + W D ε si h W G
W D = W D p + W D n W D p , n ε s i 2 C s l o t 2 + 2 ε s i | V bias | q N P , N ε s i C s l o t
R 1 p , n = ρ p , n W W G W D p , n h W G .
E bit = 1 / 4 0 1 V bias I d t
f w a l k o f f , 3 d B = 0.5 v g,opt L π | 1 v g,opt / v g,elec |
n TL,eff = c 0 C TL L TL + C D L TL 1 1 + i f BW
Z c = 1 2 1 C TL L TL + C D L TL ( 1 + i f BW )

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