Abstract

New designs are proposed for 2×2 electro-optical switching in the 1.3–12 μm wavelength range. Directional couplers are analyzed using a two-dimensional effective-index approximation. It is shown that three or four side-coupled Si or Ge channel waveguides can provide complete crossbar broad-spectrum switching when the central waveguides are injected with electrons and holes to modify the waveguides’ core index by an amount Δn+iΔk. The four-waveguide device is found to have a required active length L that is 50% shorter than L for the three-waveguide switch. A rule of ΔβL>28 for 3w and ΔβL>14 for 4w is deduced to promise insertion loss <1.5dB and crosstalk <15dB at the bar state. At an injection of ΔNe=ΔNh=5×1017cm3, the predicted L decreased from 2 to 0.5mm as λ increased from 1.32 to 12 μm. Because of Ge’s large Δk, the Ge bar loss is high in 4w but is acceptable in 3w.

© 2014 Chinese Laser Press

Full Article  |  PDF Article
OSA Recommended Articles
Electro-optical phase-change 2 × 2 switching using three- and four-waveguide directional couplers

Haibo Liang, Richard Soref, Jianwei Mu, Xun Li, and Wei-Ping Huang
Appl. Opt. 54(19) 5897-5902 (2015)

Simulation of germanium nanobeam electro-optical 2 × 2 switches and 1 × 1 modulators for the 2 to 5 µm infrared region

Richard Soref, Joshua R. Hendrickson, and Julian Sweet
Opt. Express 24(9) 9369-9382 (2016)

Wavelength-selective switching using double-ring resonators coupled by a three-waveguide directional coupler

Linjie Zhou, Richard Soref, and Jianping Chen
Opt. Express 23(10) 13488-13498 (2015)

References

  • View by:
  • |
  • |
  • |

  1. Y. Chen, S. T. Ho, and V. Krishnamurthy, “All-optical switching in a symmetric three-waveguide coupler with phase-mismatched central waveguide,” Appl. Opt. 52, 8845–8853 (2013).
    [Crossref]
  2. http://optics.synopsys.com/rsoft/rsoft-passive-device-beamprop.html .
  3. R. A. Soref and L. Friedman, “Electrooptical modulation in Si1-xGex/Si and related heterostructures,” Int. J. Optoelectron. 9, 205–210 (1994).
  4. M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14  μm infrared wavelength range,” IEEE Photon. J. 3, 1171–1180 (2011).
    [Crossref]
  5. M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” (manuscript in preparation).
  6. R. A. Soref, D. L. McDaniel, and B. R. Bennett, “Guided-wave intensity modulators using amplitude and phase perturbations,” IEEE J. Lightwave Technol. LT-6, 437–443 (1988).
  7. X. Yang, F. Cheng, and R. Soref, “Single-mode GeSn mid-infrared waveguides on group-IV substrates,” in Conference on Lasers and Electro-Optics, San Jose, California, June, 12, 2014 (Optical Society of America, 2014), paper JTh2A.
  8. O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.
  9. X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.
  10. R. A. Soref, “Electro-refraction effects,” in Handbook of Silicon Photonics, L. Pavesi and L. Vivien eds., Series in Optics and Optoelectronics (CRC Press, 2013), Chap. 8.
  11. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18, 348–363 (2010).
    [Crossref]
  12. C. Ye, Z. Li, R. Soref, and V. J. Sorger, “A compact plasmonic MOS-based electro-optic switch,” in IEEE Microwave Photonics Conference, Alexandria, Virginia, October28, 2013 (IEEE, 2013), paper WP-29.
  13. V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.
  14. J. Hendrickson, R. Soref, J. Sweet, and W. Buchwald, “Ultrasensitive silicon photonic-crystal nanobeam electro-optical modulator: design and simulation,” Opt. Express 22, 3271–3283 (2014).
    [Crossref]

2014 (1)

2013 (1)

2011 (1)

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14  μm infrared wavelength range,” IEEE Photon. J. 3, 1171–1180 (2011).
[Crossref]

2010 (1)

1994 (1)

R. A. Soref and L. Friedman, “Electrooptical modulation in Si1-xGex/Si and related heterostructures,” Int. J. Optoelectron. 9, 205–210 (1994).

1988 (1)

R. A. Soref, D. L. McDaniel, and B. R. Bennett, “Guided-wave intensity modulators using amplitude and phase perturbations,” IEEE J. Lightwave Technol. LT-6, 437–443 (1988).

Avrutsky, I.

Bennett, B. R.

R. A. Soref, D. L. McDaniel, and B. R. Bennett, “Guided-wave intensity modulators using amplitude and phase perturbations,” IEEE J. Lightwave Technol. LT-6, 437–443 (1988).

Buchwald, W.

Chen, R. T.

X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.

Chen, Y.

Cheng, F.

X. Yang, F. Cheng, and R. Soref, “Single-mode GeSn mid-infrared waveguides on group-IV substrates,” in Conference on Lasers and Electro-Optics, San Jose, California, June, 12, 2014 (Optical Society of America, 2014), paper JTh2A.

Friedman, L.

R. A. Soref and L. Friedman, “Electrooptical modulation in Si1-xGex/Si and related heterostructures,” Int. J. Optoelectron. 9, 205–210 (1994).

Hendrickson, J.

Herrera, O. D.

O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.

Himmelhuber, R.

O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.

Ho, S. T.

Hosseini, A.

X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.

Huang, C.

V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.

Jen, A.

X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.

Kim, K. J.

O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.

Krishnamurthy, V.

Li, Z.

C. Ye, Z. Li, R. Soref, and V. J. Sorger, “A compact plasmonic MOS-based electro-optic switch,” in IEEE Microwave Photonics Conference, Alexandria, Virginia, October28, 2013 (IEEE, 2013), paper WP-29.

V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.

Luo, J.

X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.

Mashanovich, G. Z.

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14  μm infrared wavelength range,” IEEE Photon. J. 3, 1171–1180 (2011).
[Crossref]

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” (manuscript in preparation).

McDaniel, D. L.

R. A. Soref, D. L. McDaniel, and B. R. Bennett, “Guided-wave intensity modulators using amplitude and phase perturbations,” IEEE J. Lightwave Technol. LT-6, 437–443 (1988).

Nedeljkovic, M.

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14  μm infrared wavelength range,” IEEE Photon. J. 3, 1171–1180 (2011).
[Crossref]

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” (manuscript in preparation).

Norwood, R. A.

O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.

Peyghambarian, N. N.

O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.

Soref, R.

J. Hendrickson, R. Soref, J. Sweet, and W. Buchwald, “Ultrasensitive silicon photonic-crystal nanobeam electro-optical modulator: design and simulation,” Opt. Express 22, 3271–3283 (2014).
[Crossref]

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14  μm infrared wavelength range,” IEEE Photon. J. 3, 1171–1180 (2011).
[Crossref]

I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18, 348–363 (2010).
[Crossref]

V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.

X. Yang, F. Cheng, and R. Soref, “Single-mode GeSn mid-infrared waveguides on group-IV substrates,” in Conference on Lasers and Electro-Optics, San Jose, California, June, 12, 2014 (Optical Society of America, 2014), paper JTh2A.

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” (manuscript in preparation).

C. Ye, Z. Li, R. Soref, and V. J. Sorger, “A compact plasmonic MOS-based electro-optic switch,” in IEEE Microwave Photonics Conference, Alexandria, Virginia, October28, 2013 (IEEE, 2013), paper WP-29.

Soref, R. A.

R. A. Soref and L. Friedman, “Electrooptical modulation in Si1-xGex/Si and related heterostructures,” Int. J. Optoelectron. 9, 205–210 (1994).

R. A. Soref, D. L. McDaniel, and B. R. Bennett, “Guided-wave intensity modulators using amplitude and phase perturbations,” IEEE J. Lightwave Technol. LT-6, 437–443 (1988).

R. A. Soref, “Electro-refraction effects,” in Handbook of Silicon Photonics, L. Pavesi and L. Vivien eds., Series in Optics and Optoelectronics (CRC Press, 2013), Chap. 8.

Sorger, V. J.

V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.

C. Ye, Z. Li, R. Soref, and V. J. Sorger, “A compact plasmonic MOS-based electro-optic switch,” in IEEE Microwave Photonics Conference, Alexandria, Virginia, October28, 2013 (IEEE, 2013), paper WP-29.

Sweet, J.

Yang, X.

X. Yang, F. Cheng, and R. Soref, “Single-mode GeSn mid-infrared waveguides on group-IV substrates,” in Conference on Lasers and Electro-Optics, San Jose, California, June, 12, 2014 (Optical Society of America, 2014), paper JTh2A.

Ye, C.

V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.

C. Ye, Z. Li, R. Soref, and V. J. Sorger, “A compact plasmonic MOS-based electro-optic switch,” in IEEE Microwave Photonics Conference, Alexandria, Virginia, October28, 2013 (IEEE, 2013), paper WP-29.

Zhang, X.

X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.

Appl. Opt. (1)

IEEE J. Lightwave Technol. (1)

R. A. Soref, D. L. McDaniel, and B. R. Bennett, “Guided-wave intensity modulators using amplitude and phase perturbations,” IEEE J. Lightwave Technol. LT-6, 437–443 (1988).

IEEE Photon. J. (1)

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14  μm infrared wavelength range,” IEEE Photon. J. 3, 1171–1180 (2011).
[Crossref]

Int. J. Optoelectron. (1)

R. A. Soref and L. Friedman, “Electrooptical modulation in Si1-xGex/Si and related heterostructures,” Int. J. Optoelectron. 9, 205–210 (1994).

Opt. Express (2)

Other (8)

http://optics.synopsys.com/rsoft/rsoft-passive-device-beamprop.html .

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” (manuscript in preparation).

X. Yang, F. Cheng, and R. Soref, “Single-mode GeSn mid-infrared waveguides on group-IV substrates,” in Conference on Lasers and Electro-Optics, San Jose, California, June, 12, 2014 (Optical Society of America, 2014), paper JTh2A.

O. D. Herrera, R. Himmelhuber, K. J. Kim, R. A. Norwood, and N. N. Peyghambarian, “Silicon/electro-optic polymer hybrid directional coupler switch,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-24.

X. Zhang, A. Hosseini, J. Luo, A. Jen, and R. T. Chen, “Hybrid silicon-electro-optic-polymer integrated high-performance optical modulator,” in SPIE Photonics West, Opto Conferences (2014), paper 8991-22.

R. A. Soref, “Electro-refraction effects,” in Handbook of Silicon Photonics, L. Pavesi and L. Vivien eds., Series in Optics and Optoelectronics (CRC Press, 2013), Chap. 8.

C. Ye, Z. Li, R. Soref, and V. J. Sorger, “A compact plasmonic MOS-based electro-optic switch,” in IEEE Microwave Photonics Conference, Alexandria, Virginia, October28, 2013 (IEEE, 2013), paper WP-29.

V. J. Sorger, Z. Li, C. Ye, C. Huang, and R. Soref, “Ultra-compact plasmonic MOS-based electro-optic switches and modulators,” in SPIE Photonics West OPTO Conference (2014), paper 8984-6.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1.

MZI 2×2 at (a) cross state with zero bias, (b) lossless bar state with π shift in one arm, and (c) bar state with π shift and free-carrier-induced loss in one arm.

Fig. 2.
Fig. 2.

MZI 2×2 bar-state IL (solid line) and CT (dashed line) versus ρ when ΔβL=π and Δk is induced in one arm.

Fig. 3.
Fig. 3.

Top view of three-waveguide directional coupler 2×2 EO switch.

Fig. 4.
Fig. 4.

4×4 crossbar matrix switch composed of 16 “2w” switches.

Fig. 5.
Fig. 5.

4×4 permutation matrix switches made from six “3w” switches.

Fig. 6.
Fig. 6.

4×4 permutation matrix switches made from six “4w” switches.

Fig. 7.
Fig. 7.

Top view of 3w symmetric coupler with one central active waveguide and two adjoining passive waveguides. CW light is launched from WG1.

Fig. 8.
Fig. 8.

“2w” and “3w” 2×2 switching characteristics compared. The output of the two outer waveguides is shown as a function of phase shift induced in the central waveguide.

Fig. 9.
Fig. 9.

Parameters of Si (a) 3w and (b) 4w used in 1.32 μm simulations.

Fig. 10.
Fig. 10.

Beam-propagation simulation at 1.32 μm for Si 4w with (a) Lc=750μm and (b) Lc=370μm when Δn=Δk=0 (solid lines), ΔβL=14.3 and Δk=0 (dashed lines), and ΔβL=14.3 and ρ=Δn/Δk=10 (dotted lines).

Fig. 11.
Fig. 11.

(a) IL and (b) CT versus ΔβL in Si 3w (dashed line) and 4w (solid line) at 1.32 μm with coupling length engineered for Lc=750μm. This is the lossless Δk=0 case.

Fig. 12.
Fig. 12.

Beam-propagation simulation at 1.32 μm for (a) Si 4w with Lc=750μm and (b) 3w with Lc=1500μm when Δn=Δk=0 (solid lines), Δn=0.004 and Δk=0 (dashed lines), and Δn=0.004 and Δk=0.001 (dotted lines).

Fig. 13.
Fig. 13.

Bar-state IL and CT as a function of ρ for both switch configurations.

Fig. 14.
Fig. 14.

Parameters of Ge (a) 3w and (b) 4w used in 12 μm simulations.

Fig. 15.
Fig. 15.

Beam-propagation simulation at 12 μm for (a) Ge 4w and (b) Ge 3w at zero bias (solid lines), lossless injection (dashed lines), and lossy injection (dotted lines).

Tables (3)

Tables Icon

Table 1. Change in Silicon Waveguide Core Index at a Carrier Injection Level of ΔNe=ΔNh=5×1017cm3

Tables Icon

Table 2. Change in Germanium Waveguide Core Index at a Carrier Injection Level of ΔNe=ΔNh=5×1017cm3

Tables Icon

Table 3. Minimum Device Length in Si and Ge Required to Meet the ΔβL>28-for-3w and ΔβL>14-for-4w Criteria at the Carrier Injection Level of ΔNe=ΔNh=5×1017cm3

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ida1dz=β1a1+κ12a2,
ida2dz=β2a2+κ21a1+κ23a3,
ida3dz=β1a3+κ32a2,
|a1|2(z)=14eαamz4γ2+b2{[Δβcosh(bz2)+2γsinh(bz2)]2+[αamcosh(bz2)+bsinh(bz2)]2(Δβ2+αam2)+[2γcos(γz)+αamsin(γz)]2+[bcos(γz)Δβsin(γz)]2}+142eαamz24γ2+b2{[(Δβγ2γ2+αamb2b22)cos(Δβ2+γ)z+(αamγΔβb2)sin(Δβ2+γ)z]ebz2+[(Δβγ+2γ2+αamb2+b22)cos(Δβ2γ)z(αamγΔβb2)sin(Δβ2γ)z]ebz2}+14,
|a2(z)|2=|κ|2eαamz4γ2+b2[ebz+ebz2cos(2γz)],
|a3|2(z)=14eαamz4γ2+b2{[Δβcosh(bz2)+2γsinh(bz2)]2+[αamcosh(bz2)+bsinh(bz2)]2(Δβ2+αam2)+[2γcos(γz)+αamsin(γz)]2+[bcos(γz)Δβsin(γz)]2}142eαamz24γ2+b2{[(Δβγ2γ2+αamb2b22)cos(Δβ2+γ)z+(αamγΔβb2)sin(Δβ2+γ)z]ebz2+[(Δβγ+2γ2+αamb2+b22)cos(Δβ2γ)z(αamγΔβb2)sin(Δβ2γ)z]ebz2}+14,
γ=[(Δβ2αam2+2π2LC02)+(Δβ2αam2+2π2LC02)2+4αam2Δβ28]12
|a1(z)|2=cos4(24πLC0z),
|a2(z)|2=12sin2(22πLC0z),
|a3(z)|2=sin4(24πLC0z),

Metrics