Abstract

The effect of adding a thin high index dielectric overlay layer onto a 3-layer slab waveguide demonstrates several interesting features that can be exploited in integrated optical device configurations. A simple modal analysis is employed to examine the behavior of guided light launched from a 3-layer waveguide structure then coupled and propagated in the 4-layer overlay region. Modal properties typically overlooked in conventional slab waveguides are made use of in the design and theoretical analysis of an MMI device and optical index of refraction sensor. The optical structure presented here can form the backdrop waveguide design for more complex and active devices.

© 2012 Optical Society of America

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References

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  1. P. K. Tien, R. J. Martin, and G. Smolinsky, “Formation of light-guiding interconnections in an integrated optical circuit by composite tapered-film coupling,” Appl. Opt. 12, 1909–1916 (1973).
    [CrossRef]
  2. T. E. Batchman and G. McWright, “Mode coupling between dielectric and semiconductor planar waveguides,” IEEE J. Quantum Electron. 18, 782–788 (1982).
    [CrossRef]
  3. H. Kumagami and M. Koshiba, “Frequency response of silicon-clad planar diffused optical waveguides,” IEE Proc. J. Optoelectronics 138, 249–252 (1991).
    [CrossRef]
  4. K. Gates, D. Summers, and T. E. Batchman, “Semiconductor clad optical waveguides,” in Proceedings of Southeastcon '80 (IEEE, 1980), pp. 151–154.
  5. T. K. Saha and W. Zhou, “High efficiency diffractive grating coupler based on transferred silicon nanomembrane overlay on photonic waveguide,” J. Phys. D 42, 085115 (2009).
    [CrossRef]
  6. K. E. Medri and R. C. Gauthier, “Patterned overlays: thin silicon layer applied to glass waveguides,” Proc. SPIE 7943, 0L-1–0L-12 (2011).
  7. J. Kim, G. Li, and K. A. Winick, “Design and fabrication of a glass waveguide optical add-drop multiplexer by use of an amorphous-silicon overlay distributed Bragg reflector,” Appl. Opt. 43, 671–677 (2004).
    [CrossRef]
  8. K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic, 2005).
  9. C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, 1977).
  10. M. F. Khodr, J. J. Sluss,, and T. E. Batchman, “Modal analysis of PbSe-clad optical waveguides,” IEE Proc. J. Optoelectronics 142, 183–189 (1995).
    [CrossRef]
  11. G. Agrawal, Lightwave Technology: Components and Devices (Wiley, 2004).
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  13. R. C. Weast, Handbook of Chemistry and Physics (CRC Press, 1977).

2011 (1)

K. E. Medri and R. C. Gauthier, “Patterned overlays: thin silicon layer applied to glass waveguides,” Proc. SPIE 7943, 0L-1–0L-12 (2011).

2009 (1)

T. K. Saha and W. Zhou, “High efficiency diffractive grating coupler based on transferred silicon nanomembrane overlay on photonic waveguide,” J. Phys. D 42, 085115 (2009).
[CrossRef]

2004 (1)

1995 (1)

M. F. Khodr, J. J. Sluss,, and T. E. Batchman, “Modal analysis of PbSe-clad optical waveguides,” IEE Proc. J. Optoelectronics 142, 183–189 (1995).
[CrossRef]

1991 (1)

H. Kumagami and M. Koshiba, “Frequency response of silicon-clad planar diffused optical waveguides,” IEE Proc. J. Optoelectronics 138, 249–252 (1991).
[CrossRef]

1982 (1)

T. E. Batchman and G. McWright, “Mode coupling between dielectric and semiconductor planar waveguides,” IEEE J. Quantum Electron. 18, 782–788 (1982).
[CrossRef]

1973 (1)

Agrawal, G.

G. Agrawal, Lightwave Technology: Components and Devices (Wiley, 2004).

Batchman, T. E.

M. F. Khodr, J. J. Sluss,, and T. E. Batchman, “Modal analysis of PbSe-clad optical waveguides,” IEE Proc. J. Optoelectronics 142, 183–189 (1995).
[CrossRef]

T. E. Batchman and G. McWright, “Mode coupling between dielectric and semiconductor planar waveguides,” IEEE J. Quantum Electron. 18, 782–788 (1982).
[CrossRef]

K. Gates, D. Summers, and T. E. Batchman, “Semiconductor clad optical waveguides,” in Proceedings of Southeastcon '80 (IEEE, 1980), pp. 151–154.

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, 1977).

Diu, B.

C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, 1977).

Gates, K.

K. Gates, D. Summers, and T. E. Batchman, “Semiconductor clad optical waveguides,” in Proceedings of Southeastcon '80 (IEEE, 1980), pp. 151–154.

Gauthier, R. C.

K. E. Medri and R. C. Gauthier, “Patterned overlays: thin silicon layer applied to glass waveguides,” Proc. SPIE 7943, 0L-1–0L-12 (2011).

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Khodr, M. F.

M. F. Khodr, J. J. Sluss,, and T. E. Batchman, “Modal analysis of PbSe-clad optical waveguides,” IEE Proc. J. Optoelectronics 142, 183–189 (1995).
[CrossRef]

Kim, J.

Koshiba, M.

H. Kumagami and M. Koshiba, “Frequency response of silicon-clad planar diffused optical waveguides,” IEE Proc. J. Optoelectronics 138, 249–252 (1991).
[CrossRef]

Kumagami, H.

H. Kumagami and M. Koshiba, “Frequency response of silicon-clad planar diffused optical waveguides,” IEE Proc. J. Optoelectronics 138, 249–252 (1991).
[CrossRef]

Laloe, F.

C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, 1977).

Li, G.

Martin, R. J.

McWright, G.

T. E. Batchman and G. McWright, “Mode coupling between dielectric and semiconductor planar waveguides,” IEEE J. Quantum Electron. 18, 782–788 (1982).
[CrossRef]

Medri, K. E.

K. E. Medri and R. C. Gauthier, “Patterned overlays: thin silicon layer applied to glass waveguides,” Proc. SPIE 7943, 0L-1–0L-12 (2011).

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic, 2005).

Saha, T. K.

T. K. Saha and W. Zhou, “High efficiency diffractive grating coupler based on transferred silicon nanomembrane overlay on photonic waveguide,” J. Phys. D 42, 085115 (2009).
[CrossRef]

Sluss,, J. J.

M. F. Khodr, J. J. Sluss,, and T. E. Batchman, “Modal analysis of PbSe-clad optical waveguides,” IEE Proc. J. Optoelectronics 142, 183–189 (1995).
[CrossRef]

Smolinsky, G.

Summers, D.

K. Gates, D. Summers, and T. E. Batchman, “Semiconductor clad optical waveguides,” in Proceedings of Southeastcon '80 (IEEE, 1980), pp. 151–154.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tien, P. K.

Weast, R. C.

R. C. Weast, Handbook of Chemistry and Physics (CRC Press, 1977).

Winick, K. A.

Zhou, W.

T. K. Saha and W. Zhou, “High efficiency diffractive grating coupler based on transferred silicon nanomembrane overlay on photonic waveguide,” J. Phys. D 42, 085115 (2009).
[CrossRef]

Appl. Opt. (2)

IEE Proc. J. Optoelectronics (2)

H. Kumagami and M. Koshiba, “Frequency response of silicon-clad planar diffused optical waveguides,” IEE Proc. J. Optoelectronics 138, 249–252 (1991).
[CrossRef]

M. F. Khodr, J. J. Sluss,, and T. E. Batchman, “Modal analysis of PbSe-clad optical waveguides,” IEE Proc. J. Optoelectronics 142, 183–189 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. E. Batchman and G. McWright, “Mode coupling between dielectric and semiconductor planar waveguides,” IEEE J. Quantum Electron. 18, 782–788 (1982).
[CrossRef]

J. Phys. D (1)

T. K. Saha and W. Zhou, “High efficiency diffractive grating coupler based on transferred silicon nanomembrane overlay on photonic waveguide,” J. Phys. D 42, 085115 (2009).
[CrossRef]

Proc. SPIE (1)

K. E. Medri and R. C. Gauthier, “Patterned overlays: thin silicon layer applied to glass waveguides,” Proc. SPIE 7943, 0L-1–0L-12 (2011).

Other (6)

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic, 2005).

C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, 1977).

G. Agrawal, Lightwave Technology: Components and Devices (Wiley, 2004).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

R. C. Weast, Handbook of Chemistry and Physics (CRC Press, 1977).

K. Gates, D. Summers, and T. E. Batchman, “Semiconductor clad optical waveguides,” in Proceedings of Southeastcon '80 (IEEE, 1980), pp. 151–154.

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Figures (15)

Fig. 1.
Fig. 1.

Design layout for the 3-layer (left) and 4-layer (right) slab waveguides.

Fig. 2.
Fig. 2.

Left- Effective index versus wavelength for the 5 modes supported by the 3-layer slab structure. Right—Effective index versus wavelength for the 5 modes supported by the 4-layer slab structure. The dashed line is along the neffective=1.6. As expected the effective indices of the 3-layer structure are pulled upwards when the overlay layer is introduced. The mode with the highest effective index is confined to values within the overlay-waveguide index range. The remaining 4 modes have effective index values confined to the waveguide-substrate range.

Fig. 3.
Fig. 3.

Left- Effective index versus wavelength for the 2 modes supported by the 3-layer slab structure. Right—Effective index versus wavelength for the 4 modes supported by the 4-layer slab structure. One mode with the highest propagation constant is confined to values within the overlay-waveguide index range. The second order mode has an effective index that starts in the overlay range and transitions into the waveguide-substrate range. The two other modes have effective indices in the waveguide-substrate range.

Fig. 4.
Fig. 4.

Effective index versus wavelength for the 3-layer (solid) and 4-layer (thin dashed) in the waveguide-substrate index range. The anti-crossing observed in the 4-layer effective index solution for the modes corresponds to the splitting of the highest order mode of the 3-layer structure. At a wavelength of 1.78 μm the 3-layer structure and 4-layer structure support a mode with the same propagation constant. Bold dashed line represents the transition effective indices for the 4-layer structure. Modes with an effective index above this dashed line have their field peak in the overlay even though their effective index is in the substrate-waveguide range.

Fig. 5.
Fig. 5.

TE03 and TE13 for λ=1.30μm.

Fig. 6.
Fig. 6.

Top row—TE04 and TE14 for λ=1.30μm. These modes are highly confined to the overlay region. Lower row—TE24 and TE34 for λ=1.30μm. These modes are highly confined to the low index waveguide region with only a small fraction of the total power confined in the overlay layer.

Fig. 7.
Fig. 7.

TE14 at λ=1.558μm (left) and λ=1.85μm (right).

Fig. 8.
Fig. 8.

Mode profiles of the 3-layer waveguide and 4-layer waveguide at the effective index crossover point at a wavelength of 1.78 μm. Due to the nature of the modal solution, the field profiles in the substrate and waveguide regions are identical.

Fig. 9.
Fig. 9.

Coupling coefficient as a function of wavelength between the lowest order mode of the input 3-layer region and available guided modes of the 4-layer region. The direct technique of transferring power to the lowest order 4-layer SOI waveguide is inefficient. The cross point between c340,1 and c340,2 indicates equal excitation of these two modes from the input waveguide.

Fig. 10.
Fig. 10.

Mode propagation for wavelengths of 1.30 μm (top), 1.55 μm (middle) and 1.78 μm (bottom) in the 3- and 4-layer waveguide segments. Lowest order mode is launched in left side 3-layer waveguide and couples to the modes supported in the 4-layer region. The field distribution and evolution in the 4-layer region is similar to that of an MMI coupler and demonstrates the characteristic beating with propagation distance. Field profiles are shown in positive grey scale. Bottom Fig. shows the dielectric layout in the (X, Z) plane.

Fig. 11.
Fig. 11.

FDTD simulation of the three systems computed using MPM and shown in Fig. 10. Mode propagation for wavelengths of 1.30 μm (top), 1.55 μm (middle) and 1.78 μm (bottom) in the 3- and 4-layer waveguide segments. FDTD includes the time dependence factor and results in sinusoidal field variations in the propagation direction in addition to any beating that occurs between modes. Field profiles are shown in positive grey scale.

Fig. 12.
Fig. 12.

Output power coupling versus 4-layer waveguide length for launched wavelengths of 1.30 μm, 1.55 μm and 1.78 μm. The trace at 1.55 μm shows a high dependence on 4-layer length as dictated by the high modulation depth of the beating between TE14 and TE24.

Fig. 13.
Fig. 13.

Output power versus superstrate index of refraction for the 4-layer length of 32.4 μm and for 262 μm. Two sensor ranges are shown for low index changes (Range 1) and for a solution between pure water and 77% sucrose solution (Range 2). The sensitivity of the sensor to index change can be increased by increasing the length of 4-layer region. This however reduces the useful non-repetitive range of the sensor.

Fig. 14.
Fig. 14.

Effective index versus wavelength for a 3-layer structure composed of superstrate, 285 nm silicon overlay and substrate. The lowest order mode is supported over the wavelength range while the second order mode is cut off for wavelengths above 1.60 μm.

Fig. 15.
Fig. 15.

Power coupled versus 4-layer interaction length when the output waveguide is conFig.d as a SOI based design for a wavelength of 1.55 μm (bold line) and 1.61 μm (thin line). The plot for the wavelength of 1.61 μm corresponds to single mode coupling to the silicon layer. Oscillations present on both lines are due to the beating that occurs between modes in the 4-layer central waveguide region.

Tables (3)

Tables Icon

Table 1. 4-layer Effective Index and Beat Length for 1.30 μm

Tables Icon

Table 2. 4-layer Effective Index and Beat Length for 1.55 μm

Tables Icon

Table 3. 4-layer Effective Index and Beat Length for 1.78 μm

Equations (14)

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

Substrate:Ey=Feξxwithξ=β2k2n42,
Waveguide:Ey=Dsin(k3x)+Ecos(k3x)withk3=k2n32β2,
Overlay:Ey=Bsin[k2(xt3)]+Ccos[k2(xt3)],k2=k2n22β2,
Superstrate:Ey=Aeσ(xt)withσ=β2k2n12.
ξst3+ξσk3ct3=k3ct3+k3σk3st3
Aξst3+Bξσk3ct3=Ak3ct3+Bk3σk3st3,
A[[k3ξ+1]ek3t3+[k3ξ1]ek3t3]=Bk3σ[[k3ξ1]ek3t3[k3ξ+1]ek3t3].
Ey=D2+E2cos(k3xϕ),
ξcos(k3t3)=k3sin(k3t3).
k2[cttk2σstt]=[σstt+k2ctt].
c34i,m=E3i(x)E4m(x)dx|E3i(x)|2dx|E4m(x)|2dx,
φ4(x)=m=0Nc340,mE4m(x)ejβmz.
LB=λΔneff.
Mixmn(x,z)=(E4m(x))2+(E4n(x))2+2E4m(x)E4n(x)cos(Δneffλz)

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