Abstract

We discuss the design of weakly guided multimode interference (MMI) devices using a genetic algorithm. For devices exhibiting a nonnegligible vertical waveguide offset, such as those produced using ion exchange in glass, three-dimensional modeling is required to properly evaluate the device performance. A combination of semivectorial finite difference modeling in two transverse dimensions and mode propagation analysis (MPA) in the propagation direction is used to evaluate the merit of each trial design. An example is provided of a 1×4 power splitter designed for ion exchange, which shows considerable improvement over that obtained by self-imaging theory.

© 2004 Optical Society of America

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References

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  1. L.H. Spiekman, Y.S.Oei, E.G. Metaal, F.H. Green, I. Moerman, and M.K. Smit, �??Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,�?? IEEE Photon. Technol. Lett. 6, 1008-1010 (1994).
    [CrossRef]
  2. T. Rasmussen, J.K. Rasmussen, and J.H. Povlsen, �??Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,�?? J. Lightwave Technol. 13, 2069-2074 (1995).
    [CrossRef]
  3. A. Bakhtazad, J.N. McMullin, C.J. Haugen, and R.G. DeCorby, �??MMI multiplexer for dual-channel erbium-doped waveguide amplifiers,�?? Opt. Express 9, 178-183 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?uri=OPEX-9-4-178">http://www.opticsexpress.org/abstract.cfm?uri=OPEX-9-4-178</a>.
    [CrossRef] [PubMed]
  4. D. Hah, E. Yoon, and S. Hong, �??An optomechanical pressure sensor using multimode interference couplers with polymer waveguides on a thin p+-Si membrane,�?? Sens. Act. A 79, 204-210 (2000).
    [CrossRef]
  5. A. Irace and G. Breglio, �??All-silicon optical temperature sensor based on multi-mode interference,�?? Opt. Express 11, 2807-2812 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2807">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2807</a>.
    [CrossRef] [PubMed]
  6. P.A. Besse, M. Bachmann, H. Melchior, L.B. Soldano, and M.K. Smit, �??Optical bandwidth and fabrication tolerances of multimode interference couplers,�?? J. Lightwave Technol. 12, 1004-1009 (1994).
    [CrossRef]
  7. L.B. Soldano and E.C.M. Pennings, �??Optical multi-mode interference devices based on self-imaging: principles and applications,�?? J. Lightwave Technol. 13, 615-627 (1995).
    [CrossRef]
  8. S.E. Yliniemi, B.R. West, T.T. Aalto, P. Madasamy, N. Peyghambarian, and S. Honkanen, �??Buried ionexchanged glass waveguides featuring low birefringence with a broad range of waveguide widths,�?? in Integrated Optics and Photonic Integrated Circuits, G. C. Righini and S. Honkanen, eds., Proc. SPIE 5451, no. 87 (2004).
  9. D.F. Geraghty, D. Provenzano, M.M. Morrell, J. Ingenhoff, B. Drapp, S. Honkanen, A. Yariv, and N. Peyghambarian, �??Polarisation-independent Bragg gratings in ion-exchanged glass channel waveguides,�?? Elect. Lett. 36, 531-532 (2000).
    [CrossRef]
  10. P. Madasamy, B.R. West, M.M. Morrell, D.F. Geraghty, S. Honkanen, and N. Peyghambarian, �??Buried ion-exchanged glass waveguides: Burial-depth dependence on the waveguide width,�?? Opt. Lett. 28, 1132- 1134 (2003).
    [CrossRef] [PubMed]
  11. Q. Wang, J. Lu, and S. He, �??Optimal design of a multimode interference coupler using a genetic algorithm,�?? Opt. Comm. 209, 131-136 (2002).
    [CrossRef]
  12. R. Ulrich and T. Kamiya, �??Resolution of self-images in planar optical waveguides,�?? J. Opt. Soc. Amer. 68, 583-592 (1978).
    [CrossRef]
  13. A.R. Gupta, �??Optimization of access waveguide width of multimode interference (MMI) couplers,�?? Opt. Commun. 221, 99-103 (2003).
    [CrossRef]
  14. B.R. West, P. Madasamy, N. Peyghambarian, and S. Honkanen, Optical Sciences Center, The University of Arizona, 1630 E. University Blvd., Tucson, AZ, 85721, are preparing a manuscript to be called �??Accurate modeling of ion-exchanged glass waveguide structures.�??
  15. C. M. Kim and R. V. Ramaswamy, �??Modeling of graded-index channel waveguides using nonuniform finite difference method,�?? J. Lightwave Technol. 7, 1581-1589 (1989).
    [CrossRef]
  16. J. Leuthold, J. Eckner, E. Gamper, P.A. Besse, and H. Melchior, �??Multimode interference couplers for the conversion and combining of zero- and first-order modes,�?? J. Lightwave Technol. 16, 1228-1239 (1998).
    [CrossRef]

Elect. Lett. (1)

D.F. Geraghty, D. Provenzano, M.M. Morrell, J. Ingenhoff, B. Drapp, S. Honkanen, A. Yariv, and N. Peyghambarian, �??Polarisation-independent Bragg gratings in ion-exchanged glass channel waveguides,�?? Elect. Lett. 36, 531-532 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L.H. Spiekman, Y.S.Oei, E.G. Metaal, F.H. Green, I. Moerman, and M.K. Smit, �??Extremely small multimode interference couplers and ultrashort bends on InP by deep etching,�?? IEEE Photon. Technol. Lett. 6, 1008-1010 (1994).
[CrossRef]

J. Lightwave Technol. (5)

T. Rasmussen, J.K. Rasmussen, and J.H. Povlsen, �??Design and performance evaluation of 1-by-64 multimode interference power splitter for optical communications,�?? J. Lightwave Technol. 13, 2069-2074 (1995).
[CrossRef]

P.A. Besse, M. Bachmann, H. Melchior, L.B. Soldano, and M.K. Smit, �??Optical bandwidth and fabrication tolerances of multimode interference couplers,�?? J. Lightwave Technol. 12, 1004-1009 (1994).
[CrossRef]

L.B. Soldano and E.C.M. Pennings, �??Optical multi-mode interference devices based on self-imaging: principles and applications,�?? J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

C. M. Kim and R. V. Ramaswamy, �??Modeling of graded-index channel waveguides using nonuniform finite difference method,�?? J. Lightwave Technol. 7, 1581-1589 (1989).
[CrossRef]

J. Leuthold, J. Eckner, E. Gamper, P.A. Besse, and H. Melchior, �??Multimode interference couplers for the conversion and combining of zero- and first-order modes,�?? J. Lightwave Technol. 16, 1228-1239 (1998).
[CrossRef]

J. Opt. Soc. Amer. (1)

R. Ulrich and T. Kamiya, �??Resolution of self-images in planar optical waveguides,�?? J. Opt. Soc. Amer. 68, 583-592 (1978).
[CrossRef]

Opt. Comm. (1)

Q. Wang, J. Lu, and S. He, �??Optimal design of a multimode interference coupler using a genetic algorithm,�?? Opt. Comm. 209, 131-136 (2002).
[CrossRef]

Opt. Commun. (1)

A.R. Gupta, �??Optimization of access waveguide width of multimode interference (MMI) couplers,�?? Opt. Commun. 221, 99-103 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

S.E. Yliniemi, B.R. West, T.T. Aalto, P. Madasamy, N. Peyghambarian, and S. Honkanen, �??Buried ionexchanged glass waveguides featuring low birefringence with a broad range of waveguide widths,�?? in Integrated Optics and Photonic Integrated Circuits, G. C. Righini and S. Honkanen, eds., Proc. SPIE 5451, no. 87 (2004).

Sens. Act. A (1)

D. Hah, E. Yoon, and S. Hong, �??An optomechanical pressure sensor using multimode interference couplers with polymer waveguides on a thin p+-Si membrane,�?? Sens. Act. A 79, 204-210 (2000).
[CrossRef]

Other (1)

B.R. West, P. Madasamy, N. Peyghambarian, and S. Honkanen, Optical Sciences Center, The University of Arizona, 1630 E. University Blvd., Tucson, AZ, 85721, are preparing a manuscript to be called �??Accurate modeling of ion-exchanged glass waveguide structures.�??

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Figures (3)

Fig. 1.
Fig. 1.

Layout of a 1×N power splitter, showing geometrical parameters.

Fig. 2.
Fig. 2.

Power in the multimode waveguide, showing region of 1×4 splitting.

Fig. 3.
Fig. 3.

Power cross-sections at the output plane of the MMI, designed using self-imaging (top) and genetic algorithm (bottom). While the inner and outer power peaks are of different magnitude, minimization of power imbalance is achieved through an intentional transverse offset of the output waveguides.

Tables (3)

Tables Icon

Table 1. Simulated effective indices of guided modes in the multimode waveguide

Tables Icon

Table 2. Results of self-imaging theory and genetic algorithm

Tables Icon

Table 3. Parameters used in the genetic algorithm

Equations (10)

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( β 0 β ν ) ν ( ν + 2 ) π 3 L π ,
Ψ ( x , y , z = 0 ) = ν a ν φ ν ( x , y ) ,
a ν = Ψ ( x , y , z = 0 ) φ ν ( x , y ) dx dy φ ν 2 ( x , y ) dx dy .
Ψ ( x , y , z ) = ν a ν φ ν ( x , y ) exp ( i ν ( ν + 2 ) π z 3 L π ) ,
L MMI = 3 L π 4 N
x i = ( 2 i ( N + 1 ) ) 2 N W e ,
XL = 10 log 10 ( i = 1 N P i ) ( excess loss ) ,
IB = 10 log 10 ( P i min P i max ) ( imbalance ) ,
PDL = 10 log 10 ( P pol min P pol max ) ( polarization dependent loss ) .
F = exp [ ( C XL XL + C IB IB + C PDL PDL ) ] ,

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