Abstract

It is shown that a nearly ideal two-dimensional focusing Gaussian beam can be synthesized by use of a linear combination of the two lowest-order even modes of an optical waveguide. This property can be used to couple laterally guided modes across slab waveguide regions with low loss. The technique is illustrated by use of a conventional multimode interference (MMI) geometry, in which the MMI coupler transforms the fundamental mode of an initial waveguide into a focusing Gaussian beam, which is then fed to a slab region. Two-dimensional beam propagation simulations show that the beam does not initially diverge in the slab region, but rather comes to a focus. A second MMI coupler then transforms the diverging beam back to the initial mode. A structure is designed that can couple the fundamental mode of a 9µm-wide waveguide across an 88µm-long slab region with only a 0.036-dB loss. This technique can be applied to improve the performance of small-angle waveguide crossings and integrated turning mirrors.

© 2003 Optical Society of America

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References

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  1. L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
    [CrossRef]
  2. P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
    [CrossRef]
  3. D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
    [CrossRef]
  4. J. Leuthold and C. H. Joyner, J. Lightwave Technol. 19, 700 (2001).
    [CrossRef]
  5. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  6. BPM simulations were performed using the formulation described in C. R. Doerr, IEEE Photon. Technol. Lett. 13, 130 (2001).
    [CrossRef]
  7. H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
    [CrossRef]
  8. R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
    [CrossRef]
  9. O. Bryngdahl, J. Opt. Soc. Am. 63, 416 (1973).
  10. R. Ulrich and T. Kamiya, J. Opt. Soc. Am. 68, 583 (1978).

2001 (2)

BPM simulations were performed using the formulation described in C. R. Doerr, IEEE Photon. Technol. Lett. 13, 130 (2001).
[CrossRef]

J. Leuthold and C. H. Joyner, J. Lightwave Technol. 19, 700 (2001).
[CrossRef]

1999 (2)

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

1997 (1)

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
[CrossRef]

1995 (1)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

1994 (1)

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

1989 (1)

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

1978 (1)

1973 (1)

Bachmann, M.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

Besse, P. A.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

Bryngdahl, O.

Bukkems, H. G.

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

Doerr, C. R.

BPM simulations were performed using the formulation described in C. R. Doerr, IEEE Photon. Technol. Lett. 13, 130 (2001).
[CrossRef]

Dries, C.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Forrest, S.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Groen, F. H.

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

Herben, C. G. P.

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

Joyner, C. H.

Kamiya, T.

Koster, A.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
[CrossRef]

Laval, S.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
[CrossRef]

Leuthold, J.

Levy, D. S.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Melchior, H.

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

Moerman, I.

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

Orobtchouk, R.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
[CrossRef]

Osgood, Jr., R. M.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Park, K. H.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Pascal, D.

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Scarmozzino, R.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Smit, M. K.

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

Studenkov, P.

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

Ulrich, R.

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

IEEE Photon. Technol. Lett. (1)

BPM simulations were performed using the formulation described in C. R. Doerr, IEEE Photon. Technol. Lett. 13, 130 (2001).
[CrossRef]

IEEE Photon. Technol. (1)

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, Jr., C. Dries, P. Studenkov, and S. Forrest, IEEE Photon. Technol. 11, 1009 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. G. Bukkems, C. G. P. Herben, M. K. Smit, F. H. Groen, and I. Moerman, IEEE Photon. Technol. Lett. 11, 1420 (1999).
[CrossRef]

J. Lightwave Technol. (4)

R. Orobtchouk, S. Laval, D. Pascal, and A. Koster, J. Lightwave Technol. 15, 815 (1997).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, J. Lightwave Technol. 12, 1004 (1994).
[CrossRef]

J. Leuthold and C. H. Joyner, J. Lightwave Technol. 19, 700 (2001).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (1)

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

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Figures (3)

Fig. 1
Fig. 1

(a) Delta 0.5% waveguide with a width of 14 µm. This structure supports three TE-polarized modes at 1.55 µm, including the two even modes shown. (b) When the two even modes are combined at a power ratio of approximately 17:1, with the proper phasing, a nearly perfect focusing (or diverging) Gaussian beam can be created. The solid curves represent quadratic phase (top) and Gaussian power (bottom). The power profile of the fundamental mode of the waveguide is shown for comparison (dashed curve).

Fig. 2
Fig. 2

BPM simulations of light propagation through the MMI lens structure. The structure is shown at left, with modal power profiles taken at 20µm increments shown at right. Within the 88µm-long slab region, there is no lateral guiding mechanism; nevertheless, the beam does not diverge in this region, but clearly comes to a focus at the center. (The second MMI structure after the slab converts the beam back to the initial mode.) The total end-to-end loss across the structure is only 0.036 dB.

Fig. 3
Fig. 3

Modal power and phase profiles at the front, center, and back of the slab region, illustrating the performance of the MMI lens. The power profiles at the front and back are nearly identical, with the beam narrowing slightly and peaking higher at the center (focal) point. The quadratic phase at the front transforms to a nearly flat phase at the center and subsequently becomes quadratic again at the back, with a sign reversal.

Tables (1)

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Table 1 Properties of MMI Lens Structures

Equations (1)

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Ef=E0+.058E2 exp-i0.73π.

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