Abstract

Using the full phase compensation method, we derive a set of precise phase compensation formulas to design a three-dimensional microprism-type Y junction. The simulated and traditional results are compared to verify that the proposed structure is better. By taking into account the orthogonality principle to estimate the branching losses, the proposed structure was improved to better than approximately 6–10% over the traditional structure.

© 1999 Optical Society of America

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References

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  1. T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1989).
  2. H. F. Taylor, “An optical analog-to-digital converter: design and analysis,” IEEE J. Quantum Electron. QE-15, 210–217 (1979).
    [CrossRef]
  3. C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
    [CrossRef]
  4. C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
    [CrossRef]
  5. S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
    [CrossRef]
  6. H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
    [CrossRef]
  7. O. Hanaizumi, M. Miyagi, Kawakami, “Wide Y-junctions with low-losses in three-dimensional dielectric optical waveguides,” IEEE J. Quantum Electron. QE-21, 168–173 (1985).
    [CrossRef]
  8. H. B. Lin, R. S. Cheng, W. S. Wang, “Wide-angle low-loss single-mode symmetric Y-junctions,” IEEE Photon. Technol. Lett. 6, 825–827 (1994).
    [CrossRef]
  9. C. T. Lee, M. L. Wu, “Microprism for wide-angle low-loss Y-junction waveguide,” Fiber Integrated Opt. 17, 213–219 (1998).
    [CrossRef]
  10. J. M. Hsu, C. T. Lee, “Systematic design of novel wide-angle low-loss symmetric Y-junction waveguides,” IEEE J. Quantum Electron. 34, 673–679 (1998).
    [CrossRef]
  11. M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
    [CrossRef]
  12. R. Baets, P. E. Lagasse, “Calculation of radiation loss in integrated-optic tapers and Y-junctions,” Appl. Opt. 21, 1972–1978 (1982).
    [CrossRef] [PubMed]
  13. M. Rangaraj, M. Minakata, S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
    [CrossRef]
  14. C. T. Lee, J. M. Hsu, “Systematic design of full phase compensation microprism-type low-loss bent waveguides,” Appl. Opt. 37, 507–509 (1998).
    [CrossRef]
  15. M. D. Feit, J. A. Fleck, “Computation of mode properties in optical fiber waveguides by a propagating beam method,” Appl. Opt. 19, 1154–1164 (1980).
    [CrossRef] [PubMed]
  16. W. Y. Hung, H. P. Chan, P. S. Chung, “Novel design of wide-angle single-mode symmetric Y-junctions,” Electron. Lett. 24, 1184–1185 (1988).
    [CrossRef]
  17. S. M. Sze, VLSI Technology (McGraw-Hill, New York, 1983).
  18. H. K. Pulker, “Characterization of optical thin films,” Appl. Opt. 18, 1969–1977 (1979).
    [CrossRef] [PubMed]
  19. C. T. Lee, M. L. Wu, J. M. Hsu, “Beam propagation analysis for tapered waveguides: taking account of the curved phase-front effect in paraxial approximation,” J. Lightwave Technol. 15, 2183–2189 (1997).
    [CrossRef]

1998 (3)

C. T. Lee, M. L. Wu, “Microprism for wide-angle low-loss Y-junction waveguide,” Fiber Integrated Opt. 17, 213–219 (1998).
[CrossRef]

J. M. Hsu, C. T. Lee, “Systematic design of novel wide-angle low-loss symmetric Y-junction waveguides,” IEEE J. Quantum Electron. 34, 673–679 (1998).
[CrossRef]

C. T. Lee, J. M. Hsu, “Systematic design of full phase compensation microprism-type low-loss bent waveguides,” Appl. Opt. 37, 507–509 (1998).
[CrossRef]

1997 (1)

C. T. Lee, M. L. Wu, J. M. Hsu, “Beam propagation analysis for tapered waveguides: taking account of the curved phase-front effect in paraxial approximation,” J. Lightwave Technol. 15, 2183–2189 (1997).
[CrossRef]

1996 (3)

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
[CrossRef]

C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
[CrossRef]

1994 (2)

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
[CrossRef]

H. B. Lin, R. S. Cheng, W. S. Wang, “Wide-angle low-loss single-mode symmetric Y-junctions,” IEEE Photon. Technol. Lett. 6, 825–827 (1994).
[CrossRef]

1993 (1)

S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
[CrossRef]

1989 (1)

M. Rangaraj, M. Minakata, S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

1988 (1)

W. Y. Hung, H. P. Chan, P. S. Chung, “Novel design of wide-angle single-mode symmetric Y-junctions,” Electron. Lett. 24, 1184–1185 (1988).
[CrossRef]

1985 (1)

O. Hanaizumi, M. Miyagi, Kawakami, “Wide Y-junctions with low-losses in three-dimensional dielectric optical waveguides,” IEEE J. Quantum Electron. QE-21, 168–173 (1985).
[CrossRef]

1982 (1)

1980 (1)

1979 (2)

H. F. Taylor, “An optical analog-to-digital converter: design and analysis,” IEEE J. Quantum Electron. QE-15, 210–217 (1979).
[CrossRef]

H. K. Pulker, “Characterization of optical thin films,” Appl. Opt. 18, 1969–1977 (1979).
[CrossRef] [PubMed]

Baets, R.

Chan, H. P.

W. Y. Hung, H. P. Chan, P. S. Chung, “Novel design of wide-angle single-mode symmetric Y-junctions,” Electron. Lett. 24, 1184–1185 (1988).
[CrossRef]

Chaudhuri, S. K.

S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
[CrossRef]

Cheng, R. S.

H. B. Lin, R. S. Cheng, W. S. Wang, “Wide-angle low-loss single-mode symmetric Y-junctions,” IEEE Photon. Technol. Lett. 6, 825–827 (1994).
[CrossRef]

Chow, Y. L.

S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
[CrossRef]

Chu, P. L.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
[CrossRef]

Chung, P. S.

W. Y. Hung, H. P. Chan, P. S. Chung, “Novel design of wide-angle single-mode symmetric Y-junctions,” Electron. Lett. 24, 1184–1185 (1988).
[CrossRef]

Fan, P. L.

C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Goss, A.

S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
[CrossRef]

Hanaizumi, O.

O. Hanaizumi, M. Miyagi, Kawakami, “Wide Y-junctions with low-losses in three-dimensional dielectric optical waveguides,” IEEE J. Quantum Electron. QE-21, 168–173 (1985).
[CrossRef]

Hatami-Hanza, H.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
[CrossRef]

Hsu, J. M.

J. M. Hsu, C. T. Lee, “Systematic design of novel wide-angle low-loss symmetric Y-junction waveguides,” IEEE J. Quantum Electron. 34, 673–679 (1998).
[CrossRef]

C. T. Lee, J. M. Hsu, “Systematic design of full phase compensation microprism-type low-loss bent waveguides,” Appl. Opt. 37, 507–509 (1998).
[CrossRef]

C. T. Lee, M. L. Wu, J. M. Hsu, “Beam propagation analysis for tapered waveguides: taking account of the curved phase-front effect in paraxial approximation,” J. Lightwave Technol. 15, 2183–2189 (1997).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Hung, W. Y.

W. Y. Hung, H. P. Chan, P. S. Chung, “Novel design of wide-angle single-mode symmetric Y-junctions,” Electron. Lett. 24, 1184–1185 (1988).
[CrossRef]

Kawakami,

O. Hanaizumi, M. Miyagi, Kawakami, “Wide Y-junctions with low-losses in three-dimensional dielectric optical waveguides,” IEEE J. Quantum Electron. QE-21, 168–173 (1985).
[CrossRef]

Kawakami, S.

M. Rangaraj, M. Minakata, S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Kuo, T. T.

C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
[CrossRef]

Lagasse, P. E.

Lai, H. H.

C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
[CrossRef]

Lederer, M. J.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
[CrossRef]

Lee, C. T.

J. M. Hsu, C. T. Lee, “Systematic design of novel wide-angle low-loss symmetric Y-junction waveguides,” IEEE J. Quantum Electron. 34, 673–679 (1998).
[CrossRef]

C. T. Lee, M. L. Wu, “Microprism for wide-angle low-loss Y-junction waveguide,” Fiber Integrated Opt. 17, 213–219 (1998).
[CrossRef]

C. T. Lee, J. M. Hsu, “Systematic design of full phase compensation microprism-type low-loss bent waveguides,” Appl. Opt. 37, 507–509 (1998).
[CrossRef]

C. T. Lee, M. L. Wu, J. M. Hsu, “Beam propagation analysis for tapered waveguides: taking account of the curved phase-front effect in paraxial approximation,” J. Lightwave Technol. 15, 2183–2189 (1997).
[CrossRef]

C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
[CrossRef]

Lee, H. C.

C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
[CrossRef]

Lee, J. C.

C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
[CrossRef]

Lin, H. B.

H. B. Lin, R. S. Cheng, W. S. Wang, “Wide-angle low-loss single-mode symmetric Y-junctions,” IEEE Photon. Technol. Lett. 6, 825–827 (1994).
[CrossRef]

Minakata, M.

M. Rangaraj, M. Minakata, S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Miyagi, M.

O. Hanaizumi, M. Miyagi, Kawakami, “Wide Y-junctions with low-losses in three-dimensional dielectric optical waveguides,” IEEE J. Quantum Electron. QE-21, 168–173 (1985).
[CrossRef]

Pulker, H. K.

Rangaraj, M.

M. Rangaraj, M. Minakata, S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

Safavi-Naeini, S.

S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
[CrossRef]

Sheu, L. G.

C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
[CrossRef]

Skinner, I. M.

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
[CrossRef]

Sze, S. M.

S. M. Sze, VLSI Technology (McGraw-Hill, New York, 1983).

Tamir, T.

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1989).

Taylor, H. F.

H. F. Taylor, “An optical analog-to-digital converter: design and analysis,” IEEE J. Quantum Electron. QE-15, 210–217 (1979).
[CrossRef]

Wang, W. S.

H. B. Lin, R. S. Cheng, W. S. Wang, “Wide-angle low-loss single-mode symmetric Y-junctions,” IEEE Photon. Technol. Lett. 6, 825–827 (1994).
[CrossRef]

Wu, M. L.

C. T. Lee, M. L. Wu, “Microprism for wide-angle low-loss Y-junction waveguide,” Fiber Integrated Opt. 17, 213–219 (1998).
[CrossRef]

C. T. Lee, M. L. Wu, J. M. Hsu, “Beam propagation analysis for tapered waveguides: taking account of the curved phase-front effect in paraxial approximation,” J. Lightwave Technol. 15, 2183–2189 (1997).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

Appl. Opt. (4)

Electron. Lett. (1)

W. Y. Hung, H. P. Chan, P. S. Chung, “Novel design of wide-angle single-mode symmetric Y-junctions,” Electron. Lett. 24, 1184–1185 (1988).
[CrossRef]

Fiber Integrated Opt. (1)

C. T. Lee, M. L. Wu, “Microprism for wide-angle low-loss Y-junction waveguide,” Fiber Integrated Opt. 17, 213–219 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. M. Hsu, C. T. Lee, “Systematic design of novel wide-angle low-loss symmetric Y-junction waveguides,” IEEE J. Quantum Electron. 34, 673–679 (1998).
[CrossRef]

H. F. Taylor, “An optical analog-to-digital converter: design and analysis,” IEEE J. Quantum Electron. QE-15, 210–217 (1979).
[CrossRef]

O. Hanaizumi, M. Miyagi, Kawakami, “Wide Y-junctions with low-losses in three-dimensional dielectric optical waveguides,” IEEE J. Quantum Electron. QE-21, 168–173 (1985).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. B. Lin, R. S. Cheng, W. S. Wang, “Wide-angle low-loss single-mode symmetric Y-junctions,” IEEE Photon. Technol. Lett. 6, 825–827 (1994).
[CrossRef]

J. Lightwave Technol. (5)

S. Safavi-Naeini, Y. L. Chow, S. K. Chaudhuri, A. Goss, “Wide angle phase-corrected Y-junction of dielectric waveguides for low loss applications,” J. Lightwave Technol. 11, 567–576 (1993).
[CrossRef]

H. Hatami-Hanza, M. J. Lederer, P. L. Chu, I. M. Skinner, “A novel wide-angle low-loss dielectric slab waveguide Y-branch,” J. Lightwave Technol. 12, 208–213 (1994).
[CrossRef]

M. L. Wu, P. L. Fan, J. M. Hsu, C. T. Lee, “Design of ideal structures for lossless bends in optical waveguides by conformal mapping,” J. Lightwave Technol. 14, 2604–2614 (1996).
[CrossRef]

M. Rangaraj, M. Minakata, S. Kawakami, “Low loss integrated optical Y-branch,” J. Lightwave Technol. 7, 753–758 (1989).
[CrossRef]

C. T. Lee, M. L. Wu, J. M. Hsu, “Beam propagation analysis for tapered waveguides: taking account of the curved phase-front effect in paraxial approximation,” J. Lightwave Technol. 15, 2183–2189 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (1)

C. T. Lee, H. C. Lee, H. H. Lai, L. G. Sheu, “Complementary optical bistable operation with integration of two directional coupler on LiNbO3 crystal,” Jpn. J. Appl. Phys. 35, 2686–2689 (1996).
[CrossRef]

Opt. Quantum Electron. (1)

C. T. Lee, P. L. Fan, J. C. Lee, T. T. Kuo, “A novel power divider with arbitrary power division and high coupling efficiency with single mode fiber,” Opt. Quantum Electron. 28, 1417–1425 (1996).
[CrossRef]

Other (2)

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1989).

S. M. Sze, VLSI Technology (McGraw-Hill, New York, 1983).

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Figures (6)

Fig. 1
Fig. 1

Top view of the full phase compensation microprism-type Y-junction waveguide.

Fig. 2
Fig. 2

Field intensity distributions of (a) approximate compensation and (b) full phase compensation microprism-type Y-junction waveguide. The normalized output intensities for (c) approximate compensation and (d) full phase compensation microprism-type Y-junction waveguide with a branching angle of ϕ = 20°.

Fig. 3
Fig. 3

Output field intensity contours and cross sections for (a) approximate compensation and (b) a full phase compensation microprism-type Y-junction waveguide. Three-dimensional plots of output field intensities for (c) approximate compensation and (d) a full phase compensation microprism-type Y-junction waveguide with a branching angle of ϕ = 20°.

Fig. 4
Fig. 4

Transmitted power efficiency η obtained with the overlap integral method and approximate method as a function of propagation distance for the half-branching angle of θ = 10°.

Fig. 5
Fig. 5

Dependence of branching loss on the half-branching angle θ for the approximate compensation and full phase compensation microprism-type Y-junction waveguides.

Fig. 6
Fig. 6

Proposed Y-junction waveguide showing only the precompensation region.

Equations (9)

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

xLτ=WA-Wp2+xp1-Wτ cos α,zLτ=zp1+Wτ sin α,xRτ=WA-Wp2cos θ+xp2-Wτ cosθ-α,zRτ=zp1+Wτ sinθ-α,
np1=ns+ngWpWA-Wp×sin2θ/2+mcosθ/21-cosθ/2+m,
np2=ngt1+tanθ/2θt-1-WgWA, t=1.011-tanθ/2θnsng-1.01 cos θ tanθ/2θ.
Pi=Lx,Ly ϕx, y, 0fx, y, 0dxdy2Lx,Ly |ϕx, y, 0|2dxdy  Lx,Ly |fx, y, 0|2dxdy,
Po=Lx,Ly ϕx, y, Lzfx, y, Lzdxdy2Lx,Ly |ϕx, y, Lz|2dxdy Lx,Ly |fx, y, Lz|2dxdy,
η=Po/Pi.
Δϕb=βOB-AA=βθCO¯-CA¯=k0neffθWp/2.
Δϕp=np1-nsk0AA-EFnp1-nsk0θ WA-Wp2×cosθ/21-cosθ/2+msin2θ/2+m,
np1=ns+neffWpWA1-Wp×sin2θ/2+mcosθ/21-cosθ/2+m.

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