Abstract

The prismless excitation of guided waves in a Bragg reflection waveguide is investigated. We show that the guided modes can be directly excited by a plane wave that is incident from the air. An excellent agreement between the effective index of the guided mode in an ideal Bragg reflection waveguide and the minimum of the reflection curve has been found for two different semiconductor multilayer compositions. With the optimization of the width of the coupling region, an almost complete transfer of the incident wave to the guided mode was accomplished. This novel guided-wave device is predicted to match well with active multilayer heterostructure devices.

© 1991 Optical Society of America

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References

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  1. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
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  3. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).
  4. J. Salzman, G. Lenz, “The Bragg reflection waveguide directional coupler,” IEEE Photon. Technol. Lett. 1, 319–322 (1989).
    [Crossref]
  5. G. Lenz, J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519–531 (1990).
    [Crossref]
  6. J. P. van der Ziel, M. Ilegems, “Multilayer GaAs–Al0.3Ga0.7As dielectric quarter wave stacks grown by molecular beam epitaxy,” Appl. Opt. 14, 2627–2630 (1975).
    [Crossref] [PubMed]
  7. M. Ogura, T. Yao, “Surface emitting laser diode with AlGaAs/GaAs multilayer heterostructures,” J. Vac. Sci. Technol. B3, 784–787 (1985).
  8. R. Ulrich, “Theory of the prism–film coupler by plane-wave analysis,” J. Opt. Soc. Am. 60, 1337–1350 (1970).
    [Crossref]
  9. G. M. Carter, Y. G. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
    [Crossref]
  10. G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
    [Crossref]
  11. G. H. Doehler, H. Kunzel, K. Ploog, “Tunable absorption coefficients in GaAs doped superlattices,” Phys. Rev. B 25, 2616–2626 (1982).
    [Crossref]
  12. A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
    [Crossref]

1990 (1)

G. Lenz, J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519–531 (1990).
[Crossref]

1989 (1)

J. Salzman, G. Lenz, “The Bragg reflection waveguide directional coupler,” IEEE Photon. Technol. Lett. 1, 319–322 (1989).
[Crossref]

1988 (2)

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
[Crossref]

1985 (1)

M. Ogura, T. Yao, “Surface emitting laser diode with AlGaAs/GaAs multilayer heterostructures,” J. Vac. Sci. Technol. B3, 784–787 (1985).

1983 (1)

G. M. Carter, Y. G. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

1982 (1)

G. H. Doehler, H. Kunzel, K. Ploog, “Tunable absorption coefficients in GaAs doped superlattices,” Phys. Rev. B 25, 2616–2626 (1982).
[Crossref]

1977 (1)

1975 (1)

1970 (1)

Assanto, G.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Carter, G. M.

G. M. Carter, Y. G. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

Chen, Y. G.

G. M. Carter, Y. G. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

Danner, A.

A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
[Crossref]

Dapkus, P. D.

A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
[Crossref]

Doehler, G. H.

G. H. Doehler, H. Kunzel, K. Ploog, “Tunable absorption coefficients in GaAs doped superlattices,” Phys. Rev. B 25, 2616–2626 (1982).
[Crossref]

Garmire, E.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
[Crossref]

Hong, C.-S.

Ilegems, M.

Kost, A.

A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
[Crossref]

Kunzel, H.

G. H. Doehler, H. Kunzel, K. Ploog, “Tunable absorption coefficients in GaAs doped superlattices,” Phys. Rev. B 25, 2616–2626 (1982).
[Crossref]

Lenz, G.

G. Lenz, J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519–531 (1990).
[Crossref]

J. Salzman, G. Lenz, “The Bragg reflection waveguide directional coupler,” IEEE Photon. Technol. Lett. 1, 319–322 (1989).
[Crossref]

Maradudin, A. A.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

Ogura, M.

M. Ogura, T. Yao, “Surface emitting laser diode with AlGaAs/GaAs multilayer heterostructures,” J. Vac. Sci. Technol. B3, 784–787 (1985).

Ploog, K.

G. H. Doehler, H. Kunzel, K. Ploog, “Tunable absorption coefficients in GaAs doped superlattices,” Phys. Rev. B 25, 2616–2626 (1982).
[Crossref]

Reinisch, R.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Salzman, J.

G. Lenz, J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519–531 (1990).
[Crossref]

J. Salzman, G. Lenz, “The Bragg reflection waveguide directional coupler,” IEEE Photon. Technol. Lett. 1, 319–322 (1989).
[Crossref]

Seaton, C. T.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Stegeman, G. I.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Ulrich, R.

van der Ziel, J. P.

Vitrant, G.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Yao, T.

M. Ogura, T. Yao, “Surface emitting laser diode with AlGaAs/GaAs multilayer heterostructures,” J. Vac. Sci. Technol. B3, 784–787 (1985).

Yariv, A.

Yeh, P.

Zanoni, R.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

G. M. Carter, Y. G. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[Crossref]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988).
[Crossref]

A. Kost, E. Garmire, A. Danner, P. D. Dapkus, “Large optical nonlinearities in a GaAS/AlGaAS hetero n-i-p-i structure,” Appl. Phys. Lett. 52, 637–639 (1988).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Lenz, J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519–531 (1990).
[Crossref]

IEEE Photon. Technol. Lett. (1)

J. Salzman, G. Lenz, “The Bragg reflection waveguide directional coupler,” IEEE Photon. Technol. Lett. 1, 319–322 (1989).
[Crossref]

J. Opt. Soc. Am. (2)

J. Vac. Sci. Technol. (1)

M. Ogura, T. Yao, “Surface emitting laser diode with AlGaAs/GaAs multilayer heterostructures,” J. Vac. Sci. Technol. B3, 784–787 (1985).

Phys. Rev. B (1)

G. H. Doehler, H. Kunzel, K. Ploog, “Tunable absorption coefficients in GaAs doped superlattices,” Phys. Rev. B 25, 2616–2626 (1982).
[Crossref]

Other (2)

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

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Figures (6)

Fig. 1
Fig. 1

(a) Profile of the dielectric constants for an ideal BRW: df, thicknesses of the guiding film, (b) Schematic of the combined coupling-waveguiding device: ε1, ε2, dielectric coefficients of the individual SL films; εf, dielectric coefficient of the guiding film; d1, d2, thicknesses of the individual SL films.

Fig. 2
Fig. 2

Real and imaginary parts of the normalized Bloch vector of an infinite SL dependent on the normalized wave-vector component β/k. The parameters are ε1 = 12.6736 + i2 × 10−4, ε2 = 11.3569, λ = 920 nm, d1 = 70 nm, d2 = 66 nm. The maximum value of the imaginary part is Im(κd) = 0.04.

Fig. 3
Fig. 3

Real part of the normalized propagation constant neff versus the guiding film thickness df for BRW modes in an asymmetric GaAs–GaAlAs multifilm configuration. The parameters are discussed in the text. The square labels the mode to be excited (df = 817 nm). The imaginary part of neff is less than 10−4. The guided-wave region (overlap of the two different stop bands) is indicated by the two curves βlower = 0.423 and βupper = 0.997.

Fig. 4
Fig. 4

Real part of the normalized propagation constant neff versus the guiding film thickness df for BRW modes in a symmetric InP–InGaAsP multifilm configuration. The parameters are discussed in the text. The square labels the mode to be excited (df = 1005 nm). The imaginary part of neff is again less than 10−4. The guided-wave region (stop band) is indicated by the curves βlower = 0.613 and βupper = 1.118.

Fig. 5
Fig. 5

Reflectivity versus the angle of incidence for a asymmetric GaAs–GaAlAs multifilm configuration consisting of a finite cladding SL2, a guiding film of thickness df = 817 nm, and an infinite substrate SL1. The numbers of unit cells of SL2 are 40 (curve 1), 45 (curve 2), 50 (curve 3), and 55 (curve 4). The arrow indicates the respective effective index neff = sin θ of the guided mode of the ideal BRW (see Fig. 3).

Fig. 6
Fig. 6

Reflectivity versus the angle of incidence for a symmetric InP–InGaAsP multifilm configuration consisting of a finite cladding SL2, a guiding film of thickness df = 1005 nm, and an infinite substrate SL1. The numbers of unit cells of SL2 are 30 (curve 1), 35 (curve 2), 40 (curve 3), and 45 (curve 4). The arrow indicates the respective effective index neff = sin θ of the guided mode of the ideal BRW (see Fig. 4).

Equations (29)

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E ( x , z , t ) = E ( x ) exp [ i ( β z ω t ) ] + c.c. ,
[ E F ] ( N + 1 ) d = m [ E F ] N d ,
m 11 = cos ( k 1 x d 1 ) cos ( k 2 x d 2 ) ( k 2 x / k 1 x ) sin ( k 1 x d 1 ) sin ( k 2 x d 2 ) ,
m 12 = [ ( 1 / k 2 x ) cos ( k 1 x d 1 ) sin ( k 2 x d 2 ) + ( 1 / k 1 x ) sin ( k 1 x d 1 ) cos ( k 2 x d 2 ) ] ,
m 21 = k 1 x sin ( k 1 x d 1 ) cos ( k 2 x d 2 ) + k 2 x cos ( k 1 x d 1 ) sin ( k 2 x d 2 ) ,
m 22 = cos ( k 1 x d 1 ) cos ( k 2 x d 2 ) ( k 1 x / k 2 x ) sin ( k 1 x d 1 ) sin ( k 2 x d 2 ) ,
[ E F ] ( N + 1 ) d = exp ( i κ d ) [ E F ] N d ,
( m μ I ) [ E F ] N d = 0 ,
μ = ( m 11 + m 22 ) 2 ± { [ ( m 11 + m 22 ) / 2 ] 2 1 } 1 / 2 .
| ( m 11 + m 22 ) / 2 | > 1 ,
[ E F ] N d = [ 1 ( μ m 11 ) / m 12 ] E N d .
[ E F ] 0 = [ 1 ( μ 1 m 11 1 ) / m 12 1 ] E 0 = [ 1 p 1 ] E 0 ,
μ 1 = ( m 11 1 + m 22 1 ) / 2 ± { [ ( m 11 1 + m 22 1 ) / 2 ] 2 1 } 1 / 2 ,
[ E F ] d f = [ 1 ( μ 2 m 11 2 ) / m 12 2 ] E d f = [ 1 p 2 ] E 0 ,
μ 2 = ( m 11 2 + m 22 2 ) / 2 ± { [ ( m 11 2 + m 22 2 ) / 2 ] 2 1 } 1 / 2 .
[ E F ] d f = m f [ E F ] 0 = [ cos ( k f x d f ) ( 1 / k f x ) sin ( k f x d f ) k f x sin ( k f x d f ) cos ( k f x d f ) ] [ E F ] 0 ,
[ 1 p 2 ] E d f = [ cos ( k f x d f ) ( 1 / k f x ) sin ( k f x d f ) k f x sin ( k f x d f ) cos ( k f x d f ) ] [ 1 p 1 ] E 0 .
tan ( k f x d f ) = k f x ( p 1 + p 2 ) k f x 2 p 1 p 2 .
[ E F ] 0 = [ 1 p 1 ] E 0 ,
[ E F ] d f = m f [ E F ] 0 = m f [ 1 p ] E 0 .
[ E F ] N ( d 1 2 + d 2 2 ) + d f = ( m 2 ) N [ E F ] d f = ( m 2 ) N m f [ 1 p 1 ] E 0 ,
[ E F ] N ( d 1 2 + d 2 2 ) + d f = [ E F ]
E a ( x ) = E i exp [ i k x ( x X ) ] + E r exp [ i k x ( x X ) ] , F a ( x ) = i k x { E i exp [ i k x ( x X ) ] + E r exp [ i k x ( x X ) ] } ,
E i + E r = E , i k x ( E i + E r ) = F ,
| E r | 2 | E i | 2 = | E + ( i / k x ) F | 2 | E ( i / k x ) F | 2 .
ɛ 1 = 12.6736 + i 2 × 10 4 , d 1 = 66 nm , ɛ 2 = 9.00 , d 2 = 80 nm ,
ɛ f = 12.6736 + i 2 × 10 4 , d f = 817 nm ,
ɛ 1 = 12.6736 + i 2 × 10 4 , d 1 = 70 nm , ɛ 2 = 11.3569 , d 2 = 66 nm .
ɛ 1 = 11.6964 + i 5 × 10 4 , d 1 = 100 nm , ɛ 2 = 10.314 , d 2 = 107 nm , ɛ f = ɛ 2 , d f = 1005 nm .

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