Abstract

We discuss coupling of ultrashort light pulses into waveguides by use of a prism waveguide coupler configuration. Theoretical analysis indicates that an extra loss induced by the short coherence times of ultrashort pulses, which has a strong effect on the reflected light and the optimum coupling condition, appears in the waveguide. Numerical simulations show that the reflectance strongly depends on the coherence times of ultrashort pulses. A method for realizing optimum coupling by compensating for the extra loss is proposed as well in this paper. A preliminary experiment of employing ultrashort pulses with different coherence times was carried out, and good agreement between theory and experiment was obtained.

© 2006 Optical Society of America

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2003

H. Li, Z. Cao, H. Lu, and Q. Shen, "Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide," Appl. Phys. Lett. 83, 2757-2759 (2003).
[CrossRef]

2002

2001

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

2000

1997

1994

1989

1988

1984

C. Liao and G. I. Stegeman, "Nonlinear prism coupler," Appl. Phys. Lett. 44, 164-166 (1984).
[CrossRef]

1981

1974

1970

1969

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

Akhouayri, H.

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, New York, 1976), pp. 1-28.

Assanto, G.

Bahtiar, A.

Best, A.

Bubeck, C.

Cao, Z.

H. Li, Z. Cao, H. Lu, and Q. Shen, "Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide," Appl. Phys. Lett. 83, 2757-2759 (2003).
[CrossRef]

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

Y. Jiang, Z. Cao, Q. Shen, X. Dou, and Y. Chen, "Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers," J. Opt. Soc. Am. B 17, 805-808 (2000).
[CrossRef]

Chen, G.

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

Chen, J. M.

Chen, W. P.

Chen, Y.

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

Y. Jiang, Z. Cao, Q. Shen, X. Dou, and Y. Chen, "Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers," J. Opt. Soc. Am. B 17, 805-808 (2000).
[CrossRef]

Dou, X.

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

Y. Jiang, Z. Cao, Q. Shen, X. Dou, and Y. Chen, "Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers," J. Opt. Soc. Am. B 17, 805-808 (2000).
[CrossRef]

Enoch, S.

Fitrilawati, F.

Fortenberry, R. M.

Goutev, N.

Herminghaus, S.

Hörhold, H.

Jiang, Y.

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

Y. Jiang, Z. Cao, Q. Shen, X. Dou, and Y. Chen, "Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers," J. Opt. Soc. Am. B 17, 805-808 (2000).
[CrossRef]

Klopfleisch, M.

Kogelnik, H.

Koynov, K.

Li, H.

H. Li, Z. Cao, H. Lu, and Q. Shen, "Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide," Appl. Phys. Lett. 83, 2757-2759 (2003).
[CrossRef]

Liao, C.

C. Liao and G. I. Stegeman, "Nonlinear prism coupler," Appl. Phys. Lett. 44, 164-166 (1984).
[CrossRef]

Lu, H.

H. Li, Z. Cao, H. Lu, and Q. Shen, "Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide," Appl. Phys. Lett. 83, 2757-2759 (2003).
[CrossRef]

Martin, R. J.

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, New York, 1976), pp. 1-28.

Okamoto, T.

Schmidt, H. J.

Seaton, C. T.

Serafin, J.

Shen, Q.

H. Li, Z. Cao, H. Lu, and Q. Shen, "Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide," Appl. Phys. Lett. 83, 2757-2759 (2003).
[CrossRef]

Y. Jiang, Z. Cao, Q. Shen, X. Dou, and Y. Chen, "Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers," J. Opt. Soc. Am. B 17, 805-808 (2000).
[CrossRef]

Spears, K. G.

Stegeman, G. I.

Tien, P. K.

P. K. Tien and R. Ulrich, "Theory of prism-film coupler and thin-film light guides," J. Opt. Soc. Am. 60, 1325-1337 (1970).
[CrossRef]

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

Ulrich, R.

Weber, H. P.

Yamaguchi, I.

Yamamoto, M.

Zhu, X.

Appl. Phys. Lett.

P. K. Tien, R. Ulrich, and R. J. Martin, "Modes of propagating light waves in thin deposited semiconductor," Appl. Phys. Lett. 14, 291-294 (1969).
[CrossRef]

C. Liao and G. I. Stegeman, "Nonlinear prism coupler," Appl. Phys. Lett. 44, 164-166 (1984).
[CrossRef]

H. Li, Z. Cao, H. Lu, and Q. Shen, "Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide," Appl. Phys. Lett. 83, 2757-2759 (2003).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Laser Technol.

Y. Jiang, Z. Cao, G. Chen, X. Dou, and Y. Chen, "Low voltage electro-optic polymer light modulator using attenuated total internal reflection," Opt. Laser Technol. 33, 417-420 (2001).
[CrossRef]

Opt. Lett.

Other

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, New York, 1976), pp. 1-28.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram for the PWC.

Fig. 2
Fig. 2

(a) Waveguide mode coupled to a semi-infinite medium n 1 through ϵ 2 , (b) two semi-infinite media n 1 and n 3 coupled through ϵ 2 , and (c) waves in a PWC.

Fig. 3
Fig. 3

Time delay between the A 3 wave and the A 3 wave in the coupling range between x n 1 and x n .

Fig. 4
Fig. 4

ATR spectra with respect to different time widths of incident pulses.

Fig. 5
Fig. 5

Spectra of reflected pulses calculated from the new amplitude reflection coefficient (solid curves) and from the conventional one (dashed curves). Dotted curves, the spectra of incident pulses.

Fig. 6
Fig. 6

Experiment arrangement.

Fig. 7
Fig. 7

Spectra of two reflected pulses.

Tables (1)

Tables Icon

Table 1 Time Delays for Different Guided Modes a

Equations (25)

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n 1 > n 3 > n 4 ,
r ( ω ) = r ( ω ) exp [ i ϕ ( ω ) ] = r 12 + r 234 exp ( 2 i κ 2 s ) 1 + r 12 r 234 exp ( 2 i κ 2 s ) ,
r 234 = r 23 + r 34 exp ( 2 i κ 3 d ) 1 + r 23 r 34 exp ( 2 i κ 3 d ) ,
r 321 = A 3 B 3 = r 32 + r 21 exp ( 2 i κ 2 s ) 1 + r 32 r 21 exp ( 2 i κ 2 s ) ,
t 31 = B 1 B 3 = ( 1 r 12 ) ( 1 r 23 ) exp ( i κ 2 s ) 1 + r 12 r 23 exp ( 2 i κ 2 s ) .
r 123 = B 1 A 1 = r 12 + r 23 exp ( 2 i κ 2 s ) 1 + r 12 r 23 exp ( 2 i κ 2 s ) ,
t 13 = A 3 A 1 = ( 1 + r 12 ) ( 1 + r 23 ) exp ( i κ 2 s ) 1 + r 12 r 23 exp ( 2 i κ 2 s ) .
A 3 = ( A 3 ) n 1 r 34 r 321 exp ( i 2 κ 3 d ) ,
A 3 = t 13 A 1 ,
( A 3 ) n = t 13 A 1 + ( A 3 ) n 1 r 34 r 321 exp ( i 2 κ 3 d ) ,
( A 3 ) 0 = t 13 A 1 ,
r 34 r 321 exp ( i 2 κ 3 d ) = α exp ( i 2 m π ) ,
exp ( i 2 κ 3 d ) = exp [ 2 i ω d ( n 3 2 N m 2 ) 1 2 c ] = exp ( i ω τ 0 ) ,
τ 1 = n 1 l sin θ c = l N m c ,
τ 2 = l v g = l [ N m c + ( n 3 2 N m 2 ) d c N m d eff ] ,
l = 2 d eff tan θ = 2 d eff N m ( n 3 2 N m 2 ) 1 2 ,
τ 2 τ 1 = 2 ( n 3 2 N m 2 ) 1 2 d c = τ 0 .
( A 3 ) n 2 = I 1 + I 2 + 2 I 1 I 2 γ ( τ 0 ) cos ( φ ) ,
( A 3 ) n 2 = [ I 1 + γ ( τ 0 ) I 2 ] 2 + [ 1 γ ( τ 0 ) 2 ] I 2 ,
( A 3 ) n = t 13 A 1 + γ ( τ 0 ) ( A 3 ) n 1 r 34 r 321 exp ( i 2 κ 3 d ) ,
( A 3 ) 0 = t 13 A 1 .
A 3 ( ω ) = t 13 ( ω ) A 1 ( ω ) { 1 + j = 1 γ ( j τ 0 ) [ r 34 r 321 exp ( i 2 κ 3 d ) ] j } .
B 1 ( ω ) = A 3 ( ω ) r 34 exp ( 2 i κ 3 d ) t 31 + r 123 A 1 ( ω ) ,
r ( ω ) = B 1 ( ω ) A 1 ( ω ) = t 31 t 13 r 34 exp ( 2 i κ 3 d ) { 1 + j = 1 γ ( j τ 0 ) [ r 34 r 321 exp ( i 2 κ 3 d ) ] j } + r 123 .
r = t 13 t 31 r 34 exp ( 2 i κ 3 d ) 1 r 34 r 321 exp ( 2 i κ 3 d ) + r 123 .

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