Abstract

Second harmonic generation in optical planar waveguides is the most promising mechanism for frequency doubling of laser emission since light can be highly confined to the nonlinear waveguide medium. However, this advantage is achievable only by precise phase matching between the fundamental wave and the doubled frequency wave, which is hard to control at the fabrication stage. Two tasks are addressed: a basic design for the layer thicknesses of a two-layer waveguide to achieve phase matching, and second, a multi-layer-waveguide design to achieve broadened phase matching bandwidth.

© 2009 Optical Society of America

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References

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  1. A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart and Winston, 1985).
  2. M. Fujimura, T. Suhara, and H. Nishihara, “Theoretical analysis of resonant waveguide optical second harmonic generation devices,” J. Lightwave Technol. 14, 1899-1905(1996).
    [CrossRef]
  3. G. Leo, R. Drenten, and M. Jongerius, “Cherenkov second-harmonic generation in multilayer waveguide structures,” IEEE J. Quantum Electron. 28, 534-546 (1992).
    [CrossRef]
  4. K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
    [CrossRef]
  5. M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
    [CrossRef]
  6. A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
    [CrossRef]
  7. W. Press, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1997).
  8. S. Chapra and R. Canale, Numerical Methods for Engineers, 3rd ed. (McGraw-Hill, 2006).
  9. C. Flueraru and C. P. Grover, “Overlap integral analysis for second-harmonic generation within inverted waveguide using mode dispersion phase match,” IEEE Photonics Technol. Lett. 15, 697-699 (2003).
    [CrossRef]

2003 (1)

C. Flueraru and C. P. Grover, “Overlap integral analysis for second-harmonic generation within inverted waveguide using mode dispersion phase match,” IEEE Photonics Technol. Lett. 15, 697-699 (2003).
[CrossRef]

2002 (1)

A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
[CrossRef]

2001 (1)

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

1996 (1)

M. Fujimura, T. Suhara, and H. Nishihara, “Theoretical analysis of resonant waveguide optical second harmonic generation devices,” J. Lightwave Technol. 14, 1899-1905(1996).
[CrossRef]

1994 (1)

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
[CrossRef]

1992 (1)

G. Leo, R. Drenten, and M. Jongerius, “Cherenkov second-harmonic generation in multilayer waveguide structures,” IEEE J. Quantum Electron. 28, 534-546 (1992).
[CrossRef]

Bogatov, A.

A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
[CrossRef]

Canale, R.

S. Chapra and R. Canale, Numerical Methods for Engineers, 3rd ed. (McGraw-Hill, 2006).

Chang, D.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Chapra, S.

S. Chapra and R. Canale, Numerical Methods for Engineers, 3rd ed. (McGraw-Hill, 2006).

Dalton, L.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Drakin, A.

A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
[CrossRef]

Drenten, R.

G. Leo, R. Drenten, and M. Jongerius, “Cherenkov second-harmonic generation in multilayer waveguide structures,” IEEE J. Quantum Electron. 28, 534-546 (1992).
[CrossRef]

Erlig, H.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Fetterman, H.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Flueraru, C.

C. Flueraru and C. P. Grover, “Overlap integral analysis for second-harmonic generation within inverted waveguide using mode dispersion phase match,” IEEE Photonics Technol. Lett. 15, 697-699 (2003).
[CrossRef]

Fujimura, M.

M. Fujimura, T. Suhara, and H. Nishihara, “Theoretical analysis of resonant waveguide optical second harmonic generation devices,” J. Lightwave Technol. 14, 1899-1905(1996).
[CrossRef]

Grover, C. P.

C. Flueraru and C. P. Grover, “Overlap integral analysis for second-harmonic generation within inverted waveguide using mode dispersion phase match,” IEEE Photonics Technol. Lett. 15, 697-699 (2003).
[CrossRef]

Jongerius, M.

G. Leo, R. Drenten, and M. Jongerius, “Cherenkov second-harmonic generation in multilayer waveguide structures,” IEEE J. Quantum Electron. 28, 534-546 (1992).
[CrossRef]

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
[CrossRef]

Kzamenets, F.

A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
[CrossRef]

Leo, G.

G. Leo, R. Drenten, and M. Jongerius, “Cherenkov second-harmonic generation in multilayer waveguide structures,” IEEE J. Quantum Electron. 28, 534-546 (1992).
[CrossRef]

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
[CrossRef]

Nishihara, H.

M. Fujimura, T. Suhara, and H. Nishihara, “Theoretical analysis of resonant waveguide optical second harmonic generation devices,” J. Lightwave Technol. 14, 1899-1905(1996).
[CrossRef]

Oh, M. C.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Press, W.

W. Press, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1997).

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
[CrossRef]

Steier, W.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Stratonnikov, A.

A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
[CrossRef]

Suhara, T.

M. Fujimura, T. Suhara, and H. Nishihara, “Theoretical analysis of resonant waveguide optical second harmonic generation devices,” J. Lightwave Technol. 14, 1899-1905(1996).
[CrossRef]

Szep, A.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Tsap, B.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart and Winston, 1985).

Yian, C.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Zhang, C.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

Zhang, H.

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Leo, R. Drenten, and M. Jongerius, “Cherenkov second-harmonic generation in multilayer waveguide structures,” IEEE J. Quantum Electron. 28, 534-546 (1992).
[CrossRef]

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596-1604 (1994).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. C. Oh, H. Zhang, C. Zhang, H. Erlig, C. Yian, B. Tsap, D. Chang, A. Szep, W. Steier, H. Fetterman, and L. Dalton, “Recent advances in electroptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

C. Flueraru and C. P. Grover, “Overlap integral analysis for second-harmonic generation within inverted waveguide using mode dispersion phase match,” IEEE Photonics Technol. Lett. 15, 697-699 (2003).
[CrossRef]

J. Lightwave Technol. (1)

M. Fujimura, T. Suhara, and H. Nishihara, “Theoretical analysis of resonant waveguide optical second harmonic generation devices,” J. Lightwave Technol. 14, 1899-1905(1996).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

A. Stratonnikov, A. Bogatov, A. Drakin, and F. Kzamenets, “A semianalytical method of mode determination for a multilayer planar optical waveguide,” J. Opt. A Pure Appl. Opt. 4, 535-539 (2002).
[CrossRef]

Other (3)

W. Press, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, 1997).

S. Chapra and R. Canale, Numerical Methods for Engineers, 3rd ed. (McGraw-Hill, 2006).

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart and Winston, 1985).

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Figures (8)

Fig. 1
Fig. 1

Two-layer waveguide assisted by top diffractive gratings for coupling the fundamental wave, a scheme that enables the design of layer thicknesses to satisfy phase matching condition.

Fig. 2
Fig. 2

(a) Three-layer waveguide assisted by top diffractive gratings for coupling the fundamental wave. A proposed scheme that enables the design of layer thicknesses to achieve a broadened conversion factor profile. (b) Modal sandwiching of the second harmonic guided mode by two fundamental guided modes. A proposed scheme that enables achieving a broadened conversion factor profile.

Fig. 3
Fig. 3

Four-layer waveguide assisted by top diffractive gratings for coupling the fundamental wave. An advanced proposed scheme that enables the design of layer thicknesses to achieve a broadened conversion factor profile. (b) Modal sandwiching of the second harmonic guided mode by three fundamental guided modes. A proposed scheme that enables achieving a broadened conversion factor profile.

Fig. 4
Fig. 4

Conversion factor versus the detuning from phase matching: the solid curve represents the behavior without modal sandwiching, and the dashed curve represents the conversion factor profile of the first scheme with modal sandwiching when a 5% ripple was allowed, whereas, the dotted curve represents the conversion factor profile when a 20% ripple was allowed.

Fig. 5
Fig. 5

(a) Evolution of layers thicknesses of the two-layer waveguide design when using the Newton method to solve Eqs. (3). (b) Error evolution of the two-layer waveguide design when using the Newton method to solve Eqs. (3).

Fig. 6
Fig. 6

(a) Evolution of layers thicknesses of the two-layer-waveguide design when using genetically assisted random search method to solve Eqs. (3). (b) Error evolution of the two-layer-waveguide design when using genetically assisted random search method to solve Eqs. (3).

Fig. 7
Fig. 7

(a) Evolution of layers thicknesses of the three-layer-waveguide design when using genetically assisted random search method to solve Eqs. (6). (b) Error evolution of the three-layer-waveguide design when using genetically assisted random search method to solve Eqs. (6). (c) The electric field intensity profile of the fundamental modes and the SH mode across the three waveguide layers for the three-layer waveguide that was proposed in example 2.

Fig. 8
Fig. 8

(a) Evolution of layers thicknesses of the four-layer-waveguide design when using genetically assisted random search method to solve Eqs. (10). (b) Error evolution of the four-layer-waveguide design when using genetically assisted random search method to solve Eqs. (10). (c) The electric field intensity profile of the fundamental modes and the SH mode across the four waveguide layers for the four-layer waveguide that was proposed in example (3).

Equations (20)

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f ( n * ) = M 11 ξ 0 M 12 1 ξ p + 1 M 21 + ξ 0 ξ p + 1 M 21 = 0 ,
M = l = 1 p m l = ( M 11 M 12 M 21 M 22 ) , m l = ( cos ( q l t l ) i ξ l 1 sin ( q l t l ) i ξ l sin ( q l t l ) cos ( q l t l ) ) , q l = k n l 2 ( n * ) 2 , ξ l = n l 2 ( n * ) 2 ,
f 1 ( n * ) = M 11 f ξ 0 M 12 f 1 ξ 3 f M 21 f + ξ 0 ξ 3 f M 21 f = 0 , f 2 ( n * ) = M 11 s ξ 0 M 12 s 1 ξ 3 s M 21 s + ξ 0 ξ 3 s M 21 s = 0 ,
M f = l = 1 2 m l f = ( M 11 f M 12 f M 21 f M 22 f ) , m l f = ( cos ( q l f t l ) i ξ l f 1 sin ( q l f t l ) i ξ l f sin ( q l f t l ) cos ( q l f t l ) ) , q l f = k n l f 2 ( n * ) 2 , ξ l f = n l f 2 ( n * ) 2 ,
M s = l = 1 2 m l s = ( M 11 s M 12 s M 21 s M 22 s ) , m l s = ( cos ( q l s t l ) i ξ l s 1 sin ( q l s t l ) i ξ l s sin ( q l s t l ) cos ( q l s t l ) ) , q l s = 2 k n l s 2 ( n * ) 2 , ξ l s = n l s 2 ( n * ) 2 .
f 1 ( n * 1 ) = M 11 f 1 ξ 0 f 1 M 12 f 1 1 ξ 4 f 1 M 21 f 1 + ξ 0 f 1 ξ 4 f 1 M 21 f 1 = 0 , f 2 ( n * 3 ) = M 11 f 2 ξ 0 f 2 M 12 f 2 1 ξ 4 f 2 M 21 f 2 + ξ 0 f 2 ξ 4 f 2 M 21 f 2 = 0 , f 3 ( n * 2 ) = M 11 s ξ 0 M 12 s 1 ξ 4 s M 21 s + ξ 0 ξ 4 s M 21 s = 0 ,
M f 1 = l = 1 3 m l f 1 = ( M 11 f 1 M 12 f 1 M 21 f 1 M 22 f 1 ) , m l f 1 = ( cos ( q l f 1 t l ) i ξ l f 1 1 sin ( q l f 1 t l ) i ξ l f 1 sin ( q l f 1 t l ) cos ( q l f 1 t l ) ) , q l f 1 = k n l f 2 ( n * 1 ) 2 , ξ l f 1 = n l f 2 ( n * 1 ) 2 ,
M f 2 = l = 1 3 m l f 2 = ( M 11 f 2 M 12 f 2 M 21 f 2 M 22 f 2 ) , m l f 2 = ( cos ( q l f 2 t l ) i ξ l f 2 1 sin ( q l f 2 t l ) i ξ l f 2 sin ( q l f 2 t l ) cos ( q l f 2 t l ) ) , q l f 2 = k n l f 2 ( n * 3 ) 2 , ξ l f 2 = n l f 2 ( n * 3 ) 2 ,
M s = l = 1 3 m l s = ( M 11 s M 12 s M 21 s M 22 s ) , m l s = ( cos ( q l s t l ) i ξ l s 1 sin ( q l s t l ) i ξ l s sin ( q l s t l ) cos ( q l s t l ) ) , q l s = 2 k n l s 2 ( n * 2 ) 2 , ξ l s = n l s 2 ( n * 2 ) 2 .
f 1 ( n * 1 ) = M 11 f 1 ξ 0 f 1 M 12 f 1 1 ξ 5 f 1 M 21 f 1 + ξ 0 f 1 ξ 5 f 1 M 21 f 1 = 0 , f 2 ( n * 2 ) = M 11 f 2 ξ 0 f 2 M 12 f 2 1 ξ 5 f 2 M 21 f 2 + ξ 0 f 2 ξ 5 f 2 M 21 f 2 = 0 , f 3 ( n * 3 ) = M 11 f 3 ξ 0 f 3 M 12 f 3 1 ξ 5 f 3 M 21 f 3 + ξ 0 f 3 ξ 5 f 3 M 21 f 3 = 0 , f 4 ( n * 2 ) = M 11 s ξ 0 M 12 s 1 ξ 5 s M 21 s + ξ 0 ξ 5 s M 21 s = 0 ,
M f 1 = l = 1 4 m l f 1 = ( M 11 f 1 M 12 f 1 M 21 f 1 M 22 f 1 ) , m l f 1 = ( cos ( q l f 1 t l ) i ξ l f 1 1 sin ( q l f 1 t l ) i ξ l f 1 sin ( q l f 1 t l ) cos ( q l f 1 t l ) ) , q l f 1 = k n l f 2 ( n * 1 ) 2 , ξ l f 1 = n l f 2 ( n * 1 ) 2 ,
M f 2 = l = 1 4 m l f 2 = ( M 11 f 2 M 12 f 2 M 21 f 2 M 22 f 2 ) , m l f 2 = ( cos ( q l f 2 t l ) i ξ l f 2 1 sin ( q l f 2 t l ) i ξ l f 2 sin ( q l f 2 t l ) cos ( q l f 2 t l ) ) , q l f 2 = k n l f 2 ( n * 2 ) 2 , ξ l f 2 = n l f 2 ( n * 2 ) 2 ,
M f 3 = l = 1 4 m l f 3 = ( M 11 f 3 M 12 f 3 M 21 f 3 M 22 f 3 ) , m l f 3 = ( cos ( q l f 3 t l ) i ξ l f 3 1 sin ( q l f 3 t l ) i ξ l f 3 sin ( q l f 3 t l ) cos ( q l f 3 t l ) ) , q l f 3 = k n l f 2 ( n * 3 ) 2 , ξ l f 3 = n l f 2 ( n * 3 ) 2 ,
M s = l = 1 4 m l s = ( M 11 s M 12 s M 21 s M 22 s ) , m l s = ( cos ( q l s t l ) i ξ l s 1 sin ( q l s t l ) i ξ l s sin ( q l s t l ) cos ( q l s t l ) ) , q l s = 2 k n l s 2 ( n * 2 ) 2 , ξ l s = n l s 2 ( n * 2 ) 2 .
F ( x ) = sin 2 ( x ) x 2 , x = k l ( δ n * ) 2 ,
F ( x ) = sin 2 ( x ) x 2 + sin 2 ( x Δ x ) ( x Δ x ) 2 , x = k l ( δ n * ) 2 , Δ x = k l ( Δ n * ) 2 ,
F ( x ) = sin 2 ( x ) x 2 + sin 2 ( x Δ x 1 ) ( x Δ x 1 ) 2 + sin 2 ( x Δ x 2 ) ( x Δ x 2 ) 2 , x = k l ( δ n * ) 2 , Δ x 1 = k l ( n 2 * n 1 * ) 2 , Δ x 2 = k l ( n 3 * n 2 * ) 2 ,
n 0 = 1 ; n 1 f = 1.6 ; n 2 f = 1.7 ; n 3 f = 1.5 ;     n 1 s = 1.625 ; n 2 s = 1.73 ; n 3 s = 1.52 ; n * = 1.59 ; λ = 1000 nm .
n 0 = 1 ; n 1 f = 1.6 ; n 2 f = 1.7 ; n 3 f = 1.75 ; n 4 f = 1.5 ; n 1 s = 1.62 ; n 2 s = 1.73 ; n 3 s = 1.77 ; n 3 s = 1.515 ; n * 1 = 1.55 ; n * 2 = 1.5515 ; n * 3 = 1.553 ; λ = 1000 nm .
n 0 = 1 ; n 1 f = 1.6 ; n 2 f = 1.7 ; n 3 f = 1.75 ; n 4 f = 1.78 ; n 5 f = 1.5 ; n 1 s = 1.62 ; n 2 s = 1.73 ; n 3 s = 1.77 ; n 4 s = 1.80 ; n 5 s = 1.515 ; n * 1 = 1.55 ; n * 2 = 1.5515 ; n * 3 = 1.553 ; λ = 1000 nm .

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