Abstract

The oxide compositions (OCs) model is established for discussing the chromatic aberrations of a gradient refractive index rod lens. The chromatic aberrations for Na+/Li+, K+/Cs+, and K+/Tl+ ion exchanges are discussed based on the OC model and the Huggins–Sun–Davis (HSD) model. Theoretical results indicate that the function value mainly depends on base glass properties and the nature of exchanging ion pairs, and rarely depends on the quantity of ion exchange. Experimental results show that the chromatic aberrations using the OC model have smaller errors than with the HSD model. The estimating average errors between the OC model and the HSD model are 0.051, 0.0067, and 0.0047 for the K+/Tl+, Li+/Na+, and K+/Cs+ ion exchanges, respectively.

© 2009 Optical Society of America

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References

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2008 (1)

1999 (1)

Y. Mitsuhashi, “Selfoc lenses: applications in DWDM and optical data links,” Proc. SPIE 3666, 246-251 (1999).
[CrossRef]

1996 (2)

1994 (2)

1986 (1)

1985 (1)

1983 (1)

1980 (1)

1942 (1)

Akazawa, N.

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamental and Applications (Springer, 2002).

Davis, D. O.

Fantone, S. D.

Fuji, K.

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamental and Applications (Springer, 2002).

Guo, L.

Huggins, M. L.

Ichikawa, H.

Kitano, I.

Krishna, K. S. R.

Liu, A.

Lv, H.

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, 1978).

Mitsuhashi, Y.

Y. Mitsuhashi, “Selfoc lenses: applications in DWDM and optical data links,” Proc. SPIE 3666, 246-251 (1999).
[CrossRef]

Moore, D. T.

Nishi, H.

Nishizawa, K.

Ogi, S.

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamental and Applications (Springer, 2002).

Ryan-Howard, D. P.

Sharma, A.

Shi, B.

Sun, K. H.

Toyama, M.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Proc. SPIE (1)

Y. Mitsuhashi, “Selfoc lenses: applications in DWDM and optical data links,” Proc. SPIE 3666, 246-251 (1999).
[CrossRef]

Other (2)

E. W. Marchand, Gradient Index Optics (Academic, 1978).

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamental and Applications (Springer, 2002).

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Figures (11)

Fig. 1
Fig. 1

Schematic illustration of fabrication process of glass rod fiber used for ion exchange.

Fig. 2
Fig. 2

Schematic diagram of the ion exchange equipment.

Fig. 3
Fig. 3

Relationship between Δ P / P and V r 0 / V 0 at different Δ n ( N 0 = 1.6 , V 0 = 50 ).

Fig. 4
Fig. 4

Relationship between Δ P / P and V r 0 / V 0 at different V 0 ( N 0 = 1.6 , Δ n = 0.05 ).

Fig. 5
Fig. 5

Relationship between Δ P / P and V r 0 / V 0 at different N 0 ( V 0 = 50 , Δ n = 0.05 ).

Fig. 6
Fig. 6

Relationship between Δ P / P and N D at different V for Na + / Li + exchange.

Fig. 7
Fig. 7

Relationship between Δ P / P and N D at different V for K + / Cs + exchange.

Fig. 8
Fig. 8

Relationship between Δ P / P and N D at different V for K + / Tl + exchange.

Fig. 9
Fig. 9

Dependence of the chromatic aberration and refractive index on the compound M m O n for K + / Tl + ion exchange: (a) HSD model and (b) OC model.

Fig. 10
Fig. 10

Dependence of the chromatic aberration and refractive index on the compound M m O n for Li + / Na + ion exchange: (a) HSD model and (b) OC model.

Fig. 11
Fig. 11

Dependence of the chromatic aberration and refractive index on the compound M m O n for K + / Cs + ion exchanges: (a) HSD model and (b) OC model.

Tables (1)

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Table 1 Basic Glass Compositions for Preparing the GRIN Rod Lens

Equations (16)

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N = N 0 ( 1 A 2 r 2 ) ,
P = 2 π A 1 / 2 .
N ( λ ) = N 0 ( λ ) ( 1 A ( λ ) 2 r 2 ) .
A ( λ ) = N 0 ( λ ) N r 0 ( λ ) N 0 ( λ ) 2 r 0 2 ,
Δ P P = 1 2 Δ A A = 1 2 N 0 · Δ N r 0 N r 0 · Δ N 0 ( N 0 N r 0 ) · N 0 ,
Δ P P = 1 2 1 V 0 ( 1 1 N 0 ) 1 V r 0 ( 1 1 N r 0 ) N 0 N r 0 1 ,
Δ P = P C P F , P = P D , Δ N 0 = 1 N 0 V 0 , Δ N r 0 = 1 N r V r 0 ,
N D , r 0 = N D , 0 + m ( R D , M in O R D , M out O ) ,
N F C , r 0 = N F , r 0 N C , r 0 = N F C , 0 + m ( R F C , M in O R F C , M out O ) ,
N F C , o = N F , 0 N C , 0 = N D , o 1 V 0 ,
V r 0 = N D , r 0 1 N F , r 0 N C , r 0 = [ N D , 0 + m ( R D , M in O R D , M out F C ) 1 ] V 0 N D , 0 1 + m ( R F C , M in O R F C , M out O ) V 0 .
Δ P P D = 1 2 1 V 0 ( 1 1 N D , 0 ) 1 V r 0 ( 1 1 N D , r 0 ) N D , 0 N D , r 0 1 .
Δ P P D = 1 2 1 V 0 N D , 0 1 N D , 0 N D , 0 1 + m ( R F C , M in O R F C , M out O ) V 0 [ N D , 0 + m ( R D , M in O R D , M out F C ) 1 ] V 0 · N D , 0 + m ( R D , M in O R D , M out O ) 1 N D , 0 + m ( R D , M in O R D , M out O ) m ( R D , M out O R D , M in O ) N D , 0 + m ( R D , M in O R D , M out O ) .
R = N 1 ρ ,
N D = 1 + M a M N M V 0 ,
N F C = 1 + M a M F C N M V 0 ,

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