Abstract

Based on precise and detailed theoretical examination of diffusion equation analysis, two-step Ag+Na+ and Na+Ag+ ion-exchange parameters were optimized in order to fabricate a gradient index (GRIN) lens in the BK7 glass rod. Using the diffusion equation, the impact of the concentration ratio of the exchanged ion during the first and second steps was examined in detail. Then, based on the calculated effective parameters such as concentration ratio and immersion time, a fabrication process was proposed. We managed to get the optimum parameters (the bath stop time, temperature, and length) to make a quarter pitch lens. As a result, some samples of the GRIN lens were fabricated and tested successfully. Theoretical considerations and experimental results are presented.

© 2012 Optical Society of America

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References

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  1. K. K. Sharma, Handbook of Optical Lasers and Optics(Springer, 2005).
  2. V. Gurfein, D. Beysens, and Y. Garrabus, “Simple grid technique to measure refractive index gradients,” Opt. Commun. 85, 147–152, (1991).
    [CrossRef]
  3. E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
    [CrossRef]
  4. X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
    [CrossRef]
  5. N. F. Borrelli, Microoptics Technology (Dekker, 2005).
  6. J. Crank, The Mathematics of Diffusion, 2nd ed. (Oxford University, 1975).
  7. A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
    [CrossRef]

2006

A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
[CrossRef]

2004

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

1998

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

1991

V. Gurfein, D. Beysens, and Y. Garrabus, “Simple grid technique to measure refractive index gradients,” Opt. Commun. 85, 147–152, (1991).
[CrossRef]

Battaglin, G.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Beysens, D.

V. Gurfein, D. Beysens, and Y. Garrabus, “Simple grid technique to measure refractive index gradients,” Opt. Commun. 85, 147–152, (1991).
[CrossRef]

Borrelli, N. F.

N. F. Borrelli, Microoptics Technology (Dekker, 2005).

Borsella, E.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Crank, J.

J. Crank, The Mathematics of Diffusion, 2nd ed. (Oxford University, 1975).

Garrabus, Y.

V. Gurfein, D. Beysens, and Y. Garrabus, “Simple grid technique to measure refractive index gradients,” Opt. Commun. 85, 147–152, (1991).
[CrossRef]

Gonella, F.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Gurfein, V.

V. Gurfein, D. Beysens, and Y. Garrabus, “Simple grid technique to measure refractive index gradients,” Opt. Commun. 85, 147–152, (1991).
[CrossRef]

Lipovskii, A. A.

A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
[CrossRef]

Ma, H.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Mazzoldi, P.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Ming, H.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Polloni, R.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Quaranta, A.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Sharma, K. K.

K. K. Sharma, Handbook of Optical Lasers and Optics(Springer, 2005).

Sun, X.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Svistunov, D. V.

A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
[CrossRef]

Tagantsev, D. K.

A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
[CrossRef]

Xie, J.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Yang, J.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Zheng, Z.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Zhurihina, V. V.

A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
[CrossRef]

Chem. Phys. Lett.

E. Borsella, F. Gonella, P. Mazzoldi, A. Quaranta, G. Battaglin, and R. Polloni, “Spectroscopic investigation of silver in soda-lime glass,” Chem. Phys. Lett. 284, 429–434 (1998).
[CrossRef]

Opt. Commun.

V. Gurfein, D. Beysens, and Y. Garrabus, “Simple grid technique to measure refractive index gradients,” Opt. Commun. 85, 147–152, (1991).
[CrossRef]

Opt. Laser Technol.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).
[CrossRef]

Opt. Mater.

A. A. Lipovskii, D. V. Svistunov, D. K. Tagantsev, and V. V. Zhurihina, “Diffusion nonlinearity in aluminumboron silicate glasses for ion-exchanged GRIN structures: a simple technique to evaluate diffusion nonlinearity of glasses,” Opt. Mater. 28, 276–284 (2006).
[CrossRef]

Other

K. K. Sharma, Handbook of Optical Lasers and Optics(Springer, 2005).

N. F. Borrelli, Microoptics Technology (Dekker, 2005).

J. Crank, The Mathematics of Diffusion, 2nd ed. (Oxford University, 1975).

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Figures (9)

Fig. 1.
Fig. 1.

Numbered curves are the calculated curves for concentration of diffused ion in terms of r/r0 (a) T2=1/2T1, (b) T2=T1, (c) T2=2T1, so that numbers on the curves indicate values of C0/C0 (ratio of diffusing ion in two baths). Meanwhile, the no-numbered curve shows the concentration distribution after the first ion-exchange process.

Fig. 2.
Fig. 2.

Numbered curves indicate concentration distributions in different values of x, T1=0.03, T2=0.15, and numbers on curves are values of x. Meanwhile, the no-numbered curve shows the concentration distribution after the first ion-exchange process.

Fig. 3.
Fig. 3.

Numbered curves indicate concentration distributions through the rod radius, Numbers on curves are values of T2, T1=0.03, and x=0.1. Meanwhile, the no-numbered curve shows the concentration distribution after the first ion-exchange process.

Fig. 4.
Fig. 4.

Numbered curves indicate concentration distributions through rod radius. Numbers on curves are values of T2, T1=0.05, and x=0.1. Meanwhile, the no-numbered curve shows the concentration distribution after the first ion-exchange process.

Fig. 5.
Fig. 5.

Numbered curves indicate concentration distributions through the rod radius. Numbers on curves are values of T2, T1=0.07, and x=0.1. Meanwhile, the no-numbered curve shows the concentration distribution after the first ion-exchange process.

Fig. 6.
Fig. 6.

Schematic of used setup for testing the samples concerning laser spot size at the output surface.

Fig. 7.
Fig. 7.

Typical experimental intensity distribution at the end of (a) a sample before and (b) after the double ion-exchange process.

Fig. 8.
Fig. 8.

(a) Comparison of intensity distribution at the end of one sample under fabrication parameters t1=13h, t2=26h after the first (dashed line) and second step of ion exchange (solid line). (b) Comparison of the output intensity between one sample with fabricated specifications, t1=13h, t2=26h (solid line), and another one with t1=15h, t2=26h (dashed line).

Fig. 9.
Fig. 9.

(a) Focal point examination using a single lens. (b) Ray tracing inside the two samples (solid line), t1=13, t2=26h (dashed line), t1=15, t2=26h.

Equations (2)

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CC0=12r01exp(Dαn2t)J0(αnr)αnJ1(αnr0),
C=C0+21[(C0C0)C0exp(βn2T1)]exp(βn2T2)J0(βnr/r0)βnJ1(βn),

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