Abstract

We examine the temperature dependence of edge-illuminated holographic filters formed in phenanthrenquinone doped poly(methyl methacrylate) (PQ∕PMMA) operating at 1550  nm. It was found that the thermally induced change to the refractive index and volume can be used to select the wavelength filtered by the grating. The temperature can be varied over a range of 15°C without introducing noticeable hysteresis effects. The wavelength can be tuned at a rate of 0.03nm/°C over this temperature range. A model for the temperature tuning effect is presented and compared to experimental results.

© 2007 Optical Society of America

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References

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  1. R. Ramaswami and K. N. Sivarajan, Optical Networks A Practical Perspective (Morgan Kaufmann, 2002).
  2. A. Sato, M. Scepanovic, and R. K. Kostuk, "Holographic edge-illuminated polymer Bragg gratings for dense wavelength division optical filters at 1550 nm," Appl. Opt. 42, 778-784 (2003).
    [CrossRef] [PubMed]
  3. R. K. Kostuk, W. Maeda, C.-H. Chen, I. Djordjevic, and B. Vasic, "Cascaded holographic polymer reflection grating filters for optical-code-division-multiple-access applications," Appl. Opt. 44, 7581-7586 (2005).
    [CrossRef] [PubMed]
  4. A. Sato and R. K. Kostuk, "Holographic grating for dense wavelength division optical filters at 1550 nm using Phenanthrenquinone doped poly(methyl methacrylate)," Proc. SPIE 5216, 44-52 (2003).
    [CrossRef]
  5. S. H. Goods, R. M. Watson, and M. Yi, "Thermal expansion and hydratation behavior of PMMA molding materials for LIGA applications," http://www.osti.gov/bridge/servlets/purl/811193-p1lH1k/native/811193.pdf.
  6. D. N. Nikogosyan, "Polymethylmethacrylate," in Properties of Optical and Laser-Related Materials: A Handbook (J Wiley, 1997).
  7. F. P. Incropera and D. P. DeWitt, "Free convection," in Fundamentals of Heat and Mass Transfer (Wiley, 2002).
  8. J. S. Simmons and K. S. Potter, "Temperature dependence of the refractive index," in Optical Materials (Academic P, 2000).
  9. I. Fanderlik, Optical Properties of Glass (Elsevier, 1983), Chaps. 3-4.
  10. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005), Appendix D.
  11. R. Kashyap, "Properties of uniform Bragg gratings," in Fiber Bragg Gratings (Academic P, 1999).

2005 (1)

2003 (2)

A. Sato and R. K. Kostuk, "Holographic grating for dense wavelength division optical filters at 1550 nm using Phenanthrenquinone doped poly(methyl methacrylate)," Proc. SPIE 5216, 44-52 (2003).
[CrossRef]

A. Sato, M. Scepanovic, and R. K. Kostuk, "Holographic edge-illuminated polymer Bragg gratings for dense wavelength division optical filters at 1550 nm," Appl. Opt. 42, 778-784 (2003).
[CrossRef] [PubMed]

Chen, C.-H.

DeWitt, D. P.

F. P. Incropera and D. P. DeWitt, "Free convection," in Fundamentals of Heat and Mass Transfer (Wiley, 2002).

Djordjevic, I.

Fanderlik, I.

I. Fanderlik, Optical Properties of Glass (Elsevier, 1983), Chaps. 3-4.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005), Appendix D.

Goods, S. H.

S. H. Goods, R. M. Watson, and M. Yi, "Thermal expansion and hydratation behavior of PMMA molding materials for LIGA applications," http://www.osti.gov/bridge/servlets/purl/811193-p1lH1k/native/811193.pdf.

Incropera, F. P.

F. P. Incropera and D. P. DeWitt, "Free convection," in Fundamentals of Heat and Mass Transfer (Wiley, 2002).

Kashyap, R.

R. Kashyap, "Properties of uniform Bragg gratings," in Fiber Bragg Gratings (Academic P, 1999).

Kostuk, R. K.

Maeda, W.

Nikogosyan, D. N.

D. N. Nikogosyan, "Polymethylmethacrylate," in Properties of Optical and Laser-Related Materials: A Handbook (J Wiley, 1997).

Potter, K. S.

J. S. Simmons and K. S. Potter, "Temperature dependence of the refractive index," in Optical Materials (Academic P, 2000).

Ramaswami, R.

R. Ramaswami and K. N. Sivarajan, Optical Networks A Practical Perspective (Morgan Kaufmann, 2002).

Sato, A.

A. Sato, M. Scepanovic, and R. K. Kostuk, "Holographic edge-illuminated polymer Bragg gratings for dense wavelength division optical filters at 1550 nm," Appl. Opt. 42, 778-784 (2003).
[CrossRef] [PubMed]

A. Sato and R. K. Kostuk, "Holographic grating for dense wavelength division optical filters at 1550 nm using Phenanthrenquinone doped poly(methyl methacrylate)," Proc. SPIE 5216, 44-52 (2003).
[CrossRef]

Scepanovic, M.

Simmons, J. S.

J. S. Simmons and K. S. Potter, "Temperature dependence of the refractive index," in Optical Materials (Academic P, 2000).

Sivarajan, K. N.

R. Ramaswami and K. N. Sivarajan, Optical Networks A Practical Perspective (Morgan Kaufmann, 2002).

Vasic, B.

Watson, R. M.

S. H. Goods, R. M. Watson, and M. Yi, "Thermal expansion and hydratation behavior of PMMA molding materials for LIGA applications," http://www.osti.gov/bridge/servlets/purl/811193-p1lH1k/native/811193.pdf.

Yi, M.

S. H. Goods, R. M. Watson, and M. Yi, "Thermal expansion and hydratation behavior of PMMA molding materials for LIGA applications," http://www.osti.gov/bridge/servlets/purl/811193-p1lH1k/native/811193.pdf.

Appl. Opt. (2)

Proc. SPIE (1)

A. Sato and R. K. Kostuk, "Holographic grating for dense wavelength division optical filters at 1550 nm using Phenanthrenquinone doped poly(methyl methacrylate)," Proc. SPIE 5216, 44-52 (2003).
[CrossRef]

Other (8)

S. H. Goods, R. M. Watson, and M. Yi, "Thermal expansion and hydratation behavior of PMMA molding materials for LIGA applications," http://www.osti.gov/bridge/servlets/purl/811193-p1lH1k/native/811193.pdf.

D. N. Nikogosyan, "Polymethylmethacrylate," in Properties of Optical and Laser-Related Materials: A Handbook (J Wiley, 1997).

F. P. Incropera and D. P. DeWitt, "Free convection," in Fundamentals of Heat and Mass Transfer (Wiley, 2002).

J. S. Simmons and K. S. Potter, "Temperature dependence of the refractive index," in Optical Materials (Academic P, 2000).

I. Fanderlik, Optical Properties of Glass (Elsevier, 1983), Chaps. 3-4.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005), Appendix D.

R. Kashyap, "Properties of uniform Bragg gratings," in Fiber Bragg Gratings (Academic P, 1999).

R. Ramaswami and K. N. Sivarajan, Optical Networks A Practical Perspective (Morgan Kaufmann, 2002).

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Figures (7)

Fig. 1
Fig. 1

(a) Sample mixture container for curing; (b) exposure setup.

Fig. 2
Fig. 2

n / T versus temperature: diamonds show values from Nikogosyan [6]; dotted curve shows a polynomial fit. For the 0 ° C 5 0 ° C temperature range n / T is approximately linear with temperature.

Fig. 3
Fig. 3

(a) Transmission and (b) reflection hologram measurement setups.

Fig. 4
Fig. 4

Reconstruction angle versus temperature: the change in the reconstruction angle is plotted along with the theoretical values using a linear CTE to predict the expansion of the period. Error bars of 0.02° are shown.

Fig. 5
Fig. 5

Transmitted power versus wavelength. The tunable laser source was set to run a sweep of wavelengths from 1546.5 to 1548.5   nm . The wavelength sweeps were run for different temperatures in the 19.82 ° C 35   ° C range.

Fig. 6
Fig. 6

Transmission minima (Bragg or reconstruction wavelength) versus temperature for samples (a) 1 and (b) 2. The Bragg wavelength of the grating decreases with temperature. The experimental results are compared to a model based on the theoretical background of Section 3 and the CTE (α) calculated in Subsection 5A.

Fig. 7
Fig. 7

Transmitted power versus wavelength. After changing the temperature of the sample several times, the temperature was restored to approximately 19. 50   ° C showing that the transmitted spectrum also returns to its original position.

Tables (1)

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Table 1 Linear Coefficients of Thermal Expansion for Undoped PMMA Materials in Units of [1∕°C]

Equations (12)

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α = 1 L L T [ 1 ° C ] ,
β = 1 V V T = ρ m ( V ρ ) ( ρ T ) = ρ m ( m ρ 2 ) ( ρ T ) = 1 ρ ( ρ T ) ,
β = 1 V V T = 1 L 3 L 3 T = 1 L 3 ( L 3 L ) ( L T ) ,
β = 1 L 3 ( 3 L 2 ) ( L T ) = 3 1 L L T = 3 α .
n r ( T ) T = ( n r 2 1 ) ( n r 2 + 2 ) 6 n r ( φ β ) ,
for   β > φ n r ( T ) T < 0 ,
θ r ( T ) = sin 1 ( λ r 2 Λ ( T ) ) .
Λ ( T ) = λ r 2   sin ( θ r ( T ) ) .
λ E d g e ( T ) = 2 n r ( T ) Λ ( T ) .
Λ ( T ) T θ r 1 T θ r 1 Λ ( T ) .
Λ ( T ) = Λ 0 ( 1 + α Δ T ) .
n r ( T ) = n 0 ( 1 1.15 α Δ T ) ,

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