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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 14 — Jul. 9, 2007
  • pp: 8857–8863
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Thermal sensitivity of tellurite and germanate optical fibers

Hongxia Li, Joris Lousteau, William N. MacPherson, Xin Jiang, Henry T. Bookey, James S. Barton, Animesh Jha, and Ajoy K. Kar  »View Author Affiliations


Optics Express, Vol. 15, Issue 14, pp. 8857-8863 (2007)
http://dx.doi.org/10.1364/OE.15.008857


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Abstract

The temperature coefficients of optical phase have been measured at 1536 nm wavelength for short fiber Fabry-Perot cavities of tellurite and germanate glass fibers spliced to silica fiber. The results are consistent with the thermal expansion and thermo-optic coefficients of the bulk glasses.

© 2007 Optical Society of America

1. Introduction

Tellurite and germanate glass fibers have potential for applications both in fundamental research and in optical device fabrication. The high refractive index and optical nonlinearity, resistance to corrosion, low melting temperature and good transmission properties in the visible to infrared region (0.35-6 μm) [1

1. S. Shen, A. Jha, X. Liu, M. Naftaly, K. Bindra, H. J. Bookey, and A. K. Kar, “Tellurite glasses for broadband amplifiers and integrated optics,” J. Am. Ceram. Soc. 85, 1391–1395 (2002). [CrossRef]

] make them promising candidates for many linear and nonlinear optical devices [2–3

2. K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observaton of multiphoton absorption,” Appl. Phys. Lett. 79, 1939–1941(2001). [CrossRef]

]. Applications may include chemical sensing, nonlinear optical signal processing, Raman amplification or mid-infrared continuum generation. In addition, tellurite glasses can be used to fabricate optical amplifiers and lasers [4–5

4. S. Sudo, Optical Fiber Amplifiers-Materials, Devices, and Applications (Artech House, 1997).

], because they are capable of incorporating large concentrations of rare-earth ions [6

6. A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5-mu m emission in Er3+-doped tellurite glasses,” Phys. Rev. B: Condens. Matter. 62, 6215–6227 (2000). [CrossRef]

] with their relatively low phonon energy (750–780 cm-1) compared with other oxide glasses such as silicate (1100 cm-1) and phosphate (1200 cm-1) glasses. These properties also make tellurite glass an ideal candidate for optical fiber and planar waveguide fabrication [7

7. V. V.Ravi Kanth Kumar, A. K. George, J. C. Knight, and P. St. J. Russell, “Tellurite photonic crystal fiber,” Opt. Express. 11, 2641–2645 (2003). [CrossRef] [PubMed]

]. Among these applications, the thermo-optical properties of fibers are important parameters which are necessary to model, design and operate fiber lasers, amplifiers and sensors.

In this paper, we report measurements on fibers drawn from tellurite glass (mol%): 75TeO2-15ZnO-10Na2O and germanate glass (mol%): 56GeO2-31PbO-9Na2O-4Ga2O3. Tellurite fibers were fabricated with 10 μm (singlemode) and 80 μm (multimode) core diameters. The fiber refractive index was measured by low-coherence interferometry and thermal sensitivity of the optical phase was determined using fiber Fabry-Perot (FFP) interferometers formed by splicing tellurite or germanate fibers to singlemode silica fiber. The temperature coefficients normalized to the fiber length L as 1LdT rad m-1 K-1 of these two material fibers have been obtained over a temperature range 280 K to 320 K, and contributions from the thermal expansion, thermal optical effects and electronic polarizability are discussed in section 4.

2. Fabrication of tellurite and germanate fiber Fabry-Perot cavities

2.1 Asymmetric fusion splicing method

Tellurite or germanate glass fibers were manufactured by a standard rod-in-tube technique. The tube was made by rotational casting. Fiber diameter was 130±20 μm with a core diameter of 80±13 μm (multimode) and 10±1.5 μm (single mode) [8

8. D. C. Tran, C. F. Fisher, and H. Sigel, “Fluoride glass performs prepared by a rotational casting process,” Electron. Lett. 18, 657–658 (1982). [CrossRef]

]. Short length FFP cavities were formed by splicing these glass fibers to singlemode silica fiber using an asymmetric fusion splicing technique [9

9. S. Jiang and J. Wang, “Method of fusion splicing silica fiber with low-temperature multi-component glass fiber,” United States Patent. Patent No. US 6,705,771 B2. (Mar. 2004).

]. This technique was necessary since the softening temperatures of tellurite and germanate glasses (approximately 590 K and 750 K respectively) are substantially lower than that of silica (~ 1470 K). This mismatch between the softening temperatures is too great for a conventional splice approach, but the asymmetric configuration, as shown in Fig. 1, is suitable for splicing lower temperature soft glass to silica fiber.

Fig. 1. Configuration for asymmetric fusion splicing method for tellurite fiber.
Fig. 2. Tellurite fiber Fabry-Perot cavity formed by splicing multimode tellurite fiber with single mode silica fiber.

In this technique, the arc electrodes are displaced a distance D along the silica fiber from the gap between the two fibers to be spliced. With a reduced arc power setting this asymmetric configuration does not soften the silica fiber, but sufficient conduction occurs to heat the soft glass fiber above its softening temperature. In this condition, the silica end of the fiber junction is hotter than the tellurite or germanate glass fiber end. This temperature gradient serves to melt the tellurite or germanate glass fiber on contact with the silica fiber thereby making a good splice when the fibers are moved towards one another. The neck formation at the gap also illustrates the evidence for significant mass transport and stress relief in Fig. 2.

2.2 Tellurite and germanate fiber Fabry-Perot cavity fabrication

A manual BFS-50 Single Mode Fusion Splicer was used. The electrode arc was placed over the silica fiber, and displaced from the end face of silica fiber by ~600 μm. The gap between two fibers was 16 μm, which further increased the temperature gradient between two fibers and provided a more uniform heating to the tellurite or germanate fiber. By optimizing the splicing parameters, such as the intial and final arc current of 5 mA, the tellurite or germanate multimode and singlemode fibers were spliced to the silica fiber with a splice loss of less than 0.53 dB, determined by a cut-back technique. Thus the fiber Fabry-Perot cavity was formed between the cleaved end face and the step change in index at the splice, as shown in Fig. 2.

3. Experimental measurement of thermal response

3.1 Fabry-Perot interferometer principle and setup

The experiment setup is shown in Fig. 3, with the tellurite (or germanate) fiber spliced to the silica fiber downlead acting as a low finesse Fabry-Perot interferometer.

Broadband light from an erbium-doped ASE source was coupled into the FFP by a 2×2 single-mode fiber coupler. Part of incident radiation is reflected by the interface between silica and tellurite fiber at the splice, the rest being coupled into the tellurite fiber and a portion reflected by the fiber end face to interfere with the light reflected from the splice. The interferogram is observed using a commercial wavelength meter. Figure 4 shows the broadband source spectrum and interference fringes observed.

Fig. 3. Scheme for thermal response experiment of tellurite fiber Fabry-Perot cavity
Fig. 4. ASE source spectrum showing interference fringes of fiber Fabry-Perot cavity
Fig. 5. Interference fringe shift as temperature is altered
Fig. 6. Comparisons of fringes and FSRs for two FFPs of different lengths

The phase of the interference fringes is given by

φ=2πλ2nl
(1)

and the free spectral range [FSR] is expressed in wavelength terms in Eq. (2)

FSR=Δλ=λ2¯2nl
(2)

where n is the refractive index of the core of tellurite or germanate fiber, λ̄ is the mean wavelength and l is the FFP cavity length. The sensitivity of the phase to temperature is used to determine the thermal response of tellurite and germanate fiber. A fringe shift was observed as the temperature of the fiber was increased (Fig. 5), caused by changes in the fiber’s physical length and core refractive index. Each fringe represents a 2π phase change, thus the phase sensitivity to temperature dφ/dT can be inferred from the slope of the temperature-phase plot.

In the experiment, two tellurite single mode and multimode FFPs were fabricated with lengths of 1.42 mm and 8.36 mm respectively. Their free spectral ranges were measured from the reflection spectra using the wavelength meter, and were found to be 0.410 nm and 0.076 nm respectively, as shown in Fig. 6.

The phase sensitivity to temperature of a fibre Fabry-Perot cavity is given by

12ldT=2πλ(n∙1LdLdT+dndT)=2πλ(nα+β)
(3)

where α=(l/L)(dL/dT) is the thermal expansion coefficient, and β=dn/dT is the thermo-optic coefficient, L is double the FFP length to allow for reflection. When the fiber temperature is changed, the interference fringes shift as a result of the change in length and refractive index. To determine the sensitivity of the phase to temperature, the FFP was placed in the centre of a temperature controlled plate for uniform heating. The plate was heated/cooled via two cascaded Peltier elements driven from a LFI-3500 series temperature controller. An erbium amplified spontaneous emission (ASE) source with a total output power of 30mW and a spectral bandwidth of around 35 nm (as shown in Fig. 4) was used. The temperature was varied from 280 K to 320 K at intervals of 1 K~2 K, and a settling time around 6 minutes was required to allow the plate and FFP to reach thermal equilibrium. At each temperature set-point, the wavelength position of one interference fringe peak was recorded and the temperature was measured at the same time. The fringe shifts were observed and recorded by a WA-7600 wavemeter. Each fringe represents a 2π-phase change, thus phase sensitivity to temperature dφ/dT can be inferred from the slope of the temperature-phase plot.

3.2 Cavity length (FSR) measurement

As well as the direct measurement from the spectrum, the FSR can also be obtained from Eq. (2), provided the FFP length and refractive index are known. We measured the refractive index independently by a low-coherence interferometer [10

10. M.J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre,” Electron.Letts. 35, 63–64 (1999). [CrossRef]

], a schematic of which is given in Fig. 7(a).

Fig. 7. Configuration of low-coherence interferometer: HeNe laser with stabilized frequency for calibration measurement.

In this configuration the fiber was placed in one arm of a scanning Michelson interferometer and illuminated with a low coherence source. The interferometer was balanced when the scanning path length was equivalent to the path length from the front face and back face of the fiber, and the interferograms from front face and back face appear as separate peaks, shown as Fig. 7(b). The separation of the interferograms and a measure of the physical length of the samples gives a value of 2.03±0.03 for the effective refractive index of the tellurite fiber and 1.83±0.03 for germanate fiber. Several samples of each fiber were tested, however we believe that the measurement accuracy is better than the scatter of ±0.03 observed in the refractive index values; this variation may be due to slight changes in the drawing condition as the fiber is fabricated.

The lengths of tellurite FFP cavities were measured by traveling microscope as 1.42 mm and 8.36 mm respectively. From Eq. (2), using the refractive index 2.03, the FSRs of the FFPs 1.42 mm and 8.36 mm in length were calculated to be 0.411 nm and 0.070 nm respectively, which compares well with the measured values of 0.410 nm and 0.076 nm. Hence the measured free spectral ranges of two different length FFPs were consistent with the values expected from independent determination of the core refractive indices. This consistency also verified the validity of the experiment setup and proved that the light was effectively coupled into the core of singlemode tellurite fiber from the silica fiber splice. From Fig. 6, it also can be seen that it is easier to resolve small spectral changes from a shorter FFP cavity for a given spectrometer resolution, and a short length also ensures a uniform heating effect over the whole length of the test fiber.

4. Results and discussions

4.1 Thermal phase sensitivity results of tellurite singlemode and multimode fibers

A 1.42 mm length tellurite singlemode FFP was used to determine the sensitivity of optical phase to temperature. By recording the wavelength shift of one interference fringe peak as a function of temperature, and dividing it by the free spectral range expressed in wavelength, a plot of a temperature-phase was obtained and dφ/dT was inferred from the slope as shown in Fig. 8(a).

Figure 8(a) shows that phase appears to be linearly proportional to the temperature and the temperature sensitivity of the tellurite optical fiber was measured to be dφ/dT=87.2±0.4 rad m-1 K-1 at a central wavelength of 1536 nm. In order to verify that the experiment setup was valid and the result meaningful, we repeated the experiment and obtained confirmatory results from a 1.38 mm long multimode tellurite FFP. Temperature sensitivity was dφ/dT=89.3±0.3 rad m-1 K-1 at central wavelength of 1536 nm, as shown in Fig. 8(b). These two results show good consistency with each other, and both are larger than the value for silica fiber, 99.8 rad m-1 K-1 at 633 nm [11

11. B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, and D. C. Larson, “Optical Fiber Thermal Modulator,” J. Lightwave Tech. 5, 1169–1175(1987). [CrossRef]

], equivalent to 41.1 rad m-1 K-1 at 1536 nm.

Fig. 8. Phase sensitivity to temperatu re of tellurite singlemode (a) and multimode (b) glass optical fiber
Fig. 9. Phase sensitivity to temperature of germanate glass optical fibre

4.2 Thermal phase sensitivity results of germanate fibers

Using the same setup and measurement method, the thermal phase sensitivity of germanate fibers 2.88 mm and 1.28 mm in length were measured to be 112.8± 0.5 rad m-1 K-1 and 116.5±0.4 rad m-1 K-1 respectively at central wavelength of 1536 nm, which also showed good consistency with each other, as displayed in Figs. 9(a) and 9(b).

4.3 Discussions

The phase sensitivity to temperature [Eq. (3)] is determined by two terms: the first factor describes the contribution from the thermal expansion coefficient, which is normally positive for optical fiber glasses, and the second factor is the contribution from the thermo-optic coefficient.

For tellurite glass fiber, the temperature sensitivity of the optical phase was measured to be about 87.2 rad m-1 K-1. Using the value of refractive index n=2.03 measured by the low-coherence interferometer, and the thermal expansion coefficient α=1.86×l0-5 which was measured using a Dynamic Mechanical Analyser, we find that thermal expansion contributes around 154 rad m-1 K-1 to the thermal phase sensitivity of tellurite fiber. This implies that the thermo-optic coefficient β of tellurite glass fibre should be negative, reducing the effect of thermal expansion. In this case the experimental result implies that β=-16.4×10-6K-1.

In order to understand the sign of β, we can use the expression (4) which is given by differentiating the Lorentz-Lorenz equation [12

12. L. Prod’homme, “A new approach to the thermal change in the refractive index of glasses,” Phys. Chem. Glasses. 1,119–122 (1960).

]

dndT=(n21)(n2+2)6n(ζ3α)
(4)

in which ζ is the temperature coefficient of the electronic polarizability, and α is the thermal expansion coefficient. This equation means that dn/dT depends on φ and α which compete with one another to give positive or negative values of thermo-optic coefficient since the term (n2-1)(n2+2)/6n is always positive.

Using Eq. (4), and ζ=40.9×10-5K-1 at 1550 nm wavelength for tellurite glass (75TeO2-20ZnO-5Na2O) [13

13. A. Koike and N. Sugimoto, “Temperature dependences of optical path length in fluorine-doped silica glass and bismuthate glass,” Proc. SPIE 6116, 61160Y1–61160Y8 (2006).

,14

14. S. M. Lima, W. F. Falco, E. S. Bannwart, L. H. C. Andrade, R. C. de Oliveira, J. C. S. Moraes, K. Yukimitu, E. B. Araújo, E. A. Falcão, A. Steimacher, N. G. C. Astrath, A. C. Bento, A. N. Medina, and M .L. Baesso, “Thermo-optical characterization of tellurite glasses by thermal lens, thermal relaxation calorimetry and interferometric methods,” J. Non-Cryst. Solids. 352, 3603–3607 (2006). [CrossRef]

], the thermo-optic coefficient of tellurite glass is calculated to be -23.3×10-6K-1, which agrees reasonably well with the negative value of-16.4×10-6K-1 from our experimental measurement. The difference between these two β values may be due to the slightly different glass compositions being compared, and also due to the changes in the glass structure during fiber drawing and the stresses induced during the preform fabrication processes [15

15. T. Nakai, N. Norimatsu, Y. Noda, O. Shinbori, and Y. Mimura, “Changes in refractive index of fluoride glass fibers during fiber fabrication processes,” Appl.Phys.Lett. 56, 203–205 (1990). [CrossRef]

] from bulk glass to fiber.

For the germanate glass fiber, using Eq. (3) and the value of refractive index n=1.83, thermal expansion coefficient α=10.9×l0-6K-1, and thermo-optic coefficient β=9.0×10-6 K-1 [16

16. S. S. Bayya, G. D. Chin, J. S. Sanghera, and I. D. Aggarwal, “Germanate glass as a window for high energy laser systems,” Opt. Express 14, 11687–11693 (2006). [CrossRef] [PubMed]

], the thermal sensitivity of the optical phase was calculated to be 118.4 rad m-1 K-1, which agrees well with our experimental measurement of 116.5 rad m-1 K-1.

5. Conclusions

Short lengths of tellurite and germanate fiber have been spliced to silica fiber to form fiber Fabry-Perot cavities. Their temperature coefficients of optical phase were measured to be 89.3±0.3 rad m-1 K-1 (tellurite) and 116.5±0.4 rad m-1 K-1 (germanate) at the mean wavelength of 1536 nm in the range 280 K to 320 K. The core refractive indices (2.03±0.3 and 1.83) were consistent with the measured free spectral ranges. The contributions from the thermal expansion coefficient and thermo-optic coefficient were broadly consistent with values for bulk glasses, and verified the negative value of thermo-optic coefficient of tellurite glass fiber which can be attributed to its higher thermal expansion coefficient compared with germanate fiber.

Acknowledgments

The authors wish to thank the UK Engineering and Physical Sciences Research Council grant nos. EP/C515226/1, EP/C515218/1 for support, including a project studentship for H. Li.

References and links

1.

S. Shen, A. Jha, X. Liu, M. Naftaly, K. Bindra, H. J. Bookey, and A. K. Kar, “Tellurite glasses for broadband amplifiers and integrated optics,” J. Am. Ceram. Soc. 85, 1391–1395 (2002). [CrossRef]

2.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observaton of multiphoton absorption,” Appl. Phys. Lett. 79, 1939–1941(2001). [CrossRef]

3.

K. S. Abedin, “Stimulated Brillouin scattering in single-mode tellurite glass fibre,” Opt.Express. 14, 11766–11772 (2006). [CrossRef] [PubMed]

4.

S. Sudo, Optical Fiber Amplifiers-Materials, Devices, and Applications (Artech House, 1997).

5.

M. J. F. Digonnet, Rare Earth Doped Fiber Lasers and Amplifiers (Marcel Dekker, 1993).

6.

A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5-mu m emission in Er3+-doped tellurite glasses,” Phys. Rev. B: Condens. Matter. 62, 6215–6227 (2000). [CrossRef]

7.

V. V.Ravi Kanth Kumar, A. K. George, J. C. Knight, and P. St. J. Russell, “Tellurite photonic crystal fiber,” Opt. Express. 11, 2641–2645 (2003). [CrossRef] [PubMed]

8.

D. C. Tran, C. F. Fisher, and H. Sigel, “Fluoride glass performs prepared by a rotational casting process,” Electron. Lett. 18, 657–658 (1982). [CrossRef]

9.

S. Jiang and J. Wang, “Method of fusion splicing silica fiber with low-temperature multi-component glass fiber,” United States Patent. Patent No. US 6,705,771 B2. (Mar. 2004).

10.

M.J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre,” Electron.Letts. 35, 63–64 (1999). [CrossRef]

11.

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, and D. C. Larson, “Optical Fiber Thermal Modulator,” J. Lightwave Tech. 5, 1169–1175(1987). [CrossRef]

12.

L. Prod’homme, “A new approach to the thermal change in the refractive index of glasses,” Phys. Chem. Glasses. 1,119–122 (1960).

13.

A. Koike and N. Sugimoto, “Temperature dependences of optical path length in fluorine-doped silica glass and bismuthate glass,” Proc. SPIE 6116, 61160Y1–61160Y8 (2006).

14.

S. M. Lima, W. F. Falco, E. S. Bannwart, L. H. C. Andrade, R. C. de Oliveira, J. C. S. Moraes, K. Yukimitu, E. B. Araújo, E. A. Falcão, A. Steimacher, N. G. C. Astrath, A. C. Bento, A. N. Medina, and M .L. Baesso, “Thermo-optical characterization of tellurite glasses by thermal lens, thermal relaxation calorimetry and interferometric methods,” J. Non-Cryst. Solids. 352, 3603–3607 (2006). [CrossRef]

15.

T. Nakai, N. Norimatsu, Y. Noda, O. Shinbori, and Y. Mimura, “Changes in refractive index of fluoride glass fibers during fiber fabrication processes,” Appl.Phys.Lett. 56, 203–205 (1990). [CrossRef]

16.

S. S. Bayya, G. D. Chin, J. S. Sanghera, and I. D. Aggarwal, “Germanate glass as a window for high energy laser systems,” Opt. Express 14, 11687–11693 (2006). [CrossRef] [PubMed]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2300) Fiber optics and optical communications : Fiber measurements

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 16, 2007
Revised Manuscript: June 15, 2007
Manuscript Accepted: June 18, 2007
Published: June 29, 2007

Citation
Hongxia Li, Joris Lousteau, William N. MacPherson, Xin Jiang, Henry T. Bookey, James S. Barton, Animesh Jha, and Ajoy K. Kar, "Thermal sensitivity of tellurite and germanate optical fibers," Opt. Express 15, 8857-8863 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-8857


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References

  1. S. Shen, A. Jha, X. Liu, M. Naftaly, K. Bindra, H. J. Bookey, and A. K. Kar, "Tellurite glasses for broadband amplifiers and integrated optics," J. Am. Ceram. Soc. 85, 1391-1395 (2002). [CrossRef]
  2. K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, "Nonlinear optical properties of chalcogenide glasses: Observaton of multiphoton absorption," Appl. Phys. Lett. 79, 1939-1941(2001). [CrossRef]
  3. K. S. Abedin, "Stimulated Brillouin scattering in single-mode tellurite glass fibre," Opt.Express. 14, 11766-11772 (2006). [CrossRef] [PubMed]
  4. S. Sudo, Optical Fiber Amplifiers-Materials, Devices, and Applications(Artech House, 1997).
  5. M. J. F. Digonnet, Rare Earth Doped Fiber Lasers and Amplifiers (Marcel Dekker, 1993).
  6. A. Jha, S. Shen, and M. Naftaly, "Structural origin of spectral broadening of 1.5-mu m emission in Er3+-doped tellurite glasses," Phys. Rev. B: Condens. Matter. 62, 6215-6227 (2000). [CrossRef]
  7. V. V. Ravi Kanth Kumar, A. K. George, J. C. Knight, and P. St. J. Russell, "Tellurite photonic crystal fiber," Opt. Express. 11, 2641-2645 (2003). [CrossRef] [PubMed]
  8. D. C. Tran, C. F. Fisher, and H. Sigel, "Fluoride glass performs prepared by a rotational casting process," Electron. Lett. 18, 657-658 (1982). [CrossRef]
  9. S. Jiang and J. Wang, "Method of fusion splicing silica fiber with low-temperature multi-component glass fiber," United States Patent. Patent No. US 6,705,771 B2. (Mar. 2004).
  10. M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight and P. St. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron.Letts. 35, 63-64 (1999). [CrossRef]
  11. B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz and D. C. Larson, "Optical Fiber Thermal Modulator," J. Lightwave Tech. 5, 1169-1175(1987). [CrossRef]
  12. L. Prod’homme, "A new approach to the thermal change in the refractive index of glasses," Phys. Chem. Glasses. 1, 119-122 (1960).
  13. A. Koike and N. Sugimoto, "Temperature dependences of optical path length in fluorine-doped silica glass and bismuthate glass," Proc. SPIE 6116, 61160Y1-61160Y8 (2006).
  14. S. M. Lima, W. F. Falco, E. S. Bannwart, L. H. C. Andrade, R. C. de Oliveira, J. C. S. Moraes, K. Yukimitu, E. B. Araújo, E. A. Falcão, A. Steimacher, N. G. C. Astrath, A. C. Bento, A. N. Medina, and M.L. Baesso, "Thermo-optical characterization of tellurite glasses by thermal lens, thermal relaxation calorimetry and interferometric methods," J. Non-Cryst. Solids. 352, 3603-3607 (2006). [CrossRef]
  15. T. Nakai, N. Norimatsu, Y. Noda, O. Shinbori and Y. Mimura, "Changes in refractive index of fluoride glass fibers during fiber fabrication processes," Appl.Phys.Lett. 56, 203-205 (1990). [CrossRef]
  16. S. S. Bayya, G. D. Chin, J. S. Sanghera, and I. D. Aggarwal, "Germanate glass as a window for high energy laser systems," Opt. Express 14, 11687-11693 (2006). [CrossRef] [PubMed]

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