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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 25 — Dec. 3, 2012
  • pp: 27288–27296
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Planar Bragg grating in bulk Polymethylmethacrylate

M. Rosenberger, G. Koller, S. Belle, B. Schmauss, and R. Hellmann  »View Author Affiliations


Optics Express, Vol. 20, Issue 25, pp. 27288-27296 (2012)
http://dx.doi.org/10.1364/OE.20.027288


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Abstract

We report on a one-step writing process of a planar waveguide including a Bragg grating structure in bulk Polymethylmethacrylate (PMMA). A KrF excimer laser and a phase mask covered by an amplitude mask were used to locally increase the refractive index in PMMA and thereby generate simultaneously the planar waveguide and the Bragg grating. Our results show a reflected wavelength of the Bragg grating of about 1558.5 nm in accordance to the phase mask period. The reflectivity of the grating is about 80%. Initial characteristics of the Bragg grating structure towards humidity are investigated.

© 2012 OSA

1. Introduction

Integrated optical elements continuously attract considerable interest in applied and basic research. Due to miniaturization and modularity especially sensing applications benefit from the advantages of elements such as ring resonators or planar Bragg gratings, which have been successfully implemented for the detection of aromatic compounds, aqueous alcohol solution and biochemical reactions [1

1. A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30(24), 3344–3346 (2005). [CrossRef] [PubMed]

6

6. M. Rosenberger, S. Belle, and R. Hellmann, “Detection of biochemical reaction and DNA hybridization using a planar Bragg grating sensor,” Proc. SPIE 8073, 80730C, 80730C-7 (2011). [CrossRef]

]. Bragg gratings are filters reflecting a small wavelength band according to the Bragg Eq.:
mΔλB=2neffΛB,
(1)
with m describing the order of the Bragg reflection, neff being the effective refractive index and ΛB the period of the Bragg grating [7

7. K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]

]. Current planar Bragg grating sensors are commonly based on silica and are therefore time-consuming to fabricate and cost intensive [8

8. G. Emmerson, S. Watts, C. Gawith, V. Albanis, C. Riziotis, A. Fu, M. Ibsen, R. B. Williams, and P. G. Smith, “Directly UV-written planar channel waveguides containing simultaneously defined Bragg gratings,” Opt. Fiber Comm. Conf. MF52 (2003).

10

10. G. Emmerson, S. Watts, C. Gawith, V. Albanis, M. Ibsen, R. Williams, and P. Smith, “Fabrication of directly UV-written channel waveguides with simultaneously defined integral Bragg gratings,” Electron. Lett. 38(24), 1531–1532 (2002). [CrossRef]

]. Polymer materials provide an alternative due to their low price and good processability and have already been used for the fabrication of optical devices [11

11. L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000). [CrossRef]

]. In addition, several polymers have distinguished material parameters such as a high strain-optical coefficient or a negative thermo-optical coefficient and are therefore promising candidates for sensing elements with divergent characteristics as compared to silica based components [12

12. N. G. Harbach, “Fiber Bragg gratings in polymer optical fibers” Ecole Polytechnique Federale de Lausanne (2008).

15

15. H. Y. Liu, G. D. Peng, and P. L. Chu, “Thermal tuning of polymer optical fiber Bragg gratings,” IEEE Photon. Technol. Lett. 13(8), 824–826 (2001). [CrossRef]

]. As a result, fiber based Bragg gratings (FBG) in polymer optical fibers have been intensively studied during the last decade [16

16. W. Zhang, D. Webb, and G. Peng, “Investigation into time response of polymer fiber Bragg grating based humidity sensors,” J. Lightwave Technol. 30(8), 1090–1096 (2012). [CrossRef]

19

19. I. P. Johnson, W. Yuan, A. Stefani, K. Nielsen, H. K. Rasmussen, L. Khan, D. J. Webb, K. Kalli, and O. Bang, “Optical fibre Bragg grating recorded in TOPAS cyclic olefin copolymer,” Electron. Lett. 47(4), 271–272 (2011). [CrossRef]

]. Among others it has been demonstrated by Stefani et al. that compared to silica FBGs polymer based gratings are advantageous for strain sensing [20

20. A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High sensitivity polymer optical fiber-Bragg-grating-based accelerometer,” IEEE Photon. Technol. Lett. 24(9), 763–765 (2012). [CrossRef]

]. Additionally, a planar sensing element could easily be applied to a work piece with a simplified load transmission and might therefore be well-suited for strain sensing. Moreover, refractive index sensors based on planar Bragg grating structures benefit from the possibilities of various coating techniques to functionalize the grating surface to any specific sensing application. Furthermore, fluidic structures can be integrated on chip, thus enabling the fabrication of lab on chip devices comparable to FBGs integrated on a biochip [21

21. L. Rindorf, P. E. Høiby, J. B. Jensen, L. H. Pedersen, O. Bang, and O. Geschke, “Towards biochips using microstructured optical fiber sensors,” Anal. Bioanal. Chem. 385(8), 1370–1375 (2006). [CrossRef] [PubMed]

].

Here, we report on the fabrication of an integrated planar Bragg grating sensor in bulk PMMA using a KrF-laser in a one-step writing technique. The bulk PMMA acts as the substrate including the optical device requiring no additional production step. The surface of the irradiated PMMA chip was investigated using confocal imaging to verify the period of the Bragg grating. To create a compact sensor element the polymer chip was pigtailed to a single mode fiber and the reflected Bragg wavelength was characterized. The one-step UV writing process leads to a reflectivity of up to 35 dB with regard to the baseline. In addition, the dependence of the Bragg wavelength towards humidity was investigated.

2. Experimental

Commercially available bulk PMMA was used for the fabrication of the planar polymer Bragg grating due to its availability and easy handling but basically because of its photosensitivity which makes this polymer a qualified material for the fabrication of integrated optical elements like waveguides or Bragg gratings [22

22. W. J. Tomlinson, “Photoinduced refractive index increase in Poly(methylmethacrylate) and its applications,” Appl. Phys. Lett. 16(12), 486 (1970). [CrossRef]

27

27. C. Wochnowski, M. Shamseldin, and S. Metev, “UV-laser-assisted degradation of poly(methyl methacrylate),” Polym. Degrad. Stabil. 89(2), 252–264 (2005). [CrossRef]

].

For the UV-writing process a KrF-laser with an emission wavelength of 248 nm (Bragg Star, Coherent) was employed. A specifically designed lens system is used to deliver the laser beam to the writing station providing the required energy density and the appropriate beam geometry. The arrangement of the phase and amplitude mask during the writing process is illustrated in Fig. 1(a)
Fig. 1 (a) Configuration of the amplitude and the phase mask upon the PMMA chip for simultaneous writing of the optical waveguide and the Bragg grating. (b) Schematic drawing of the waveguide and the Bragg grating in bulk PMMA.
. The amplitude mask was positioned right on top of the phase mask (Ibsen Photonics) which itself was placed with the corrugation side in contact with the bulk PMMA. The amplitude mask with the waveguide structure consists of fused silica and is covered with chrome leaving only a 20 mm long and 15 µm wide area for the UV-light to pass allowing to modify the refractive index of PMMA in the defined region. The periodical structure of the phase mask with a period of 1053 nm covers 10 mm of the waveguide structure, thus making it possible to write a waveguide and a Bragg grating simultaneously. A schematic illustration of the configuration of the waveguide and the Bragg grating in bulk PMMA is depicted in Fig. 1(b). The fabrication of Bragg gratings in bulk PMMA in a single writing step was performed in 14x17 mm2 PMMA chips. These chips were laser cut out of a 300x300 mm2 PMMA plate with a thickness of 1.1 mm using a 200W CO2 laser (Synrad F200). Afterwards the PMMA samples were cleaned with isopropanol. The writing process was performed with a pulse duration of 15 ns and a spatial coherence larger than 1500 µm. The Bragg grating structure and the waveguide were manufactured using a fluence of 8 mJ/cm2, 3000 pulses and a repetition rate of 200 Hz. After the writing process the PMMA chips were stored in an oven for 24h at a temperature of 60°C accelerating the chemical reaction triggered by the UV radiation [26

26. M. Koerdt and F. Vollertsen, “Fabrication of an integrated optical Mach–Zehnder interferometer based on refractive index modification of polymethylmethacrylate by krypton fluoride excimer laser radiation,” Appl. Surf. Sci. 257(12), 5237–5240 (2011). [CrossRef]

].

Subsequently, the front and back surface of the PMMA chip were polished down to 0.3 µm minimizing coupling losses. The topographical structure of the waveguide surface and the Bragg grating were characterized and measured by confocal imaging (Fries Research & Technology) with a nominal lateral resolution of 0.3 μm and a nominal vertical resolution of 1 nm, respectively. The characterization of the reflected Bragg wavelength λB and the spectral shift of λB due to humidity were performed with a Braggmeter (Stratophase) having a spectral resolution of 1pm at a sampling rate of 2Hz. The measurement setup is depicted in Fig. 2
Fig. 2 Experimental setup for analyzing the reflectance of polymer planar Bragg gratings.
. The basic setup of the Braggmeter consists of a tunable laser diode emitting in the spectral range of 1510-1590 nm, a circulator and a photo diode. Light is launched into the polymer Bragg grating by the laser diode and the back reflected light is detected by a photo diode. The planar polymer Bragg grating chip was connected with a single mode fiber. The alignment was done by active fiber-chip-coupling with micro-mechanical actuators (Thorlabs) and was optimized by simultaneously monitoring the reflected spectrum and the transmitted intensity at the back of the chip. Subsequently, the fiber was connected to the PMMA chip applying UV curable glue. Beyond the reflected spectrum the transmission of a planar Bragg grating is recorded using a multi-mode fiber. To analyze the mode field distribution a near infrared laser (Toptica) was used emitting a wavelength of 830 nm. The transmitted light was evaluated using an objective lens and a CCD camera (Coherent).

To assess the vertical position of the generated waveguide in the PMMA chip Bromonaphtalene (Sigma Aldrich) was used as an index matching liquid (IML) having a higher refractive index of 1.62 as compared to PMMA (1.48). Dropped on the surface of the structure, light is supposed to couple out of a potential surface waveguide while a buried waveguide would not be affected.

To evaluate the behavior of the polymer Bragg gratings against relative humidity (RH), the polymer chips including Bragg grating was stored in an environmental chamber (Weiss Umwelttechnik) at a constant temperature of 25°C while the relative humidity (RH) was raised successively. The environmental chamber exhibits an accuracy of ± 2% RH and ± 1°C. The relative humidity was increased in 10% steps over a time of one hour from 35% to 85% RH while each step was maintained for another hour to ensure stable conditions. During the whole measurement the reflected wavelength was monitored online with a sampling rate of 2Hz.

3. Results and discussion

After the UV one-step writing process no significant and visible ablation of the PMMA can be observed. However, after the subsequent heating process the waveguide structure gets visible due to the compaction of the exposed regions [32

32. M. Koerdt, Herstellung von integiert-optischen Sensorstrukturen in Polymersubstraten basierend auf Brechzahländerungen durch ultraviolette Laserstrahlung (BIAS Verlag Bremen, 2011).

]. The width of the observable waveguide amounts to 26 µm, i.e. 11 µm wider than the structure of the amplitude mask. This deviation can be attributed to diffraction as the amplitude mask is not in direct contact with the PMMA but is located on top of the phase mask. After cleaning the PMMA chip with Isopropanol a 200 nm deep trench is measurable in the waveguide region. The PMMA being additionally irradiated through the phase mask shows a periodical grating structure at the surface (Fig. 3
Fig. 3 Planar Bragg grating structure in a PMMA chip written with a single writing step using UV radiation. (a) confocal image of the PMMA surface; (b) topography of the grating located on top of the PMMA chip.
). Bright light microscopy and confocal imaging reveal a grating period of 1063 nm averaged over 20 periods and a depth of 100 nm for this grating structure. Taking into account the lateral resolution of the used confocal microscope this grating period is in agreement with the period of the phase mask [33

33. C. Wochnowski, M. Abuelqomsan, W. Pieper, K. Meteva, S. Metev, G. Wenke, and F. Vollertsen, “UV-laser assisted fabrication of Bragg sensor components in a planar polymer chip,” Sens. Actua. A. 120(1), 44–52 (2005). [CrossRef]

]. This grating extends uniformly over the entire region that is irradiated through the phase mask. No further significant and visible degradation of the PMMA is found.

The investigation of the mode field emitted on the back side of the PMMA chip in transmission reveals an intensity distribution (Fig. 4
Fig. 4 Mode field distribution measured at the back side of a planar Bragg grating.
), indicating that as a result of the UV radiation the refractive index of PMMA was raised and therefore light is propagating in an integrated waveguide in bulk PMMA.

Figure 5
Fig. 5 (a) Reflected spectrum of a polymer planar Bragg grating showing a Bragg wavelength at 1558.5 nm and a flat baseline.(b) Transmission spectrum of a polymer Bragg grating measured with a multi-mode fiber showing a Bragg notch at 1558.5 nm.
shows the reflected spectrum of the Bragg grating in planar PMMA with a FWHM of 240 pm and a peak wavelength of 1558.5 nm. The relative reflected intensity is about 35 dB in reference to the flat baseline.

Using a refractive index of 1.48 for PMMA, as determined using the Sellmeier Eq., and the nominal grating period of 1053 nm, we calculate a Bragg wavelength of 1558.5 nm indicating a second order Bragg grating [34

34. T. Ishigure, E. Nihei, and Y. Koike, “Optimum refractive-index profile of the graded-index polymer optical fiber, toward gigabit data links,” Appl. Opt. 35(12), 2048–2053 (1996). [CrossRef] [PubMed]

]. This value is in excellent agreement with the measured spectrum. Moreover, this result is in agreement with the grating structures generated in two consecutive writing steps [33

33. C. Wochnowski, M. Abuelqomsan, W. Pieper, K. Meteva, S. Metev, G. Wenke, and F. Vollertsen, “UV-laser assisted fabrication of Bragg sensor components in a planar polymer chip,” Sens. Actua. A. 120(1), 44–52 (2005). [CrossRef]

]. The transmission spectrum of the polymer Bragg grating is shown in Fig. 6(b)
Fig. 6 Reflection of a planar Bragg grating in PMMA with and without index matching liquid (IML).
. At a wavelength of 1558.5 nm a transmission dip Td of about 7 dB is detectable which corresponds to a reflectivity R of 80% according to the formula [35

35. Raman Kashyap, Fiber Bragg Gratings (Academic Press, 2010).

].

R=110Td/10,
(2)

In order to determine whether the UV irradiation leads to a near surface or a buried waveguide, we employed bromonaphthalene as an index matching liquid on the PMMA surface, having a refractive index of 1.62. Please note that the confocal imaging revealed a periodical structure on top of the PMMA (Fig. 3). In case of a near surface waveguide light would couple out of the waveguide once bromonaphthalene covers the waveguide region resulting in a decrease of the reflected intensity [36

36. C. Wochnowski, M. T. Kouamo, W. Pieper, K. Meteva, S. Metev, G. Wenke, and F. Vollertsen, “Fabrication of a planar polymeric deformation Bragg sensor component by excimer laser radiation,” IEEE J. Sens. 6(2), 331–339 (2006). [CrossRef]

]. Figure 6 shows the reflection of the planar Bragg grating structure with and without the index matching liquid. It can be clearly seen that the liquid does neither result in any decrease of the reflected intensity nor in a spectral shift of the Bragg wavelength. Hence, we conclude that both the waveguide and the grating being responsible for the reflection are buried in the planar polymer chip.

As PMMA can assimilate moisture causing both expansion and a change of the refractive index [12

12. N. G. Harbach, “Fiber Bragg gratings in polymer optical fibers” Ecole Polytechnique Federale de Lausanne (2008).

,14

14. C. Zhang, W. Zhang, D. J. Webb, and G. D. Peng, “Optical fibre temperature and humidity sensor,” Electron. Lett. 46(9), 643–644 (2010). [CrossRef]

,15

15. H. Y. Liu, G. D. Peng, and P. L. Chu, “Thermal tuning of polymer optical fiber Bragg gratings,” IEEE Photon. Technol. Lett. 13(8), 824–826 (2001). [CrossRef]

], we investigated the relationship between the reflected Bragg wavelength and the relative humidity.

Figure 7
Fig. 7 Relationship between the reflected Bragg wavelength and the relative humidity.
reveals the Bragg wavelength response as a result of an increasing relative humidity. It shows both the preset and the actually measured humidity in the climate chamber as well as the detected spectral shift Δλ of the Bragg wavelength. In this case, the planar waveguide structure including Bragg grating can be referred to as being a polymer planar Bragg grating humidity sensor (PPBG sensor).

It is evident from the results shown in Fig. 7 that the signal of the PPBG sensor (the Bragg wavelength) follows the changes of the relative humidity. At higher relative humidity above 75% RH the climate chamber requires a longer time to accomplish the set climate conditions. Even under these conditions the PPBG sensor follows precisely the actual relative humidity in the chamber and therefore reveals a slower increase of the Bragg wavelength. While the intensity of the reflected wavelength remains almost constant during these experiments, λB changes almost linearly over the entire range of RH at a rate of 42 ± 2 pm/%RH (see inset of Fig. 7). This spectral shift can be attributed to the absorption of water in PMMA causing changes in the effective refractive index as well as of the grating pitch. The rate of 42 ± 2 pm/%RH corresponds well to recently reported values for Bragg gratings in polymer optical fibers which showed a sensitivity of 35 pm/%RH [12

12. N. G. Harbach, “Fiber Bragg gratings in polymer optical fibers” Ecole Polytechnique Federale de Lausanne (2008).

15

15. H. Y. Liu, G. D. Peng, and P. L. Chu, “Thermal tuning of polymer optical fiber Bragg gratings,” IEEE Photon. Technol. Lett. 13(8), 824–826 (2001). [CrossRef]

]. As the temperature deviation of the climate chamber is only ± 0.2 K, we do not register any cross sensitivity against temperature during our measurements. Please note that in case sensitivity towards relative humidity is objectionable, polymer optical fiber Bragg gratings in other polymers such as TOPAS exhibit a significantly lower humidity sensitivity [37

37. W. Yuan, L. Khan, D. J. Webb, K. Kalli, H. K. Rasmussen, A. Stefani, and O. Bang, “Humidity insensitive TOPAS polymer fiber Bragg grating sensor,” Opt. Express 19(20), 19731–19739 (2011). [CrossRef] [PubMed]

].

Since waveguide and Bragg grating are buried in bulk PMMA it takes some time for the sensor signal before going into saturation due to the fact that the adsorption process depends on the material thickness which has already been shown using polymer optical fibers with different diameters [15

15. H. Y. Liu, G. D. Peng, and P. L. Chu, “Thermal tuning of polymer optical fiber Bragg gratings,” IEEE Photon. Technol. Lett. 13(8), 824–826 (2001). [CrossRef]

].

4. Conclusion

We have demonstrated the fabrication of a buried waveguide including a planar Bragg grating in bulk PMMA. To the best of our knowledge, these structures are written for the first time in a one-step writing process with an afore unreported short process time of 15 seconds. This one-step writing process provides a fast and cost effective method for the fabrication of planar polymer Bragg grating sensors (PPBG sensor). Butt coupling of a single mode fiber yields a portable sensor chip. Using this sensor structure, we determine a reflected wavelength of 1558.5 nm with a relative reflected intensity of up to 35 dB in reference to the baseline and a reflectivity of 80%. Measuring the transmission spectrum reveals the same Bragg wavelength proving a continuous integrated waveguide structure throughout the PMMA chip. Initial investigations towards a potential sensor application have been presented with the focus on relative humidity. The planar polymer Bragg grating sensor shows a sensitivity towards relative humidity of about 42 ± 2 pm/%RH over a range from 35% to 85% RH.

Acknowledgment

This work was supported by the German Federal Ministry of Education and Research (BMBF) under the Project Number 17PNT016.

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M. Rosenberger, S. Belle, and R. Hellmann, “Detection of biochemical reaction and DNA hybridization using a planar Bragg grating sensor,” Proc. SPIE 8073, 80730C, 80730C-7 (2011). [CrossRef]

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K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]

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G. Emmerson, S. Watts, C. Gawith, V. Albanis, C. Riziotis, A. Fu, M. Ibsen, R. B. Williams, and P. G. Smith, “Directly UV-written planar channel waveguides containing simultaneously defined Bragg gratings,” Opt. Fiber Comm. Conf. MF52 (2003).

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G. Emmerson, C. Gawith, S. Watts, R. Williams, P. Smith, S. McMeekin, J. Bonar, and R. Laming, “All-UV-written integrated planar Bragg gratings and channel waveguides through single-step direct grating writing,” Proc Optoelectron, IEEE. 151(2), 119–122 (2004). [CrossRef]

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L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6(1), 54–68 (2000). [CrossRef]

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N. G. Harbach, “Fiber Bragg gratings in polymer optical fibers” Ecole Polytechnique Federale de Lausanne (2008).

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C. Zhang, X. Chen, D. J. Webb, and G.-D. Peng, “Water detection in jet fuel using a polymer optical fibre Bragg grating,” Proc. SPIE 7503, 750380, 750380-4 (2009). [CrossRef]

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C. Zhang, W. Zhang, D. J. Webb, and G. D. Peng, “Optical fibre temperature and humidity sensor,” Electron. Lett. 46(9), 643–644 (2010). [CrossRef]

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H. Y. Liu, G. D. Peng, and P. L. Chu, “Thermal tuning of polymer optical fiber Bragg gratings,” IEEE Photon. Technol. Lett. 13(8), 824–826 (2001). [CrossRef]

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W. Zhang, D. Webb, and G. Peng, “Investigation into time response of polymer fiber Bragg grating based humidity sensors,” J. Lightwave Technol. 30(8), 1090–1096 (2012). [CrossRef]

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W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. K. Nielsen, S. Andresen, O. B. Sørensen, K. S. Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber Bragg gratings,” Opt. Commun. 284(1), 176–182 (2011). [CrossRef]

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20.

A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High sensitivity polymer optical fiber-Bragg-grating-based accelerometer,” IEEE Photon. Technol. Lett. 24(9), 763–765 (2012). [CrossRef]

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W. J. Tomlinson, “Photoinduced refractive index increase in Poly(methylmethacrylate) and its applications,” Appl. Phys. Lett. 16(12), 486 (1970). [CrossRef]

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33.

C. Wochnowski, M. Abuelqomsan, W. Pieper, K. Meteva, S. Metev, G. Wenke, and F. Vollertsen, “UV-laser assisted fabrication of Bragg sensor components in a planar polymer chip,” Sens. Actua. A. 120(1), 44–52 (2005). [CrossRef]

34.

T. Ishigure, E. Nihei, and Y. Koike, “Optimum refractive-index profile of the graded-index polymer optical fiber, toward gigabit data links,” Appl. Opt. 35(12), 2048–2053 (1996). [CrossRef] [PubMed]

35.

Raman Kashyap, Fiber Bragg Gratings (Academic Press, 2010).

36.

C. Wochnowski, M. T. Kouamo, W. Pieper, K. Meteva, S. Metev, G. Wenke, and F. Vollertsen, “Fabrication of a planar polymeric deformation Bragg sensor component by excimer laser radiation,” IEEE J. Sens. 6(2), 331–339 (2006). [CrossRef]

37.

W. Yuan, L. Khan, D. J. Webb, K. Kalli, H. K. Rasmussen, A. Stefani, and O. Bang, “Humidity insensitive TOPAS polymer fiber Bragg grating sensor,” Opt. Express 19(20), 19731–19739 (2011). [CrossRef] [PubMed]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(160.5470) Materials : Polymers
(220.4610) Optical design and fabrication : Optical fabrication

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 22, 2012
Revised Manuscript: October 18, 2012
Manuscript Accepted: October 19, 2012
Published: November 20, 2012

Citation
M. Rosenberger, G. Koller, S. Belle, B. Schmauss, and R. Hellmann, "Planar Bragg grating in bulk Polymethylmethacrylate," Opt. Express 20, 27288-27296 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-25-27288


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