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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2739–2747
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Broadening of the light self-trapping due to thermal defocusing in PQ-PMMA polymeric layers

E. Tolstik, O. Kashin, V. Matusevich, and R. Kowarschik  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2739-2747 (2011)
http://dx.doi.org/10.1364/OE.19.002739


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Abstract

The channel formation by the self-trapping of a (1 + 1)D beam in polymeric media based on a polymethylmethacrylate (PMMA) matrix containing phenanthrenequinone (PQ) molecules is predicted theoretically and observed experimentally for the first time. Particular attention is paid to the effect of thermal beam expansion, which in conjunction with the photorefractive nonlinearity of the medium results in the possibility to control optically the geometrical parameters of the generated channel.

© 2011 OSA

1. Introduction

Among the optical effects, which are intensively investigated in recent decades, is the phenomenon of self-action of light beams in nonlinear optical media, e.g. self-trapping and self-focusing of optical beams, self-phase modulation of optical pulses etc. It allows to realize the direct optical conversion of images and to control their space-time light structure [1

1. G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000). [CrossRef]

3

3. G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999). [CrossRef] [PubMed]

]. The practical realization of self-trapping depends to a large extent on the choice of a suitable photosensitive material. The splicing of damaged waveguides, the confinement of light beams to guarantee conditions for a steady-state information transfer and the fabrication of a variety of different optical splitters and switching systems for optical signals require the formation of waveguide channels that conserve their properties for a long time without a supporting radiation source. These tasks, as well as constantly emerging new problems in fiber-optical technologies determine the need for further research and the development of new photosensitive materials for the generation of optical waveguide structures. Owing to their high nonlinear optical susceptibilities and the ability to maintain diffracted structures for long periods of time photopolymers became attractive media in this field [4

4. J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001). [CrossRef]

8

8. A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996). [CrossRef] [PubMed]

].

The presented work demonstrates for the first time to our knowledge good results of the straight self-trapping channel generation in polymethylmethacrylate (PMMA) with distributed phenanthrenequinone (PQ). The self-trapping process occurs due to the compensation of the natural beam diffraction by the positive change of the refractive index that leads to a stable cross-section of the propagating laser beam to travel within the media by self-focusing. Polymers based on PMMA with addition of PQ molecules show a light-induced change of the refractive index up to 10−3 [9

9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

,10

10. U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006). [CrossRef]

]. The photoaddition of PQ molecules to the polymeric matrix leads to the generation of the photoproduct in the illuminated area changing thereby the refractive index. The holographic relaxation technique was used previously in order to study the optical properties of the PQ-PMMA material [9

9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

15

15. V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

].

The results of the numerical simulation of self-trapping in PQ-PMMA polymeric layers due to the nonlinear properties of the medium were shown in our theoretical work [16

16. O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009). [CrossRef]

]. The experimental confirmation of the formation of a straight waveguide channeling as a result of Ar-laser beam self-action in PQ-containing media is demonstrated in this paper. The numerical model of the description of the laser beam propagation in PQ-PMMA is improved by taking the heat conduction equation into consideration. The acquired effect of the self-trapping broadening is caused by the PQ-PMMA properties of nonlinear focusing and thermal defocusing of the light beams. Moreover, the dependence of the generated channel cross-section on the input beam power is shown.

2. Experimental self-trapping in PQ-PMMA

The polymeric layers were prepared by the solution of PQ and PMMA, which was previously purified from the monomer, in the chloroform. The solution was filtrated after mixing in order to decrease the quantity of light-scattering centers. The glass substrates were coated with the liquid solution of the various ingredients to form polymeric films of the necessary dimensions and shape. The mechanical rigidity that is required for waveguiding application was obtained by subsequent drying. For a slow removal of the solvent, the samples were placed in a Petri dish for 20 hours at temperature of 100°C, which is below the glass transition temperature of the PMMA (105°C). The obtained samples have good optical quality and high thicknesses (up to 200 µm - 400 µm) [9

9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

11

11. V. Matusevich, A. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Holographic volume absorption grating in glass-like polymer recording material,” Opt. Express 16(3), 1552–1558 (2008). [CrossRef] [PubMed]

].

The generation of the refractive index change in the PQ-PMMA occurs as a result of the modulation of optical parameters in the course of the photochemical hydrogen reduction by the redox cycling agent PQ with the formation of a semiquinone radical [9

9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

,10

10. U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006). [CrossRef]

]. Its subsequent addition to a polymer macromolecule forms a stable photoproduct. This mechanism can be provided in real time by using a laser source which irradiates in the absorption band of PQ (480-540 nm).

Experiments for the self-trapping generation were carried out for the samples with a layer thickness of 400 µm and a PQ concentration of 2.5-3 mol.%. To generate a waveguiding structure in the polymer an Ar-laser was used (Fig. 1(a)
Fig. 1 Schematic setup for formation of a self-trapped channel using Ar-laser illumination and a microobjective (a); Self-trapping in a PQ-PMMA polymeric layer, top view (b).
). The laser power required to form a channel was found experimentally to be in the range of milliwatts. That is an order of magnitude higher than the values obtained previously from our theoretical model [16

16. O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009). [CrossRef]

]. The laser beam was focused on the front surface of the polymeric layer using a microscope objective with a focal length of 16 mm. The PQ-PMMA sample was placed on a mechanical stage which allows to control the position of the input beam. The beam diameter at its waist behind the microobjective was 16 µm (FWHM). A CCD-camera was used to detect the self-trapping formation.

The polymeric layers have a yellow colour with an absorption band up to about 540 nm. Under Ar-laser illumination (514.5 nm) the colour changed from yellow to almost transparent, which means that all photosensitive PQ molecules join the polymeric matrix with subsequent formation of stable photoproducts. The self-induced waveguiding structure in the PQ-PMMA medium is shown in Fig. 1(b).

The experiment was carried out with several identical samples. The illumination of the samples with a power of 8 mW was made for periods of 60 min. The generation of the planar straight channel induced by the incident light itself was observed in the PQ-PMMA layer during an irradiation period of 12 min (Figs. 2(a)-(e)
Fig. 2 Experimental self-trapping formation in the PQ-PMMA layer by Ar-laser illumination during 12 min (a)-(e); and Ar-laser-light propagation in a pure PMMA medium through the microobjective with a magnification factor of 10 and a focal length of 16 mm (f) [laser power is 8 mW, PQ-concentration is 2.5 mol%, layer thickness is 400 µm].
). The photoattachment of PQ molecules to the polymeric matrix resulted in a necessarily nonlinear change of the refractive index by which a stable waveguiding structure was produced under the Ar-laser illumination. The formed channel has a length up to 4-5 mm after an exposure time of 6-10 min. By further illumination (15-60 min) the distortion of the self-trapping channel started. This happens due to the absorption of PQ molecules in the peripheral areas of the channel, leading to a multiple broadening of the channel and to a loss of the self-trapping property.

In spite of the small input beam diameter (16 µm) the width of the achieved channel was about 500 µm (Figs. 2(b)-(e)). The additional investigation of the Plexiglas PMMA material without PQ molecules under Ar-light illumination revealed a high divergence of the propagating beam (Fig. 2(f)). This led us to suggest that as a result of the high input power at the beam focus the polymeric material starts warming up due to the absorption with the consequently large increase of the light scattering.

The activation of the warming-up effect in the PQ-PMMA film results in the formation of a thermal lens and increases the divergence of the laser beam, starting just after beginning of the illumination. Normally Plexiglas is almost transparent for Ar-laser radiation, being subjected to the natural diffraction of light. According to the parameters of the laser and the microobjective, the light divergence in the PMMA layer should be equal to 10-12 mrad. The thermal lens formed in the layer increases the light divergence even under the influence of minor absorption (α a tens of cm−1) [11

11. V. Matusevich, A. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Holographic volume absorption grating in glass-like polymer recording material,” Opt. Express 16(3), 1552–1558 (2008). [CrossRef] [PubMed]

]. However, the high intensities in the focal region (I1kW/cm2) lead to a broader distribution of light (Fig. 2(f)).

The injection of the light sensitive PQ components into the polymeric matrix causes the photoproduct formation and generates a straight channel (Figs. 2(a)-(e)). The process of fast heating appears at the point of maximum input intensity till the PQ-phototransformation is completed and proceeds within the layer. The formation of the self-channeling with a large cross section can be associated with two competitive mechanisms: thermal beam expansion together with the variation of the photoinduced nonlinear refractive index.

Thereby, the experimental results indicate the possibility of the formation of straight waveguides in PQ-PMMA media. The broadening of the channel can be connected with the activation of the thermal defocusing in the material due to the high input power. This defocusing effect is compensated by the effect of nonlinear self-focusing of the light beam generating a waveguide structure. This thermal expansion of self-trapping can be included in our numerical model by taking the heat conduction equation into consideration.

3. Mechanism of light-channel broadening

The special characteristic of the light beam distribution in polymeric materials is a nonlinear change of the absorption coefficient during the PQ-photoattachment process. Thus, along with the variation of the refractive index caused by the photoreaction of PQ (ΔnPQ), a thermal change of the refractive index (ΔnT) is closely connected with this and has to be taken into account for any simulation. Under steady-state conditions the influence of the thermal effect on the change of the refractive index can be calculated as [17

17. F. Kan, and F. Gan, Laser Materials (World Scientific Pub. Co. Inc., 1995).

]
ΔnT=αItCρnT,
(1)
where α is the absorption coefficient of the medium, I is the beam intensity with the Gaussian distribution [I=I0exp[(x2/x02)]], t is the effective interaction time, Cρ is the heat capacity of the unit volume, called also the volumetric heat capacity, and n/T is the thermooptical coefficient. Since the medium is normally hotter on the beam axis, compared with the outer regions, a transverse gradient of the refractive index appears, called the thermooptical effect, which is quantified by the coefficient n/T [18

18. S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968). [CrossRef]

]. Index changes can be caused by the temperature dependence of the refractive index and by the thermally induced mechanical stress (photoelastic effect). Both mechanisms can lead to bulging of the end faces of the gain medium, which leads to the effect of thermal lensing. In a medium withn/T<0, there is a defocusing effect caused by the temperature, which eliminates the process of self-focusing. In rare cases, if n/T>0, one can observe the reverse situation, i.e. a heating of the medium generates self-focusing.

The variation of the refractive index due to warming can be essentially higher at a certain area in the polymeric layer and can compensate accordingly the Δn- change caused by photoattaching. The position of this area corresponds to the maximum light intensity and results in a channel widening. To investigate the complete change of the refractive index in the PQ-PMMA material during the self-trapping generation, we have included the mechanism of the thermal nonlinearity in the numerical simulations.

The change of the temperature (ΔT) in the illuminated area can be calculated using the heat conduction equation along the two orthogonal coordinates x and z [19

19. H. S. Carslaw, and J. C. Jaeger, Conduction of heat in solids, 2nd ed. (Oxford Univ. Press, 1959).

]
ΔTtaT(2ΔTx2+2ΔTz2)+bΔT=αICρ,
(2)
where b is the coefficient of the heat transfer and Cρ=cTρ is the volumetric heat capacity with the specific heat capacity cT and the density ρ of the material.

The solution of Eq. (2) provides the value of ΔT (temperature difference between the waveguide structure and the surrounding material), which can be calculated by separation of the linear (Eq. (3)) and nonlinear (Eq. (4)) parts of Eq. (2) applying the split-step method [20

20. T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984). [CrossRef]

]

ΔTLt=aT(2ΔTx2+2ΔTz2)bΔT,
(3)
ΔTNLt=αICρ.
(4)

The change of the refractive index due to the heating (ΔnT) results in the thermal defocusing of the beam and can be calculated by
ΔnT=nTΔT,
(5)
where n/T=1.3104K-1 is the thermooptical coefficient of PMMA [21

21. Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006). [CrossRef]

]. Because of the negative value of the thermooptical coefficient the thermal change of the refractive index leads to an absolute magnitude with opposite sign as compared with the magnitude of ΔnPQ. This results in a thermal defocusing of the light beam with the corresponding channel broadening.

The change of the refractive index due to the photoreaction of PQ determines by the difference between the refraction coefficients of the photoproduct (RHPQR) and phenanthrenequinone (RPQ). Based on the values for the variations of their concentrations (photoproduct CHPQR(x,z,t) and PQ molecules CPQ(x,z,t)) and using the Lorentz-Lorenz formula, the following expression for the change of the refractive index is obtained [9

9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

,22

22. M. Born, and E. Wolf, Principles of Optics (Oxford, Pergamon, 1968).

]

ΔnPQ=(n2+2)26n[RHPQRCHPQR(x,z,t)RPQCPQ(x,z,t)].
(6)

Thus, the sum of the two contributions to the change of the refractive index (ΔnΣ) is decreasing according to

ΔnΣ=ΔnPQ+ΔnT.
(7)

4. Numerical simulation of channel broadening

The calculations are based on the PQ-PMMA parameters used in the experiment presented above: laser input power 8 mW, input-beam radius x0=9.6 µm (at 1/e mean), initial PQ concentration 2.5 mol.%, n=1.5, λ0=514.5 nm, ΔR=1.4cm3/mol [9

9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

]. The absorption coefficient α varies in a range of about tens of cm1. For the solution of Eq. (3) the thermal diffusivity coefficient of aT=107m2/s and a heat capacity of Cρ=1.7106J/(m3K) were used in correspondence with the parameters of the PQ-PMMA material [21

21. Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006). [CrossRef]

,23

23. K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004). [CrossRef] [PubMed]

,24

24. M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005). [CrossRef]

]. The magnitude of the heat transfer coefficient was found to be inversely proportional to the velocity of the heat propagation in the polymeric medium. In the numerical calculations b=0.2s1 was chosen for a polymeric layer thickness of 400 µm [19

19. H. S. Carslaw, and J. C. Jaeger, Conduction of heat in solids, 2nd ed. (Oxford Univ. Press, 1959).

,23

23. K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004). [CrossRef] [PubMed]

].

The obtained changes of the refractive indexΔnTdue to thermal defocusing in dependence on the illumination time for different layer lengths are presented in Fig. 3
Fig. 3 Distribution of the thermal changes of the refractive index in dependence on the illumination time for different lengths of the polymeric layer [1.5 mm, 3 mm, 4.5 mm and 6 mm].
. As a point of ΔnT-measurements the coordinate x in the middle of the beam width is taken. The decrease of the change of the thermal refractive index reaches values of ΔnT=1102. The interplay of thermal defocusing and nonlinear properties of the medium causes a channel widening at this point. The negative value of ΔnT substantially exceeds the positive change of the refractive index ΔnPQ104 at the local point where the laser has a higher intensity [16

16. O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009). [CrossRef]

]. The superposition of both processes at this point leads in total to a negative change of the refractive index. Since the values of the thermal refractive index change are presented as local magnitudes at a particular time, they are decreasing in time due to the heat transfer. At the point, where the radiation is already absorbed, ΔnT becomes equal to zero. Then the sum change of the refractive index ΔnΣdetermines by the positive values of the ΔnPQ due to the photoreaction.

Thus, the mechanism of channel formation and broadening can be described like a heat wave propagating together with a light wave through the polymer (Fig. 5
Fig. 5 Evolution of the spreading of temperature in the polymeric layer during an illumination period of 300 s (Media 1).
, (Media 1)). At the point of maximum intensity the formation of a thermal lens occurs with subsequent activation of the thermal defocusing effect. The main broadening of the channel is observed during the first 15 s after starting the illumination process. At the place of the maximal beam intensity the temperature of the polymeric layer achieves a peak value of about 100°C (for an input beam power of 8 mW) due to the thermal absorption of the PQ-PMMA material. After finishing the PQ-photoaddition process the layer becomes transparent to the laser light and the illuminated area cools down. At this time the warming-up process is stopped. The area of the maximal temperature, a heat wave, moves forward together with the propagating light beam with a velocity determined by the speed of the reaction of the PQ-photoattaching process to the polymeric matrix.

5. Control of the width of the generated waveguide

In consideration of the dependence of the thermal defocusing on the beam power, we examined the possibility of the self-trapping formation using specific cross-section parameters of the channel. A numerical simulation of the channel formation provides a possibility to control the development of the channel width and allows producing waveguiding structures of desired dimensions.

Figure 6
Fig. 6 Simulation of the refractive-index profiles for input powers of 2 mW (dotted line) and 8 mW (solid line).
demonstrates the results of the numerical calculation of the profile of the refractive-index change for input powers of 8 mW and 2 mW. The diameter of the channel is reduced by a factor of about 2, if the power decreases by a factor of 4.

6. Conclusion

The possibility of the (1 + 1)D beam self-trapping formation in PQ-PMMA polymeric layers due to the photoinduced nonlinear refractive index modulation and the effect of thermal beam expansion was shown experimentally and theoretically for the first time. The recording of self-trapping structures implemented in layers of purified PMMA with a high PQ concentration has been performed under the action of an argon laser of 8 mW input power. A comparison of the propagation of light beams in pure PMMA and in PMMA containing sufficient amounts of PQ molecules confirmed the decisive role, which the photoattachment process of the light-sensitive PQ molecules to the polymeric matrix plays for the formation of the waveguide channel. A width of the channel in the polymer of 500 µm was achieved with an incident beam of 16 µm diameter and remained constant along a distance of 4-5 mm.

It was found that the formation of the waveguide is strongly influenced by heating of the medium, which results in an additional thermal defocusing of the light beam. The theoretical modeling of the light propagation under conditions of the mutual action of the processes of PQ-photoattachment and thermal nonlinearity has confirmed the validity of the proposed approach. Heating produces a negative change of the refractive index in the photopolymer, which leads to the reduction of the resulting Δn and to a channel widening. The formation of a self-trapped channel with a length of 6 mm was observed by applying Ar-laser illumination for a duration of 5-6 min. This is in good agreement with the experimental results.

Moreover, a new method for controlling the waveguide cross-sections by changing the ratio of the two competing mechanisms of the nonlinear refractive-index variation (namely the formation of the photoproducts and the heating of the medium while varying the power of the light beam) was proposed. The experimental results were confirmed by the theoretical modeling of the self-trapping process. With a diameter of the channel much larger than the diameter of the laser beam waist in the focal plane the following simple relation has been derived: the square of the ratio of the diameters of the two beams is equal to the ratio of their powers. By using this relation it is possible to generate channels with well defined and suitable cross-sections.

References and links

1.

G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000). [CrossRef]

2.

Y. S. Kivshar, and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (San Diego, Academic Press, 2003).

3.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999). [CrossRef] [PubMed]

4.

J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001). [CrossRef]

5.

B. L. Booth, “Photopolymer material for holography,” Appl. Opt. 14(3), 593–601 (1975). [CrossRef] [PubMed]

6.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004). [CrossRef] [PubMed]

7.

Y. Ichihashi, P. Henzi, M. Bruendel, J. Mohr, and D. G. Rabus, “Polymer waveguides from alicyclic methacrylate copolymer fabricated by deep-UV exposure,” Opt. Lett. 32(4), 379–381 (2007). [CrossRef] [PubMed]

8.

A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996). [CrossRef] [PubMed]

9.

U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]

10.

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006). [CrossRef]

11.

V. Matusevich, A. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Holographic volume absorption grating in glass-like polymer recording material,” Opt. Express 16(3), 1552–1558 (2008). [CrossRef] [PubMed]

12.

L. P. Krul, V. Matusevich, D. Hoff, R. Kowarschik, Y. I. Matusevich, G. V. Butovskaya, and E. A. Murashko, “Modified polymethylmethacrylate as a base for thermostable optical recording media,” Opt. Express 15(14), 8543–8549 (2007). [CrossRef] [PubMed]

13.

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009). [CrossRef]

14.

E. Tolstik, O. Kashin, A. Matusevich, V. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Non-local response in glass-like polymer storage materials based on poly (methylmethacrylate) with distributed phenanthrenequinone,” Opt. Express 16(15), 11253–11258 (2008). [CrossRef] [PubMed]

15.

V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

16.

O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009). [CrossRef]

17.

F. Kan, and F. Gan, Laser Materials (World Scientific Pub. Co. Inc., 1995).

18.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968). [CrossRef]

19.

H. S. Carslaw, and J. C. Jaeger, Conduction of heat in solids, 2nd ed. (Oxford Univ. Press, 1959).

20.

T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984). [CrossRef]

21.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006). [CrossRef]

22.

M. Born, and E. Wolf, Principles of Optics (Oxford, Pergamon, 1968).

23.

K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004). [CrossRef] [PubMed]

24.

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005). [CrossRef]

OCIS Codes
(160.2900) Materials : Optical storage materials
(160.5470) Materials : Polymers
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4870) Nonlinear optics : Photothermal effects

ToC Category:
Materials

History
Original Manuscript: October 26, 2010
Revised Manuscript: December 13, 2010
Manuscript Accepted: December 22, 2010
Published: January 28, 2011

Citation
E. Tolstik, O. Kashin, V. Matusevich, and R. Kowarschik, "Broadening of the light self-trapping due to thermal defocusing in PQ-PMMA polymeric layers," Opt. Express 19, 2739-2747 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2739


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References

  1. G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000). [CrossRef]
  2. Y. S. Kivshar, and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (San Diego, Academic Press, 2003).
  3. G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999). [CrossRef] [PubMed]
  4. J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001). [CrossRef]
  5. B. L. Booth, “Photopolymer material for holography,” Appl. Opt. 14(3), 593–601 (1975). [CrossRef] [PubMed]
  6. K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004). [CrossRef] [PubMed]
  7. Y. Ichihashi, P. Henzi, M. Bruendel, J. Mohr, and D. G. Rabus, “Polymer waveguides from alicyclic methacrylate copolymer fabricated by deep-UV exposure,” Opt. Lett. 32(4), 379–381 (2007). [CrossRef] [PubMed]
  8. A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996). [CrossRef] [PubMed]
  9. U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008). [CrossRef]
  10. U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006). [CrossRef]
  11. V. Matusevich, A. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Holographic volume absorption grating in glass-like polymer recording material,” Opt. Express 16(3), 1552–1558 (2008). [CrossRef] [PubMed]
  12. L. P. Krul, V. Matusevich, D. Hoff, R. Kowarschik, Y. I. Matusevich, G. V. Butovskaya, and E. A. Murashko, “Modified polymethylmethacrylate as a base for thermostable optical recording media,” Opt. Express 15(14), 8543–8549 (2007). [CrossRef] [PubMed]
  13. E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009). [CrossRef]
  14. E. Tolstik, O. Kashin, A. Matusevich, V. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Non-local response in glass-like polymer storage materials based on poly (methylmethacrylate) with distributed phenanthrenequinone,” Opt. Express 16(15), 11253–11258 (2008). [CrossRef] [PubMed]
  15. V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).
  16. O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009). [CrossRef]
  17. F. Kan, and F. Gan, Laser Materials (World Scientific Pub. Co. Inc., 1995).
  18. S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968). [CrossRef]
  19. H. S. Carslaw, and J. C. Jaeger, Conduction of heat in solids, 2nd ed. (Oxford Univ. Press, 1959).
  20. T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984). [CrossRef]
  21. Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006). [CrossRef]
  22. M. Born, and E. Wolf, Principles of Optics (Oxford, Pergamon, 1968).
  23. K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004). [CrossRef] [PubMed]
  24. M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005). [CrossRef]

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