The formation speed of a self-written waveguide structure formed owing to the propagation of surface waves in a photorefractive polymer composite is measured. The formation speed linearly increases with the power of a laser beam. From the measurements of the dynamics of photorefractive grating and the photocurrent output of the polymer, it is revealed that the waveguide structure is formed by a single photorefractive grating, which is identical for the different power levels of the injected pump beam.
©2012 Optical Society of America
Self-guiding optical waves have been observed in several photorefractive (PR) materials including polymers. A laser beam injected into a PR material propagates such that it maintains its beam width within the small dimension of the material, resulting in the self-formation of waveguide structures [1–4]. Such a self-guiding optical wave can transport a high-density optical field and achieve high efficiency pumping of PR materials to enhance their photophysical or photochemical effects.
PR self-guiding waves can be categorized into two types on the basis of their generation mechanism. One is the soliton-like self-trapped wave generated owing to the self-focusing and self-defocusing effects of the laser beam in PR materials [1,2]. The other is considered to be the surface wave originating from the self-bending effects [3,4] of the laser beam injected into PR materials, which is caused by the formation of the PR index grating . PR surface waves can concentrate and propagate along the boundary between a PR medium and a dielectric layer of a lower refractive index, bringing about a strong enhancement of the optical field near the interface. The mechanism of the near-boundary beam propagation can be explained by the reflection of light toward the PR medium-dielectric layer boundary due to the PR index grating which is formed between the incident and the reflected beams near the interface [3,4]. These surface waves are applied to enhance surface second harmonic generation and surface Raman scattering , excite long-range surface plasmon polaritons , and to accelerate the coupling of a PR beam in fiber-like PR crystals . Most studies on PR surface waves have been conducted only in inorganic PR crystals, although some experimental  and theoretical  studies have recently been conducted in PR polymers.
Optical field enhancement by PR surface waves is attributed to the waveguide structure formed near the boundary. The formation time of the waveguide structure is an important parameter for the above mentioned applications. Especially, a shorter formation time of the waveguide structure can be a critical factor for PR beam coupling. One promising way of accelerating the formation time is to enhance the power of the incident laser beam (pump beam), because this increase in power can increase the photoconductivity and consequently the response speed of the PR material. Furthermore, in order to accelerate the surface waveguide formation process, it is important to study the trend of reduction in the build-up time with increasing pump power. Such studies would also aid in the understanding of the formation mechanism of the waveguide structure. However, to the best of our knowledge, the pump power dependence of the build-up time has not been investigated thus far. In this paper, we examine the pump power dependence of the build-up time and the formation speed of PR surface wave-based waveguides in PR polymers. Previously, we studied the waveguide structure formation process in a PR polymer composite, PVK/PDCST/BisCzPro/C60, through a specially designed pumping geometry with prism couplers and asymmetric sandwich cells in which the polymer composite was placed . This unique geometry allowed the separation of propagation areas for a pump beam and a surface wave, so that we could directly observe the formation of the waveguide structure through a charge-coupled device (CCD) camera. With this geometry, we observed a surface wave caused by PR amplified scattering, which was similar to that observed in thin PR crystals . The surface wave propagated along the boundary for 1.7 mm, confining the power to a constant area of ca. 30 μm . In this study, we essentially use the same setup as the one used in our previous study, except for a fast response photodiode and an optical slit to measure the formation speed of the waveguide structure with respect to the pump beam intensity. Further, we use the same PR polymer composite (PVK/PDCST/BisCzPro/C60), because it is an efficient material for generating PR surface waves; the PR surface waves are generated by PR amplified scattering through the orientationally enhanced PR effect . In addition, we characterize the PR dynamics of the material by performing four-wave mixing (FWM) experiments and photocurrent measurements to study the formation mechanism of the waveguide structure.
2. Sample preparation and optical measurements
The molecular structures of the components of the PR polymer composite PVK/PDCST/BisCzPro/C60 are shown in Fig. 1 . A well-dissolved toluene–cyclohexanone solution of PVK(45 wt.%)/PDCST(25 wt.%)/BisCzPro(29.9 wt.%)/C60(0.06 wt.%) was dried in vacuum and hot-pressed between two glass substrates coated with conductive indium tin oxide (ITO) layers. The glass substrates were selected such that their refractive indices were suitable for the experiments. The preparation details of the composite polymer and the conditions for hot pressing are given in .
In order to measure the formation speed of surface wave-based waveguides, we used the asymmetric sample cell and the pumping geometry with a prism coupler same as those used in ; however, the method for detecting the surface waves was not the same. The asymmetric optical cell was composed of two different glass substrates, one with a refractive index almost same as that of the polymer (S2) and another with a refractive index lower than that of the polymer (S1) (Fig. 2 ). The polymer thickness was ca. 100 μm. The prism coupler was placed under substrate S1 to inject a pump beam (p-polarized He-Ne laser; λ = 0.63 μm) into the polymer at a large angle of incidence (54°). The polarization of a pump beam and the direction of an electric field were chosen so as to enhance the beam fanning as shown in Fig. 2. Owing to the above mentioned configuration, the pump beam was able to escape from the polymer layer through the other substrate S2 after exciting the PR medium, and consequently, only the surface waves that were excited in the pumped region could travel along the polymer–substrate (S1) interface. The propagation length of the surface waves (L) was fixed to 2.0 mm, which was the maximum length achievable using the above mentioned setup. Because the formation of the waveguide structure began around the pumped region andgradually advanced toward the end face of the polymer layer , the formation time was evaluated by measuring the power of the light (i.e., surface waves) emitted from the small region in the polymer end face that corresponds to the aperture of the waveguide to be formed. The light power from the aperture area of the waveguide structure was obtained through an optical slit located in the image plane of the objective lens and measured using a photodiode. After the measurement, the waveguide structure formed in the PR medium was removed by irradiating it with an erase beam (λ = 0.63 μm). This procedure was carried out for various pump power levels ranging from 70 μW to 1100 μW, which were measured before coupling the pump beam to the polymer composite through the prism coupler. During the measurements, an electric field of 45 V/μm was applied to the polymer layer. It should be noted that the spacing and the position of the slit in the image plane of the experimental setup were the same for all the measurements.
For the purpose of characterizing the PR dynamics of the composite polymer material, the pump power dependence of the formation time of a PR index grating formed using two beams was investigated (Fig. 3 ). Two writing beams from an s-polarized He-Ne laser (λ = 0.63 μm) were used to irradiate the sample and induce a refractive index grating having a single grating spacing Λ (Λ = 6.3 μm). Here, a symmetric sample cell with the thickness of ca. 50 μm, in which two glass substrates had the same refractive indices, was used. Further, the refractive index values of the glass substrates were close to that of the polymer, and therefore, we considered only the optical reflection loss at air–substrate interfaces in evaluating the pump beam intensity within the polymer. The power level of a diffracted light wave owing to the grating formation at a fixed power level of the writing beams was measured using a p-polarized laser diode emitting a wavelength of 0.81 μm at which negligible absorption was observed in the sample. After this measurement, a single writing beam was used to irradiate the sample for erasing the grating so as to conduct the same measurement for different power levels of the writing beam. The temporal change in the measured power levels was analyzed using a biexponential equation, where τ1 < τ2 (τ1, 2: time constants; m1, 2: prefactors), frequently used for PR polymers . The inverse of the time constant obtained from the equation shows the response speed of a refractive index change induced in the grating by the light excitation of the PR medium. In addition, the pump power dependence of the photocurrent generated by the polymer was measured. For this measurement, a pulsed light beam (pulse width: 0.5 ms) from a laser diode (λ = 0.64 μm) was used as a pumping source. The photocurrent was evaluated by observing the difference between the currents produced with and without sample irradiation using a light beam, through an oscilloscope.
3. Results and discussion
Figure 4 shows temporal changes in the light power collected through the slit. The pump beam was injected at t = 0. For all pump power levels, the output power increases abruptly during the initial stage. Gradually, the output power becomes stable, indicating the gradual formation of the waveguide structure. The inset in Fig. 4 shows a light pattern at the polymerend face projected on the image plane; this light pattern corresponds to the aperture of the formed waveguide (the slit is not located in the image plane in this photo image). During the initial stage, the formation of the waveguide should begin just near the pumped area ; therefore, the light wave should follow an expanding path in the polymer layer to facilitate the transmission of a small amount of power through the slit. The lag period observed at pump power levels below 280 μW should correspond to the time period during which a very small amount of power, under the detection limit of the photodiode, is transmitted through the aperture owing to the considerably expanded path followed by the light wave. Gradually, as the waveguide structure forms toward the end face, the path of the light wave should become narrow so that it can pass through the slit more efficiently. Therefore, the time at which the light power saturates corresponds to the time at which the waveguide formation is completed. Further, the higher the pump power level, the larger the output light power. The saturated output intensities are evaluated as 14, 33, 96, 320, 530 mW/cm2 at pump power levels of 70.5, 140, 280, 560, 1100 μW, respectively, showing a superlinear relation which is attributed to a leaky propagation of surface waves . The output light intensity was calculated from the detected power and the aperture area of the completely formed waveguide structure, i.e., 30 μm × 200 μm (6.0 × 10−5 cm2), already reported in . The output intensity shows the light power transferred through the waveguide and therefore, corresponds to the light intensity required for the formation of a waveguide structure. It is found that thetemporal changes are well fitted by biexponential functions, , where τ1 < τ2 (τ1, 2: time constants; m1, 2: prefactors), as shown in Fig. 4. Figure 5 shows the saturated output intensity dependence of the waveguide formation speed that was calculated using a small time constant value τ1 obtained from Fig. 4. It should be noted that the ratio of the prefactors for the small time constant (m1 / (m1 + m2)) is almost the same (~60%) for all output intensity levels. The formation speed of the waveguide structure has a linear relation with the output intensity. The reason why the extrapolation of the speed to zero of the output intensity shows a certain value is that the waveguide can still grow near the pumped region although it does not reach the polymer end face .
The waveguide structure was formed by surface waves having light intensity ranging from 14 to 530 mW/cm2 as described above. The FWM experiment was performed to study the PR dynamics in the composite material at the corresponding pump power levels. The material, however, was found to exhibit considerable beam fanning owing to the amplified scattering above the writing beam intensity of ca. 60 mW/cm2, resulting in the distortion of the diffraction power trace; therefore, the output power measurement was performed only in the low pump beam intensity region. Figure 6 shows a typical plot of the response speed 1/τ1 versus the pump beam intensity obtained at an external electric field of 40 V/μm, which is comparable to that used in the experiment described above. We can observe that the PR polymer shows a linear relation between the response speed and the pump beam intensity. This result suggests that the polymer composite should follow a simple band model (Kukhtarev model) for PR index changes in which the following relation exists for the response speed,13]. However, in order to apply Eq. (1) to PR polymers, it is provided that the orientation speed of chromophores should be much faster than the buildup time of PR gratings. We have checked that the chromophore orientation was more than three orders of magnitude faster (below 1 ms) from Mach-Zehnder interferometer experiments, which will be reported in detail elsewhere. We find that the photocurrent is linearly proportional to the pump beam intensity up to ca. 250 mW/cm2 in the polymer composite (Fig. 7 ) and confirm that the linearity of the speed of the PR grating index change with the pump beam intensity holds in the high pump beam intensity above 60 mW/cm2; Eq. (1) should hold in the light intensity range achieved by surface waves in thepolymer composite. It should be noted that the response speed shows large difference between the waveguide and the PR grating formations at the similar pump intensity, which should be attributed to the differences in a grating spacing and an optical interaction length .
As described above, the surface wave is generated from a PR index grating which is formed between an incident beam and a reflected beam near the photorefractive-dielectric interface. In our case, owing to the experimental geometry separating the propagation areas for a pump beam and a surface wave (Fig. 2), the incident beam for the grating formation may correspond to the bent beam separated from the pump beam due to PR amplified scattering . Considering the result given in Fig. 5 and obtained by Eq. (1), it is suggested that the waveguide structure in the polymer should be formed by identical PR gratings with single grating spacing, because σph has a linear relation with I, as shown in Fig. 7, so that or Λ should be the same for all the pump beam intensities in Fig. 5. As a result, the identical single PR grating should play a dominant role in shaping the waveguide structure in this experiment. In fact, surface waves in a thin PR inorganic crystal are explained by a single PR grating in which the grating vector is perpendicular to the interface of the PR medium and air . Moreover, the recent theoretical study of surface waves in PR polymer materials  demonstrates the intensity distribution of the optical field in the PR medium, which will further help in conducting a detailed study of the grating structure formed in the PR medium.
The pump power dependence of the formation speed of a waveguide structure formed owing to the propagation of surface waves in the PR polymer composite was investigated. A linear relation was observed between the pump beam intensity and the formation speed of the waveguide structure. From the measurements of the dynamics of PR gratings and photocurrent of the polymer with respect to the pump beam intensity, it is indicated that the PR grating that contributes to the formation of the waveguide structure should be a single grating and identical at different power levels of the pump beam.
This research is partially supported by Iketani Science and Technology Foundation (Grant No. 0231044-A).
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