1. Introduction

Nonlinear polymer films are expected to offer a number of advantages over inorganic crystals, including their relatively large second-order susceptibility, fast response time and simple processing techniques. It has been more than 20 years since the first electric field poled second-order nonlinear polymers were reported. During this period numerous investigations have been published to study the physical and chemical properties of second-order nonlinear polymers and their potential applications in electrooptics and frequency-doubling devices[1,2]. Photobleaching is an attractive method for fabricating optical waveguide in polymeric materials[3–7]. The variation in optical nonlinearity and chemical stability of NLO polymer during the photobleaching is an important characteristic for its application in waveguide devices. In this paper, a real-time scheme is proposed to test the performance of different dyed polymeric systems during photobleaching process through monitoring the SHG intensity enhanced by SPR. By comparing the SPR enhanced SHG intensity generated from the NLO polymer with that from calibrated quartz crystal, the NLO coefficient d₃₃ is quantitatively determined in our experiment. The merit of the method is that the changes of both the refractive index and thickness of the NLO poled-polymer film during the photobleaching have little effect on the SHG intensity enhanced by the SPR and that the derived mathematical expression for determining the NLO coefficient is much simplified. The results show that photobleaching process has less effect on the second-order nonlinearity of a poled cross-linked polymer than that of a poled side-chain polymer.

2. Theory

Attenuated total reflection geometry utilized in our experiments is shown in Fig. 1, where medium 1 is a glass prism with refractive index n ₁ for the fundamental frequency ω and refractive index N ₁ for the harmonic frequency 2ω; medium 2 is a metal film with thickness d, the complex dielectric constants of the metal film at frequency ω and 2ω are ε₂(ω) and ε₂(2ω), respectively; medium 3 is an NLO poled-polymer film with the nonlinear coefficient d₃₃ ; medium 4 is air. A p-polarized laser beam with intensity I(ω) is incident on prism-metal film interface. At the SPR incidence angle a surface plasmon resonance is excited at the interface between the metal and the polymer, the intensities I(2ω) of second harmonic generation enhanced by SPR is measured against the incidence angle under scanning. According to the theoretical analyses by Sipe et al in [8], it is recognized that the SHG signals from the silver film are resulting from a bulk current within the film and two surface currents which could be characterized as two dipole sheets situated in the immediate vicinity of the prism-metal interface and metal-polymer interface, respectively, which is illustrated in Fig. 1(b). Nonlinear interaction between the excited SPR and the medium can cause a strong peak of the SHG, up to four orders of SHG magnitude above the background in the direction determined by wave vector matching condition n ₁ sinθ₀ 2N ₁ sinθ_r, where θ₀ and θ_r are the incidence angle of fundamental field and reflection angle of second-harmonic generation, respectively. From the hydrodynamic theory of electron gas, the SPR-enhanced SHG intensity for total internal reflection at the SPR incidence angle can be expressed as[8–10]

where R is the linear reflectivity of the incident fundamental beam for the ATR configuration, $A_s^{*}$ is the ratio $E_{1-}^{2\omega }$/$E_{1+}^{\omega }$ resulted from the NLO poled polymer, where $E_{1+}^{\omega }$ is the downward-propagating incident field and $E_{1-}^{2\omega }$ is the upward-propagating second-harmonic field. The ratios $E_{1+}^{\omega }$ resulted from the bulk metal and two dipole sheets are much smaller than $A_s^{*}$ and can be neglected. $A_s^{*}$ is given in the following formation [8]:

where $a=\frac{n_1\sin {\theta }_0}{n_3}\frac{t_{23}{t}_{12}{e}^{i\left(w_2-w_3\right)d}}{1-r_{23}{r}_{21}{e}^{2i{w}_{2}d}},b=-\frac{\sqrt{n_3^2-n_1^2{\sin }^2{\theta }_0}}{n_3}\frac{t_{23}{t}_{12}{e}^{i\left(w_2-w_3\right)d}}{1-r_{23}{r}_{21}{e}^{2i{w}_{2}d}},w_i=k_0\sqrt{n_{\mathrm{i}}^2-n_1^2{\sin }^2{\theta }_0},r_{\mathit{ij}}$ and t_ij are the Fresnel coefficients at ω for reflection and transmission, k ₀ is the wave vector in vacuum at ω. The corresponding capital letters indicate these quantities evaluate at 2ω. According to the simulated results as shown in Fig. 2, the coupling efficiency (1-R) in Eq. (1) at SPR incidence angle remains unchanged as the refractive index of the NLO polymer changes from 1.413 to 1.643 with fixed thickness of silver film. The absorption of polymer remains almost unchanged at fundamental frequency which is far away from the absorption region, with the result that the photo-induced absorption has little effect on R in Eq. (1). The penetration depth of SPR in the NLO polymer is so thin that the thickness change of polymer film during bleaching can be ignored. Therefore, in our case, the changes in refractive index, absorption and thickness of polymer film during the photobleaching process have little effect on the change of SHG intensity enhanced by SPR. The changes of NLO coefficient d₃₃ of polymer film is the main causes for the change of the SPR-enhanced SHG intensity during the bleaching process. Moreover, the prism configuration seperates the fundamental wave and the SHG light by prism dispersion so that SHG beam can be observed easily[11].

 

Fig. 1. ATR configuration. (a) The schematic drawing for sample; (b) Theoretical mode.

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From Eq. (1), by comparing the SPR-enhanced SHG intensity generated from the interface of metal-polymer with that from interface of metal-quartz, the formulation to calculate the nonlinear coefficient d₃₃ of polymer film is derived to be

where I _j(2ω) and I_j (ω) (j = p, q) represent the SPR-enhanced SHG intensity and incident intensity of fundamental wave, respectively; the superscript and subscript p and q in Eq. (3) represent the parameters of polymer and quartz, respectively; the coefficient B can be expressed as

where R_p and R_q are the linear reflectivity of the incident fundamental beam at the SPR incidence angle. The contour diagram of the coefficient B which indicates the relation between n _ω and Δ_n = n _ω-n _2ω for different kinds of NLO polymers is shown in Fig. 3. In it, the refractive indices of the prism for the fundamental frequency ω and for the harmonic frequency 2ω are assumed to be known. Then the NLO coefficient d₃₃ can be determined with Eq. (3) since the coefficient B for different kinds of polymer can be found directly in Fig. 3.

 

Fig. 2. Simulated SPR curves showing the reflectivity R versus angle of incident at 1.064μm; the thickness of silver film is 45nm; the refractive index the NLO polymer decreases from 1.643 to 1.413. The refractive index of prism at 1.064μm is 1.775.

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Fig. 3. The contour of coefficient B for different kinds of NLO polymer with refractive index of n _ω and Δn; Ag film, 45nm; at the SPR incidence angle, R_p=1% ; prism, ZF7; λ =1.064μm.

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3. Experiment

In our experiment, two samples with different kinds of EO materials were fabricated. For the first sample, (NCO)₂DR-19 was synthesized from nonlinear chromophore disperse red(DR-19) and toluene diisocyanate, then a cross-linked polyurethane was prepared by mixing (NCO)₂DR-19 with trimer of toluene diisocyanate and triehtanolamine at 80°C, in which the concentration of DR-19 is 30wt%[12]. The molecular structure of (NCO)2DR-19 and absorption spectrum of polyurethane are shown in Fig. 4. The polymer material (before bleached: B=0.595, n _ω=1.591, n _2ω=1.665; after bleached B=0.696, n _ω=1.583, n _2ω=1.655; λ=1.064μm) in N,N-dimethyl formamide solution was spin-coated on the base of a glass prism (ZF7, n ₁=1.775, λ=1.064μm) which was precoated with a 45-nm-thin silver layer(ε₂(ω)=-52.4+i3.74, ε₂(2ω)=-10.6+i0.91) by sputtering technique. The thickness of the polymer film was 3.4μm. The refractive index and the thickness of polymer film were measured with the conventional m-line method. Thickness and complex dielectric constant of the metal film was measured by the double wavelength method[13]. In order to remove the centrosymmetric structure of polymer, the film was corona-poled in the air by an applied electric voltage of 4.3kV at 160°C for 25 minutes with interelectrode distance being 2cm, and cooled down to room temperature with the field still applied.

 

Fig. 4. The chemical structure of (NCO)₂DR-19 and absorption spectrum of polyurethane

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The second sample was fabricated with the same procedures as the first one. The EO material is a side-chain polymer PEI which was prepared from a chromophore-containing dianhydride based on 2, 2-[4-[(4-hitrophenhl)-azo]phenyl] iminobisethanol, benzophenone-3, 3 , 4, 4 -tetracarboxylic dianhydride, and 4, 4 -diamino-3,3 -dimethyl diphenyl-methane[14]. The chemical structure and absorption spectrum of PEI is shown in Fig. 5. The thickness of the polymer film (before bleached: B=0.242, n _ω=1.658, n2ω=1.752; after bleached: B=0.251, n _ω=1.649, n _2ω=1.744) was 3.5μm. The poling temperature was 170oC and poling voltage was about 4.2kV.

 

Fig. 5. The chemical structure and absorption spectrum of PEI (x = 30)

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An X-cut quartz reference sample was prepared for measuring NLO coefficient d₃₃ of the two kinds of poled polymer. A silver film of thickness 45nm was deposited on the surface of the X-cut quartz flat to serve as the light-coupling layer. The quartz flat with Ag film was located closely to the base of the prism, with the index matching liquids(Certified Refractive Index Liqids, Series M, 1.755±0.0005; Structure Probe, Inc) filled in the gap between the prism and Ag film.

The experiment setup is shown in Fig. 6. A p-polarized Q-switched Nd:YAG laser (pulse width 16ns, λ=1.064μm, maximum output energy, 300mJ; maximum repeat frequency, 10Hz) was used as a fundamental light. The sample was placed on a θ/2θ goniometer to adjust the incident angle to the SPR incidence angle accurately. An UV light with power of 140mW/cm² was placed in front of the prism base with the distance about 5cm. The relative spectral power distribution of UV light is show at the upper right corner of Fig. 6. The incident laser intensity was carefully controlled to avoid the damage of the thin metal film. Output signal from the sample was transmitted through an absorption cell and a filter to block the fundamental wave. The SHG light was observed in the reflective direction to be at an angle of 4° with the reflected fundamental laser, and collected by a photomultiplier tube, then amplified and averaged in a boxcar integrator. Output signal from the boxcar was treated by a computer and visualized on an oscillograph.

 

Fig. 6. The experimental set-up. The upper right corner is the relative spectral power distribution of UV light.

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Fig. 7. Time dependence of SHG intensity for two kinds of NLO polymer.

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The SHG intensities of the poled-polymer samples were monitored during the whole bleaching process. For each measurement, only slight adjustment of the previously fixed incident angle was made to reach the SPR incident angle by θ/2θ goniometer while the light path remained unchanged because the refractive index change of polymer is small through bleaching and the reception area of photomultiplier tube is relatively large. As shown in Fig. 7, the SHG intensities in the bleaching procedure had undergone first a slow decay and then a fast decay for both poled cross-linked polymer and poled side-chain polymer. For the first 30 minutes, the SHG intensity decreased very slowly. This is due to the fact that in a strongly absorbing material the photons responsible for the bleaching reaction cannot penetrate deeply into the film, thus converting only chromophores near the surface. Once these molecules are bleached their absorptivity decreases and the light can penetrate deeper inside the film. The SHG intensity decreased very quickly from 30 to 100 minutes. 125 minutes later from the beginning, the SHG intensity almost kept its value invariable. After the bleaching process, it was found that the SHG intensity of poled cross-linked polymer still remained 72% of the initial value whereas the SHG intensity of poled side-chain polymer only remained 25% of the initial value. The predominant bleaching process is an irreversible decomposition of the NLOmoieties accompanied by a broadening of the polymer molecular weight distribution[3], which cause the decrease of SHG intensity enhanced by SPR. The different ranges of change in SHG intensities show that the poled cross-linked polymer is more stable than the poled side-chain polymer in photobleaching.

The main reason that causes the decreasing of the SHG intensities of poled-polymer samples is the degradation of NLO coefficient d₃₃ . By comparing the SHG intensities of the two poled-polymer samples with that of the X-cut quartz reference sample, the NLO coefficient d₃₃ of the two kinds of poled-polymer films before and after the bleaching process were calculated from Eq. (3) and calibrated by X-cut quartz reference sample(d₁₁ =0.42pm/V, which was measured using conventional SHG measurement technique by comparing with standard quartz before silver film was deposited). The results are listed in Table 1.

Table 1. The NLO coefficient d₃₃ of two kinds of poled-polymer before and after photobleaching process.

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4. Conclusion

In conclusion, we demonstrate a new scheme to monitor the degradation of the SPR-enhanced SHG intensity of NLO poled-polymer during photobleaching, and the NLO coefficient d₃₃ of poled-polymer is determined by comparing the SPR-enhanced SHG intensity with that from calibrated quartz. The advantages of this technique lie in its simplicity and ignoring the effect of the changes in refractive index and thickness of poled-polymer film on the SHG intensity. First of all, compared with the conventional technique[15–17], since the SHG beam based on SPR radiates in the reflected direction to be at an angle of 4° with the reflected fundamental laser light as a result of the prism dispersion, the fundamental wave can be blocked and the SHG beam can be observed easily. Second, the derived mathematical expression in this paper for determining the NLO coefficient is much simplified than those in [16,17], in which only two parameters(the coefficient B, the ratio $\sqrt{\frac{I_p\left(2\omega \right)}{I_q\left(2\omega \right)}}\frac{I_q\left(\omega \right)}{I_p\left(\omega \right)}$) are needed for the measurement. Third, the SHG intensity is independent of the changes in refractive index and thickness of poled-polymer film during the bleaching process. For most of NLO polymer, the contour diagram shown in this paper can be used directly(ZF7 prism). Before the coefficient B is obtained, four parameters (n _ω and n _2ω of prism and NLO polymer, respectively) should be achieved in advance.