1. Introduction

Whispering gallery mode (WGM) optical resonators have been extensively studied in a large variety of geometries either for fundamental physics or for practical applications [1]. High quality factor (Q-factor) WGM microcavities store light at resonant frequencies into extremely small volumes for extended periods of time enhancing dramatically the light-matter interaction [2]. This property allows studying non-linear optical phenomena like second harmonic generation [3]. These studies may be performed either on bulk materials, which are shaped into WGM resonators, or on thin layers deposited on passive WGM cavities. For this latter purpose silica microspheres are typically used as they can be easily fabricated with high Q-factors (10⁸) and they can be simply excited with tapered fibers

Resonance positions of coated WGM resonators depend on the size, shape and refractive index of the resonator, on the dielectric properties of the surrounding media, on the thickness and refractive index of the coating. Furthermore, it also depends on thermo-optic effect due to the heat induced by light absorption [4,5]. All-optical switch at low powers has been theoretically proposed in microspheres coated by a Kerr material [6] and very recently demonstrated experimentally [7,8]. The main advantage of using the electronic Kerr effect for all-optical switching of WGM resonators is that large refractive index changes can be easily obtained on fast time scales using intensities well below the damage thresholds of the polymers [9]. For optically induced refractive index changes, a strong third order optical nonlinearity of the involved materials is required. The material refractive index n and the absorption coefficient α depend on the light intensity I in the material according to the equations n = n₀ + n₂I + n₄I² + … (with the nonlinear refractive index n₂ ∝ Re (χ⁽³⁾), n₄ ∝ Re (χ⁽⁵⁾), where χ⁽³⁾ and χ⁽⁵⁾ are the third- and fifth- order nonlinear optical susceptibilities) and α = α₀ + βΙ + ... (with the nonlinear absorption coefficient β ∝ Im(χ⁽³⁾)). All-optical switching for a probe signal I_probe, which is resonant with the microsphere, can be realized using a resonant pump beam I_pump, which affects the coated cavity resonance position by changing the refractive index of the coating in the corresponding wavelength range [10].

If the χ⁽³⁾ and χ⁽⁵⁾ are caused by fast electronic Kerr nonlinearity, then the nonlinear switching is on a picosecond time scale, that is the most desired situation for the optical switching. However, thermal nonlinearities can restrict the use of the hybrid devices because the spectral response is sensitive to the input power of the probe signal as well [11]. In that case, the light-induced changes in the refractive index can be described phenomenologically by n₂ = (dn/dT) T_L, where T_L is the laser-induced change of the temperature of the nonlinear medium, the corresponding switching time being about 10⁻³ – 10⁻⁵ s. In other words, the thermal switching of a nonlinear medium for the case of a standard Ti-sapphire laser should be the same for the pulsed or CW mode operation regime. Besides, an intrinsically weak but highly localized probe beam can also participate in this type of the light-induced WGM switching.

In this work we present our investigation on the all-optical switching of WGM in silica microspheres with two types of coatings, an active one based on a Kerr polymeric material (polyfluorene derivative, PF(o)n) and an inert polymer based on an anionic copolymer made of metacrylic acid and methyl methacrylate (Eudragit® L100) [12]. We also modeled the overlap of the coupled optical field with the polymer layer and verified the role of the probe field experimentally for both polymer coatings.

2. Experimental set-up

The setup was designed to combine high spatial and temporal interaction of the light propagating in the optical microspheres as WGMs and an intense pump pulsed beam which can cause the fast Kerr-like switching of the WGMs of the microsphere.

As a probe beam for the excitation of the WGM a semiconductor external-cavity laser tunable in the spectral range of 1.55 ÷ 1.6 μm and with 300 kHz linewidth (Tunics Plus) was used. The probe laser radiation was coupled in and out of the WGM resonator (WGMR) by means of a home-made tapered fiber. The transmission of the coupler-WGMR system was monitored using an amplified InGaAs photodiode detector connected to an oscilloscope. A Ti:sapphire laser tunable in the NIR region, with the pulse width of 100 fs, mean energy up to 1 W and repetition rate of 80 MHz was used. The radiation of Ti:sapphire was sent to a multimode optical fiber illuminating an hemisphere of the WGMR. The pump intensity on the sample was varied by a set of appropriate color filters.

Figure 1 shows an sketch of the optical pump-and probe set-up and an optical picture of a microspherical WGMR, with a diameter of about 260 μm. To make a polymer coverage, clean microspheres were immersed in different solutions: a) 0.1 mg/ml in toluene PF(o)n and b) 10 mM Eudragit® L100 (Degussa) in ethanol. After 1 minute of dip coating, the microspheres were let to dry until total solvent evaporation. All reactions were performed under a chemical hood. We obtained layers of about 100 nm thickness for PF(o) coatings and of about 50 nm thickness for Eudragit coatings. The Q values were obtained by measuring the resonance linewidth of the WGM modes around 1.55 μm [13]: they were higher than 10⁸ for bare microspheres and higher than 10⁶ after polymer coating. The chosen polyfluorene derivative, PF(o)n, was functionalized at the C9 position of the fluorine ring with two pendant octyl chains for attaining adequate solubility in common organic solvents and mesogenic behavior. It shows a maximum absorption at λ_abs = 379 nm, and the measured n₂ and β coefficient are n₂ = 2 10⁻¹⁰ cm²/W and β = 7 10⁻⁷ cm/W [8,14].

 

Fig. 1 Experimental pump-and-probe set-up. Left hand side inset: optical image of the WGMR. The typical size of the WGMR is of about 260 μm of diameter

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3. Results

The inset of Fig. 2 shows a typical resonance and the corresponding Lorentzian fit from which the Q value can be obtained (Q = ω/δω) for the case of bare microspheres. We obtained a Q factor value of 8 x 10⁷. We have also checked that the quality factor decreases down to 10⁶ after the polymer coating. As the first step, pump-induced effects on the WGM in as-prepared microspheres were studied. No effect was seen, i.e. the WGM resonances were not shifted as the averaged pump power was increased up to 30 mW. Thus we may assume that the Kerr nonlinearity and the thermal nonlinear effects of pure fused silica were negligible for these pump and probe levels.

 

Fig. 2 Frequency center of the WGMR resonance versus pump power. The red line is a guide to the eye. Inset: Zoom of a typical resonance for a bare microsphere, the red line is a Lorentzian fit (R² = 0.97) with a FWHM of about 2.4 MHz

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On the contrary to bare microspheres, we observed that a spectral shift of the resonant WGM in polymer-coated microspheres is achieved. By systematically tuning the wavelength of the pump and the probe, and by changing the polymer material, we have mapped out the interaction of the optical fields with the polymer layer. Figure 3(a) shows the WGM spectrum measured for the probe wavelength of 1600 nm and for two different pump powers for the mode-locked regime of the Ti:Sapphire laser. The Ti:Sapphire was tuned at 775 nm in order to generate the two photon absorption in the PF(o)n coating of the WGMR. As it can be clearly seen, no broadening of the resonance, hysteresis or asymmetries could be observed in the transmission spectra. Thermal nonlinearities can be ruled out.

 

Fig. 3 a) Typical WGM spectra measured for a polymer-coated microsphere for two different pump powers: (black) pump laser off and (blue) 32 mW. λ_pump = 775 nm, λ_probe = 1600 nm. B) Pump power dependence of the detuning of WGM in PF(o)n coated microspheres for mode-locked regime of the Ti-sapphire pump laser: 825 nm (filled squares) and 775 nm (empty circles); and CW at 775 nm (empty downside triangles).

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The results of the pump-and-probe experiments are shown in Fig. 3(b), where a frequency shift of 2 GHz is obtained in pulsed regime for an average pump power of 35 mW at 775 nm for a probe of 1600nm. In order to discriminate the thermal shift from the Kerr shift, we have performed measurements in CW and pulsed regime for the same average pump powers, similarly to a previous work [8]. For the same wavelength and average pump power, we obtained a much lower spectral shift of 250 MHz in the CW regime (Fig. 3(b)). In here, we have also tested the influence of the wavelength of the pump beam. Figure 3(b) also shows a frequency shift of 200 MHz obtained in the mode locked regime for an average pump power up to 21 mW at 825 nm. The detuning is of the same order of magnitude as the CW regime. We have chosen 825 nm as a pump beam because two photon absorption (TPA) is not feasible since λ_{abs = 0} = 425 nm; and because it is also far from the second harmonic of the probe beam. In that case the pump beam acts as a spectrally broad thermal source only.

Figure 4 shows the frequency shift versus pump power for λ_probe = 1558 nm at two different laser regimes for the PF(o) coated WGMR. At λ_pump = 775 nm a clear quadratic dependency can be observed, whereas at λ_pump = 825 nm the dependency is linear and the detuning is of the same order of magnitude as the CW regime, indicating again that in absence of TPA, the pump acts as a thermal source. It can also be observed that in the case of λ_probe = 1558 nm the magnitude of the shift is greater than in the case of λ_probe = 1600 nm, for both regimes, pulsed and CW.

 

Fig. 4 Pump power dependence of the detuning of WGM in PF(o)n coated microspheres for mode-locked regime of the Ti-sapphire pump laser for two different regimes: CW (filled circles), mode locked at 775 nm (empty circles) and mode locked at 825 nm.

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In order to understand the role of the Kerr effect and thermal nonlinearities, we tested the microspheres coated with an inert polymer, Eudragit ®L100. This polymer is an anionic copolymer made of metacrylic acid and methyl methacrylate, which has a negative thermo-optic coefficient. In these experiments, thinner films thicknesses are used because we wanted to have similar Q values [12] for both polymers. As it can be observed in Fig. 5 , the hybrid device shows an almost null red-shift up to 20 mW of pump power. The Eudragit ®L100 hybrid WGMR clearly shows a different behavior than the PF(o) one.

 

Fig. 5 Eudragit coated microspheres for mode-locked regime of the Ti-sapphire pump laser for two different regimes: CW (empty circles) and pulsed (filled squares) The probe wavelength is set at 1558 nm.

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4. Discussion

A specific dedicated software, based on the Mie theory [15], has been developed in the MATLAB environment in order to simulate the WGM - electrical field distribution (inside and outside) in any kind of microresonators with spherical symmetry. Using our software we are also able to investigate the shift (δλ) of the resonant wavelength due to the effect of different kinds (RI change - δn_c) and/or thickness (δh) of the coating layer outside the microsphere.

Figure 6(a) shows the resonance shift induced by a change in the refractive index for a fixed polymer thickness of 100 nm. In Fig. 6(b), we show the variation of the percentage of the radial field inside the coating layer as a function of the layer thickness, evaluated at two different resonance wavelengths (1558 and 1600 nm). The plot shows that there is an increment in the field inside the coating region as the layer becomes thicker. Our results are in agreement with previous studies [4], where it was shown that nanometer-scale changes in the film thickness result in a significant change in the optical field.

 

Fig. 6 a): shift of the resonance wavelength at 1558 nm due to the variation of the refractive index of the coating layer. b): variation of the radial field inside the coating layer as a function of the layer thickness at two different resonance wavelengths (1558 nm, black line, and 1600 nm, red line).

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Two main scenarios of the WGM switching dependencies were observed, namely, nonlinear and linear switching of the resonant modes versus the pump power. In the first case, the light-induced effect is caused by the fast electronic Kerr nonlinearity of the PF(o)n layer, as no such effects were observed for bare microspheres at the same pump power values and was larger for the mode-locked regime of the Ti-sapphire laser, i.e. both terms in the expression n = n₀ + n₂I + n₄I² participate in the process.

In the case of λ_probe = 1558 nm, the confinement of the optical field is greater due to the fulfillment of the resonant condition for the pump beam and of the second harmonic of the probe beams, thus increasing the percentage of the optical field that resides in the polymer layer compared to the longer wavelength. In consequence, the sensitivity of the mode is higher and we observed the appearance of higher-order induced nonlinearities and the corresponding changes in the refractive index under high pump intensity.

In the case of Eudragit coatings, the WGM detuning as a function of the pump power was nearly the same for mode-locked pump laser regime and for a CW one.

7. Conclusion

In conclusion, we have shown experimentally that external pump radiation can result in the spectral tuning of WGM in polymer-coated fused silica microspheres. Depending on the composition of the polymer, its state and the geometry of the light-MS interaction, different regimes of the switching can be attained: fast electronic Kerr switching, as well slow thermal modification of the WGM spectra that exist even for the CW mode of laser operation. Higher order induced nonlinearities were observed when the sensitivity of the mode was greater, due to a better confinement of the field. No effects were observed for bare microspheres.