1. Introduction

Optical microresonators supporting whispering gallery modes (WGMs) have attracted great interest in recent years because of their applications in many various fields of science and technology [1–5]. For example, they are used to test fundamental physical concepts, to achieve high-performance sensors, to do nonlinear optics at weak power levels, to fabricate low-threshold on-chip microlasers, and to perform as filters and modulators in optical communication networks [6–8]. A waveguide coupled WGM resonator is a widely used configuration in aforementioned applications. It has been shown that a waveguide coupled WGM resonator system can be operated in three distinct regimes — under-coupling, over-coupling or critical coupling, by controlling the balance between coupling loss and other losses experienced by optical modes in the resonator.

An important figure-of-merit (FOM), quality factor Q, quantifies the loss of a resonator through the expression Q = ω_c/γ with ω_c and γ denoting the resonance frequency and the energy decay rate, respectively. The energy decay rate γ mainly comprises of two main parts, the coupling loss associated with energy exchange between the waveguide and the resonator and the intrinsic loss which is limited by the resonator itself, such as losses coming from material absorption, scattering, and radiation, etc. Scattering losses can be minimized, if not completely eliminated, by adopting higher fabrication standards to ensure optically smooth surfaces and homogenous surface and refractive index throughout the resonator structure. Similarly, radiation losses can be minimized by appropriate design of the shape and the size of the resonators. Coupling losses can be controlled by adjusting the distance between the waveguide and the resonator.

Operating the waveguide-coupled resonator system in one of the three distinct regimes — under-coupling, over-coupling or critical coupling depends on how the coupling losses compare with other losses (i.e., intrinsic losses) experienced by the optical modes. Recent studies have shown that by doping the resonator with an optical gain providing material such as rare earth ions during the fabrication process helps to lower the losses in the system [4, 9–20]. Such resonators are called as active resonators, and they have higher Q factors and narrower linewidths than their passive (no gain dopant) counterparts. Active resonators have been used as optical amplifiers [21–26], optical sensors [3,13,27], and optical filters [28]. The characterization of doped active resonator, such as laser threshold, laser behavior above threshold, evolution of transmission spectra below lasing threshold (i.e., loss compensation) have been extensively studied both theoretically and experimentally [4,15,19,29–31].

Although widely used in active resonators, rare-earth dopants introduce additional steps and cost to the fabrication process; require pump laser suitable for the used rare-earth-ion dopant (i.e., each rare-earth ion has its own specific pumping and emission band); lowers the quality factor in the absence of the pump laser (i.e., if one wants to switch on and off the pump for specific applications); and more importantly they are suitable for loss compensation only for specific bands of the spectrum where they have emission. For example, while erbium ions are very good in compensating losses in the 1550 nm band with a pump at 980 nm or 1450 nm bands, they cannot provide gain for compensation in the visible spectrum which is suitable to operate resonator-based sensors in aqueous environments. In addition, most of the rare-earth ions are not biocompatible, and are not suitable for bio-particle sensing. Thus, a dopant-free loss compensation and Q -enhancement process is highly desirable.

The requirement of dopant-free system implies that we are limited with the optical activity (Raman scattering, photoluminescence, fluorescence, etc.) of the material used for fabricating the resonator. Recent research has shown that Raman process can be efficiently realized in most of the common materials used to fabricate WGM resonator. For example, WGM Raman lasing with very low thresholds has been demonstrated in silica, silicon, and CaF₂ WGM resonators [4, 11,32–41]. Below laser threshold, these microcavities serve as amplifiers when the waveguide-resonator system is set in over-coupling region [42,43]. Recently use of Raman gain and Raman lasing in a WGM resonator has been shown to provide a very high-performance platform for nanoparticle detection with single particle resolution in various bands of the spectrum [44,45].

In this paper, we report the use of Raman gain in silica microresonators for loss-compensation in the presence of modesplitting, and on-demand adjustment of cavity-waveguide coupling to control effective cavity loss and coupling regime. We demonstrate the evolution of the transmission spectra of a WGM microresonator in different coupling regimes, linewidth narrowing (i.e., Q enhancement) and signal amplification controlled by the Raman gain. The change of effective loss due to provided Raman gain affect the coupling regime, which depends on the balance between the coupling loss and other losses in the resonator. As a result we can simply control the light transmission in the system by injecting pump light. This provides a practical and effective method to change the coupling condition and minimum transmission, especially for systems where the coupling gap is fixed after fabrication, such as monolithically integrated microcavity systems (silicon microring resonators, etc.) and microresonators encapsulated in polymers together with their fiber couplers [46]. Moreover, compared to the previous Raman loss method, our scheme makes it possible to tune the system in different coupling regimes and releases it from the side effect of decreased Q factor [47].

2. Theoretical model and simulations

For a fiber-taper coupled active resonator, we consider the round-trip energy gain provided by the Raman process and denote it by ξ. The effective loss κ_eff is defined as κ_eff = κ₀−ξ. The time evolution of the intracavity electric field is given by [23,29,49]

Equation (2) shows that the transmission will go through three different regimes as the coupling loss characterized by κ_ex increases. First, its the under-coupling regime in which T decreases as κ_ex increases. When κ_ex is equal to κ_eff, the system reaches critical coupling point at which the transmission becomes zero. After the system passes the critical point, it enters over-coupling regime in which further increase of κ_ex is accompanied by the increase of the T.

It has been demonstrated that ultra-high Q microresonators are very sensitive to scattering centers in the mode volume of the resonator [50–52], which can induce the splitting of a resonance mode into two. In the presence of Raman gain, the evolution of the intracavity field amplitudes a_CW and a_CCW of the clockwise (CW) and counterclockwise (CCW) modes are described as

We use the expression in Eq. (5) to perform curve fitting to the experimentally-obtained transmission spectra, and to extract the values of the relevant parameters κ₀, κ_ex, g and Γ_R. The value of κ₀ that defines the intrinsic loss is extracted from experimentally-obtained transmission spectra when the system is in the deep under-coupling regime. In this regime, κ_ex ≪ κ₀, thus the linewidth of the resonances measured will provide a good estimation of κ₀. Similarly, the amount of mode splitting g and the scatterer-induced loss Γ_R can also be obtained from curve fitting to the experimentally obtained transmission spectra in the deep undercoupling regime. As the system is moved from deep under-coupling to under-coupling, critical or over-coupling regime, κ_ex becomes comparable or even higher than κ₀, thus to estimate κ_ex at other coupling conditions we assume the value of κ₀ doesn’t change (i.e., the value got in the deep under-coupling region). Subsequently, with the information of κ₀, and κ_ex known and fixed, one can get the value of provided Raman gain ξ when the pump is turned on.

Figure 2 shows the simulated evolution of transmission spectra for different Raman gain in various coupling conditions. When the system is initially in the under-coupling regime and the optical gain is zero, i.e. ξ = 0, the minimum transmission is non-zero (Fig. 2(a)). Increasing the gain reduces κ_eff so that its value approaches to κ_ex and the resonance mode becomes deeper. When the system is initially set at critical coupling, i.e., transmission vanishes, increasing ξ reduces κ_eff such that balance among different losses at the maintained critical coupling condition is broken and the system is pushed to the over-coupling regime which is also characterized with non-zero minimum transmission (Fig. 2(b)). Before κ_eff reaches zero the mode goes shallower and shallower. Further decrease of κ_eff (when κ_eff < 0) evolves the system from a resonance dip to a resonance peak (Fig. 2(b)). Finally, if the system is initially in the over-coupling regime, increasing the gain pushes the resonance from a dip to a peak (Fig. 2(c)). Figures 2(d), 2(e) and 2(f) illustrate the effect of the Raman gain on the mode splitting spectra in each coupling condition corresponding to Figs. 2(a), 2(b) and 2(c), respectively. It is clearly seen that Raman gain does not only allow tuning the minimum transmission but also narrows down the linewidths of the resonances making it easier to resolve split modes, which is important for the applications of mode splitting such as particle sensing [44].

3. Experiments and discussions

The setup used in our experiments is shown in Fig. 1. We used silica microtoroid resonators of approximately 43 µm in diameter with a Q factor about 6×10⁷. The resonator-fiber taper coupling was adjusted using a nanopositioning system. To investigate the Raman gain effect on a cavity mode, we used a pump-probe configuration in which a pump laser excited the Raman gain and a probe laser monitored the effect of the Raman gain on a resonance mode.

 

Fig. 1 Experimental setup. (a) Schematic illustration of the experimental setup. A pump laser excites the Raman gain to compensate the losses in the spectral band of a probe laser that is used to probe and monitor the resonances. A fiber-taper is used to couple the pump and probe light into and out of the silica microtoroid. The transmitted pump and probe lights are separated using a wavelength-division-multiplexer (WDM), and then detected with photodiodes (PD) connected to an oscilloscope (OSC). Laser power is controlled by variable optical attenuators (VOA), and polarization state is changed by fiber polarization controllers (PC). (b) Energy level diagrams describing Raman scattering. (c) Normalized Raman gain spectra of bulk silica [48].

Download Full Size | PDF

 

Fig. 2 Theoretical transmission spectra showing the effect of Raman gain. (a, b, c) are transmission spectra without mode splitting. Initial coupling conditions (i.e., before the Raman gain is introduced) are set as: (a) under coupling, (b) critical coupling, and (c) over-coupling. The values of the Raman gain used in the calculations are given in the plots. (d, e, f) are transmission spectra with scatterer-induced mode splitting, with the same ξ and Raman gain κ_ex corresponding to (a, b, c).

Download Full Size | PDF

Both the pump and probe were coupled to the WGM resonator via the same fiber-taper. The light at the output of the fiber-taper was directed to a wavelength division multiplexer (WDM) to separate the pump from the probe. The two outputs of the WDM were connected to photodetectors, followed by a multi-channel oscilloscope to monitor the transmission spectra as the wavelength of the probe laser was scanned. The amount of optical gain provided by the Raman process into the probe band was controlled by adjusting the power of the pump laser. The probe power was kept as small as possible to minimize, if not to eliminate, thermal effects and possible probe induced nonlinear processes [53]. We note here that a higher probe power would result in thermal broadening (narrowing) of the resonance in the probe band when the probe wavelength is scanned from shorter (longer) to longer (shorter) wavelenths, and subsequently Eqs. (1)–(5) should be modified to take this dynamic process into account as was done in Ref. [53] and Ref. [54]. In this work, we limit the probe power to low levels to prevent such thermal effects.

We obtained transmission spectra in the experiments and then employed curve fitting to extract the relevant parameters as discussed in the previous section. Here, we present our results which clearly explains the evolution of transmission spectra of microcavities with mode splitting in the presence of Raman gain. Figure 3 represents a typical set of mode splitting spectra demonstrating the effect of Raman gain in different coupling conditions. All data were measured on the same resonance modes with a pump wavelength of 1449.3 nm (Q = 6.71×10⁷) and a probe wavelength of 1545.7 nm (Q = 6.84 × 10⁷). The first column of Fig. 3 (i.e., Figs. 3(a) 3(d) and 3(g)) exhibit the transmission spectra in the absence of Raman gain. The amount of Raman gain of the second and third column is controlled by the power of the pump laser. Since the Raman gain comes from stimulated Raman scattering and we input Stokes mode photons by injecting probe laser, Raman gain exists as long as the pump power is above zero [55].

 

Fig. 3 Experimentally obtained transmission spectra at various values of Raman gain for different initial coupling conditions. Blue curves are obtained in the experiments and the red curves are the fitting curves using Eq. (5). Pump power is measured at the fiber-taper input port. Raman gain ξ of fitting curves is marked on each plot. When the pump is OFF (no Raman gain), the parameters extracted from the deep under-coupling regime are κ₀ = 1.97MHz, 2g = −2.47κ₀ and Γ_R ≪ κ₀.

Download Full Size | PDF

Figures 3(a) 3(b) and 3(c) (κ_ex ~ 0.5κ₀) show that increasing the pump power and hence the Raman gain decreases the linewidth of the splitting modes thereby increasing the resolvability of the splitting. Moreover, the resonance dips approach zero implying that the system is moving from under-coupling regime closer to the vicinity of critical coupling point. In Fig. 3(c), it is clearly seen that the depths of both splitting modes are close to zero. Noting that during the experiments, the distance between the fiber-taper and the resonator is kept constant, the transition of the system from under-coupling regime to zero mininum transmission at critical coupling point can be explained only with the decrease in κ_eff with increasing gain. This hints that one can effectively move the system among different mode depth by decreasing the loss in the system while κ_ex (i.e., determined by the waveguide-resonator distance) is kept constant.

Figures 3(d) 3(e) and 3(f) are get when system is initially set in critical coupling (κ_ex ~ κ₀). Since the space between two splitting modes |2g| is larger than the total loss κ_eff + κ_ex + Γ_R, two splitting modes can be resolved. Increasing κ_ex from 0.5κ₀ (Fig. 3(a)) to κ₀ (Fig. 3(d)) pushes the minimum transmission closer to zero and makes the linewidth broader due to increased coupling loss. We gradually increase the Raman gain characterized by ξ to make the system closer to critical coupling point (Fig. 3(e)). The spectra presented in Figs. 3(c) and 3(e) show that smaller Raman gain is required to adjust the system to critical coupling point if the coupling loss of the mode is larger. When the Raman gain is large enough the mode transits from resonance dips to resonance peaks (Fig. 3(f)).

Finally in the initially over-coupling regime (Figs. 3(g), 3(h) and 3(i), κ_ex ~ 11κ₀, as the total loss κ_eff + κ_ex + Γ_R becomes larger than the detuning |2g| [29,56], we know that the two split resonance modes become one resonance dip (Fig. 3(g)). As the Raman gain increases, the transmission changes from one resonance dip to one resonance peak (Figs. 3(h) and 3(i)).

In short, Fig. 3 exhibits the mode evolution with increasing Raman gain when system is set initially in different coupling conditions. For each κ_ex, the resolvability of splitting dips is gradually enhanced by increasing Raman gain. During this process, although coupling loss of the system is kept the same, with the variation in the effective cavity loss, the transmission spectra can experience great changes. When Raman gain is high enough, the mode transmission goes from dips to peaks. These experimental results are in good agreement with the theoretical simulation curves in Fig. 2.

As we have discussed above and in the previous section, tuning κ_eff using Raman gain provides a practical method to control the minimum transmission of the cavity-waveguide system without changing the distance between them. In Fig. 4, we present the evolution of mode splitting spectra and the curve fitting values of κ_eff, κ_ex and minimum transmission as the Raman gain is varied. In this set of experiments, we kept the distance between the resonator and the fiber-taper fixed and varied only the pump power (Raman gain). As shown in Fig. 4, κ_eff decreases with the increasing pump power. It is seen in Figs. 4(a) and 4(b) that the system is operated in under-coupling regime in which the minimum transmission decreases gradually with the decreasing κ_eff when initially κ_ex is much smaller than κ_eff (i.e., coupling loss is much smaller than other losses experienced by light in the resonator). The increases of the pump power will boost the optical Raman gain and hence decrease the effective loss in the resonator. Fig. 4 shows that the cavity can transit from under-coupling to critical coupling and over-coupling regimes with the decreasing loss due to the help of Raman gain. The critical coupling point, at which transmission reaches zero, separates the under-coupling and over-coupling regimes. In the under-coupling regime, the minimum transmission decreases with the decrease of loss in the resonator. While in the over-coupling regime, opposite trend is observed, that is, minimum transmission increases with the decrease of loss in the resonator. Depending on the initial coupling loss κ_ex and its difference from the effective loss in the resonator κ_eff, the amount of pump power required to push the system to reach the critical coupling condition is different.

 

Fig. 4 Mode splitting spectra and the curve fitting values with increasing pump power. (a), (c) and (e) are splitting spectra in different coupling (κ_ex = 0.28κ₀, κ_ex = 0.49κ₀ and κ_ex = 1.05κ₀), blue curves are obtained in experiments and the red curves are the fitting. (b), (d) and (f) are curve fitting parameters of κ_eff (red circles— linear fitted with red line), κ_ex (blue squares— linear fitted with blue line), and minimum transmission of two splitting modes (green diamonds for one and black hexagonal for the other, with corresponding dashed lines for visual guides). The maximum injected pump power is 1.57 mW, and the injected probe power is kept at 21.0 µW, measured at the fiber-taper input port.

Download Full Size | PDF

Different from the case for transmission with single resonance, for which critical coupling condition is reached when the coupling loss characterized by κ_ex is equal to the effective loss in the resonator κ_eff, for the typical case with two split modes separated by |2g| at the same order of the intrinsic cavity loss κ₀, even if κ_eff = κ_ex the minimum transmission as shown in Figs. 4(b), 4(d) and 4(f). The κ_ef f has to be smaller than κ_ex for the split modes to reach critical coupling point. Note that if the splitting mode detuning |2g| is small enough and extra loss introduced by the light scatter Γ_R is negligible, at the intersection point of the curves for κ_eff and κ_ex, the minimum transmission is zero, i.e., critical coupling point, which is similar to the case for single resonance.

With increasing pump, κ_eff decreases and can become negative, i.e., optical gain, ultimately the resonance dips can turn into resonance peaks, and because of splitting the turning point from resonance dip to peak is not when κ_eff = 0 but after it. It is worth noting that all the κ_eff -pump power points in Figs. 4(b), 4(d) and 4(f) are found to be in the same straight line, which implies a linear development between Raman gain and pump power, so these measured points have not reached saturation or Raman laser threshold.

4. Conclusion

In this paper we systematically investigated both theoretically and experimentally the evolution of mode splitting spectra under Raman gain in various initial coupling conditions. We showed that Raman gain compensates losses leading to narrower linewidths and higher quality factors. The narrowing of the linewidths increases the resolvability of mode splitting. This will significantly increase the detection limits of various sensors based on monitoring splitting spectra. We have also demonstrated that providing gain enables us to drive the cavity-waveguide system to different coupling regimes and the minimum transmission to desired values just by tuning the gain (i.e., pump power). This all-optical scheme is a useful tool to control the loading condition and minimum transmission after the fabrication of waveguide-coupled resonator systems without moving any part of the system. Note that one can use Raman loss instead of Raman gain to tune the coupling conditions of waveguide-coupled microresonators [47]; however, the Raman loss method is limited to tune a system from over-coupling to under-coupling but not the other way around. Our demonstrated method, on the other hand, has good performance in driving the system from under-coupling to over-coupling regime, which makes the control a complete and practical tool in cavity-waveguide systems. The combination of Raman gain method and Raman loss method may help to realize a bidirectional, on-demand all optical control of cavity resonances.