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## 1 Introduction

Electromagnetically induced transparency (EIT) in photonic structures is a phenomenon which arises from the destructive quantum interference effect [1], [2], [3], [4] and has potential applications including all-optical switching [5], slow light [6], light storage [7], optical sensing [8], and quantum information processing [9]. In photonic structures, the EIT effect can be realized through several different paths, such as photonic crystals [10], plasmonic nanostructures [11], [12], [13], [14], and whispering-gallery-mode (WGM) optical microcavities [15]. WGM optical microcavities are excellent candidates for achieving a narrowband transparency window of the EIT spectrum, due to their high-quality (Q) factors [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]. WGM-microcavity-based EIT has been realized in a single microcavity and coupled microcavities. EIT based on a single microcavity has been studied in different kinds of structures, such as microspheres [33], microbottles [34], microbubbles [35], and microtoroids [36], [37]. However, to achieve the EIT effect in a single microcavity, two conditions are required: first, resonance frequencies of two optical modes with different Q factors are close enough to each other; second, there exists energy coupling between them. Furthermore, it is difficult to control the frequency detuning in a large range [34], [35], [37]. Therefore, coupled-microcavity-based EIT has been intensively investigated in recent years. So far, the EIT effect has been illustrated with coupled microspheres [6], coupled microtoroids [15], [38], coupled microtoroid–microdisk [39], and coupled microrings [40]. However, there exist some challenges for these schemes. For coupled microtoroids, it is difficult for the edge-located microtoroid to achieve a Q factor of up to 108, which is limited by the fabrication process. Due to low Q factors, silicon-based microcavities cannot be applied when ultrahigh Q factors are required [41]. For coupled microspheres, there is no effective scheme to tune the resonant frequency of a single microsphere.

The silica microbottle cavity, which is fabricated from the standard single-mode fiber (SMF), possesses an ultrahigh Q factor of ~108 and is a good candidate for realizing the EIT effect [42], [43]. Apart from that, the resonance tuning of the microbottle cavity is generally realized by the stretching method [42], which could make the resonant frequencies of two involved WGMs matched. However, the stretching method requires extra piezoelectric bending actuators, and the coupled-microcavity system is easy to be disturbed. In order to avoid this problem, nonmechanical methods ought to be adopted, especially all-optical methods. So far, for the silica microcavity, several all-optical tuning methods have been reported [44], [45], [46]. However, those methods lead to degradation of Q factors at different levels and/or realize relatively small tuning ranges. Therefore, it is extremely important to propose an all-optical scheme, which can maintain ultrahigh Q factors during the tuning process and realize a large tuning range.

Here, two coupled silica microbottle cavities coated with iron oxide nanoparticles are proposed and fabricated to achieve all-optical tunable EIT. As shown in Figure 1, the system consists of two coupled silica microbottle cavities, both of which possess short and spherical ends. The original microbottle cavity is fabricated from two SMFs using a fusion splicer [47]. The microbottle cavity with a short and spherical end is fabricated with the help of a carbon dioxide (CO2) laser. (For details of the CO2 laser fabrication platform, see part S1 in the Supporting Information). Iron oxide nanoparticles are coated in the tapered area of the microbottle where there is no WGM field distribution. Pump light is fed through the axial direction of the microbottle and absorbed by iron oxide nanoparticles. Due to the strong photothermal effect of iron oxide nanoparticles [48], heat generated in this area is transferred to the locations of WGM fields to change the resonances of the microbottle cavity. In this work, the microbottle cavity with a Q factor of 1.39×108 is utilized and the resonant frequency is tuned by 282.32 GHz (2.25 nm @ 1550 nm band), while the ultrahigh Q factor is maintained during the tuning process. By changing the frequency detuning between the two coupled WGMs, we can precisely control the EIT spectrum with a transparency window bandwidth as narrow as 2.3 MHz and a transparency depth of 99%. Especially, we have also realized all-optical control of the whole EIT spectrum in a range of 71.52 GHz by tuning the two microcavities separately.

Figure 1:

Schematic of all-optical controllable EIT based on coupled silica microbottle cavities.

## 2.1 Fabrication method

A microbottle fabricated by a fusion splicer is vertically fixed on a three-dimensional (3-D) displacement stage and is attached with a small weight on the bottom. Counterpropagating CO2 beams are focused on the bottleneck, and a taper emerges due to gravity. Then, we change the locations of the laser beams and obtain a fiber tip. The laser beams are focused on the fiber tip and consequently a spherical end forms. After that, a drop of water-based iron oxide nanoparticle solution is dropped on the surface of a metal platform. By precisely adjusting the relative position between the microbottle and the nanoparticle solution, the spherical end is gradually immerged into and pulled out of the solution. Since there exists a depression between the microcavity and the spherical end, a lot of iron oxide nanoparticles are located in this area after the carrier liquid is evaporated, which can absorb enough pump power.

## 2.2 Experimental test setup

A tunable laser source (TLS) in the 1550 nm band with a fine scanning range of 30 GHz is utilized in the experiment. Signal light derived from the TLS is controlled by a polarization controller (PC). The signal light is coupled into the microbottle cavity and the transmission light coming from the other end of the microfiber is detected by a photodetector (PD). A digital storage oscilloscope (DSO) is utilized to analyze the transmission spectrum. In order to tune the transparency window, continuous-wave pump light at 1550 nm from a TLS is amplified by a high power erbium-doped fiber amplifier (EDFA) and then is fed into a 10/90 optical splitter through a variable optical attenuator (VOA), which is used to tune the pump power. In order to control the whole EIT spectrum, two TLSs are needed to pump light into the two microcavities separately.

## 3 Results and discussion

The equatorial diameters of the higher-Q and the lower-Q microbottle cavities are 173 μm and 144 μm, respectively. The microfiber with a diameter of around 2.5 μm is utilized as the coupling fiber [49], [50]. Figure 2A shows the fabrication process of the proposed microbottle cavity. Figure 2B shows the fabricated microbottle with a short and spherical end. The coating area seems black because of iron oxide nanoparticles. We also find that there exists a boundary (red line) on the surface of the microbottle, which means the coating range of iron oxide nanoparticles. It could suppress the higher-order WGMs and has no influence on the Q factors of the lower-order WGMs. (For details of WGM field distributions, see part S2 in the Supporting Information). Due to the special structure of the microbottle, the guided mode propagating in the fiber core will convert into leaky modes in the tapered area and then absorbed by iron oxide nanoparticles. In order to verify this point, a red beam is fed through the axial direction of the microbottle. As shown in Figure 2C, there exists large light field intensity in the tapered area, which indicates that a lot of optical energy leaks out due to disappearance of the guided mode. Figure 2D shows the scanning electron micrograph (SEM) of the microbottle. In order to intuitively demonstrate a fact that iron oxide nanoparticles are coated in the tapered area, we measure the energy dispersive X-ray spectroscopy (EDX) of this area, as shown in Figure 2E. The measured area is shown in the red box of the inset, in which more iron oxide nanoparticles exist. There are several obvious peaks in the spectroscopy result, which represent the consistence of the atomic ratio of oxygen (O), ferrum (Fe), silicon (Si), and carbon (C), and this indicates that there are only iron oxide nanoparticles on the microcavity. The existence of carbon is due to the conductive plastic around the end, which can enhance its conductivity.

Figure 2:

Fabrication process and characterization of the proposed silica microbottle cavity.

(A) Fabrication process of the proposed silica microbottle cavity. (B) Optical micrograph of the higher-Q microbottle cavity with a short and spherical end. (C) Close-up view of the coating area. (D) SEM micrograph of the higher-Q microbottle cavity. (E) Measured energy dispersive X-ray (EDX) spectroscopy of the tapered area coated with iron oxide nanoparticles. Inset: close-up SEM micrograph of the coating area.

The EIT spectrum of the coupled microcavities can be explained by coupled mode equations:

$\frac{d{a}^{CW}}{dt}=\left(i\Delta {\omega }_{a}-\frac{1}{2\tau }\right){a}^{CW}-i\mu {b}^{CCW}+\sqrt{{\kappa }_{ex}{S}_{in}}$(1)$\frac{d{b}^{CCW}}{dt}=\left(i\Delta {\omega }_{b}-\frac{1}{2{\tau }_{o}}\right){b}^{CCW}-i\mu {a}^{CW}$(2)${S}_{\text{out}}={S}_{\text{in}}-\sqrt{{\kappa }_{ex}}{a}^{CW}$(3)$T={|\frac{{S}_{\text{out}}}{{S}_{\text{in}}}|}^{2}$(4)

where aCW and bCCW are the mode field amplitudes in the two microcavities, τ and τo represent the total and intrinsic lifetimes of photons in the two microcavities, κex denotes the coupling strength between the microfiber and the lower-Q microcavity, μ is the coupling strength between aCW and bCCW modes, Δωa/b=ωωa/b are the frequency detunings in the two microcavities, Sin and Sout represent the incident and transmitted light field amplitudes, T denotes the transmission coefficient of the signal light. By combining Eqs. (1), (2), (3), and (4), T can be expressed as:

$T={\left[1-\frac{2\tau {\kappa }_{ex}-i4\tau {\tau }_{o}{\kappa }_{ex}\Delta {\omega }_{b}}{-4\tau {\tau }_{o}\Delta {\omega }_{a}\Delta {\omega }_{b}-i2{\tau }_{o}\Delta {\omega }_{b}-i2\tau \Delta {\omega }_{a}+1+4\tau {\tau }_{o}{\mu }^{2}}\right]}^{2}$(5)

From Eq. (5), we can find that the transmission coefficient T depends on Δωa/b and μ. We first measure the Q factor and the tuning performance of the higher-Q microbottle cavity based on Figure 3. Figure 4A shows the measured transmission spectrum of a single resonance mode, which possesses a loaded Q factor of 1.39×108 by Lorentzian fitting. The apparent ring down phenomenon results from the ultrahigh Q factor of the microcavity [51]. For achieving controllable EIT, the tunability of a single microcavity is critical. Therefore, we also test the all-optical tuning performance of the microcavity, as shown in Figure 4B and C. Heat generated in the tapered area is transmitted to the microcavity. Due to the positive thermo-optic and thermal expansion coefficients of silica, the resonant frequency generates the redshift [44], [45], [46]. (For details of the response time of the tuning process, see part S3 in the Supporting Information). Figure 4B shows the transmission spectra at different pump powers in a small range, and there still exist apparent ring down phenomena in the transmission spectra. Meanwhile, we find that the ultrahigh Q factor of the microcavity is still maintained during the tuning process. As shown in Figure 4C, the red circle dotted line represents the resonant frequency shift with the pump power. A total tuning range of 282.32 GHz (2.25 nm) is achieved as the pump power increases to 260.28 mW. The overcoupling condition between the microfiber and the lower-Q microcavity is reached by enabling them to get in touch with each other, which also can make the coupling system stable. Figure 4D represents the transmission spectrum of the lower-Q microcavity with a loaded Q factor of 1.8×106. The red line represents Lorentzian fitting. The measured asymmetric spectrum may result from the excitation of spiral modes in the microcavity [52].

Figure 3:

Experimental setup for performance test of all-optical controllable EIT. AWG: arbitrary waveform generator. TLS: tunable laser source, PC: polarization controller, PD: photodetector, DSO: digital storage oscilloscope, EDFA: erbium-doped fiber amplifier, VOA: variable optical attenuator, PM: power meter.

Figure 4:

Optical performance and tunability of the fabricated microbottle cavity.

(A) Transmission spectrum of a single resonance mode of the higher-Q microbottle cavity. The red line is corresponding Lorentzian fitting. (B) 30-GHz range transmission spectra of the higher-Q microbottle cavity with different pump powers. (C) Resonant frequency shift versus the pump power, with the measured data in the red dot and the fitted data in the red line. (D) Transmission spectrum of a single resonance mode of the lower-Q microbottle cavity. The red line is corresponding Lorentzian fitting.

To obtain the EIT spectrum, the two microcavities are fixed on two three-dimensional displacement stages and couple with each other. In order to optimize the depth and the bandwidth of the transparency window, we can control the EIT spectrum by changing the coupling gap between the two microcavities. When the microfiber couples with the lower-Q microcavity, which is away from the higher-Q microcavity, there is only the transmission spectrum of the lower-Q microcavity. Then, we gradually decrease the gap between the two microcavities. In Figure 5A, when the gap is adjusted to a specific value, a narrow transparent window appears in the center of the lower-Q mode due to destructive interference between two optical pathways in the coupled microcavities [6]. Then, the gap is keeping decreased. From Figure 5A–E, it can be seen that both the transparency peak and the bandwidth gradually increase as the calculated coupling strength increases from 2π×0.0029 to 2π×0.074 GHz. The red lines represent the theoretical fitting calculated from Eq. (5), which is well agreed with the experimental results. Besides, due to the ultrahigh Q factor of the higher-Q microcavity, the bandwidth of the transparency window achieves 2.3 MHz, which is the narrowest compared with the previous work based on microcavities [6], [33], [34], [35], [37], [38], [39], [40], as shown in Figure 5B. From Figure 5E, as the gap is further decreased, the transmission spectrum splits into two separate dips and the maximum transparency depth of 99% is achieved. However, the bandwidth of the transparency window is about 115.4 MHz, which may result from the loss induced by the large coupling strength [6]. Besides, the transmission phase shift of the EIT spectrum, which indicates the change of the coupling strength, is also calculated based on the measured transmission spectrum. (For details of the transmission phase shift, see part S4 in the Supporting Information).

Figure 5:

Transmission spectra for different gaps between the coupled microcavities.

(A–E) Measured EIT spectra (black lines) of the coupled microcavities for different coupling strengths. (Inset) Close-up to the transparency window with a bandwidth of 2.3 MHz. Theoretical fittings are represented by the red lines calculated from Eq. (5) and in excellent agreement with the experimental results.

After that, we demonstrate the all-optical tuning of the transparency window. The transparency window is derived from the presence of the higher-Q microcavity and thus can be precisely controlled by changing its resonant frequency. Figure 6A shows the transmission spectrum with two independent dips, and the frequency detuning of the two modes is 171.07 MHz, when there is no pump power to the higher-Q microcavity. Then, pump light is fed into the axial direction of the higher-Q microcavity. As shown in Figure 6B and C, as the increase of the pump power, the frequency detuning decreases, and the Lorentzian line shape evolves to the asymmetric Fano resonance line shape. As the pump power increases to 0.47 mW, the frequency detuning is reduced to zero, and the asymmetry of the Fano resonance disappears while the EIT spectrum emerges. As the pump power further increases, the frequency detuning increases and the asymmetric line shape appears again, as shown in Figure 6E and F. Finally, two modes with the Lorentzian line shapes and the frequency detuning of 381.02 MHz appear again as the pump power increases to 1.64 mW. We find that the coupling strength in Figure 6G is larger than that in Figure 6A, because the thermal expansion will lead to the increase of the microcavity diameter, and then the decrease of the gap between the coupled microcavities. Furthermore, we also find that, though only the higher-Q microcavity is pumped, the resonant frequency of the lower-Q microcavity also changes a little. It is because that heat generated in the higher-Q microcavity is transferred to the lower-Q microcavity, leading to the redshift of its resonant frequency. In Figure 6H, the tuning sensitivity of the lower-Q microcavity is smaller than that of the higher-Q microcavity, because a smaller portion of the generated heat is transferred to the lower-Q microcavity, when only the higher-Q microcavity is pumped.

Figure 6:

Transmission spectra for different frequency detunings between the coupled WGMs.

(A–G) Measured EIT spectra (black lines) of the coupled microcavities for different pump powers. Frequency detunings are 171.07, 65.89, 30.36, 0, −33, −83.61, and −381.02 MHz, respectively. (H) Frequency shifs of the higher-Q and the lower-Q modes as a function of the pump power.

Since the lower-Q microcavity is also coated with iron oxide nanoparticles, its resonant frequency can be tuned by pumping light through its axial direction. Therefore, the whole EIT spectrum can be controlled by feeding the pump light through the axial directions of the lower-Q and the higher-Q microcavities. The frequency detuning can be precisely controlled by separately tuning the two microcavities with different pump powers. From Figure 7A, by increasing the pump powers of the two microcavities, the whole EIT spectrum can be shifted by 71.52 GHz. We also find that the tuning sensitivities of the two microcavities are slightly different, because the sizes and the mode orders of the two microcavities are different. It is the first time to all-optically control the whole EIT spectrum compared with reported studies [33], [34], [35], [36], [37], [38], [39], [40]. Figure 7B–D are three specific EIT spectra at different pump powers, which demonstrate that the EIT spectrum profile can always be maintained during the tuning process. When the EIT spectrum is located at a specific resonant frequency, the transparency window can be flexibly shifted due to the large tunability of the higher-Q microcavity. Based on this method, a specific EIT spectrum can emerge in a relatively large frequency range. In this way, based on two tunable and coupled microcavities, it is possible for us to realize all-optical control of the transparency window and the whole EIT spectrum.

Figure 7:

Tuning of the whole EIT spectrum.

(A) Frequency shift of the whole EIT spectrum as a function of the pump power (pump power I in the lower-Q microcavity; pump power II in the higher-Q microcavity). (B–D) Three specific EIT spectra with different pump powers.

## 4 Conclusion

In conclusion, we achieved all-optical controllable EIT based on two coupled silica microbottle cavities coated with iron oxide nanoparticles. Due to the large tunability, we achieved all-optical control of the transparency window. Due to the ultrahigh-Q factor of the microcavity, a transparency depth of 99% and a transparency window bandwidth as narrow as 2.3 MHz were obtained. Besides, we realized all-optical control of the whole EIT spectrum with a range of 71.52 GHz for the first time. Therefore, based on this scheme, the transparency window and the whole EIT spectrum can be all-optically and independently controlled. We believe this work can be utilized in optical sensing, slow light, and quantum optics.

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