1. INTRODUCTION

Electromagnetically induced transparency (EIT) is a phenomenon deriving from destructive quantum interference between various excitation pathways in a multilevel atomic system, permitting the propagation of light through an otherwise opaque atomic medium [1–3]. Stemming from the ability of greatly enhancing nonlinear susceptibility in the transparency spectral region of the medium [1], EIT has broad implications in fields ranging from nonlinear optics to quantum information science [4]. A remarkable feature of EIT is the drastically reduced group velocity, which leads light passing through the material to be slowed or even stopped. This feature enables EIT to play important roles in photon storage [5–11] and sensitivity-enhanced optical gyroscopes [12–14]. Optical pulse propagation velocity reduced to 17 m/s has been experimentally demonstrated in ultracold sodium atoms [9]. Besides, compared with passive dielectric gyroscopes, a slow light gyroscope with group velocity of meters per second could achieve significant improvement of sensitivity by eight orders of magnitude [12]. Nevertheless, the classical EIT systems require either the atoms to be gaseous or the experimental conditions to be rigorously controlled, impeding the connection with the popular fiber communication systems [15,16]. Additionally, the available frequencies in atomic systems are intrinsically restrained by the discrete atomic transitions, severely limiting the bandwidth of the light pulses that can be slowed in the atomic medium [16–19].

Alternatively, EIT-like effects can be established in coupled-resonator systems due to classical destructive interference between frequency-detuning modes [20–25], which are often called coupled resonator induced transparency (CRIT). In the coupled-resonator system, CRIT does not suffer from the bandwidth limitation of EIT as a result of controlled field absorption [3]. Additionally, the dispersion induced by the coupled resonators can achieve superluminal signal velocity without violating Einstein causality [26,27], which is highly desired by the optical communication for optical signal regeneration [28], the laser gyroscope for enhancing absolute rotation measurement sensitivity [11], and the interferometry for detecting gravitational waves [29]. However, previous experimental and theoretical analyses reveal that CRIT only occurs when the mode detuning between the two ring resonators is less than the width of an individual silicon resonator, or the coupled resonators differ by no less than two orders of magnitude in quality factors [3,6,21], which brings serious challenges to the device fabrication and control process. Moreover, planar waveguide based CRIT is lossy when coupling with the popular fiber systems, causing significant obstacles to practical applications.

Naturally, one is led to ask whether an EIT-like effect can be generated by a monolithic optical resonator. “Spectacles-” or “yin-yang-” shaped optical fiber resonators represent a cost-effective alternative solution [30]. In the spectacles-shaped cavity, degenerate two-wave mixing can bring about the simultaneous occurrence of the first and second resonances, analogue to the classical EIT phenomenon [31]. The spectacles-shaped optical fiber resonators have been used to achieve passive devices such as bandpass/bandstop filters [32] and wavelength division multiplexers/demultiplexers [33], as well as active systems such as isolator-free unidirectional fiber lasers [34,35]. Nevertheless, previous spectacles-shaped resonators are constructed by standard optical fiber and fiber couplers, whose bulky sizes would go against the integration concept. Recently, Zhou et al. proposed a self-coupled optical waveguide (SCOW) resonator that is based on the above spectacles-shaped resonator [36,37]. Despite the compact size and nontrival resonance features of the SCOW, its slow/fast light characteristics have not been systematically investigated yet.

Benefitting from the advantages of large evanescent field, supreme mechanical properties, and intrinsic compatibility with fiber devices, micro/nano fiber (MNF) is an excellent platform for highly integrated photonic devices [38,39]. Many types of microfiber resonators including microfiber loop, knot, and coil configurations have been proposed for applications including sensing, filtering, and light velocity control [40–46]. Particularly, for light velocity control, a maximum of merely $\sim 25\mathrm{ps}$ pulse advancement in a microfiber knot resonator with a Sagnac loop reflector has been reported [45]. Slow light of about 70 ps was also achieved in a microfiber double knot resonator [46]. Beyond that, it is of fundamental interest that both slow light and fast light are achieved within one microfiber resonator.

In this work, motivated by the classical EIT effect and the spectacles-shaped resonator structure, we achieve, to the best of our knowledge, the first experimental observation of an all-fiber-based EIT-like effect in a monolithic microfiber bridged ring resonator (MBRR). This EIT-like effect, interpreted as microfiber resonator induced transparency (MRIT), is originated from destructive interference between two degenerate counter-propagating modes in the cavity. Because of the MRIT, the MBRR exhibits excellent light velocity control ability. Both fast light and slow light up to several nanoseconds can be expected in theory by refining the coupling parameters of the MBRR. Experimentally, continuous pulse delay tuning from $-60\mathrm{ps}$ (fast light) to $+160\mathrm{ps}$ (slow light) is achieved, breaking through the values of the prior microfiber resonators. The proposed MBRR with unique advantages of multi-channels, compact size, and compatibility with optical fiber systems has promising applications in all-fiber light storage, dispersion management, and optical fiber sensing.

2. MICROFIBER BRIDGED RING RESONATOR AND FABRICATION

A schematic diagram of the proposed MBRR is shown in Fig. 1(a). A “micro-bridge” is within the main cavity to route signal between the two ports of the device. Two knot areas labeled by I and II are referred to as two couplers of the MBRR since they resemble conventional fiber couplers. Eight ports defined by the two couplers in total can be found in the MBRR device. Referring to Fig. 1(a), light is launched into the cavity through port 1, and clockwise (CW) mode oscillation along the path of 2–5–7–4–2–5–7–… is initially generated. In the propagation process, the CW mode arriving at coupler I or coupler II will be divided into two branches. One branch straightly passing through the coupler maintains oscillation as the CW mode, while the other branch being routed to the micro-bridge is converted into a counterclockwise (CCW) mode along the path of 4–7–5–2–4–7–5–…. Optical powers of the two branches are determined by the coupling efficiencies and coupling losses of the two couplers, which will be discussed in the following. The micro-bridge plays a crucial role in unidirectionally converting the CW mode to the CCW mode. Generally, light going across one coupler experiences a $\pi /2$ phase lag [47]. Because the CW mode needs to cross over two couplers to be converted into the CCW mode, the CCW mode experiences $\pi$ phase lag from the CW mode. Therefore, interference between the CW mode and the CCW mode is destructive and hence induces a MRIT spectrum.

 

Fig. 1. (a) Schematic diagram of the proposed MBRR. (b) MBRR sandwiched between two Teflon-coated silica substrates with the help of glue (right), and its exploded view (left). (c) Photo of an experimentally fabricated MBRR transmitting red light (upper), and microscopic image of the adopted microfiber (lower).

Download Full Size | PDF

Since the MRIT spectrum derives from the destructive interference, the available wavelength bandwidth of the MRIT in the MBRR is much broader than that of the classical EIT case. The electric fields at the eight ports are related by the coupled mode equations. Then, the reflectance at port 1 and the transmittance at port 8 can be respectively derived as

The reflection and transmission intensities of the MBRR can be defined as $R={|r|}^2$ and $T={|t|}^2$, respectively. When calculating the reflection and transmission intensities, the term $\exp (j\beta l_0)$ is eliminated after multiplying its conjugate. Therefore, the length of micro-bridge $l_0$ has no influence on the reflection and transmission spectra. Group delay in the MBRR can be obtained by $\tau =d\varphi (\omega )/d\omega$, where $\varphi$ is the phase of the reflection or transmission light and $\omega$ is the angular frequency of the degenerate CW and CCW modes in the MBRR. Since the term $\exp (j\beta l_0)$ plays a role in the phase of the reflection and the transmission light, the length of micro-bridge $l_0$ will hence affect the group delay. A larger value of $l_0$ will give a larger group delay because of a longer optical path. However, a longer $l_0$ will also increase the overall size of the MBRR, which is undesired to the integrated systems. Therefore, a trade-off should be made between the group delay and the size of the MBRR. The coupling strength in the MBRR is characterized by the coupling efficiencies and coupling losses of couplers I and II. In the following discussion, we assume that the coupling efficiencies and the coupling losses of couplers I and II are the same for simplicity, i.e., ${\kappa }_1={\kappa }_2=\kappa$, ${\gamma }_1={\gamma }_2=\gamma$.

In order to fabricate a MBRR, a microfiber is first tapered from a single-mode fiber (SMF) by utilizing the flame-brushing technique. Then it is cut off to form two sections of microfiber. Both sections contain a SMF end and a microfiber pigtail. After one section of microfiber is anchored on a substrate by pasting its SMF end, the microfiber pigtail is twice bended and wrapped, forming a reflective-type MBRR. Thereupon, a transmissive-type MBRR can be assembled by joining another section of microfiber to the microfiber pigtail of the reflective-type MBRR. In this work, we adopt a microfiber with diameter of 2 μm to fabricate a MBRR with size of $3\mathrm{mm}\times 2\mathrm{mm}$, as shown in Fig. 1(c).

To achieve a robust and reliable device, the MBRR is packaged by homemade Teflon-coated silica substrates. Teflon is adopted here due to its low RI ($<1.3100$) and high optical transmission ($>95\%$). At first, 1.8 g Teflon amorphous fluoroplastic (DuPont Teflon AF1600) is dissolved in 100 ml fluoric solvent (FC-40) to produce 1% AF1601S2 Teflon solution. Then, the Teflon solution is dip-coated on a $60\mathrm{mm}\times 20\mathrm{mm}\times 1\mathrm{mm}$ cuboid silica substrate. The coating thickness is about 0.01 mm. Afterwards, the Teflon coating layer is dried in an oven for 5 min at a temperature of 120°C to complete the preparation of the Teflon-coated silica substrate. Finally, the fabricated MBRR is sandwiched between two fabricated Teflon-coated substrates with the help of polymer glue, as illustrated in Fig. 1(b).

3. RESULTS AND DISCUSSION

A. Coupling Parameters Dependency of the MRIT Effect

First, we study the MRIT characteristics of the MBRR by investigating the optical transmission spectrum. Equation (1) indicates that the coupling strength characterized by the coupling parameters $\kappa$ and $\gamma$ has influence on the transmission spectra of the MBRR. Figures 2(a) and 2(b) give the simulated transmission spectra of the MBRR under different coupling efficiencies $\kappa$ and coupling losses $\gamma$, respectively. Under conditions of low coupling efficiency [$\kappa =0.1$ in Fig. 2(a)] and high coupling loss [$\gamma =0.5$ in Fig. 2(b)], a transparent window does not show up in the transmission spectrum. As the coupling efficiency gets higher [$\kappa =0.5,0.9$ in Fig. 2(a)] or the coupling loss gets lower [$\gamma =0.5,0.9$ in Fig. 2(b)], the MRIT peak gradually emerges and becomes sharp.

 

Fig. 2. Coupling parameters dependency of MRIT effect in the MBRR. (a) Theoretical transmission spectra with different coupling efficiencies $\kappa$, where the coupling loss is set as $\gamma =0.01$. (b) Theoretical transmission spectra with different coupling losses $\gamma$, where the coupling efficiency is set as $\kappa =0.99$. (c) Experimental transmission spectra (red solid lines) and theoretical fitting curves (blue dashed lines) with different coupling parameters, which verifies the MRIT effect of the MBRR.

Download Full Size | PDF

Experimentally, the above point was validated by measurement of the transmission spectra under different coupling parameters. Both the coupling efficiency and the coupling loss were determined by using numerical simulations. The solid red lines and dashed blue lines in Fig. 2(c) are transmission spectra obtained experimentally and theoretically, respectively. When the coupling parameters are $\kappa =0.12$, $\gamma =0.56$, the intensity of the CCW mode is quite weak so that it could be neglected. Therefore, the MRIT does not occur and no transparent window is observed. When the coupling strength gets stronger, with the coupling parameters being $\kappa =0.96$, $\gamma =0.439$, a transparent window appears in the valley of the transmission spectrum due to the MRIT effect, as shown in Fig. 2(c). As the coupling strength further increases to the coupling parameters being $\kappa =0.6$, $\gamma =0.25$, the MRIT is enhanced, leading to increased amplitude and reduced bandwidth of the transparent window.

B. Coupling Parameters Dependency of the Group Delay

Resulting from the MRIT effect, the phase of the propagated modes changes rapidly near the resonant wavelength, giving rise to a large group delay. However, unlike the rigorous EIT case, the dispersion relation in the MRIT is not significantly distorted because the linewidth of the MBRR is much broader compared with the atomic resonators’ linewidth [15]. Therefore, in addition to slow light, fast light can also be realized in the MBRR. The group delay as a function of coupling efficiency under different coupling losses is calculated, as shown in Fig. 3(a). In the simulation, the main cavity length of MBRR $L$, the length of micro-bridge $l_0$, and the microfiber diameter are set as 10 mm, 3.6 mm, and 2 μm, respectively. The simulation result suggests that zero group delay can be achieved with appropriate interplay between coupling efficiency and coupling loss, through which the light propagation is able to turn from fast light to slow light. These transient points are extracted and displayed in the coupling efficiency–coupling loss ($\kappa -\gamma$) plane, as shown by the blue square in Fig. 3(b). By fitting the transient points with a polynomial curve, the whole $\kappa -\gamma$ plane is divided into two regions, namely the fast light region and the slow light region, respectively. Group delay spectra of a typical fast light point A ($\kappa =0.1$, $\gamma =0.01$) and a typical slow light point B ($\kappa =0.999$, $\gamma =0.01$) are calculated, respectively, with results being shown in the top row of Fig. 3(c). The maximum group delay difference occurs between the off-resonant position (phase $\text{detun}\text{in}g=\pm \pi$) and the on-resonant position (phase $\text{detun}\text{in}g=0$). Taking the off-resonant position as the reference, the MBRR can achieve fast light of $-5047\mathrm{ps}$ as $\kappa =0.1$, $\gamma =0.01$ and slow light of $+5156\mathrm{ps}$ as $\kappa =0.999$, $\gamma =0.01$.

 

Fig. 3. Theoretical and experimental group delay performance of the MBRR. (a) Group delay as a function of coupling efficiency under different coupling losses. (b) $\kappa -\gamma$ plane showing the critical coupling efficiency and coupling loss for fast/slow light, where the lower triangular is the fast light region and the upper triangular is the slow light region. In the simulation, the following parameters are adopted: microfiber diameter 2 μm, surrounding medium Teflon, and cavity length $L=10\mathrm{mm}$. (c) Simulated group delay spectra of points A, B, C, D, E, and F. Points A–F are labeled in (b). (d) Experimentally measured pulse temporal profiles with the group delay values being $-60$, $-10$, 80, and 160 ps, respectively, which verifies the tunability of the group delay. Coupling parameters of the reflection spectra corresponding to the pulse profiles from top to bottom are $\kappa =0.1$, $\gamma =0.518$, $\kappa =0.4$, $\gamma =0.7$, $\kappa =0.89$, $\gamma =0.28$, and $\kappa =0.9$, $\gamma =0.15$, respectively.

Download Full Size | PDF

C. Wavelength Dependency of the Group Delay

We experimentally investigated the group delay characteristics of the MBRR using setup depicted in Fig. 4(a). In the experiment, a continuous-wave laser from a tunable laser source (TLS, Alnair Labs TLG-200) with linewidth of 100 kHz was modulated into a 1.7 GHz sinusoidal pulse by an electro-optic modulator (EOM, SWT-MOD21212) driven through a clock signal of a bit error rate tester (BERT, Tektronix BSA125C). After being amplified by an erbium-doped fiber amplifier (EDFA, Connect MFAP-EY-B-MP), the pulse was exerted by the MBRR via a circulator. Subsequently, the reflective pulse from the MBRR passed through a variable optical attenuation (VOA, Exfo FVA-3150) for optical intensity equilibrium, and then was divided by an optical coupler (OC) into two parts. One part was detected by a photoelectric detector (PD, New Focus 1647) incorporated with a digital storage oscilloscope (DSO, Tektronix DSA8200) to record the pulse trains, where the DSO was synchronized with the EOM through the clock signal from the BERT. The other part was connected to an optical spectrum analyzer (OSA ANDO AQ6370C) to monitor the reflection spectra. In order to examine the wavelength dependency of the group delay, the wavelength of the laser pulse was successively tuned from 1559.915 to 1560.077 nm. The measured group delay and reflection spectra of the MBRR are both presented in Fig. 4(b). The zero group delay point is taken at the position of the off-resonant wavelength 1559.905 nm, as marked in Fig. 4(b). Assisted with Lorentz fitting, we obtain the maximum group delay of $+80\mathrm{ps}$ at the on-resonant wavelength 1560.01 nm. The group delay gradually decreases on both sides of the on-resonant wavelength.

 

Fig. 4. (a) Experimental setup for group delay characterization of the MBRR. TLS, tunable laser source; PC, polarization controller; EOM, electro-optic modulator; BERT, bit error rate tester; EDFA, erbium-doped fiber amplifier; VOA, variable optical attenuation; OC, optical coupler; PD, photoelectric detector; DSO, digital storage oscilloscope; OSA, optical spectrum analyzer. (b) Experimentally measured group delay spectrum and optical spectrum of the MBRR. The green solid line and green dashed line respectively mark the positions of on-resonant wavelength 1560.01 nm and off-resonant wavelength 1559.905 nm for the reflection spectrum of the MBRR.

Download Full Size | PDF

D. Continuous Tunablity of the Group Delay

The dependences of the group delay on the coupling parameters of the MBRR are experimentally studied. In the experiment, the coupling parameters are tuned by manually adjusting the coupling length and coupling angle of the two couplers. Figure 3(d) presents four different pulse temporal profiles, which correspond to reflection spectra with coupling parameters being $\kappa =0.1$, $\gamma =0.518$; $\kappa =0.4$, $\gamma =0.7$; $\kappa =0.89$, $\gamma =0.28$; and $\kappa =0.9$, $\gamma =0.15$, respectively. The four sets of coupling parameters respectively correspond to points C, D, E, and F in the $\kappa -\gamma$ plane of Fig. 3(b). Theoretical values of group delay for points C, D, E, and F are calculated to be $-67.6$, $-6.3$, $+86.7$, and $+92.2\mathrm{ps}$, as illustrated in Fig. 3(c), while the experimental counterparts are $-60$, $-10$, $+80$, and $+160\mathrm{ps}$, respectively.

The discrepancy between the experimental observation and the theoretical calculation can be attributed to two reasons. First, in the theoretical model, we assume that the two couplers have identical coupling parameters for simplicity. But in the real condition, the coupling parameters of the two couplers would actually be different depending on the length and the cross angle of the coupler. Besides, theoretically we refer to the off-resonance position as the zero-delay point. Nevertheless, in the experiment, the linewidth of the source laser is not narrow enough. In this case, the locations of off-resonance and on-resonance in the experiment might be inaccurate. Of course, there are several methods to further reduce the discrepancy between the experimental observation and the theoretical calculation. First, a more accurate theoretical model can be developed by concerning the difference of the two couplers in the MBRR. Second, a tunable laser with narrower linewidth can be used as the light source to increase the wavelength location accuracy.

Besides, although the experimentally obtained values of group delay are not large enough to be used for real applications currently, the pulse delay demonstrated in this work is one order of magnitude larger than that in the previously reported microfiber resonators [45,46], which is a step forward for the all-fiber-based delay line. In addition, the largest pulse advancement and pulse delay are theoretically calculated to be $-5047$ and $+5156\mathrm{ps}$. By building the experimental platform in an ultra-clean lab, adopting a thinner microfiber with better diameter uniformity to enhance the coupling strengths, and exploring a stable packaging method, we can be ceaselessly close to the theoretical values and make the proposed MBRR useful for real applications. Moreover, in order to achieve automatic tuning of the group delay, we could tune the refractive index around the MBRR by packaging the MBRR into a fluidic device, or control the temperature around the MBRR by putting the MBRR on a temperature-controllable hotplate.

4. CONCLUSIONS

In summary, we have experimentally demonstrated a monolithic MBRR with the MRIT effect and proved its distinguished group delay characteristics. Beginning with the coupled mode equations, we show that the interference between two counter-propagating modes in the unique cavity of the MBRR prompts the MRIT effect, depending on the coupling parameters of the two couplers in the MBRR. By accommodating the coupling parameters in trial, we observe the evolution process of the MRIT effect in the MBRR, which signifies, to the best of our knowledge, the first experimental proof of the EIT-like effect in an all-fiber structure. The MRIT effect bypasses the material limitation in classical EIT and avoids the connection difficulties with fiber systems in CRIT, opening a route for all-fiber photon storage and sensitivity-enhanced optical fiber gyroscope. Resulting from the MRIT effect, the phase of the propagated modes changes rapidly near the resonant wavelength, giving rise to a large group delay. Moreover, because of the relatively broad linewidth of the MBRR, apart from slow light, fast light can also be realized in the MBRR. Our theoretical and experimental results verify the above expectation. Theoretically, we show that the group delay can be continuously tuned from fast light $-5047\mathrm{ps}$ to slow light $+5156\mathrm{ps}$ by tailoring the coupling parameters of the two couplers in the MBRR. Meanwhile, we verify that both fast light and slow light ($-60\mathrm{ps}$ to $+160\mathrm{ps}$) within one MBRR are achievable in experiment. The value of slow light obtained in the MBRR is a more than one order of magnitude improvement over prior microfiber resonators. The proposed MBRR featuring multi-channels, all-fiber structure, and compact size paves the way for quantum computation, information storage, optical processing, and precision measurement.