Tunable Fano resonances based on microring resonator with feedback coupled waveguide

Guolin Zhao; Ting Zhao; Huifu Xiao; Zilong Liu; Guipeng Liu; Jianhong Yang; Zhaoyu Ren; Jintao Bai; Yonghui Tian

doi:10.1364/OE.24.020187

1. Introduction

The Fano resonance originates from interference between a discrete state and a continuum state [1,2], which has been attracted extensive attentions in the field of atom physics. The main feature of the Fano resonance is asymmetric line shapes caused by possible destructive interference. The similar asymmetric line shapes which named as Fano resonance can be also achieved in the field of integrated optics. Recently, the Fano resonance has induced wide research interests in aspects of optical switching/modulating [3–6], filtering [7], high-sensitivity sensing [8–10], laser [11], nonlinear and slow-light [12–15] owing to its sharp asymmetry. Currently, the Fano resonance can be achieved through many approaches in the field of integrated optics, such as waveguide-coupled-cavities [4–6,9,10], photonic crystals [4,16], nanostructures [15], and metamaterials [17], etc. In fact, the resonant cavities is the most important building block for achieving the Fano resonance due to its high quality factor, and among all types of resonant cavities, the microring resonant cavities have got the favor of researchers due to its unique features such as compact size, low power consumption, large-scale integration, etc. The resonance line-shape of a microring resonator (MRR) is symmetrical (Lorenz-shape) with respect to its resonant wavelength, and the quality factor of such MRR is generally low. Therefore, the performance of traditional optical switching [18,19], modulating [20,21], filtering [22] and sensing [23,24] based on MRR is generally limited by the low quality factor of MRR. Recent decade, the asymmetric Fano resonance based on MRR has attracted extensive attentions from researcher in the field of integrated optics. Some research groups [4,6,10] have investigated the Fano resonance by means of external feedback couple. However, to the best of our knowledge, such the Fano resonance tuning characteristics and its dependence on the feedback coupled waveguide have not been investigated in detail.

In this paper, we experimentally demonstrate a tunable Fano resonance based on a MMR and a U-bend feedback coupled waveguide (FCW) on the silicon-on-insulator (SOI) substrate (Fig. 1). We also theoretically analyze the physical essence of the Fano resonance of the device. Mode amplitude transmission factor $α_{L}$ of the FCW is the asymmetric parameter which can control the Fano profile [1,2]. In this system, the Fano resonance line-shape can be periodically tuned by two ways: tuning the MRR and FCW based on thermo-optic effect [25–27] or electro-optic effect [28]. Here we demonstrate thermal tuning the MRR/FCW by the microheaters based on the thermo-optic effect, and tuning the FCW transmission loss based on the electro-optic effect by the lateral p-i-n diode. At last, we experimentally demonstrate the ER of the proposed device can achieve as high as 30.8dB, which has many potential applications in the field of optical switching/modulating, filtering, biochemical sensing, etc.

Fig. 1 (a) Schematic and (b) micrograph of the Fano resonance device. Inset: cross-section view schematic of the rib waveguide with top TiN microheater and lateral p-i-n diode. V_R and V_L are the DC bias voltages applied to the microheater top the MRR and FCW, respectively. V is the DC bias voltage applied to the lateral p-i-n diode.

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2. Device design, fabrication and modeling

2.1 Device design and fabrication

The tunable Fano resonances device consists of a MRR and a U-bend FCW, which is shown in the Fig. 1. The radius of MRR and the length of the FCW are $10 μ m$ and $642.3 μ m$ , respectively. The gap between the MRR and FCW is $0.45 μ m$ . The remaining parameters of rib waveguide are shown in Fig. 1. A long doped FCW is designed to obtain the good Fano resonances through increasing the loss of the FCW in the resonance system [7].

The device is fabricated on silicon-on-insulator (SOI) wafer with 2μm buried SiO₂ layer and 220 nm top silicon layer using the standard Complementary-Metal-Oxide-Semiconductor (CMOS) process and the micrograph of the device is shown in Fig. 1(b). Titanium nitride (TiN) microheaters with the thickness of 150nm are fabricated on the top of the MRR and FCW to thermally tune its resonant wavelength and/or phase shifts. An embedded lateral p-i-n diode is fabricated around the FCW to tune the transmission loss of the FCW by injecting free-carriers into the FCW. Aluminum traces are formed to connect the microheaters/p-i-n diode and pads at last.

2.2 Device modeling

Utilizing the scattering matrix method [29], we theoretically analyze the Fano resonances. The relationship between the input and output electric-fields is given by

(\begin{matrix} E_{o} \\ E_{1} \end{matrix}) = (\begin{matrix} t & k e^{- i π / 2} \\ - k e^{i π / 2} & t \end{matrix}) (\begin{matrix} α_{L} e^{- i ϕ^{'}} & 0 \\ 0 & α^{1 / 2} e^{- i θ^{'} / 2} \end{matrix}) (\begin{matrix} t & k e^{- i π / 2} \\ - k e^{i π / 2} & t \end{matrix}) (\begin{matrix} 1 & 0 \\ 0 & α^{1 / 2} e^{- i θ^{'} / 2} \end{matrix}) (\begin{matrix} E_{i} \\ E_{1} \end{matrix}) .

where

E_{i}

and

E_{o}

are the input and output electric field amplitudes in the bus waveguide, respectively,

E_{1}

is the electric field amplitude in the MRR through the coupler close to the output port (see Fig. 2), t and k are the transmission and coupling coefficients of the couplers, respectively. For simplicity, we assume the two couplers are identical and lossless (

t^{2} + k^{2} = 1

).

α

and

α_{L}

are amplitude transmission factors of the micro-ring and FCW, respectively.

θ^{'} = θ + Δ θ

and

ϕ^{'} = ϕ + Δ ϕ

are the phase shifts of the round trip ring and through the FCW, respectively, where

θ =4 π r k_{0} (n_{e f f} + Δ n_{R e f f}) / λ

,

ϕ = k_{0} (n_{e f f} + Δ n_{L e f f}) L

.

n_{e f f}

is the effective refractive index,

Δ n_{R e f f}

and

Δ n_{L e f f}

are the refractive index variations of the ring and FCW due to thermo-optic effect [25–27] or electro-optic effect [28], respectively,

r

and

L

are the radius of the ring and FCW length, respectively.

Δ θ

and

Δ ϕ

represent the other disturbing factors of

θ

and

ϕ

, respectively, such as the thermal crosstalk between the MRR and FCW. Assuming the input power is normalized, the power of output is then obtained as

Fig. 2 Three paths of the mode propagating from point A to point B: (a) two paths indicated with red and blue dashed line correspond to the first two terms of the fraction of Eq. (2), respectively, and (b) the third paths indicated with red and blue dashed lines, which corresponding to the third term of Eq. (2) (there are two possible transmission paths for the third path indicated with red and blue dashed lines, in fact, the two transmission paths are equivalent).

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I_{o} = {| E_{o} |}^{2} = {| \frac{α^{1 / 2} k^{2} e^{- i (θ^{'} / 2 + π)} + α_{L} t^{2} e^{- i ϕ^{'}} + α_{L} α e^{- i (ϕ^{'} + θ^{'} + π)}}{1 - α t^{2} e^{- i θ^{'}} - α_{L} α^{1 / 2} k^{2} e^{- i (ϕ^{'} + θ^{'} / 2 + π)}} |}^{2} .

Two coupling resonant cavities, namely MRR and racetrack-like resonator (RTR) formed by a semi-ring and the FCW, exist in the proposed device. The term $1 - α t^{2} e^{- i θ^{'}}$ of the denominator in Eq. (2) is the resonance of the MRR, which can be regarded as discrete resonant states; considering the small coupling coefficient and large cavity length, the term $| 1 - α_{L} α^{1 / 2} k^{2} e^{- i (ϕ^{'} + θ^{'} / 2 + π)} | \approx 1$ belongs to the RTR, which can be regarded as continuum state. Figure 2 illustrates the three paths of the modes propagating from the first coupler (denoted with A) to the second coupler (denoted with B). The three paths correspond to the three terms of the fraction of the Eq. (2), respectively. The first two terms ( $α^{1 / 2} k^{2} e^{- i (θ^{'} / 2 + π)}$ and $α_{L} t^{2} e^{- i ϕ^{'}}$ ) represent the modes propagating from A to B merely via MRR and FCW, respectively; the last one ( $α_{L} α e^{- i (ϕ^{'} + θ^{'} + π)}$ ) represents the modes interaction between the MRR and RTR. When these modes are coupled by three paths, interference may occur and the resonances with asymmetric line-shape may appear. Fano [1] first described the asymmetric line shape which originated from the interference of the discrete and continuum states.

We analyze the influence of thermo-optic effect on the Fano resonance spectra. We firstly discuss the case of thermally tuning the MRR herein. A DC voltage $V_{R}$ is applied to the microheater over the MRR to change $θ^{'}$ and then tune its resonant wavelength. Equation (2) shows that the resonant wavelength of the RTR can also be tuned simultaneously. However, the tuning ranges of the two resonant wavelengths are different. Under the configuration of the parameters mentioned above, changing $Δ n_{R e f f} = 9.7 \times 10^{- 4}$ , the ratio of two resonant wavelengths shifts ( $Δ λ_{M R R} / Δ λ_{R T R}$ ) is 17.5. The asynchronous shift leads to the variable modes interference of the three paths. Therefore, the shape and ER of the Fano resonance will vary with the voltage $V_{R}$ . Then we discuss the case of thermally tuning the FCW. The resonant wavelength of RTR can be tuned when a DC voltage $V_{L}$ is applied to the microheater over the FCW. The thermal crosstalk between the RTR and MRR results in a slight shift of resonant wavelength of the MRR. The resonant wavelength shifts of the two cavities are also different. Therefore, the line-shape of the Fano resonance will vary with the voltage $V_{L}$ .

For the resonant system, the Fano resonance can also be controlled by asymmetry parameter $α_{L}$ [1,2]. If $α_{L} = 1$ , this means the FCW is lossless, and the resonant system is equivalent to the notch filter [30] consisting of a MRR and a bus waveguide, and its resonant line-shape is shown in Fig. 3 with black line; if $α_{L} =0$ , this means the light signal cannot transmit through the FCW, and the resonant system is equivalent to the add-drop filter [31] consisting of a MRR and two bus waveguide, and its resonant line-shape at output port is shown in Fig. 3 with red line. These two resonance line-shapes are symmetrical with respect to its resonant wavelength (Lorenz shape), sometimes called antiresonance [2]. In order to obtain a Fano resonance, the parameter $α_{L}$ must satisfy with the condition of $0 < α_{L} < 1$ (see Fig. 3, $α_{L} = 0.65$ ). In fact, the transmission loss of the fabricated waveguide can never be zero or infinity. In other words, the condition of $0 < α_{L} < 1$ is always satisfied for the proposed device, therefore, the proposed device can appear the Fano resonance [Fig. 4(a)]. In addition, the value $α_{L}$ of the proposed device can be dynamically tuned by changing the transmission loss of the FCW, which can be achieved through injecting free carriers to the FCW using the p-i-n diode embedded around the FCW. Increasing the loss of the FCW contributes to the continuum state ( $| 1 - α_{L} α^{1 / 2} k^{2} e^{- i (ϕ^{'} + θ^{'} / 2 + π)} |$ ) closer to unity but without affecting the discrete state. Therefore, increasing the transmission loss of the FCW can also tunes the Fano resonance line-shape and increases the ER.

Fig. 3 Normalized Fano profiles for various values of the asymmetry parameter $α_{L}$ (amplitude transmission factors of the FCW), $λ_{0}$ is the MRR’s resonant wavelength.

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Fig. 4 (a) Measured static spectrum, and (b)-(h) measured (black line) and simulated (red dashed line) resonance spectra when different bias voltages applied to the MRR. The black and red labels indicate the experimental and simulated data, respectively. In addition, the animation for the case has been given in Visualization 1. (IL: insertion loss).

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3. Results and discussions

A beam of continuous broadband light is coupled into the devices by the lensed fiber. The measured static transmission spectrum of the device is shown in Fig. 4(a), which exhibits uniformity span over multiple FSRs. A FSR is 9.912 nm which equals to the FSR of the MRR. The slight fluctuation is caused by the resonance of the RTR. We experimentally demonstrate the shape and ER of the Fano resonance can be periodically tuned via applying bias voltage on the MRR ( $V_{R}$ ) or FCW ( $V_{L}$ ).

We firstly demonstrate the case of only applying $V_{R}$ . Figure 4(b)-4(h) show the measured and simulated transmission spectra under different DC bias voltages (marked in the corresponding sub figures). The wavelength region near the fourth resonance peak is selected for clearly displaying the variation of the Fano resonance spectra. The average slope between the maximum and minimum transmission is 101.3dB/nm. In the simulation, we choose $α = 0.998, t = 0.983$ and $α_{L} = 0.65$ , and the values of $Δ n_{R e f f}$ and $Δ ϕ$ are given in the corresponding sub-figures directly. Increasing the bias voltage V_R, the left dip will uplift and the right dip will drop slowly, which decreases the ER. The resonance spectrum becomes symmetric (EIT-like) at $V_{R} = 0.81 V$ [Fig. 4(c)]. A phase shift with 0.03π of the FCW can be introduced due to the thermal crosstalk between MRR and FCW. Continuing to increase the bias, the left trough slowly uplift and the right dip gradually becomes deeper. Figure 4(d) shows that the resonance spectra at $V_{R} = 1.16 V$ becomes mirror symmetrical with one at $V_{R} = 0$ . However, the resonant wavelength red shifts 0.260nm owing to the thermo-optic effect. Further increasing the bias, the left trough still slowly uplift and the right dip become deeper, the Fano resonance becomes sharpest and the maximum ER is 25.8dB at $V_{R} = 1.38 V$ [Fig. 4(e)]. The wavelength span between the maximum and minimum transmission is 0.116nm. Thereafter, the right dip rapidly uplifts and the resonance peak red shifts with further increasing the V_R. The dip disappears entirely and the spectrum exhibits a symmetric spike when $V_{R} = 1.92 V$ [Fig. 4 (f)]. Then continue to raise the voltage, a dip generates from the left side and rapidly gets deeper. As before, the dip falls to the deepest form [Fig. 4(g)] and then rapidly uplifts. At a certain voltage (2.44V), the spectrum is same as the one at $V_{R} = 0$ except for a resonant wavelength red shift 1.148nm [Fig. 4(h)]. Thus, a cycle tune of the MRR is completed. The thermal crosstalk between the MRR and FCW is enhanced with the increasing bias voltage $V_{R}$ .

For merely thermal tuning the FCW, the resonance spectra display the opposite variation trend compare to thermal tuning of the MRR, which are shown in Fig. 5(a)-5(g), owing to asynchronous tuning ranges of the two resonant wavelengths. Herein the wavelength region near the fourth resonance peak [Fig. 4(a)] is selected for clearly displaying the variation of the Fano resonance spectra. The experimental and simulated data are given in the corresponding subfigures with black and red color, respectively. The thermal crosstalk between the MRR and FCW is weak because the heating area is far from the MRR [Fig. 1(b)]. As a result, the resonant wavelength red shifts are much less relative to the former case. In addition, the applied modulation voltages are greater owing to the long microheater at top of the FCW. Therefore, it is generally wiser to choose the former way to tune the Fano resonance for saving energy.

Fig. 5 Measured (black line) and simulated (red dashed line) resonance spectra: (a)-(g) when different bias voltages applied to the FCW and (h) of increasing the transmission loss of the FCW. The black and red labels indicate the experimental and simulated data, respectively. In addition, the animations for two cases of applying the voltage V_L and V have been prepared (see Visualization 2 and Visualization 3). (IL: insertion loss).

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The transmission loss of FCW can be changed by injecting free carriers into the FCW using the embedded lateral biased p-i-n diode around the FCW. According to the Eq. (2), the continuum state can be closer to unity by modestly increasing the loss of the FCW, which can result in the sharper asymmetry of Fano resonance and the increase of the ER. However, further increasing the FCW loss weakens the feedback coupling effect of the FCW, and the Fano resonance will gradually disappear (see Visualization 3). The measurement maximum ER of the Fano resonance is 30.8dB when the voltage V is 1.26V [Fig. 5(h)]. Compared with the existing results (20~23dB) [27,32–34], the ER of the proposed device is excellent. In addition, numerical simulation shows that the free-carrier concentration in the core region of FCW can reach to 3.45 × 10¹⁸cm⁻³ [35] when the voltage V is 1.26V, and the average slope between the maximum and minimum transmission is 226.5dB/nm, which means the ER and the corresponding spectral slope are improved.

4. Conclusion

In conclusion, we experimentally demonstrated the tunable Fano resonance based on a MRR and a U-bend FCW on the SOI substrate. The Fano resonance spectra can be well tuned by thermally tuning the MRR / FCW or by increasing the loss of the FCW based on the electro-optic effect. In order to intuitively show the dynamic tuning processes of the Fano resonance, the animations of the tuning behavior for three cases are given in supplementary files respectively (see Visualization 1, Visualization 2, and Visualization 3). The proposed device has high ER (30.8dB) and wavelength sensitivity (226.5dB/nm), which has many potential applications in the field of high on/off ratio optical switching & modulating, narrow-band filtering, and high-sensitivity biochemical sensing, etc.

Funding

National Natural Science Foundation of China (NSFC) (61405082); Natural Science Foundation of Gansu Province (145RJZA110); Fundamental Research Funds for the Central Universities (lzujbky-2015-k08).

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Name	Description
Visualization 1: MOV (693 KB)	Thermal tuning the MRR
Visualization 2: MOV (748 KB)	Thermal tuning the FCW
Visualization 3: MOV (1581 KB)	Tuning the transmission loss of the FCW

Tunable Fano resonances based on microring resonator with feedback coupled waveguide

Abstract

1. Introduction

2. Device design, fabrication and modeling

2.1 Device design and fabrication

2.2 Device modeling

3. Results and discussions

4. Conclusion

Funding

References and links

Supplementary Material (3)

Cited By

Figures (5)

Equations (2)

Optics Express