Electromagnetically induced transparency-like effect in microring-Bragg gratings based coupling resonant system

Zecen Zhang; Geok Ing Ng; Ting Hu; Haodong Qiu; Xin Guo; Mohamed Saïd Rouifed; Chongyang Liu; Hong Wang

doi:10.1364/OE.24.025665

1. Introduction

In the past decades, the electromagnetically induced transparency (EIT) [1] in photonics, which possesses a narrow optical transparency peak residing in a broader absorption valley [2], has attracted considerable research interests for its wide applications in slow and fast light [3], modulation [4,5], optical signal processing [6] and sensing [7]. Similar to the quantum interference in a multi-level atomic system, the EIT originates from the coupling between two resonators such as microring resonators. Microring resonators which act as the basic resonant elements with acceptable extinction ratio (ER), bandwidth and compactness are being used for various applications, including filters [8–10], modulators [11], and sensors [12]. In addition, microring resonators have also been widely employed to construct the EIT systems. In 2006, Q. Xu first observed experimentally the EIT-like spectrum in an integrated two micro-size silicon microring resonators based system with a quality factor (Q factor) of 17000 [13,14]. In 2011, S. Darmawan and Y. Zhang observed a EIT-like spectrum in a ring-bus-ring geometry synergistically integrated with Mach-Zehnder interferometer with a Q factor of 18000 [15,16]. For these two systems, one of the drawbacks is that they required a very tight perimeter difference (< 10 nm) between these two microrings which is not easy to control in fabrication. Another drawback is its large footprint due to the use of two microrings. Besides microring resonators, there are also some EIT systems based on other types of resonators being reported. For example, C. Zhang obtained a EIT-like spectrum in a system consisting of two coupled microtoroids with diameters of 60.4 µm and 67.5 µm which makes it non-compact [17]. K. Totsuka proposed a microsphere based coupled system to realize the EIT-like spectrum [18]. However, the microsphere structure is not compatible with the standard complementary-metal-oxide-semiconductor (CMOS) fabrication process and cannot be fabricated by the planar lightwave technology.

In this paper, an all-pass microring-Bragg gratings (APMR-BG) based coupling resonant system is proposed and experimentally demonstrated to generate the EIT-like spectrum. In this system, the EIT-like spectrum originates from the light coupling between two resonators. It consists of a Fabry–Pérot (F-P) resonator formed by two sections of Bragg gratings and a microring resonator. Different from the above reported structures, the proposed resonant coupling system has only one microring resonator thus making it very compact. Besides, due to the large bandwidth of the F-P resonance spectrum, it is easier to overlap the resonance wavelengths of the microring resonator and the F-P resonator to obtain the EIT-like spectrum. As a result, the fabrication tolerance can be improved. In section 2, a numerical model based on the transfer matrix method is built to investigate the working principle and the influence of the physical dimensional parameters on the device performance. In section 3, details of an APMR-BG based coupling resonant system realized on a SOI platform and its characteristics will be reported. The EIT-like spectrum with an ER of 12 dB and a Q factor of 20200 was obtained experimentally. Based on our numerical model, a slow light with a group delay of 38 ps is obtained.

2. Device design and performance analysis

The schematic of the APMR-BG based coupling resonant system is shown in Fig. 1. Two sections of Bragg gratings are located in the bus waveguide at the two sides of the microring. They perform as partially reflective elements to form an F-P resonator. The coupling between the micro-ring resonator and the F-P resonator gives rise to the EIT-like spectrum. For the all-pass microring resonator, the transmission can be expressed as [19]:

t_{r i n g_t h r u} = \frac{- α + t e^{- i φ}}{- α t^{*} + e^{- i φ}}

where

φ = \frac{2 π n_{e f f} L_{r}}{λ}

is the round-trip phase;

t = \sqrt{1 - {| k |}^{2}}

is the transmission coefficient and

k

is the coupling coefficient;

t^{*}

is the conjugation of

t

;

α^{2} = e^{- δ_{r} L_{r}}

is the round-trip-power-attenuation in which the

δ_{r}

is the propagation loss of microring waveguide per unit length;

L_{r} = 2 π R

is the cavity length of the microring in which the

R

is the radius;

λ

is the wavelength;

n_{e f f}

is the effective refractive index of the microring waveguide.

Fig. 1 The schematic of the APMR-BG based coupling resonant system.

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Because the Bragg gratings act as partially reflective elements, a part of the light in the bus waveguide is reflected and then transmits inversely. The transfer matrix of the microring should take this part of light into account. Hence, it can be written as:

T_{r i n g} = (\begin{matrix} 1 / t_{r i n g_t h r u} & 0 \\ 0 & t_{r i n g_t h r u_i n v} \end{matrix})

where

t_{r i n g_t h r u_i n v} = \frac{- α + t^{*} e^{i φ}}{- α t + e^{i φ}}

is the inverse transmission of the microring resonator. For the Bragg grating, it can be regarded as a periodic structure consisting of wide waveguide segments, narrow waveguide segments and reflective interfaces. The transfer matrix of the Bragg grating can be written as [19]:

T_{B g} = {(T_{w_w g_s g m t} \cdot T_{w_t o_n} \cdot T_{n_w g_s g m t} \cdot T_{n_t o_w})}^{N}

where

T_{w_w g_s g m t} = (\begin{matrix} e^{- i β_{w} l_{w}} & 0 \\ 0 & e^{i β_{w} l_{w}} \end{matrix})

and

T_{n_w g_s g m t} = (\begin{matrix} e^{- i β_{n} l_{n}} & 0 \\ 0 & e^{i β_{n} l_{n}} \end{matrix})

are the transfer matrices of the wide and the narrow waveguide segments respectively; the

β_{w} = \frac{2 π n_{e f f_w}}{λ} - i \frac{δ_{w}}{2}

is the complex propagation constant of the wide waveguide segments and

l_{w}

is the length;

β_{n} = \frac{2 π n_{e f f_n}}{λ} - i \frac{δ_{n}}{2}

is the complex propagation constant of the narrow waveguide segments and

l_{n}

is the length;

n_{e f f_w}

and

n_{e f f_n}

are the effective refractive indices of the wide and narrow waveguide segments;

δ_{w}

and

δ_{n}

are the propagation loss of the wide and narrow waveguides per unit length;

T_{w_t o_n} = (\begin{matrix} \frac{n_{1} + n_{2}}{2 \sqrt{n_{1} n_{2}}} & \frac{n_{1} - n_{2}}{2 \sqrt{n_{1} n_{2}}} \\ \frac{n_{1} - n_{2}}{2 \sqrt{n_{1} n_{2}}} & \frac{n_{1} + n_{2}}{2 \sqrt{n_{1} n_{2}}} \end{matrix})

and

T_{n_t o_w} = (\begin{matrix} \frac{n_{2} + n_{1}}{2 \sqrt{n_{1} n_{2}}} & \frac{n_{2} - n_{1}}{2 \sqrt{n_{1} n_{2}}} \\ \frac{n_{2} - n_{1}}{2 \sqrt{n_{1} n_{2}}} & \frac{n_{2} + n_{1}}{2 \sqrt{n_{1} n_{2}}} \end{matrix})

are the transfer matrices of the ‘wide-to-narrow’ and the ‘narrow-to-wide’ reflective interfaces respectively;

n_{1}

and

n_{2}

are the effective refractive indices of the wide and narrow waveguide segments respectively. The whole section of Bragg grating is periodic and the exponent

N

is the number of Bragg grating periods. With all the basic components defined, the equation for the APMR-BG based coupling resonant system can be expressed by combining these transfer matrices as:

T_{i n} = T_{B g} \cdot T_{w g} \cdot T_{r i n g} \cdot T_{w g} \cdot T_{B g} \cdot T_{o u t}

where

T_{w g} = (\begin{matrix} e^{- i β_{w} \frac{L}{2}} & 0 \\ 0 & e^{i β_{w} \frac{L}{2}} \end{matrix})

is the matrix of the waveguide of the F-P cavity, in which

L

is the cavity length. In this paper, the inverse transfer matrix expression for the structures is adopted. The effective indices for the waveguides of the different widths and wavelengths are calculated with the BeamPROP module of Rsoft software by taking the dispersion into account.

When only the F-P resonator is present and $L$ is an integral multiple of Bragg grating pitch, a ‘U’-like spectrum can be observed as shown in Fig. 2(a). The Bragg resonance wavelength (λ_B) is the center wavelength of the ‘U’ lineshape. When the resonance peaks of the microring overlap with the ‘U’ lineshape, the resonances are formed in both the F-P resonator and the microring resonator. Consequently, at the wavelengths of the microring peaks, the coupling between them occurs and generates the EIT-like spectra (circled by red dashed lines) as shown in Fig. 2(b). It is noteworthy that, because the EIT-like spectra happens at the slope region of the ‘U’ lineshape, the two dips beside the EIT peak are not completely symmetrical. As shown in the inset of Fig. 2(b), here we define the ER as the transmission difference between the EIT peak and the dip closer to the λ_B.

Fig. 2 (a) The normalized transmission spectra of the microring and the F-P resonator. (b) The normalized EIT-like spectrum of the APMR-BG based coupling resonant system.

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For the Bragg gratings, there are three main parameters influencing the device performance. They are the pitch, the number of Bragg grating periods (N) and the width of Bragg grating corrugation (dw). For the microring resonator, there are two main influencing parameters, the coupling coefficient (k) and the round-trip-power-attenuation (α²). In this paper, the influence of the above five parameters on two most important properties of the EIT-like spectrum namely the insertion loss (IL) and the full-width-at-half-maximum (FWHM) are discussed. A low IL is a guarantee of good transmission transparency at the wavelength of the EIT peak. A small FWHM represents a high Q factor which gives rise to a sharp EIT lineshape. In this work, we aim at building highly sensitive sensors and low switching power modulators based on this APMR-BG system. Hence, our focus is to optimize the system for a high Q factor and a sharp EIT lineshape. Besides, as shown in Fig. 2(b), the overlap between two microring resonance peaks and the ‘U’ lineshape generates two EIT-like spectra (circled by red dashed lines). The generation and working principles of these two EIT-like spectra are the identical. The EIT-like spectra occur at the left side can be analyzed with the same approach as the ones occur at the right side. In the following theoretical analysis, we only discuss the right EIT-like spectrum to avoid repetition. Furthermore, two different group delays in one device could be realized with appropriate designs.

Firstly, in order to investigate the influence of the pitch, we set the other parameters as: N = 90, dw = 20 nm, k = 0.35i, α² = 0.9981. Figure 3(a) illustrates the normalized EIT-like spectra at several different pitches. When the pitch increases, the ‘U’ lineshape moves to the longer wavelength but the resonance peak of the microring resonator stays at the original wavelength, which means the resonance peak of the microring resonator is closer to the λ_B. At the same time, the FWHM is improved but the transmission is degraded. As shown in Fig. 3(b), when the pitch < 319.6 nm, the FWHM decreases rapidly and the IL increases rapidly with the increase of the pitch. Although the IL is low in this region, the FWHM is too wide for realizing highly sensitive sensors and low switching power modulators. When the pitch > 320.3 nm, the rates of change of the FWHM and the IL both drop significantly and their values become saturated. However, the IL is too high in this region. So in order to achieve a small FWHM and a low IL at the same time, it is necessary to keep the pitch size between 319.6 nm and 320.3 nm.

Fig. 3 (a) The normalized EIT-like spectra of different pitches under N = 90, dw = 20 nm, k = 0.35i, α² = 0.9981. (b) The relation between the pitch, IL and FWHM under N = 90, dw = 20 nm, k = 0.35i, α² = 0.9981.

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The influence of N is also examined. By controlling the N, the depth of the ‘U’ lineshape can be manipulated. A larger N leads to a deeper ‘U’ lineshape. As a result of the above discussion, we set the pitch = 320 nm and maintain the rest of parameters. As shown in Fig. 4(a), the FWHM becomes smaller with the increasing value of N, which results in a higher Q factor and a sharper curve but at expense of a higher IL. Although the FWHM at N = 130 is only one-sixth of the value at N = 50, the IL at N = 130 is 16 times higher than that at N = 50. So there is a trade-off between FWHM and IL. As plotted in Fig. 4(b), the IL rises with the increase of N. It is noteworthy that the rate of change of the IL slightly increases when N > 100 and the rate of change of FWHM slows down significantly when the N > 80. Besides, when N < 70 the FWHM is too large and when N > 100 the IL is too high. So in order to achieve a balance between the FWHM and the IL, setting the N between 70 and 100 is a reasonable choice.

Fig. 4 (a) The normalized EIT-like transmission spectra at different N under pitch = 320 nm, dw = 20 nm, k = 0.35i, α² = 0.9981. (b) The relation between the N, IL and FWHM under pitch = 320 nm, dw = 20 nm, k = 0.35i, α² = 0.9981.

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The width of the Bragg grating corrugation is also a very important parameter controlling the width and the depth of the ‘U’ lineshape. Figure 5(a) shows the influence of different dw on the EIT-like spectrum. As discussed above, the pitch and the N are set as 320 nm and 90 respectively. The rest of the parameters are set as the same as dw = 20 nm, k = 0.35i, α² = 0.9981. The increase of dw gives rise to a blue-shift and the deepening of the ‘U’ lineshape, which results in the increase of the IL and the decrease of the FWHM. As depicted in Fig. 5(b), the rate of change of the FWHM drops when dw > 17 nm and the increasing of IL slows down when dw > 21nm. Besides, the IL is too high when dw > 21 nm and the FWHM is also too large when dw < 17nm. Therefore, in order to have a small FWHM with a low IL, the dw is chosen to be between 17 nm and 21 nm.

Fig. 5 (a) The normalized EIT-like transmission spectra at different dw under pitch = 320 nm, N = 90, k = 0.35i, α² = 0.9981. (b) The relation between the dw, IL and FWHM under pitch = 320 nm, N = 90, k = 0.35i, α² = 0.9981.

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Next, the influence of the microring resonator related parameters, the coupling coefficient k and the round-trip-power-attenuation α², will be discussed. Several spectra of different k are presented in Fig. 6(a). The pitch, N and dw are chosen as 320 nm, 90 and 20 nm respectively from the optimal ranges as discussed above. α² is kept the same as 0.9981. It is observed that while k value is increasing, IL decreases along with a broadening of the EIT peak. Besides, with the increase of k, the ER of the microring resonance peak decreases and the bandwidth increases. The broader overlap region between the microring resonance peak and the ‘U’ lineshape gives rise to the simultaneous broadening of the two dips and a more symmetrical EIT peak. The value of k can be manipulated by controlling the width of the waveguides and the gap width between the microring and the bus waveguide. A smaller gap width gives rise to a larger k. As shown in Fig. 6(b), when k_{real part} > 0.3, the rate of increase of the FWHM rises. The rate of change of the IL slightly decreases when k_{real part} < 0.25 and k_{real part} > 0.5. The regions k_{real part} < 0.3 and k_{real part} > 0.5 should be avoided due to the high IL and the large FWHM respectively. In order to balance the IL and FWHM, setting the k in between 0.3i and 0.5i is preferred.

Fig. 6 (a) The normalized EIT-like transmission spectra at different k under pitch = 320 nm, N = 90, dw = 20 nm, α² = 0.9981. (b) The relation between the k, IL and FWHM under pitch = 320 nm, N = 90, dw = 20 nm, α² = 0.9981.

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The round-trip-power-attenuation α² acts as another crucial parameter indicating the intrinsic Q factor of the microring. As shown in Fig. 7(a), it can be noticed that the sharper lineshape and the higher transmission can be achieved by reducing the round trip loss. So a higher α² is preferred. Figure 7(b) shows the IL and the FWHM as functions of α². It can be observed that both the IL and the FWHM decrease with the increase of α². This is because the light propagation in a low-loss microring resonator brings about a high optical transparency and intrinsic Q factor. In order to achieve a high α², the fabrication process needs to be improved to smoothen the surface of the microring waveguide. Besides, the radius of microring (R) needs to be large enough to avoid the radiation loss. From simulation results, the radiation loss can be neglected when R > 10 µm at the wavelength of 1.55 µm.

Fig. 7 (a) The normalized EIT-like transmission spectra at different α² under pitch = 320 nm, N = 90, dw = 20 nm, k = 0.35i. (b) The relation between the α², IL and FWHM under pitch = 320 nm, N = 90, dw = 20 nm, k = 0.35i.

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3. Experiment and discussion

An APMR-BG based coupling resonant system was fabricated on a SOI wafer with a 220-nm-thick top silicon layer and a 2-µm-thick buried oxide (BOX) layer. Both the grating layer and the waveguide layer are defined with electron beam lithography (EBL). The grating layer is partially etched to the depth of 70 nm with reactive ion etching (RIE). The waveguide layer is fully etched to BOX layer with deep reactive ion etching (DRIE). Then the sample is coated with a cladding layer of 1 µm SiO₂ with plasma-enhanced chemical vapor deposition (PECVD). The radius of the APMR is designed to be 10 µm and the width of waveguides is designed to be 500 nm. The width of the gap between the bus waveguide and the microring is set to be 130 nm. The pitch of Bragg gratings and the depth of corrugations are designed to be 320 nm and 20 nm respectively. The number of periods is 100 for each Bragg grating. The duty cycle is 50%. The cavity length of the F-P resonator between two Bragg gratings is 3.4 µm which equals to 10 times of the pitch.

Figures 8(a) and 8(b) show the SEM images of the APMR-BG based coupling resonant system and the Bragg grating respectively. As presented in Fig. 9(a), by using the proposed numerical model, the theoretical calculation result agrees well with the experimental result. The input light power is + 5 dBm. The grating couplers are utilized to couple light into and out from the waveguide. The coupling loss is about 4.5 dB for each grating coupler. The imbalance of the transmission curve at the two sides of the ‘U’ lineshape is due to the uneven coupling efficiency of the grating couplers at different wavelengths. Due to some roughness of the Bragg gratings, the bottom of the ‘U’ lineshape is not as smooth as the fitting curve but this will not influence the EIT-like spectra in this device. As shown, the bandwidth of the ‘U’ lineshape is slightly larger than the free spectrum range (FSR) of the microring resonator, which results in the dual EIT-like spectra. The measured ILs of these two EIT-like spectra are 7 dB and 7.5 dB. The FWHMs are 0.124 nm and 0.077 nm which correspond to the Q factors of 12500 and 20200 respectively. The ERs are 11.5 dB and 12 dB. The fitting parameters are obtained as follows: P = 321.6 nm, N = 100, dw = 11.4 nm, R = 10.2 µm, k = 0.53i, α² = 0.9778.

Fig. 8 (a) The SEM image of the APMR-BG based coupling resonant system. (b) The zoomed-in SEM image of the Bragg grating.

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Fig. 9 (a) The fitting between the experimental result and the theoretical calculation result. (b) The light propagation of the EIT-like spectrum peak at the wavelength of 1560.432 nm. (c) The light propagation of the EIT-like spectrum dip at the wavelength of 1560.252 nm.

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As shown in Fig. 8(b), the Bragg grating corrugations are not in the desired rectangular shape, thus the actual dw (11.4 nm) is smaller than the designed value of 20 nm. So more periods (N = 100) are needed to increase the reflectivity to compensate the effects of the actual smaller value of dw. Besides, due to the fabrication roughness, the relatively high propagation loss of the microring waveguide results in the low round-trip-power-attenuation α² (0.9778), which suppresses the Q factor and results in the high IL (7.5 dB). The high coupling coefficient k = 0.53i, caused by the narrow gap (130 nm) between the bus waveguide and the microring, also influences the Q factor. Further improvements can be achieved through further process optimization, for example, to improve the sharpness of the corrugation of the Bragg gratings and to smoothen the surface of waveguides through thermal oxidation followed by buffer oxide etching [20]. Increasing the gap width to have a smaller k will also improve the Q factor.

By using the Lumerical FDTD software, the light propagations at the peak and the dip of the EIT-like spectrum in the right part of the ‘U’ lineshape can be obtained as shown in Figs. 9(b) and 9(c) with normalized power. It can be clearly seen that the microring is in resonance at both of these two wavelengths. Due to the phase shift, constructive coupling and destructive coupling are formed at the wavelengths of the peak and the dip respectively. A measured ER value of 12 dB was obtained experimentally.

For the EIT system, one of the important properties is the ability to produce slow light. The microring resonator has already been known to be able to generate slow light at the wavelengths of resonance peaks. However, the transmission at these resonance peaks is too low for practical applications. By contrast, the EIT system can generate slow light with a high transmission at the wavelength of the EIT peak. In order to study the properties of slow light, the phase of the transmission can be utilized to calculate the group delay between the input and the output light. In this paper, the initial phase of the input light is normalized to 0. In Fig. 10(a), the phase of the output light is extracted from the fitted transmission spectrum. The EIT peak region (the dashed circle line) is zoomed in as shown in Fig. 10(b). At the wavelength of the EIT peak (the dashed line), there is an abrupt slope change of the phase curve indicating a sudden and drastic change of the phase. With the phase curve, the group delay can be calculated by

τ = \frac{d φ}{d ω}

where

φ

is the phase;

ω = \frac{2 π c}{λ}

is the angular frequency, in which

c

is the speed of light in vacuum and

λ

is the wavelength. The group delay curve and the transmission spectrum have been plotted in Fig. 10(c). The EIT peak region (the dashed circle line) is magnified in Fig. 10(d). It can be seen that the group delay peak and the EIT transmission peak match exactly at the same wavelength (the dashed line), which verifies the characteristic of the EIT effect. The EIT effect can offer a group delay with a high transmission transparency. Calculation shows that a slow light with a group delay of 38 ps is obtained. Since the theoretical fitted transmission spectrum is optimized in terms of the measured data, we believe the calculated group delay is able to provide a good prediction on the actual performance. According to the simulation results, if we increase the reflectivity of the Bragg gratings by increasing dw and N, the group delay can be much higher but at the cost of higher IL as discussed above. In addition, by smoothening the surface of waveguides and reducing the round trip loss of the microring to achieve a higher α², not only the IL can be reduced but also the group delay can be further improved.

Fig. 10 (a) The phase curve and the EIT-like transmission spectrum. (b) The zoomed-in curves of the phase and EIT-like transmission circled by the dashed line. (c) The group delay curve and the EIT-like transmission spectrum. (d) The zoomed-in curves of the group delay curve and the EIT-like transmission circled by the dashed line.

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4. Conclusion

In summary, an EIT-like spectrum has been successfully demonstrated theoretically and experimentally in an APMR-BG based coupling resonant system for the first time. The EIT-like spectrum originates from the coupling between two resonators namely the F-P resonator which is formed by two sections of Bragg gratings and the microring resonator. The influence of five main dimensional parameters have been investigated, including the pitch of Bragg grating, the number of Bragg grating periods (N) and the depth of Bragg grating corrugation (dw), the coupling coefficient (k) and the round-trip-power-attenuation (α²). The EIT-like spectrum is experimentally observed in a compact and fully integrated APMR-BG based coupling resonant system on a SOI wafer. The FWHM is 0.077 nm corresponding to a Q factor of 20200. The IL and the ER are 7.5 dB and 12 dB respectively. The experimental result fits well with the numerical model. Based on the fitted transmission curve, the phase and the group delay have been studied. The slow light with the group delay of 38 ps is obtained at the wavelength of the EIT peak. As our proposed APMR-BG based coupling resonant system can offer attractive features such as compactness, process compatibility with silicon CMOS technology, large fabrication tolerance, group delay with high Q factor, it can be a promising candidate for applications such as on-chip time delay lines, highly sensitive sensors, low switching power modulators [21] and optical buffering [22]. By modifying the single microring to multiple microrings structure, a broadband group delay could be realized with the proposed system [23].

Funding

This work is supported in part by the National Research Foundation of Singapore (NRF-CRP12-2013-04) and NTU-A*Star Silicon Technologies Centre of Excellence.

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Electromagnetically induced transparency-like effect in microring-Bragg gratings based coupling resonant system

Abstract

1. Introduction

2. Device design and performance analysis

3. Experiment and discussion

4. Conclusion

Funding

References and Links

Cited By

Figures (10)

Equations (5)

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