Simulation and Analysis of Microring Electric Field Sensor Based on a Lithium Niobate-On-Insulator

crystals

Article Simulation and Analysis of Microring Electric Field Sensor Based on a Lithium Niobate-on-Insulator

Zhenlin Wu 1, Yumeng Lin 1, Shaoshuai Han 1, Xiong Yin 1, Menghan Ding 1 , Lei Guo 2, Xin Yang 3 and Mingshan Zhao 1,*

1 School of Optoelectronic Engineering and Instrumentation Science, Dalian University of Technology, Dalian 116024, China; [email protected] (Z.W.); [email protected] (Y.L.); [email protected] (S.H.); [email protected] (X.Y.); [email protected] (M.D.) 2 School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China; [email protected] 3 Department of Electrical and Electronics Engineering, School of Engineering, Cardiff University, Cardiff CF10 3AT, UK; [email protected] * Correspondence: [email protected]; Tel.: +86-138-8960-3037

Abstract: With the increasing sensitivity and accuracy of contemporary high-performance electronic information systems to electromagnetic energy, they are also very vulnerable to be damaged by high-energy electromagnetic fields. In this work, an all-dielectric electromagnetic field sensor is proposed based on a microring resonator structure. The sensor is designed to work at 35 GHz RF field using a lithium niobate-on-insulator (LNOI) material system. The 2.5-D variational finite difference time domain (varFDTD) and finite difference eigenmode (FDE) methods are utilized to analyze

the single-mode condition, bending loss, as well as the transmission loss to achieve optimized waveguide dimensions. In order to obtain higher sensitivity, the quality factor (Q-factor) of the 6 Citation: Wu, Z.; Lin, Y.; Han, S.; Yin, microring resonator is optimized to be 10 with the total ring circumference of 3766.59 µm. The X.; Ding, M.; Guo, L.; Yang, X.; Zhao, M. lithium niobate layer is adopted in z-cut direction to utilize TM mode in the proposed all-dielectric Simulation and Analysis of Microring electric ﬁeld sensor, and with the help of the periodically poled lithium niobate (PPLN) technology, Electric Field Sensor Based on a the electro-optic (EO) tunability of the device is enhanced to 48 pm·µm/V. Lithium Niobate-on-Insulator. Crystals 2021, 11, 359. https://doi.org/ Keywords: LNOI; microring resonator; electro-optical; PPLN 10.3390/cryst11040359

Academic Editor: Marco Bazzan 1. Introduction Received: 3 March 2021 As a key component of modern photonic integrated circuits, microring resonator Accepted: 26 March 2021 Published: 30 March 2021 (MRR) shows great performance in ﬁltering [1,2], sensing [3–6], ultra-fast electro-optic modulation (EOM) [7–10], optical frequency comb generation [11,12] and wavelength

Publisher’s Note: MDPI stays neutral division multiplexing [13] due to its unique characteristics such as wavelength selection, with regard to jurisdictional claims in compact structure and high quality factor (Q-factor). In the past decades, various material published maps and institutional affil- systems of MRR structures have been investigated for opto-electric applications, including iations. graphene [14,15], silicon (Si) [16–18], indium phosphide (InP) [19], polymer [20] and lithium niobate [8,10,21]. Among these materials, Si and InP structures rely on plasma dispersion effect and quantum-confined Stark effect, respectively, which are not suitable for ultra-high-speed data transmission purposes. For graphene, the technical difficulty lies in the separation of monolayer structure and limitation for mass production [15], which Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. makes it hard for commercialization. In addition, although the EO polymer has high EO This article is an open access article coefficient, the thermal instability might cause the material decrease gradually with time. distributed under the terms and Lithium niobate (LiNbO3, LN) is a synthetic material with excellent electro-optic, acoustic- conditions of the Creative Commons optic, nonlinear-optic properties and good transmittance in the near-infrared band [22]. Attribution (CC BY) license (https:// Lithium niobate-on-insulator (LNOI) has been developed as the platform for a variety of creativecommons.org/licenses/by/ waveguide structures, such as LN waveguide [8,23,24], proton-exchange waveguide [25] 4.0/). and strip-loaded waveguide [26]. Due to the high electro-optic coefficient (γ33 = 31 pm/V)

Crystals 2021, 11, 359. https://doi.org/10.3390/cryst11040359 https://www.mdpi.com/journal/crystals Crystals 2021, 11, 359 2 of 10

and large refractive index (ne = 2.138 and no = 2.21 at 1550 nm), lithium niobate-based EOM devices have been developed rapidly in recent years. In addition, several hybrid waveguide modulators have been proposed, such as Si-LiNbO3 [9], Si3N4-LiNbO3 [27]. However, as the RI of Si-Si3N4 is higher than or close to LN, the proportion of optical modes in LN will be decreased, reducing the interaction between electric and optical field, lowering the overall EO modulation efficiency of the device. In order to fabricate LN structure directly from the thin film, a series of work has been carried out to process this hard-to-etch material, and to date, ultra-low-loss LiNbO3 waveguide has been proved to be as low as 2.7 dB/m [24,28]. With the miniaturization of electronic devices, the maximum voltage they can with- stand is constantly reduced, which makes them very vulnerable to damage by high electromagnetic energy; therefore, several all-dielectric receivers based on bulk LN crystals have been investigated [29,30]. They use all dielectric antenna to receive the RF electric field in space, and then amplify by dielectric resonant antenna (DRA) resonance and utilize a LN disc resonator to modulate the optical field. However, this bulk structure is not conducive for integration. Another all-dielectric microring electric field sensor device proposed by Chen et al. using Si3N4-LiNbO3 heterostructure has shown the ability for the detection of electric field of 1.86 GHz [3]. However, due to the small proportion of light which can propagate in the LN layer, it will lead to a lower EO overlap factor, giving rise to lower sensitivity of the device. In this paper, LNOI structure is used as an EO platform to analyze the single-mode conditions, transmission loss, optical power distribution in LN, cladding thickness and finally determine the waveguide size, so that it has high EO overlap factor and low transmission loss. After strict theoretical calculation and software simulation, the design of microring electric field sensor which works at 35 GHz can be achieved. In order to avoid the phenomenon that net modulation is zero, a traditional receiving front end adopts the method of adjusting the distribution of resonant electrodes [31]. There are also proposed electrode-free front-ends to avoid zero modulation by exposing half of the receiving unit to the electric field [29,30]. However, neither of these two methods makes full use of the electro-optical performance of the RF receiving unit. Unlike any traditional methods, PPLN technology is introduced in this design. It makes full use of the electro- optical characteristics of the entire microring and improves the electro-optical tuneability to 48 pm·µm/V. Compared with the traditional electro-optic modulator with electrodes, the designed microring sensor does not involve any metal structure, which is able to avoid serious damages caused by external high-energy electromagnetic field.

2. Structure The structure of the proposed device is illustrated in Figure1. In this design, Si is used as the bottom substrate with a 2 µm thick SiO2 layer on top as the lower cladding. A layer of z-cut lithium niobate film is selected as the core layer of the waveguide whose refractive index can vary with applied electric field. A layer of SiO2 is covered on top of the whole device as a protection layer. The resonator is designed as an add-drop structure, the light satisfying the resonance condition oscillates continuously in the ring and interacting with the external electric field, thus realizing the efficient electro-optical modulation. The variational finite difference time domain (varFDTD) method as a new solution for solving complex Maxwell equations can efficiently model microring resonators and have better time efficiency compared with 3-D FDTD. Finite difference eigenmode (FDE) is considered to be the most effective way to analyze mode distribution and calculate bending loss. In both cases, rectangular Cartesian grids are used to divide the waveguide geometry, and perfectly matched layer (PML) is used as the boundary condition. In order to ensure the accuracy of the results, the grid density is increased in the region with large refractive index change. Crystals 2021, 11, x FOR PEER REVIEW 3 of 10

Crystals 2021, 11, 359 3 of 10 to ensure the accuracy of the results, the grid density is increased in the region with large refractive index change.

1 Figure 1. A schematic of periodically poled lithium niobate (PPLN) microring resonator (MRR) structure (blue and purple areas representrepresent lithium lithium niobate niobate ﬁlms films with with opposite opposite polarization polarization direction). direction). Inset: Inset: schematic schemati ofc cross-section of cross-section of the of waveguide the waveguide structure, where w is the width of the waveguide and hslab is the thickness of the residual layer. structure, where w is the width of the waveguide and hslab is the thickness of the residual layer.

3. Results and Discussion In this this work, work, a a 1550 1550 nm nm laser laser is is adopted adopted as as carrier carrier wave. wave. At Atthis this wavelength, wavelength, the theex- traordinary and ordinary refractive indices of LN are ne = 2.138 and no = 2.211 [32], respec- extraordinary and ordinary refractive indices of LN are ne = 2.138 and no = 2.211 [32], tively, and the refractive index of SiO2 is 1.444. The waveguide structure has a strong re- respectively, and the refractive index of SiO2 is 1.444. The waveguide structure has a strong strictionrestriction on on light light energy energy due due to to the the high high-refractive-index-refractive-index difference difference (> (>0.7)0.7) of LNOI. The parameters of 600 nm LNOI film,film, which is used as the basic platform for the design, comes from NANOLN company (Jinan, China). To To ensure that the signal will not decay due toto modal dispersion, the single single-mode-mode condition in the waveguide should be be satisf satisfied.ied. Firstly, Firstly, the effect of thethe LNLN slabslab thicknessthickness onon thethe effectiveeffective refractiverefractive indexindex nneffeff isis calculated,calculated, asas shown in Figure Figure 22a.a. With h TETE-slab-slab < 0.5< 0.5 μmµ mand and hTM h-TM-slabslab < 0.6< μm, 0.6 µthem, transverse the transverse electric electric (TE) (TE)and transverse and transverse magnetic magnetic (TM) modes (TM) modes can be can realized be realized in the vertical in the vertical direction direction for single for- modesingle-mode transmission, transmission, respectively. respectively. Figure Figure 2b shows2b shows the bending the bending loss losscorresponding corresponding to dif- to ferentdifferent LN LN slab slab thickness thickness with with fixed fixed 0.8 0.8 μmµm waveguide waveguide width width and and 100 100 μmµm bending bending radius. radius. It can be found that the reduction in the thicknessthickness of the slab areaarea cancan leadlead toto enhancedenhanced waveguide mode mode confinement confinement and and reduced reduced bending bending loss; loss; however, however, at the at the same same time time it can it alsocan alsocause cause difficulty difficulty in coupling in coupling between between waveguides. waveguides. In order In order to obtain to obtain the same the same couplingcoupling efficiency, efficiency, the thecoupling coupling distance distance gap gapis usually is usually small, small, which which requires requires complex complex fab- ricationfabrication procedures procedures for forthe theetching etching of the of LN the LNfilms. films. Figure Figure 2c shows2c shows the results the results of the of pre- the previousvious analysis, analysis, where where it can it canbe found be found that thatthe coupling the coupling efficiency efficiency gradually gradually descends descends with withdecreasing decreasing hslab. hByslab considering. By considering both boththe low the-loss low-loss transmission transmission in the in waveguide the waveguide and and the effectivethe effective coupling coupling between between waveguides, waveguides, a thickness a thickness of 0.22 of μm 0.22 ofµ mthe of slab the area slab of area LN of layer LN islayer eventually is eventually chosen chosen to achieve to achieve better better optical optical carrier carrier transmission transmission characteristics. characteristics. The thickness of the LN slab area is fixed at 0.22 µm, and the dependence of the effective refractive index on the ridge waveguide width w is shown in Figure3a. The effective refractive index increases with increasing width of the waveguide, generating higher-order of waveguide modes. For TE and TM, the single-mode and multi-mode critical values appear near w = 1.1 µm and 0.9 µm, respectively. Therefore, it is necessary to select w smaller than the critical value to satisfy the single-mode condition. At the same time, since the transmission loss and the optical power in the lithium niobate showed a positive trend with the increase of w, it is necessary to choose a larger w so that the waveguide has low transmission loss and high mode confinement, as shown in Figure3b . The higher the ratio of optical power in lithium niobate PLN is, the larger the photo-electric overlap factor is, resulting in the greater electro-optical modulation efficiency of the device [26], as shown in Figure3c. By weighing the relationship between the parameters, the waveguide width is determined to be 0.8 µm, and more than 80% of optical power is confined in LN waveguide area. Therefore, the TE and TM optical mode-field profile of the finally

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designed LiNbO3 ridge waveguide are obtained as shown in Figure3d. It can be seen that this structure has good capability of modal constraint. For z-cut LN film, TE and TM mode accesses electro-optic coefficients γ13 = 8 pm/V and γ33 = 31 pm/V, respectively [33], so we choose 1550 nm TM polarized light as the carrier. In this case, the effective refractive index neff = 1.78596, group refractive index ng = 2.27407, transmission loss can be calculated as −5 1.06670 × 10 dB/cm, and the optical power in lithium niobate PLN = 81%. In order to prevent external dust, humidity and other pollutants from changing the effective refractive index of the waveguide and thus affecting the performance of the microring, an upper cladding layer of SiO2 is adopted on top of the LN film as the protection layer to increase the stability of the device. The effect of SiO2 thickness on the Crystals 2021, 11, x FOR PEER REVIEW effective refractive index is also simulated, as shown in Figure4. When the SiO thickness 4 of 10 2 is more than 1 µm, neff tends to be stable, therefore, the thickness of SiO2 protection layer is set to be 3 µm.

Figure 2. (a) Relationship between effective refractive index of lithium niobate-on-insulator (LNOI) slab waveguide with Figure 2. (a) Relationship between effective refractive index of lithium niobate-on-insulator (LNOI) slab waveguide with 1 µm upper cladding thickness and slab thickness. (b) The inﬂuence of the thickness of LN slab layer on bending loss with 1 μm upperthe waveguidecladding thickness width of 0.8 andµm andslab the thickness. bending radius (b) The of 100influenceµm. (c) Theof the dependence thickness of theof LN coupling slab layer efﬁciency on andbending the loss with the waveguithicknessde width of the of lithium 0.8 μm niobate and (LN) the slabbending layer with radius coupling of 100 distance μm. ( gapc) The = 0.5 dependenceµm. of the coupling efficiency and the thickness of the lithium niobate (LN) slab layer with coupling distance gap = 0.5 μm.

The thickness of the LN slab area is fixed at 0.22 μm, and the dependence of the effective refractive index on the ridge waveguide width w is shown in Figure 3a. The effective refractive index increases with increasing width of the waveguide, generating higher- order of waveguide modes. For TE and TM, the single-mode and multi-mode critical values appear near w = 1.1 μm and 0.9 μm, respectively. Therefore, it is necessary to select w smaller than the critical value to satisfy the single-mode condition. At the same time, since the transmission loss and the optical power in the lithium niobate showed a positive trend with the increase of w, it is necessary to choose a larger w so that the waveguide has low transmission loss and high mode confinement, as shown in Figure 3b. The higher the ratio of optical power in lithium niobate PLN is, the larger the photo-electric overlap factor is, resulting in the greater electro-optical modulation efficiency of the device [26], as shown in Figure 3c. By weighing the relationship between the parameters, the waveguide width is determined to be 0.8 μm, and more than 80% of optical power is confined in LN waveguide area. Therefore, the TE and TM optical mode-field profile of the finally designed LiNbO3 ridge waveguide are obtained as shown in Figure 3d. It can be seen that this structure has good capability of modal constraint. For z-cut LN film, TE and TM mode accesses electro-optic coefficients γ13 = 8 pm/V and γ33 = 31 pm/V, respectively [33], so we choose 1550 nm TM polarized light as the carrier. In this case, the effective refractive index neff = 1.78596, group refractive index ng = 2.27407, transmission loss can be calculated as 1.06670 × 10−5 dB/cm, and the optical power in lithium niobate PLN = 81%.

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Figure 3. Dependence of (a) effective refractive index (b) transmission loss of straight waveguide/100 μm radius curved waveguide and (c) optical power ratio in lithium niobate on waveguide width. (d) Simulated transverse electric (TE) and transverse magnetic™ optical mode-field profile of a LiNbO3 ridge waveguide with 0.22 μm thickness of slab layer and 0.8 μm width of waveguide at 1550 nm. Material boundaries are indicated by the black solid lines.

layer to increase the stability of the device. The effect of SiO2 thickness on the effective FigureFigure 3. Dependence 3. Dependence of of(a) ( aeffective) effective refractive refractive index ((bb)) transmission transmission loss loss of straightof straight waveguide/100 waveguide/µ100m radius μm radius curved curved refractive index is also simulated, as shown in Figure 4. When the SiO2 thickness is more waveguidewaveguide and and (c) optical (c) optical power power ratio ratio in in lithium lithium niobate onon waveguide waveguide width. width. (d )( Simulatedd) Simulated transverse transverse electric electric (TE) and (TE) and µ transversetransverse magnetic magnetic™ optical™ opticalthan mode mode-ﬁeld 1-field μm, profile proﬁle neff tendsof of a LiNbOLiNbO to 3be3ridge ridge stable, waveguide wavegui therefore,de with with 0.22 0.22 them μm thickness thickness thickness of slab ofoflayer slab SiO andlayer2 protection and layer is set to 0.8 μm0.8 widthµm width of waveguide of waveguide atbe at1550 15503 μm.nm. nm. Material Material boundaries are are indicated indicated by by the the black black solid solid lines. lines.

In order to prevent external dust, humidity and other pollutants from changing the effective refractive index of the waveguide and thus affecting the performance of the microring, an upper cladding layer of SiO2 is adopted on top of the LN film as the protection layer to increase the stability of the device. The effect of SiO2 thickness on the effective refractive index is also simulated, as shown in Figure 4. When the SiO2 thickness is more than 1 μm, neff tends to be stable, therefore, the thickness of SiO2 protection layer is set to be 3 μm.

Figure 4. Figure 4.Relationship Relationship between between the SiO2 thicknessthe SiO and2 thickness the effective and refractive the effective index. refractive index.

Figure 4. Relationship between the SiO2 thickness and the effective refractive index.

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As the radio frequency field ﬁeld is incident on the LNOI microring resonator, the output light intensity will change with the RF field ﬁeld intensity, asas shownshown inin FigureFigure5 5a.a. ForFor betterbetter detection sensitivity, thethe inputinput lightlight needsneeds toto be set at the maximum slope of the resonance peak, so that even if the received RF signal is very weak, the modulated light intensity can still have a large variation. Figure5b shows that when f = f , RF modulation can be still have a large variation. Figure 5b shows that when RFfRF = fFSRFSR, RF modulation can be achieved as lo longng as the modulation sidebands are located in the adjacent resonances.resonances.

Figure 5.5. ((aa)) IntensityIntensity modulationmodulation of of microring microring resonator. resonator. The The periodic periodic change change of RFof RF signal signal (yellow (yellow line) line) causes causes the leftthe andleft and right drift of the microring transmission spectral line, which eventually leads to the periodic change of the intensity right drift of the microring transmission spectral line, which eventually leads to the periodic change of the intensity of the of the output laser (red line). (b) Microring modulation mechanism. The optical carrier is biased at the maximum slope of output laser (red line). (b) Microring modulation mechanism. The optical carrier is biased at the maximum slope of the the microring transmission curve. When the RF frequency is equal to the free spectrum range (FSR) of the microring, the microringRF signal resonates transmission in the curve. loop Whentogether the with RF frequencythe optical is carrier equal to perform the free spectrumefficient electro range- (FSR)optical of conversion. the microring, the RF signal resonates in the loop together with the optical carrier to perform efficient electro-optical conversion. The free spectrum range (FSR) of the LN waveguide microring resonator is also ana- The free spectrum range (FSR) of the LN waveguide microring resonator is also lyzed. FSR represents the distance between two adjacent resonance peaks, which can be analyzed. FSR represents the distance between two adjacent resonance peaks, which can expressed as: be expressed as: λ2휆2 푓퐹푆푅 = , (1) fFSR = 퐿⋅푛푔, (1) L·ng where L is the circumference of the microring, ng is the group refractive index and λ is the where L is the circumference of the microring, ng is the group refractive index and λ is the optical carrier wavelength. wavelength. For For the the radio radio frequency frequency at at 35 35 GHz, GHz, the the calculated calculated perimeter perimeter L =L 3766.59= 3766.59 μm.µm In. Inorder order to to concentrate concentrate the the electric electric field field on on the the microring, microring, special special design is needed for the shape of the mi microring,croring, as shown in Figure1 1.. ItIt hashas severalseveral arcsarcs withwith smallsmall bending radii and several straight lines. The bending loss of the structure is simulated, as shown in Figure 66.. InIn orderorder toto showshow thethe influenceinfluence ofof thethe bendingbending radiusradius RR onon thethe opticaloptical mode field field d distributionistribution more more intuitively, intuitively, the the logarithmic logarithmic mode mode profile profile corresponding corresponding to toR =R 30 = μm, 30 µ 60m, μm, 60 µ100m, μm 100 andµm straight and straight waveguide waveguide is simulated. is simulated. With the With increasing the increasing of bend- ingof bending radius, the radius, symmetry the symmetry of the profile of the becomes profile becomes better and better closer and to closer the case to theof straight case of wstraightaveguide. waveguide. When the When bending the bendingradius is radius greater is than greater 100 thanμm, 100the µlossm, tends the loss to tendsbe flat to and be closeflat and to closethe straight to the straightwaveguide waveguide loss. Therefore, loss. Therefore, the bending the bending radius of radius 100 μm of100 is finallyµm is selected.finally selected. As another important parameter of the microring, quality factor Q indicates the ability of the microring to store photons. As for a RF receiver, Q-factor can reflect the interaction between the carrier light wave and the incident RF electric field, where a high Q value means sharper resonance peaks, which can lead to longer lifetime of the photon in the ring and further generate strong interactions between the light field, enhancing the electric field, which ultimately make a higher sensitivity of the receiver. The value of Q can be expressed as: p πng L A(1 − κ2) Q = , (2) λ 1 − A(1 − κ2) where A = exp(−αL) is the loss coefficient, α is the transmission loss of the waveguide and κ is the coupling coefficient. For the device design, the transmission loss is set to be Figure2.7 dB/m 6. Relationship [24] which between is the minimum the bend lossradius value and thatoptical can loss. be achievedSimulations by of the the current logarithmic process- modeing technology, profile corresponding and the relationship to R = 30 μm, between 60 μm, quality100 μm factorand straight Q and waveguide coupling coefficientare reportedκ canin the insets.

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As the radio frequency field is incident on the LNOI microring resonator, the output light intensity will change with the RF field intensity, as shown in Figure 5a. For better detection sensitivity, the input light needs to be set at the maximum slope of the resonance peak, so that even if the received RF signal is very weak, the modulated light intensity can still have a large variation. Figure 5b shows that when fRF = fFSR, RF modulation can be achieved as long as the modulation sidebands are located in the adjacent resonances.

Figure 5. (a) Intensity modulation of microring resonator. The periodic change of RF signal (yellow line) causes the left and right drift of the microring transmission spectral line, which eventually leads to the periodic change of the intensity of the output laser (red line). (b) Microring modulation mechanism. The optical carrier is biased at the maximum slope of the microring transmission curve. When the RF frequency is equal to the free spectrum range (FSR) of the microring, the RF signal resonates in the loop together with the optical carrier to perform efficient electro-optical conversion.

The free spectrum range (FSR) of the LN waveguide microring resonator is also analyzed. FSR represents the distance between two adjacent resonance peaks, which can be expressed as:

휆2 푓퐹푆푅 = , (1) 퐿⋅푛푔

where L is the circumference of the microring, ng is the group refractive index and λ is the optical carrier wavelength. For the radio frequency at 35 GHz, the calculated perimeter L = 3766.59 μm. In order to concentrate the electric field on the microring, special design is needed for the shape of the microring, as shown in Figure 1. It has several arcs with small bending radii and several straight lines. The bending loss of the structure is simulated, as Crystals 2021, 11, 359 7 of 10 Crystals 2021, 11, x FOR PEER REVIEWshown in Figure 6. In order to show the influence of the bending radius R7 of on 10 the optical

mode field distribution more intuitively, the logarithmic mode profile corresponding to R = 30 μm, 60 μm, 100 μm and straight waveguide is simulated. With the increasing of bend- be analyzed, see Figure7a. In the case of fixed gap, the length of coupling region L couple ising directly Asradius, another affected the important bysymmetry the value parameter ofofκ .the As theprofileof the coupling microring, becomes coefficient quality better increased, factor and Qcloser Q indicates showed to the a the caseabil- of straight itydownwardwaveguide. of the microring trend. When To obtainto the store abending high-quality-factor,photons. radius As for ais aRF greater smaller receiver, coupling than Q- factor100 coefficient μm, can thereflect should loss the be tends interac- to be flat and selected, but this is at the cost of decreasing extinction ratio, as shown in Figure7b. As tionclose between to the the straight carrier lightwaveguide wave and loss. the incidentTherefore, RF electric the bending field, where radius a high of Q100 value μm is finally meansthe coupling sharper coefficient resonance is set peaks, to be κwhich= 0.08, can the lead corresponding to longer Q-factorlifetime isof calculatedthe photon to in be the ring aroundselected. 106 , and the coupling length L = 0.7 µm. and further generate strong interactionscouple between the light field, enhancing the electric field, which ultimately make a higher sensitivity of the receiver. The value of Q can be expressed as:

휋푛 퐿 √퐴(1−휅2) 푄 = 푔 , (2) 휆 1−퐴(1−휅2) where A = exp(−αL) is the loss coefficient, α is the transmission loss of the waveguide and κ is the coupling coefficient. For the device design, the transmission loss is set to be 2.7 dB/m [24] which is the minimum loss value that can be achieved by the current processing technology, and the relationship between quality factor Q and coupling coefficient κ can be analyzed, see Figure 7a. In the case of fixed gap, the length of coupling region Lcouple is directly affected by the value of κ. As the coupling coefficient increased, Q showed a downward trend. To obtain a high-quality-factor, a smaller coupling coefficient should be

selected, but this is at the cost of decreasing extinction ratio, as shown in Figure 7b. As the couplingFigure 6. 6.Relationship coefficientRelationship between is setbetween to the be bend κthe = radius bend0.08, and theradius optical corresponding and loss. optical Simulations Qloss.-factor ofSimulations the is logarithmic calculated of the to logarithmic be mode proﬁle corresponding to R = 30 µm, 60 µm, 100 µm and straight waveguide are reported in aroundmode profile 106, and corresponding the coupling lengthto R = 30Lcouple μm, = 600.7 μm, μm. 100 μm and straight waveguide are reported in the insets. insets.

FigureFigure 7. 7.(a)( Functiona) Function relationship relationship between between quality quality factor (Q)(Q) andand couplingcoupling coefficient coefficientκ. κ. Inset: Inset: function function of of coupling coupling coef- coefficient κ and coupling length L when gap = 0.8 µm. (b) Transmission line with coupling coefficient κ of 0.04, 0.06 ficient κ and coupling length Lcouplecouple when gap = 0.8 μm. (b) Transmission line with coupling coefficient κ of 0.04, 0.06 and 0.08and around 0.08 around 1550 nm. 1550 nm. After the analysis and design mentioned above, the parameters of each part of the microringAfter have the beenanalysis determined. and design It should mentioned be noted above, that when the the parameters modulated electricof each field part of the microringis uniformly have distributed been determined. on the microring, It should zero modulation be noted that phenomenon when the will modulated occur [34], electric fieldand the is uniformly phase change distributed of photons on moving the microring, around in thezero ring modulation is represented phenomenon by [29]: will occur [34], and the phase change of photons moving around in the ring is represented by [29]: πn3 γ E LΓ e f f 33 3z ∆ϕ = − 휋푛 훾33,퐸푧퐿훤 (3) Δ휑 = −λ 푒푓푓 , (3) 휆 where Ez is the z-component of the electric with the direction perpendicular to the device where Ez is the z-component of the electric with the direction perpendicular to the device surface, and Γ is the electro-optic overlap factor. Since fFSR = fRF, the time for the photon to surface, and Γ is the electro-optic overlap factor. Since fFSR = fRF, the time for the photon to travel a week in the ring is exactly equal to the time for the RF electric field to change for travelone cycle, a week resulting in the in ring zero phaseis exactly change, equal as shownto the intime Figure for 8the. In RF this electric work, a field PPLN to thin change for one cycle, resulting in zero phase change, as shown in Figure 8. In this work, a PPLN thin film is introduced to have the left and right parts of the microring polarized with opposite directions, so that the maximum electro-optic modulation efficiency can be achieved. When a vertical electric field is applied to the surface of the chip, the modulated effective refractive index of the waveguide can be given by [35]:

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film is introduced to have the left and right parts of the microring polarized with opposite directions, so that the maximum electro-optic modulation efficiency can be achieved. When 3 a vertical electric field is applied to the surface of the chip, the푛 modulated훾33퐸푧훤 effective refractive 푛 = 푛 − 푒푓푓0 , (4) index of the waveguide can be given by [푒푓푓35]: 푒푓푓0 2 Crystals 2021, 11, x FOR PEER REVIEW 8 of 10

eff0 3 where n is the effective refractive indexne f f 0ofγ33 waveguideEzΓ without electric field. The simu- n = n − , (4) lation is performed using thee f ffollowinge f f 0 parameters:2 γ33 = 31 pm/V, neff0 = 1.78596, Г = 0.81.

To observe the electro-optic effect, assuming3 that the applied electric field is uniform, the where neff0 is the effective refractive index of waveguide푛푒푓푓0훾33 without퐸푧훤 electric ﬁeld. The simula- 푛푒푓푓 = 푛푒푓푓0 − , (4) drifttion of is the performed resonance using thepeak following near 1550 parameters: nm is γinvestigated33 =2 31 pm/V, nateff 0different= 1.78596, electricΓ = 0.81. field intensities

of To0 whereV/μm, observe neff 1 the0 isV/μm, the electro-optic effective 2 V/μm, refractive effect, 3 V/μm assuming index and of that waveguide 4 theV/μm, applied respectively,without electric electric ﬁeld is asfield. uniform, shown The simu- thein Figure 9a,b, the drift of the resonance peak near 1550 nm is investigated at different electric ﬁeld intensities electrolation-optical is performed tunability using the of following the RF receiverparameters: can γ33 =be 31 determinedpm/V, neff0 = 1.78596, as 48 Г pm·μm/V,= 0.81. which is ofTo 0 V/observeµm, 1 V/theµ electrom, 2 V/-opticµm, 3effect, V/µ massuming and 4 V/ thatµm, the respectively, applied electric as shown field in is Figure uniform,9a,b, the comparable to that of the structure with electrodes [36,37]. ·µ thedrift electro-optical of the resonance tunability peak near of the 1550 RF receivernm is investigated can be determined at different as electric 48 pm fieldm/V, intensities which isof comparable 0 V/μm, 1 toV/μm, that 2 of V/μm, the structure 3 V/μm withand 4 electrodes V/μm, respectively, [36,37]. as shown in Figure 9a,b, the electro-optical tunability of the RF receiver can be determined as 48 pm·μm/V, which is comparable to that of the structure with electrodes [36,37].

Figure 8. Zero modulation principle of uniform field. The blue area represents the microring, and FigureFigure 8. Zero8. Zero modulation modulation principle principle of uniform of uniform field. The field. blue The area bluerepresents area the represents microring, theand microring, and the Vm-t curve below represents the change of electric field intensity over time. Since fFSR = fRF, the the Vm-t curve below represents the change of electric field intensity over time. Since fFSR = fRF, the timethe forVm the-t curve photon below to travelrepresents one cycle the change in the ringof electric is exactly field equal intensity to the over time time. for Since one period fFSR = f ofRF, RFthe time for the photon to travel one cycle in the ring is exactly equal to the time for one period of RF timeelectric for field.the photon When the to uniform travel electricone cycle field actsin the on thering microring is exactly and theequal photon to the is transmitted time for inone period of RF electric field. When the uniform electric field acts on the microring and the photon is transmitted electricregion field. A of the When microring, the theuniform RF electric electric field is field positive, acts and on the the corresponding microring resultsand the in Equation photon is transmitted in region A of the microring, the RF electric field is positive, and the corresponding results in in (3)regionEquation is ∆ϕ .A Similarly, (3)of isthe Δφ. microring, as Similarly, the photon as the travelsthe photonRF through electric travels the field through B region is positive, the of theB region microring, and of the the the microring, corresponding RF electric the field RF results in Equationreverseselectric and(3) field is the reverses Δφ. corresponding Similarly, and the corresponding phase as the change photon phase is − ∆travelsϕ change. As a through result,is −Δφ. theAs overallthea result, B region phase the overall difference of the phase microring, of the RF electricphotonsdifference field around ofreverses photons the microring aroundand the is the zero. corresponding microring is zero. phase change is −Δφ. As a result, the overall phase difference of photons around the microring is zero.

FigureFigure 9. 9.(a )(a The) The transmission transmission spectrum spectrum and and (b ()b wavelength) wavelength offsets offsets of of the the microring microring when when the the electric electric ﬁeldfield intensityintensity isis 0 0 V/V/μm,µm, 1 V/V/μm,µm, 2 2 V/μm, V/µm, 3 3V/μm V/µm and and 4 4V/μm, V/µm, respectively. respectively.

4. Conclusions In conclusion, a microring -based electrode-free radio frequency receiver is designed Figure 9. (a) The transmission spectrumusing varFDTD and ( band) wavelength FDE solution offsets methods, of the operating microring at 35 when GHz RFthe electricelectric field. field Key intensity is 0 V/μm, 1 V/μm, 2 V/μm, 3 V/μmparameters and 4 V/μm, such respectively. as the coupling length of single-mode conditional transmission loss are analyzed and calculated. The Q-factor of the resonator is up to 106 and the total length of the ring is 3766.59 μm. PPLN technology is used to improve the electro-optic modulation 4. Conclusionsefficiency, and the electro-optic tuneability reaches 48 pm·μm/V. This proposed device In conclusion, a microring-based electrode-free radio frequency receiver is designed using varFDTD and FDE solution methods, operating at 35 GHz RF electric field. Key parameters such as the coupling length of single-mode conditional transmission loss are analyzed and calculated. The Q-factor of the resonator is up to 106 and the total length of the ring is 3766.59 μm. PPLN technology is used to improve the electro-optic modulation efficiency, and the electro-optic tuneability reaches 48 pm·μm/V. This proposed device

Crystals 2021, 11, 359 9 of 10

4. Conclusions In conclusion, a microring-based electrode-free radio frequency receiver is designed using varFDTD and FDE solution methods, operating at 35 GHz RF electric field. Key parameters such as the coupling length of single-mode conditional transmission loss are analyzed and calculated. The Q-factor of the resonator is up to 106 and the total length of the ring is 3766.59 µm. PPLN technology is used to improve the electro-optic modulation efficiency, and the electro-optic tuneability reaches 48 pm·µm/V. This proposed device can be used with all dielectric antenna as a metal-free receiving front-end which will eliminate the weakness of traditional receivers and expect to play a key role in the field of anti-electromagnetic damage.

Author Contributions: Z.W. and M.Z. proposed the conceptualization and methodology; Z.W. analyzed the data, reviewed and modified the manuscript; Y.L. carried out the simulations, and wrote the paper; S.H., X.Y. (Xiong Yin) and M.D. contributed investigation; L.G. and X.Y. (Xin Yang) contributed data analysis and modification of the paper; M.Z. managed the project. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Natural Science Foundation of China (NSFC) (61704017) and Dalian Science and Technology Innovation Fund (2018J11CY006). Institutional Review Board Statement: The study was not applicable involving humans or animals. Informed Consent Statement: The study was not applicable involving humans or animals. Data Availability Statement: Data available in a publicly accessible repository. Acknowledgments: Z. Wu, L. Guo and M. Zhao would like to acknowledge the support from the Natural Science Foundation of China (NSFC) (61704017) and Dalian Science and Technology Innovation Fund (2018J11CY006). Conflicts of Interest: The authors declare no conflict of interest.

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