I J P R A INTERNATIONAL JOURNAL OF 2766-2748 PHYSICS RESEARCH AND APPLICATIONS

Review Article More Information *Address for Correspondence: Anjan Samanta, Sabang Sajanikanta Mahavidyalaya, Lutunia, Tunable induced transparency and Paschim Medinipur, 721166, India, Email: [email protected]

Fano-resonance in double cavity Submitted: October 19, 2020 Approved: April 06, 2021 optomechanical system Published: April 07, 2021 How to cite this article: Samanta A, Anjan Samanta1,2*, Kousik Mukherjee2,3 and Paresh Mukherjee K, Jana PC. Tunable induced transparency and Fano-resonance in double 2 Chandra Jana cavity optomechanical system. Int J Phys Res Appl. 2021; 4: 019-025. 1 Sabang Sajanikanta Mahavidyalaya, Lutunia, Paschim Medinipur, 721166, India DOI: 10.29328/journal.ijpra.1001036 2Vidyasagar University, Medinipur, Paschim Medinipur, 71102, India Copyright: © 2021 Samanta A, et al. This is 3Government General Degree College, Gopiballavpur-II 721517, India an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and re- Abstract production in any medium, provided the original work is properly cited.

We analyze optomechanically induced Transparency and asymmetric Fano-line shape Profi le Keywords: Transparency; Fano-Resonance; in a two-mode cavity system, coupling at weak and strong coupling regimes. The model system Optical switches consists of one mechanical mode and two optical modes. The transmission shows nonreciprocal behavior. Both the forward transmission and backward refl ection for the system are analyzed for both optic-optic and mechanical-optic cavities by considering various system parameters. The output spectra lead to sharp asymmetric Fano-resonance and tunable transparency. Double OPEN ACCESS line-shape profi le is observed in the output Spectrum. Our proposal provides a new platform for application in quantum telecommunications and a photonic device like optical Switches.

Introduction many applications in ultra-slow wave propagation [13], Single-photon source [14], Photo Switch [15], Quantum Induced transparency with detuning parameters for opti- wavelength conversion [16], Optical narrow cavity system like cal systems has the impact to be used for potential applications microresonator, four-wave mixing [17], Quantum Trampling such as power switching, quantum computing, etc. Different [18], ultra-high-precision assessment [19,20]. Squeezing of a types of induced transparency are electromagnetically, mechanical observation in the sideband state [21,22] can’t be optomechanically, optically, coupled mode induced trans- solved in the traditional Opto-mechanical way. parency, etc. In this regard, we have discussed the tunable line-shaped fano proile in a double cavity optomechanical It requires a new technique. Chen, et al. [23] build a new system. technique in which a slow light is realized in BEC. A tunable Fano-resonance can be achieved via the Passive - Passive In cavity optomechanics, the investigation of Controlled regime [6]. In recent times the Fano-resonance property has induced transparency and Fano-resonance clearly describe been shown for double cavity coniguration [24]. The induced the controlled behavior of Electromagnetically induced transparency and Fano-resonance have been achieved by transparency (EIT) for a hybrid Bose-Einstein condensate the study of absorption and dispersion proiles for output (BEC) and signiicantly uses in quantum, engineering [1]. ield probe frequency [25]. The correlation function has Electromagnetically induced transparency a phenomenon of been calculated [26]. Controlled behavior of EIT has been direct development of quantum systems exclusively observed shown for transverse ields [1]. Fano-resonance has also been [2,3] and inds tremendous application [4,5]. Tunable presented in a hybrid cavity system for different parameters asymmetric Fano property and optically induced transparency [27,28]. However, to the best of our knowledge multiple Fano- (OIT) for weak ield clearly show the application in telecom resonances useful in three-dimensional Plasmon ruler [29], system [6], in double EIT phenomena with lab-application highly directive antenna [30], Humble Waveguide [31]. EIT [7] switches, sensors, and selection of single-mode laser is a result of the Interference effect which is known as Fano [8]. A Fano-like asymmetric resonance is induced with time interference [32,33]. Fano resonance and EIT Occurs in single [9] and shows a description of Ugo-Fano [10], nanoscale silica - iber taper [34]. In Quantum optics it has also been Structure [11,12]. The purpose of this type of research has shown that by using a microcavity it is possible to design an

https://doi.org/10.29328/journal.ijpra.1001036 https://www.heighpubs.org/jpra 019 Tunable induced transparency and Fano-resonance in double cavity optomechanical system

optical switch and also optical sensor [36]. So to understand Calculation of dynamics the quantum interference in EIT we have focused on this type In the mechanical displacement at a frequency ω for the of research. Our study concentrates the tunable transparency m input control ield, the total Hamiltonian is transformed by and Fano resonance for the system. We theoretically solved g and plot via different experimental data which is published aa††  b b , the nonlinear coupling can be Diagonalized m [6]. Ve g2 g as ()aa†2under week Optomechanical coupling  1 and In this paper ‘Fano-resonance and tunable transparency in m m double cavity Opto-mechanical system’, has been investigated the transformed Hamiltonian can be written as as ref. 6. We represent a model: Hamiltonian with double HaaccbbacacaaEcEc' †††     ( †††2†*  )  ( )   (2) cavity coupled mechanically which is controlled by a control 12m g2 ield and probe ield. The system is illuminated by a laser Where  Kerr type nonlinear strength induced by  ield. In this paper, we present the solution for the proposed m optomechanical coupling. Hamiltonian and have discussed dynamically the Heisenberg- Langevin equations for input-output theory. We have shown Considering the effect of quantum noise term the forward and backward relection rates by varying different Heisenberg-Langevin equations for the ield modes are system parameters. We present here the induced tunable written as transparency and asymmetric Fano-resonance for two  †2  different situations, one for coupling parameter and detuning a iaic 1    2 iaaka  – a , b ibibm   term. For their application in Quantum Opto-mechanics. ipt c  iciaiEkcie 2  –  cp  (3) Theoretical calculation The perturbation operators satisfy the following The model consists of one mechanical mode (b) and two correlations optical modes (a and c). They are coupled within the cavities aatt†'  bt' bt †  ct'  ct †   tt’  by mechanical mode via optomechanical interaction. The (4) ††† cavity is externally driven by a laser ield which is expressed atat'    bt  bt'   ct  c t'   0 by Where the equation [3] satisies the following equation.

in it12 i t øEte12 E e ddd (aFaic )  – , ( bFb ) ,   c Fciaie  – ipt dt123 dt dt p The Hamiltonian of the system can be written as (ħ = 1) For this purpose, we use the following parameters ††† †††††* HaaccbbacacgaabbEcEc 12   m ( )      (1) 2 Fi123 asam  4|| iakFi      iFi    cc  k Here ∆j = ωj - ωl (j = 1,2) is the corresponding cavity To examine the expectation values of small quantum laser detuning. ωj & ωm are resonance Frequencies of the luctuations of the above equation we use the matrix corresponding optical cavity and mechanical resonator. ∆1 is formation to calculate the luctuations components of Optic the frequency detuning ∆2 is the probe frequency detuning. and mechanical ield’s modes for solving the Eigenvalue    Here a(α ), b(b ), c(c ) are annihilation (creation) equation. We obtain the luctuation parameters which help us operators for the cavity ield modes. to calculate the forward and backward relection proile. In the Hamiltonian, the irst & second part describes the Fi1 p 0  i  A 0 fundamental and second harmonic optical ield mode with  (6) 000Fi2 p  B  frequency ωa & ωc and the third term represents mechanical  iFiCi0 3 pp mode, with frequency ωb. Here λ represents tunneling strength, which interacts between two modes with a photon. After matrix transformations, we get Now the nonlinear term of the system represents by g. The iFi () A  pp2 (7) last two parts are the intense control and weakened probe  2222 RQiPppp     i  pm()  ield. The ield strengths are related to the control ield power 4 Pk B = 0 by the relation E  c , + h iFi pp()()21 Fi  p C  P = Laser power. kj = corresponding cavity decay rate. The 222 (8) RQiPppp     i()  m classical laser ield is applied to the ordinary cavity, we can’t use it for the optomechanical cavity [38]. Here we use three For this calculation, we have used the constants situations of coupling coeficients μ, it deines three situations Pkka( (   )  (   )  )  4 | |2 (    ) μ < 1/2, μ = 1/2, μ > 1/2. It is referred to as under coupling, ac m cm ac s m c ik(( ) k (  )4| a |)22  critical coupling, and over coupling. am c cm a s

https://doi.org/10.29328/journal.ijpra.1001036 https://www.heighpubs.org/jpra 020 Tunable induced transparency and Fano-resonance in double cavity optomechanical system

5.5 MHz, and it can be timbre by changing the gap between Qi(4||)()      a2   kk  acm s ac the cavities. The optical kerr medium strength ≈ -2π × 1.05 Rkk()()4()     akk2     MHz. The gain to loss ratio for this cavity system varies from ca ac m s c m c -3 to +3 [40-46]. We propose the transmission and relection ikka(4)()2 1 ca  ca   s  c  m proiles over critical region μ  . Figures 2-4 represent 2 For a laser ield, the input-output information is photon tunneling strength on the forward transmission and backward relection rate for the double cavity mechanical

out in μkt (), out  μ()kt (9) system. It is seen from igure 2 that forward transmission rate T has a single transparent peak around ∆ /k 0 and two dips Here α β represents the input, output signal information F p a = are there on both sides of it. So it represents symmetric dip respectively. peak –dips spectral structure and conirms the IT effect. In Applying standard input-output theory for this model igure 3 if we increase the cavity coupling strength λ = 0.4, and  kc pp it2c 1 itc it p p  0.6 the two dips around 2 and 2 appear and the akaekAekAeout[μ c c s  p a a ] (10) k kk μk a aa a width of the transparency increases. Hence one may tune the it2c itc it p p ckbeBeBeoutμ[ c s   ] IT by increasing detuning parameter and coupling strength (here relection rate is very small due to the small gain to So in equation (10) both the input and output ields have the loss ratio). If we choose coupling strength 1.67 (Figure 3) their frequency components. The irst two indicate input the relection proile splits into two peaks and expiates the and output ield frequency and the third one is for additional forward rate and the separation between two peaks depends frequency component 2ωc - ωp called stokes ield frequency on the tunneling strength and weak coupling parameters. [37]. To study forward power transmission and backward Next, we have studied the variation of forward transmission power relection we are interested in the component of output rate with strength. ield frequency.

For the probe ield frequency, the ratio of output to input 8 ield amplitude for forward transmission and backward

6 relection is given by B , T μkA F 4 a  T p 1  p 2 kkμ B   ca  0 p -20 -10 0 10 20  p 'p/ka The forward transmission rate T |( )|2 and backward F  Figure 1 2 relection rate TB |( )| of the probe, ield are derived as

20 k Äpm (11) T |1 |2 F w 15 ikk[4()      a2   ikk   k  3 ac a p m p m s m p ma a a p p 2 TB | | (12) B w 10 , T F

22 T Where w = RQiPppp     i 12 (   m )  5

Results and discussions 0 -20 -10 0 10 20

In this section, we have discussed the transmission of the 'p/ka probe ield with respect to system parameters. We present Figure 2 different situations by using forward and backward relection rates as a function of normalized probe detuning and different ield parameters. The tunable external laser having 1350 nm 15 band is used as control or pump laser and other with 1450 nm 10

band is used as probe laser. A cavity resonator can be designed B , T

from silica. This setup can emit photons in the wavelength F 5 band 1500 nm band for a laser driving wavelength 900 nm T or 1350 nm bands. By slit change of the resonator gap the 0 total loss rate can be tuned via external coupling loss rate. -20 -10 0 10 20 'p/ka The effective gain rate in the cavity is ≈ -2π × 10.5 MHz. The photon tunneling rate between the two cavities is ≈ -2π × Figure 3

https://doi.org/10.29328/journal.ijpra.1001036 https://www.heighpubs.org/jpra 021 Tunable induced transparency and Fano-resonance in double cavity optomechanical system

 c 14 0.006, 0.66, 5aksa 0.06, / 0.26 kkaa 12 10 k (1)  /kk 0.133, c 1.33, / 0.6 aa 8 ka F 6 T kcm (2) 0.0006, 0.6, 0.06 , 26.67 4 kkkkaaaa 2

kcm ë 0 (3) 0.133, 0.6, 0.06 , 1.67 -20 -10 0 10 20 kkkkaaaa 'p/k'a p/ka

Figures 4-7 show the variation of forward transmission Figure 4 rate with probe strength for the Optic-Optic system. Now we have plotted line shape transmission spectra for a double

Optomechanical system. In igure 5 we have taken Optic cavity 8 detuning ∆a = - 0.01ka; the plot of TF has a sharp peak around 6

the center i.e. ∆ = 0 and two symmetric dips around both sides

p F of the peak. In igure-6 all the parameters remain the same T 4 as in igure 5 except the passive cavity detuning ∆ = - 0.02k . a a 2 There is an increase in transparency peak and the dips nature 0 are asymmetric. It is also called a two-sided coupled cavity -20 -10 0 10 20 system. The frequency of this line always is close to the cavity 'p/ka mode which indicates the origin of the Fano [39]. For the Figure 5 same cavity detuning if we decrease the value of effective gain kc = - 1.0ka then the peak height also reduces as shown in igure

7. At kc = - 2.0ka with all other parameters remain unchanged 8 the transparency peak disappears. So the transmission rate is controlled by changing the gain to lose ratio. In igure 8 if 6

we use λ = 0.067 then the proile is highly asymmetric. This F 4 proile shows an asymmetric Fano line Shape. T 2

Figures 4-7 Plot of forward transmission rates (blue line) 0 for normalized probe -20 -10 0 10 20 'p/ka' p/ka cm 0.66, 5, |as | 0.06,  0.133,  0.2, Figure 6 kkkaaa ë kk 0.26(4)ac 0.0066, 1.66, (5) ac 0.06,, 1.0, kkkaaa kk aa 14 kkëë12 (6)ac 0.0133,  1.0,  0.067, ac  0.0133,  1.0,  0.067 kkkkkkaaaaaa 10 8 Now we calculate the forward transmission and F T backward relection in the over- coupling region by taking 6 μ = 2. The interference between two optical systems excited 4 simultaneously in a resonator creates EIT otherwise Fano- 2 0 resonance. The several transmission line shape is manipulated -20 -10 0 10 20 by γ + ω Σ(j = 1, 2) with kk between two optical cavities 'p/ka j j ac which affect the transmission relection proile. In our Figure 7 calculation, both the cavity photon and incident laser source have the same polarization. When Σ >> γj + ωj i.e no interaction between these cavities then there are two separate dips 2.0 in transmission spectrum but if Σ < γj + ωj then two modes 1.5 interact, and the Fano line shape is formed. If Σ (Kerr-type nonlinear strength) is decreased further i. e. the interaction F T 1.0 between two optic modes is stronger than the Fano lineshape has more contrast as shown in igures 8-11 and when it 0.5 becomes zero that means Fano line Shape became EIT. It also 0.0 clear from igure 12, the case zero asymmetries, which shows -6 -4 -2 0 2 4 6 symmetrical resonance which is referred to as anti-resonance 'p/ka [39]. Figure 8

https://doi.org/10.29328/journal.ijpra.1001036 https://www.heighpubs.org/jpra 022 Tunable induced transparency and Fano-resonance in double cavity optomechanical system

Figures 8-11 Plot of forward transmission rate TF (blue line) for normalized probe: 3.0 2.5

kca c m 2.0  0.2, 0.1,as  0.06,  1, 0.05, 0.5,  0.005,

kkaa k a ka F

T 1.5 8 160. 9  100. 10 70 11kk /  1,  / k  0.067,  5,      ca aa 1.0 ma/kk 0.2,  /a  0.67,  0.4 0.5 0.0 Figures 12-15 shows the variation of forward -6 -4 -2 0 2 4 6 transmission rate with probe detuning in over coupling 'p/ka regime for Optic-mechanical System. It is to be noted that Figure 10 if the coupling parameters are 0.1 then there is no effect in output transmission. Figure 12 shows absorptive properties of the system if we change the coupling parameter ratio from 8

kkcc 1.0 to  1.25. The Transmission line shape changes 6 kkaa more drastically. In igures 13-15 line shape picture is F T 4 generated and the result has zero probe asymmetric Fano line shape due to the presence of the coupling term gaa (b + b) 2 in the Hamiltonian. Figure 15 is a mirror type image of igures 0 15,16 where other variables remain unchanged but coupling -10 -5 0 5 10 kk 'p/ka constant changes from cc1 to  1 as is indicated by kk the input power of laser sources.aa Asymmetric nature can be Figure 11 tuned via gain to lose ratio as shown in igures 13,14. Figure 13 indicates a sharp Fano line with a resonance peak at 1.5

∆p = 0.00341ka and dip at ∆p = -0.00567ka, the Fano spectral

1.0 width is of 0.00908ka. The forward transmission contrast with

Fano resonance by approximately 60% which satisies the F T minimum criterion for a telecommunication system [35]. 0.5

Figures 12-15 Plot of forward transmission rate TF (blue 0.0 line) constant variables: -6 -4 -2 0 2 4 6 'p/ka

1,  0.1,  0.3,asm  0.06,   0.31,  10, Figure 12 (12)kkac 2,  2.0,  c  2, 13 kk ac  2,  2.5,  c  3,

14kkac 2,  2.5,  c  2(15) kk ac  1,  2.0,  c  2

Again if we decrease the non linear coupling parameters 1.5 then the transmission proile almost remain same but its peak 1.0

become sharp and increases height. From this study the Fano F T line shape is ruled out and transmission proile is absorptive. 0.5

Conclusion 0.0 -6 -4 -2 0 2 4 6 In conclusion, we have investigated the tunneling effect 'p/ka and Fano resonance for double cavity Optomechanical system Figure 13 via Forward transmission and backward relection proile.

2.5 2.0

2.0 1.5 F

F 1.5 T

T 1.0 1.0 0.5 0.5

0.0 0.0 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 'p/ka 'p/ka

Figure 9 Figure 14

https://doi.org/10.29328/journal.ijpra.1001036 https://www.heighpubs.org/jpra 023 Tunable induced transparency and Fano-resonance in double cavity optomechanical system

with a doubled free spectral range for sensing application. Optics 3.0 communications. 2011; 284. 2.5 9. Peng LF, Ozdemir B, Long SK, Yang GL. Applied Phys Letter. 2014;

2.0 105: 1101112. 1.5 F 10. Miroshnichenko AE, Flach S, Kivshar YS. Fano resonances in T 1.0 nanoscale structures. Rev Mod Phys. 2010; 82: 2257. 0.5 11. Yanchuk BL, Zheludev NI, Maier SA, Halas NJ, Nordlander P, et al. 0.0 The Fano resonance in plasmonic nanostructures and metamaterials. -6 -4 -2 0 2 4 6 Nat Mater. 2010; 9: 707-715. PubMed: https://pubmed.ncbi.nlm.nih.gov/20733610/ 'p/ka

Figure 15 12. Christ A, Tikhodeev SG, Gippius NA, Kuhl J, Giessen H, Waveguide- Plasmon Polaritons: Strong Coupling of Photonic and Electronic Resonances in a Metallic Photonic Crystal Slab. Phys Rev Lett. 2003; These results support how Fanoresonance is controlled in 91: 183901. various optical systems. The results are very interesting for PubMed: https://pubmed.ncbi.nlm.nih.gov/14611284/ destructive and constructive line shape with anti-symmetric 13. Teufel JD, Li D, Allman MS, Cicak K, Sirois AJ, et al. Circuit cavity tunable Fano-resonance. we have focused here on how Fano electromechanics in the strong-coupling regime. Nature. 2011; 471: 204-208. resonance in light, propagates through the optical device PubMed: https://pubmed.ncbi.nlm.nih.gov/21390127/ and how we can use this type of research in quantum optical 14. Agarwal GS, Huang S. Optomechanical systems as single-photon communications and can enrich our optical device for using routers. Phys Rev A. 2012; 85: 021801. line optical switches. We model this for two coupling schemes 15. Qu K, Agarwal GS. Phonon-mediated electromagnetically induced i.e for critical and over coupling. Here we have shown that absorption in hybrid opto-electromechanical systems. Phys Rev A. both the proile continuously changes due to gain to loss ratio 2013; 87: 031802. and coupling strength with coupling parameter. For the Optic- 16. Hill JT, Safavi-Naeini AH, Chan J, Painter O. Coherent optical wavelength Optic cavity coniguration, the transmission spectra show conversion via cavity optomechanics. Nat Commun. 2012; 3: 1196. PubMed: https://pubmed.ncbi.nlm.nih.gov/23149741/ asymmetric behavior which can be controlled by an input/ output probe. In our study, we use coupling parameters 17. Huang S, Agarwal GS. Normal-mode splitting and antibunching in Stokes and anti-Stokes processes in cavity optomechanics: Radiation- opposite sign for an active-passive and the same sign for pressure-induced four-wave-mixing cavity optomechanics. Phys Rev the passive-passive system. This study is useful for different A. 2010; 81: 033830. optical switching systems and also telecom systems. 18. Agarwal GS, Huang S. Optomechanical systems as single-photon routers. Phys Rev A. 2012; 85: 021801. Author contribution statement 19. Zhang JQ, Li Y, Feng M, Xu Y. Precision measurement of electrical This worked was discussed by three authors and careful charge with optomechanically induced transparency. Phys Rev A. reading veriied the output proile. AS performed theoretical 2012; 86: 053806. calculations and wrote the paper. 20. Wang Q, Zhang JQ, Ma PC, Yao CM, Feng M. Tunable high-order sideband spectra generation using a photonic molecule optomechanical References system. Phys Rev A. 2015; 91: 063827. 21. Wang DY, Bai CH, Wang HF, Zhu AD, Zhang S. Steady-state 1. Kashif AY, Wu-Ming Liu. Nature. Scientifi c. Report, 2016; 10. 1038- mechanical squeezing in a double-cavity optomechanical system. Sci 22651. Rep. 2016; 6: 24421. 2. Scully MO, Zubairy MS. Quantumn Optics (Cambridge University PubMed: https://pubmed.ncbi.nlm.nih.gov/27917939/ Press). 1997; 67. 630. 43458. 22. Dalafi A, Naderi H, Motazedifard. Eff ects of quadratic coupling and 3. Safavi-Naeini AH, Mayer Alegre TP, Chan J, Eichenfi eld M, Winger squeezed vacuum injection in an optomechanical cavity assisted with M, et al, Electromagnetically induced transparency and slow light with a Bose-Einstein condensate. Phy Rev A. 2018; 97: 043619. optomechanics. Nature. 2011; 472: 69-73. 23. Chen B, Jiang C, Zhu KD. Manipulation of slow and superluminal light PubMed: https://pubmed.ncbi.nlm.nih.gov/21412237/ based on a graphene nanoribbon resonator. Phys Rev A. 2011; 83: 4. Harris SE, Field JE, Imamoglu, A, Nonlinear optical processes using 055803. electromagnetically induced transparency. Phys Rev Lett. 1990; 64: 24. Wallauer J, Walther M. Fano line shape and phase reversal in a split- 1107-1110. ring resonator based metamaterial. Phys Rev B. 2013; 88: 195118. PubMed: https://pubmed.ncbi.nlm.nih.gov/10041301/ 25. Qu K, Agarwal GS. Phonon-mediated electromagnetically induced 5. Boller KJ, Imamoglu A, Harris S. Observation of electromagnetically absorption in hybrid opto-electromechanical systems. Phys Rev A. induced transparency. Phys Rev Lett. 1991; 66; 2593-2596. 2013; 87: 031802. PubMed: https://pubmed.ncbi.nlm.nih.gov/10043562/ 26. Samanta A, Jana PC. Study of First & Second order Correlation 6. Mukherjee K, Jana PC. Optically induced transparency in coupled Function for Two Composite State. IJERD. 2020; 16. micro-cavities: tunable Fano resonance. Eur Phys JD. 2019; 73: 264. 27. Qu K, Agarwal GS. Fano resonances and their control in optomechanics. 7. Akram MJ, Ghafoor F, Saif F. Electromagnetically induced transparency Phys Rev A. 2013; 87: 063813. and tunable fano resonances in hybrid optomechanics. J Phys B At Mol 28. Akram MJ, Ghafoor F, Sair F. Electromagnetically induced transparency Opt Phys. 2015; 48: 065502. and tunable fano resonances in hybrid optomechanics. J Phys B. 2015; 8. Lu Y, Fu X, Chu D, Wen W, Yao J. Nested microring resonator 48: 065502.

https://doi.org/10.29328/journal.ijpra.1001036 https://www.heighpubs.org/jpra 024 Tunable induced transparency and Fano-resonance in double cavity optomechanical system

29. Liu N, Hentschel, Weiss T, Alivisatos AP, Giessen H. Three- 38. Wang DY, Wu Q, Yu YF, Zhang ZM. Optical nonreciprocal response dimensional plasmon rulers. Science. 2011; 332: 1407-1410. and conversion in a Tavis-Cummings coupling optomechanical system. PubMed: https://pubmed.ncbi.nlm.nih.gov/21680838/ Phys Rev A. 2019; 99: 043818.

30. Artar A, Yanik AA, Altug H. Multispectral Plasmon Induced Transparency 39. Miroshnichenko AE, Flach S, Kivshar YS. Fano resonances in in Coupled Meta-Atoms. Nano Lett. 2011; 11: 3694. nanoscale structures. 2003; 0902: 3014.

31. Liu N, Mukherjee S, Bao K, Brown LV, Dorfmuller J, et al. Magnetic 40. Chang JH, Lin WH, Wang PC, Taur J, Ku TA, et al. Solution-processed plasmon formation and propagation in artifi cial aromatic molecules. transparent blue organic light-emitting diodes with graphene as the top Nano Lett. 2012; 12: 364 -369. cathode. Sci Rep. 2015; 5: 9693. PubMed: https://pubmed.ncbi.nlm.nih.gov/22122612/ PubMed: https://www.ncbi.nlm.nih.gov/pubmed/25892370 32. Fano U. Eff ects of Confi guration Interaction on Intensities and Phase 41. Vahala KJ. Optical microcavities. Nature. 2003; 424: 839-846. Shifts. Phys Rev. 1961; 124: 1866. PubMed: https://pubmed.ncbi.nlm.nih.gov/12917698/ 33. Miroshnichenko AE, Flach S, Kivshar YS. Fano resonances in 42. Vahala KJ. Optical Microcavities in Advanced Series in Applied nanoscale structures. Rev Mod Phys. 2010; 82: 2257-2298. Physics, World Scintifi c. 2004; 5. 34. Li BB, Xiao YF, Zou CL, Jiang XF, Liu YC, et al. Fano resonances in metallic grating coupled whispering gallery mode resonator. Appl Phys 43. Peng B. Parity–time-symmetric whispering-gallery microcavities. Nat Lett. 2012; 100: 021108. Phys. 2014; 10: 394. 35. Reed GT. Silicon optical modulators. Nat Photon. 2010; 4: 518. 44. Peng B, Özdemir SK, Rotter S, Yilmaz H, Liertzer M, et al. Loss-induced suppression and revival of lasing. Science. 2014; 346: 328-332. 36. Mukherjee K, Jana PC. Tunable terahertz optical bistability and PubMed: https://pubmed.ncbi.nlm.nih.gov/25324384/ multistability in photonic metamaterial multilayers containing nonlinear dielectric slab and graphene sheet. Physics. 2020; 117: 113780. 45. Reed GT. Silicon optical modulators. Nat Photon. 2010; 4: 518. 37. Hung S, Agarwal GS. Normal-mode splitting and antibunching in 46. Li S, Ge Q, Wang Z, Martín JC, Yu B. Optical bistability via an external Stokes and anti-Stokes processes in cavity optomechanics: Radiation- control fi eld in all-fi ber ring cavity. Sci Rep. 2017; 7: 8992. pressure-induced four-wave-mixing cavity optomechanics. Phys Rev A. PubMed: https://pubmed.ncbi.nlm.nih.gov/28827618/ 2010; 81: 033830.

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