Abstract

Nonreciprocal light phenomena, including one-way wave propagation along an interface and one-way optical tunneling, are presented at terahertz frequencies in a system of magnetically controlled multi-layered structure. By varying the surface termination and the surrounding medium, it is found that the nonreciprocal bound or radiative Tamm plasmon polartions can be supported, manipulated, and well excited. Two different types of contributions to the non-reciprocity are analyzed, including the direct effect of magnetization-dependent surface terminating layer as well as violation of the periodicity in truncated multi-layered systems. Calculations on the asymmetrical dispersion relation of surface modes, field distribution, and transmission spectra through the structure are employed to confirm the theoretical results, which may potentially impact the design of tunable and compact optical isolators.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical non-reciprocity refers to the asymmetrical characteristics in the transmission of the field when the source and detector are exchanged in their locations. This property is of immense importance for devices such as optical isolators [1–3], which allows light to propagate one single direction but blocks light in the opposite direction. The traditional way for realizing optical non-reciprocity relies on magneto-optical (MO) Faraday effects in a system based on ferrite materials, i.e. Yttrium Iron Garnet (YIG). However, owing to the intrinsic weakness of Faraday effects, such ferrite-based systems are generally bulky, thereby hindering the miniaturization of optical devices. Over the past two decades, enhanced nonreciprocal response is investigated in photonic crystals (PCs) by use of optical resonances. For example, resonant Faraday rotation response can be achieved by use of Bragg scattering in a magnetic photonic crystal waveguide [4], and also based on guided resonances [5], it is possible to obtain strong nonreciprocal response in a MO photonic crystal slab. Nonreciprocal behavior has also been demonstrated by considering numerous other techniques or methods, such as spatio-temporal dynamic modulation [6–9], opto-mechanical coupling effects [10–12] and the use of nonlinear optical processes [13–16].

It is well known that surface waves may possibly show nonreciprocal properties when the time-reversal symmetry is broken in a system [17–22]. Recently, Raghu and Haldane [17, 18] predicted firstly that the 2D MO PCs system can possess unidirectional photonic modes, which are direct analogs of chiral edge states of the electron in the quantum Hall effect. The field of such modes is bounded by the surface of PCs, exhibiting one-way wave propagation characteristics. Followed by the proposed theoretical prediction, several research groups [19, 20] realized and observed experimentally the electromagnetic one-way edge states in different MO PCs. The existence of one-way surface plasmon polaritons (SPPs) is also demonstrated in a plasmonic waveguide under a static magnetic field [21]. However, the working frequency for this device is limited at visible spectral ranges, and meanwhile the required magnetic field is very high (B>103 T) and not achievable to date.

On the other hand, Tamm plasmon-polaritons (TPPs) are surface localized waves bounded at the interface between a metal and a dielectric Bragg mirror and were proposed theoretically and confirmed experimentally by Kaliteevski and co-workers [23–25]. As for conventional SPPs, the confinement of TPPs on the metal side originates from the fact of the metal’s negative dielectric constant at a frequency below its bulk plasma frequency. However, on the side of the Bragg mirror, the confinement is not due to total internal reflection but to the photonic band gap arising from the dielectric multilayer structure. Furthermore, TPPs can be supported in both the TE and TM polarizations and be excited without the use of special optical techniques such as prism or grating coupling. Due to the rapid growing interest in their properties, a number of potential applications on TPPs have been found in the realization of various optical components, such as absorbers [26], filters [27], optical switches [28, 29], polariton lasers [30–32], and single photon source [33] or the novel promising tool to engineer fluorophores emission [34–36].

Recently, great attention has been devoted to Terahertz (THz) science and technology due to its real-world applications, including sensing, imaging and wireless communications [37–39]. However, there still exists a challenge on the realization of high-performance, tunable, broadband and compact THz isolators, due to inadequate research of non-reciprocity mechanisms. In this work, we aim to examine significant non-reciprocity for TPPs at terahertz frequencies based on magnetically tunable multi-layered structure, when the external static magnetic field is less than 1 Tesla. It is shown that asymmetrical dispersions of TPPs can be obtained, leading to one-way wave propagation at the surface of semi-infinite structure or one-way optical tunneling when the structure becomes finite. Distinct nonreciprocal behavior can be tuned flexibly by varying geometrical or external parameters, i.e. surface terminations, the surrounding medium or external magnetic field. Moreover, the robustness of unidirectional propagation by the influence of a obstacle, as well as non-reciprocity in transmission related to loss effect of MO materials, is also investigated in our numerical simulations.

 figure: Fig. 1

Fig. 1 (a) Schematic diagram of the proposed MPC structure, formed by alternating magneto-optical active [permittivity ϵ1¯] and isotropic dielectric layers [permittivity ϵ2]. The semi-infinite MPC structure with a top magneto-active layer is embedded into a kind of homogeneous background dielectric material with its permittivity ϵb. (b) Dispersion of bound TPPs at the surface of MPCs. Gray and red lines correspond to the TPPs solutions when the external magnetic field is absent [B = 0T] or present [B=0.1T], respectively. f+ and f denote respectively the cutoff frequencies where the forward- and backward-propagating modes vanish, then representing the one-way wave propagation by light blue region. Yellow and white regions correspond to pass-bands and stop-gaps of an infinite MPC. Light lines for the background material are also shown by dotted lines.

Download Full Size | PPT Slide | PDF

2. Model and methods

Let us start with a one-dimensional magnetoplasmonic crystal (MPC) as schematically illustrated in Fig. 1(a). The unit cell of the MPC consists of one magneto-optical active layer (ML), i.e. gyrotropic material, and one non-magnetic isotropic dielectric, with thicknesses d1, d2, and permittivities ϵ¯1, ϵ2, respectively. The external static magnetic field is applied along z direction, forming a Voigt configuration with magnetization in the plane of the MPC interface and perpendicular to the wave vector of TPPs. The optical property of ML is characterized by a permittivity tensor,

ϵ¯1=(ϵ1iΔ10iΔ1ϵ1000ϵ1).

We take the following parameters for ML, i.e. ϵ1=ϵ[1ωp2(1+iα/ω)/((ω+iα)2ωc2)], Δ1=ϵωp2ωc/[ω((ω+iα)2ωc2)] and ϵ1 '=ϵ[1ωp2/(ω(ω+iα))]. Here ϵ is the high-frequency permittivity, ωp is the plasma frequency of ML, the collision frequency α characterizes loss strength in the ML, ωc=eB/m* is the cyclotron frequency, e is the electron charge, and m* is the effective mass of electrons. Here we take a typical kind of semiconductor material for the ML layer, i.e. the indium antimonide (InSb), which can have a permittivity at THz frequencies similar to that of metals at optical frequencies, therefore using the Drude model [40, 41] for the permittivity of ML layer. It should be noted that the studied nonreciprocal behavior throughout the paper is only limited to the case of TM-polarized light beam (magnetic field along z direction), because the TE mode solutions (electric field along z direction) for this system still possess time-reversal symmetry and Lorentz reciprocity. And the eiωt time-dependent convention for harmonic field is used in this work.

The entire MPC structure is embedded into a kind of homogeneous surrounding material with permittivity ϵb. To study wave propagation behavior in this system, we may firstly find the solution of the band structure for 1D infinite periodic structure of MPCs by using standard transfer-matrix approach [42, 43]. Let us consider a unit cell by starting from the interface of ML, and finishing the next such location after going through a full period Λ=d1+d2, and the total transfer matrix T^ associated with such a particular choice of the unit cell gives T^=P^1M^21P^2M^12. M^ij is the interface matrix associated with the magnetic field at the interface between the layer i and j,taking the following form

M^ij=ϵj2Δj22ϵjkxj(Fj*+FiFj*Fi*FjFiFj+Fi*),
where Fm=(ϵmkxm+iΔmky)/(ϵm2Δm2), m=i,j. The propagation matrix P^m= diag[eikxmdm, eikxmdm] describes the phase shift of the propagation wave in the m-th layer. By solvingthe eigenvalue problem on the matrix T^,
T^(a0b0)=eiKΛ(a0b0).
one can obtain the Bloch modes for the infinite MPC, where K is the Bloch wave vector.

Since the photonic band structure is only associated with the eigenvalues of transfer matrix, which is independent of the particular choice of a unit cell, one can consider a more general transfer matrix Tσ with a top layer, i.e. MO material with thickness σd1 (σ[0,1], a geometrical parameter determining the truncation of the terminating layer of MPCs), which is given by T^σ=P^σ1T^P^σ, where P^σ= diag[eikx1σd1,eikx1σd1]. That is, T^σ and T^ have the same eigenvalues, and the eigenvectors for them satisfy the relations

(aσbσ)=P^σ1(a0b0).

With the boundary condition that the tangential field components should be continuous across the interface, one can find the dispersion relation for TPPs,

qb=ikx1ϵbϵ1ϵ12Δ12T12e2ikx1σd1+T11eiKΛT12e2ikx1σd1T11+eiKΛkyϵbΔ1ϵ12Δ12,lmodes
where qb is defined as
qb=ky2(ωc)2ϵb,
describing the wave decay rate in the background material.

Eigenmode solutions of Eq. (5) for our proposed structure could be found by using a commercial root solver (Mathematica FindRoot), to search the numerical root ky of Eq. (5) at a fixed frequency. The non-reciprocity of TPPswhich comes from the contribution of the first and second item on the right hand of Eq. (5) will be analyzed below.

3. One-way wave propagation at the interface of semi-infinite MPCs

Without loss of generality, we consider a typical kind of semiconductor material for the ML layer, i.e. the indium antimonide (InSb), the dielectric layer in the MPC, i.e. germanium (Ge) with high permittivity ϵ2=16 in THz region, which can provide good index contrast with InSb, thereby forming the band gap of the MPC, and low-loss background materials SiO2 with permittivity ϵb=4 in the THz region for our calculation. The corresponding parameters of InSb at room temperature are taken as m*=0.014m0 (m0 is the free electron mass in vacuum), ωp=2×1013 rad/s, and ϵ=15.68 [40, 44]. We neglect the influence of the absorption in InSb by setting α=0 for initial calculations. The MO and dielectric layer have identical thickness with d1=d2=10μm throughout this work.

 figure: Fig. 2

Fig. 2 Steady-state field distribution Hz at a frequency f=2.8 THz with the applied magnetic field (a) B = 0T; (b) B=0.1T, in the absence of the scatterer; (c) B=0.1T, when a large PEC obstacle [height 40μm and width 8μm] is inserted. The line source at the interface is marked with "" in the figure.

Download Full Size | PPT Slide | PDF

Fig. 1(b) depicts regions of photonic pass-bands (yellow regions) and stop-gaps (white regions), together with the dispersion of the forward (ky>0) and backward (ky<0) TPPs, where the surface termination is the InSb layer with σ=1. In the absence of external magnetic field, B = 0 T, modes solution of TPPs is symmetrical and reciprocal, f(ky)=f(ky). However, when the magnetic field turns on, i.e. B=0.1 T, it is seen that there exists distinct and asymmetrical TPPs modes with f(ky)f(ky), and the branches of forward and backward TPPs approach and vanish, respectively, at different cutoff frequencies f+ and f, which implies the THz waves in the frequency region of [f,f+] (the light blue region) can only propagate forward. For the range of results shown, the dispersion curves of TPPs lie in the band gap of the MPC and simultaneously outside the light cone of the surrounding medium. This indicates the associated modes are localized at the surface of MPC, and meanwhile not accessible to direct excitation by incident radiation.

As a direct illustration of wave transport properties for our system, we plot in Fig. 2 the out-of-plane magnetic field profile by using a finite element solver (COMSOL Multiphysics). A magnetic line current as the source is located at the surface of the MPC, radiating waves of various wave vectors. Those matching up with the dispersion curves may be picked up to excite the TPPs. The working frequency is set to f=2.8 THz. As expected, surface waves, propagating forward or backward, are both well excited shown in Fig. 2(a), when the external static magnetic field is absent. In contrast, with the introduction of magnetic field, i.e. B=0.1 T, the source radiates forward, and only along a single direction [Fig. 2(b)], implying the excitation of one-way TPPs identical with the prediction shown in Fig. 1(b). Moreover, the unusual property of such one-way edge mode on strong suppression of backscattering is also examined in Fig. 2(c). A slab of perfect electrical conductor (PEC) is inserted on the interface, and it is observed that forward propagating waves choose another route to go around the obstacle to avoid being backscattered.

 figure: Fig. 3

Fig. 3 Effect of (a) applied magnetic field B and (b) the permittivity ϵb of the background material on the cutoff frequency f+ and f, and the bandwidth Δf=f+f of one-way wave propagation band. Note that ϵb=4 and B=0.1T are used in (a) and (b), respectively. Other parameters are the same as Fig. 1.

Download Full Size | PPT Slide | PDF

The performance of the one-way propagating frequency band may be affected by geometrical parameters or external factors applied to the proposed system. Next, We calculate the cutoff frequencies of the forward (f+) and backward (f) propagating modes, as well as the one-way transport regions, as a function of the applied magnetic field and permittivity of surrounding medium, shown in Fig. 3(a) and 3(b), respectively. With the increase of magnetic field, from 0 T to 0.2 T, the cutoff frequency starts to experience a splitting, giving rise to an increase of f+ but a decrease in f. Consequently, the bandwidth Δff+f of one-way propagating band exhibits a nearly linear variation from 0 to 0.4 THz, as the magnetic field increases. On the other hand, it depends little on the permittivity ϵb of the surrounding medium as seen in Fig. 3(b). Both f+ and f decrease dramatically as ϵb increases from 1.5 to 10, but Δf=0.2 THz remains almost unchanged.

We remark that in this regime, the field [seen from Fig. 2] is strongly localized at the interface and just penetrates into the first layer of multilayer systems. Therefore, such non-reciprocity on TPPs develops mainly from contribution of the magnetization effect in the top layer of MPCs, directly related to the second item in Eq. (5). Meanwhile, in the limit of kyω/c, the TPPs tends to be far away from the photonic band edge, and our proposed system in Fig. 1(a) may be considered as a simple waveguide structure formed at the interface of MO and background materials. Under this circumstance, the dispersion for the interface mode is given by

qb=ϵbϵ12Δ12(kyΔ1+kx1ϵ1)
and the cutoff frequencies of the forward and backward propagating mode f+ and f can be expressed analytically as [21, 41]
f+=12π[ωc24+ϵωp2ϵb+ϵ+ωc2],
f=12π[ωc24+ϵωp2ϵb+ϵωc2].

Thereby, the one-way-propagating bandwidth Δf=ωc/2π is proportional to the magnetic field B, and independent of the permittivity of the surrounding medium, which is in excellent agreement with the results shown in Fig. 3.

We turn to investigate in Fig. 4 the impact of the surface termination by vary σ on the manipulation of TPPs. As the thickness of the top layer decreases from σ=0.8 to 0.1, the cutoff frequencies f+ and f move to higher ones, and the bandwidth Δf tends to zero, resulting in weaker non-reciprocity effect shown in Fig. 4. Nevertheless, at smaller σ, i.e. σ<0.5, it is seen that there exists the radiative mode solutions for nonreciprocal TPPs inside the light cone of surrounding medium. We explain the formation of such radiative modes as below: when the top layer InSb layer shrinks to be a thin film, i.e. σ<0.5, the localized field for interface modes starts to extend into the multilayer structure more deeply than in the case of σ=1 shown in Fig. 3, the above mode of simple waveguide structure becomes not applicable, and new solutions including radiative modes may arise within the band gap of the MPCs. It should be noted that, different from the completely localized modes, the field for those radiative TPPs is not well confined at the interface, and can propagate in the background material.

 figure: Fig. 4

Fig. 4 (a) Dispersion for bound (or radiative) TPPs lying outside (inside) the light cone for the background material by tuning the surface terminating layer from σ=0.8 to σ=0.1. (b) Effect of surface terminating layer on the cutoff frequency f+ and f, and the bandwidth Δf=f+f of one-way wave propagation band. Note that ϵb=4 and B=0.1T are used in (b). Other parameters are the same as Fig. 1.

Download Full Size | PPT Slide | PDF

 figure: Fig. 5

Fig. 5 (a) The schematic diagram is the same as Fig. 1(a) except that the top layer of the MPC and the surrounding materials are replaced by the dielectric and metallic material, respectively. (b) Dispersion for TPPs [the red line] consists of radiativesolutions lying inside the light cone for the background material (with permittivity, ϵe=16). The applied magnetic field B=0.3 T and the parameter γ for surface terminating layer is set to γ=0.4. All other parameters and settings are the same as in Fig. 1.

Download Full Size | PPT Slide | PDF

4. One-way optical tunneling through finite-size MPCs

We proceed to explore the possibility to see a kind of completely localized TPPs with non-reciprocity, which are different from those shown in Fig. 1(b). They may be excited directly by incident plane waves. Based on the previous system in Fig. 1(a), we simply change the surface termination layer from magnetized InSb to the dielectric, and simultaneously the background from dielectric to the semiconductor material, i.e. unmagnetized InSb, as shown in Fig. 5(a). The parameter γ is used to tune the thickness of top dielectric layer of the MPC. All other geometrical parameters and settings remain unchanged. Correspondingly, by replacing the ϵ1, σ by ϵ2, γ, respectively, and meanwhile setting Δ1 to be zero in Eq. (5), we can obtain the dispersion for TPPs in this system shown in Fig. 5(a),

qb=ikx2ϵbϵ2T12e2ikx2γd2+T11eiKΛT12e2ikx2γd2T11+eiKΛ,
where the transfer matrix T^ is also changed by T^=P^2M^12P^1M^21.

Likewise with Fig. 1(b), we plot in Fig. 5(b) the complete dispersion of forward and backward TPPs with a particular case of the external magnetic field B=0.3 T and the parameter γ=0.4. Asymmetrical and nonreciprocal TPPs [f(ky)f(ky)] are supported. Here, another type of contribution to the non-reciprocity of TPPs is revealed. It comes from the periodic violation of MPCs due to the surface termination [42, 43], which results in the removal of the spatial symmetry for the MPCs structure, i.e. the mirror reflection symmetry. The non-reciprocity for TPPs may be directly seen from Eq. (10), in which the off-diagonal elements for the transfer matrix show asymmetrical properties, i.e. T12(ky)T12(ky). It is emphasized that the Bloch band for 1D infinite two-component MPCs remains symmetrical, i.e. the Bloch number K(ky)=K(ky), due to the maintenance of spatial symmetry induced by periodicity of the structure. Notice that such TPPs mode solutions are bounded at the interface. The wave evanescent decay in the semiconductor is due to the negative dielectric constant, and meanwhile waves are falling within the band gap of MPCs. The lightlines for the dielectric material (permittivity ϵ2) are also shown by dotted lines. The localized TPPs lying inside the light cone are expected to be directly excited by incident plane waves propagating at the dielectric.

 figure: Fig. 6

Fig. 6 Steady-state field patterns Hz for the finite-size structure consisting of a unmagnetized InSb layer (with thickness a=28μm) on the surface of a 3-period MPC plus with a dielectric first layer under the back illumination (a) and front illumination (b), when the incident angle θ is chosen to be θ=17.720. The proposed finite-size structure is embedded into a uniform surrounding medium with permittivity ϵe=ϵ2=16. Here f=2.67 THz is used. Other parametersare identical with those in Fig. 5. In (a), the TPPs are well excited at the interface between non-magnetized InSb and MPCs, exhibiting strong enhancement on the magnetic field by the white color with its magnitude beyond the scope of the colorbar.

Download Full Size | PPT Slide | PDF

The excitation of such nonreciprocal TPPs is further confirmed by using COMSOL Multiphysics. We show in Fig. 6 the steady-state field patterns for a finite structure consisting of a unmagnetized InSb layer (with thickness a=28μm) on the surface of three complete period MPCs plus with a first dielectric layer (γ=0.4), in the presence of external incident radiation. Counter propagating plane waves are incident from the surrounding dielectric material, with its permittivity, i.e. ϵe=ilon2=16. Other parameters are chosen with B=0.3T and f=2.67 THz. For the case of backward incidence, at a particular incident angle θ=17.720, strong field enhancement is seen at the surface of MPCs, and backward TPPs (ky<0) is well excited, giving rise to full transmission through the whole structure [Fig. 6(a)]. In contrast, for the case of forward incidence, θ=+17.720 [Fig. 6(b)], strong reflection is observed, resulted from the suppression of the excitation of forward TPPs (ky>0). Therefore, one-way optical tunneling through such a finite-size structure could be achieved. Notice that other selection for the thickness of unmagnetized InSb has no intrinsic influence on the non-reciprocity effect, but change slightly the intensity of light tunneling.

 figure: Fig. 7

Fig. 7 Nonreciprocal transmittance T through the finite-size structure in Fig. 6.

Download Full Size | PPT Slide | PDF

 figure: Fig. 8

Fig. 8 The calculated isolation spectra for positive and negative incident angles when the loss in ML is absent (a) α=0, and present (b) α=0.1 THz.

Download Full Size | PPT Slide | PDF

As a validation of the above results, we can also directly determine the response of a finite structure illuminated by light by using transfer-matrix formalism. Figure 7 presents the transmittance through the same structure as Fig. 6 as a function of incident angle θ and frequency ω. It is observed that there exists distinct and asymmetrical transmission peaks, T(θ)T(θ), over a certain of frequency range around 2.462.85 THz. Such pronounced non-reciprocity of transmittance reveals that the optical properties are dependent of the specific direction, which is not observed in nonmagnetic, linear, and time-independent structures. Moreover, the transmission peaks could map well onto the dispersion curves for TPPs shown in Fig. 5 (b). Thus, the nonreciprocal character of TPPs may bring the directional dependence in transmission and result in one-way behavior for this finte-size system.

For the purpose of clearly demonstrating the performance of the non-reciprocity in transmission, which is strongly dependent on the incident angle of light, we define the isolation between the forward transmittance T(θ) and backward transmittance T(θ) expressed by Iso=10log[T(θ)/T(θ)] and show in Fig. 8 the isolation spectra as a function of frequency and the incident angle θ of light illumination. Here we take a particular case with the applied magnetic field B=0.3T. In the absence of loss in ML, α=0 [Fig. 8(a)], it is found that the best isolator performance could exceed 70 dB at a specified incident angle when the nonreciprocal TPPs are excited. Moreover, over the range of frequencies f=2.72.85 THz, there exist two different incident angles to achieve high isolation in transmission. When the loss in ML is introduced [here in Fig. 8(b) we use a realistic typical value of α=0.1 THz for InSb in the terahertz region], the transmission peaks for both directions are suppressed and broaden, and the non-reciprocity becomes weaker. Nevertheless, the isolation can approach as high as 35 dB, resulting in pronounced non-reciprocity for the proposed structure.

5. Conclusions

In summary, we investigate optical non-reciprocity behaviors associated with asymmetrical TPPs in terahertz MPCs. Nonreciprocal bound TPPs could be supported with a top ML for the MPC, giving rise to the observation of one-way wave propagation at the surface of semi-infinite MPCs. Such non-reciprocity can be attributed to the contribution of direct magnetization effect of surface terminating layer of MPCs. By varying the top layer of MPCs to the dielectric and the other side of the interface by metallic materials, radiative TPPS with non-reciprocity could be seen, originating from the periodicity violation in truncated MPCs. In comparison with the bound TPPs, radiative mode solutions lie inside the light cone for the surrounding materials, and can be well excited directly by incident plane waves, which enables us to see one-way optical tunneling through a finite-size structure. It is expected that those results may provide potential applications on the design of tunable and compact optical isolators. Compared to other metal-dielectric MO structures based on InSb materials that have been proposed for THz isolators [45, 46], the proposed nonreciprocal structure is simple in the geometry design, and compact with thickness less than 100 μm. Meanwhile, our isolator exhibits high non-reciprocity at its operating frequency which can be broadly tuned by changing the incident angles, surface termination as well as external magnetic field.

Funding

Natural Science Foundation of Jiangsu Province (BK20160878, BK20181263); National Natural Science Foundation of China (NSFC) (11774053); The General Research Fund from Hong Kong RGC (15300315).

References

1. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004). [CrossRef]  

2. D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013). [CrossRef]  

3. B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018). [CrossRef]  

4. R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005). [CrossRef]  

5. K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011). [CrossRef]  

6. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009). [CrossRef]  

7. N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014). [CrossRef]  

8. H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012). [CrossRef]   [PubMed]  

9. S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015). [CrossRef]  

10. F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016). [CrossRef]   [PubMed]  

11. M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017). [CrossRef]  

12. K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012). [CrossRef]  

13. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001). [CrossRef]  

14. M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003). [CrossRef]  

15. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012). [CrossRef]  

16. Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014). [CrossRef]  

17. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008). [CrossRef]  

18. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008). [CrossRef]  

19. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009). [CrossRef]   [PubMed]  

20. Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011). [CrossRef]   [PubMed]  

21. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008). [CrossRef]  

22. J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015). [CrossRef]  

23. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007). [CrossRef]  

24. I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007). [CrossRef]  

25. M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008). [CrossRef]  

26. Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011). [CrossRef]   [PubMed]  

27. H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010). [CrossRef]   [PubMed]  

28. W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010). [CrossRef]  

29. K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013). [CrossRef]  

30. A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005). [CrossRef]  

31. C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012). [CrossRef]  

32. G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015). [CrossRef]  

33. O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012). [CrossRef]  

34. R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014). [CrossRef]  

35. Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014). [CrossRef]  

36. Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014). [CrossRef]   [PubMed]  

37. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007). [CrossRef]  

38. S. Lin, K. Bhattarai, J. Zhou, and D. Talbayev, “Thin InSb layers with metallic gratings: a novel platform for spectrally-selective THz plasmonic sensing,” Opt. Express 24, 19448–19457 (2016). [CrossRef]   [PubMed]  

39. M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38, 3437–3440 (2013). [CrossRef]   [PubMed]  

40. J. G. Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13, 847–859 (2005). [CrossRef]  

41. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012). [CrossRef]   [PubMed]  

42. H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013). [CrossRef]  

43. A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009). [CrossRef]  

44. B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015). [CrossRef]  

45. F. Fan, S. Chen, X. Wang, and S. Chang, “Tunable nonreciprocal terahertz transmission and enhancement base on metal/magneto-optic plasmonic lens,” Opt. Express 21, 8614–8621 (2013). [CrossRef]   [PubMed]  

46. S. Chen, F. Fan, X. Wang, P. Wu, H. Zhang, and S. Chang, “Terahertz isolator based on nonreciprocal magneto-metasurface,” Opt. Express 23, 1015–1024 (2015). [CrossRef]   [PubMed]  

References

  • View by:

  1. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
    [Crossref]
  2. D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
    [Crossref]
  3. B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
    [Crossref]
  4. R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
    [Crossref]
  5. K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
    [Crossref]
  6. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
    [Crossref]
  7. N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
    [Crossref]
  8. H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
    [Crossref] [PubMed]
  9. S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015).
    [Crossref]
  10. F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
    [Crossref] [PubMed]
  11. M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
    [Crossref]
  12. K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
    [Crossref]
  13. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
    [Crossref]
  14. M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
    [Crossref]
  15. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
    [Crossref]
  16. Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
    [Crossref]
  17. F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
    [Crossref]
  18. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
    [Crossref]
  19. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
    [Crossref] [PubMed]
  20. Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
    [Crossref] [PubMed]
  21. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
    [Crossref]
  22. J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
    [Crossref]
  23. M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
    [Crossref]
  24. I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
    [Crossref]
  25. M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
    [Crossref]
  26. Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
    [Crossref] [PubMed]
  27. H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
    [Crossref] [PubMed]
  28. W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
    [Crossref]
  29. K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
    [Crossref]
  30. A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
    [Crossref]
  31. C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
    [Crossref]
  32. G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
    [Crossref]
  33. O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
    [Crossref]
  34. R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
    [Crossref]
  35. Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
    [Crossref]
  36. Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
    [Crossref] [PubMed]
  37. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
    [Crossref]
  38. S. Lin, K. Bhattarai, J. Zhou, and D. Talbayev, “Thin InSb layers with metallic gratings: a novel platform for spectrally-selective THz plasmonic sensing,” Opt. Express 24, 19448–19457 (2016).
    [Crossref] [PubMed]
  39. M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38, 3437–3440 (2013).
    [Crossref] [PubMed]
  40. J. G. Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13, 847–859 (2005).
    [Crossref]
  41. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
    [Crossref] [PubMed]
  42. H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
    [Crossref]
  43. A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
    [Crossref]
  44. B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
    [Crossref]
  45. F. Fan, S. Chen, X. Wang, and S. Chang, “Tunable nonreciprocal terahertz transmission and enhancement base on metal/magneto-optic plasmonic lens,” Opt. Express 21, 8614–8621 (2013).
    [Crossref] [PubMed]
  46. S. Chen, F. Fan, X. Wang, P. Wu, H. Zhang, and S. Chang, “Terahertz isolator based on nonreciprocal magneto-metasurface,” Opt. Express 23, 1015–1024 (2015).
    [Crossref] [PubMed]

2018 (1)

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

2017 (1)

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

2016 (2)

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

S. Lin, K. Bhattarai, J. Zhou, and D. Talbayev, “Thin InSb layers with metallic gratings: a novel platform for spectrally-selective THz plasmonic sensing,” Opt. Express 24, 19448–19457 (2016).
[Crossref] [PubMed]

2015 (5)

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

S. Chen, F. Fan, X. Wang, P. Wu, H. Zhang, and S. Chang, “Terahertz isolator based on nonreciprocal magneto-metasurface,” Opt. Express 23, 1015–1024 (2015).
[Crossref] [PubMed]

S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015).
[Crossref]

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

2014 (5)

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
[Crossref]

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

2013 (5)

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

F. Fan, S. Chen, X. Wang, and S. Chang, “Tunable nonreciprocal terahertz transmission and enhancement base on metal/magneto-optic plasmonic lens,” Opt. Express 21, 8614–8621 (2013).
[Crossref] [PubMed]

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
[Crossref]

M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38, 3437–3440 (2013).
[Crossref] [PubMed]

2012 (6)

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

2011 (3)

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

2010 (2)

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

2009 (3)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
[Crossref]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

2008 (4)

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
[Crossref]

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

2007 (3)

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

2005 (3)

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
[Crossref]

J. G. Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13, 847–859 (2005).
[Crossref]

2004 (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[Crossref]

2003 (1)

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

2001 (1)

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Abram, R. A.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Alù, A.

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Azzini, S.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Badugu, R.

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Baets, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Baryshev, A. V.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Bellessa, J.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

Bhattarai, K.

Bolivar, P. H.

Brand, S.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Brucoli, G.

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Chamberlain, J. M.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

Chan, C. T.

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Chang, K. J.

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

Chang, S.

Chen, H. W.

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

Chen, S.

Chen, Y.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Cheng, B. H.

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Clerk, A. A.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Cui, T. J.

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
[Crossref]

de Vasconcellos, S. M.

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

Descrovi, E.

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Doerr, C. R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Dong, H. Y.

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
[Crossref]

Egorov, A. Y.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Eich, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Estep, N. A.

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

Fan, F.

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Fan, S.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
[Crossref]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

Fang, K.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Freude, W.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Fung, K. H.

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Gauthron, K.

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

Gazzano, O.

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

Gong, Y.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

Greffet, J.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Grischkowsky, D.

Guebrou, S. A.

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
[Crossref]

He, B.

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

Homeyer, E.

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Hu, B.

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

Hugonin, J.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Inoue, M.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Iorsh, I.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

Jalas, D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Janke, C.

Jiang, X.

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

Joannopoulos, J. D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

Jomaa, M. H.

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Kaliteevski, M.

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

Kaliteevski, M. A.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Kavokin, A.

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

Kavokin, A. V.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Khanikaev, A. B.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Kim, K.

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

Kivshar, Y. S.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Kurz, H.

Lakowicz, J. R.

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Lan, Y.

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

Lee, K. J.

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

Lemaître, A.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Levy, M.

R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
[Crossref]

Lheureux, G.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Li, R.

R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
[Crossref]

Lin, S.

Lin, Z.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Ling, C. W.

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

Lipson, M.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

Lira, H.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

Liu, V.

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Liu, X.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

Long, H.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015).
[Crossref]

Lu, H.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

Lu, P.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

Luo, C.

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

Luo, J.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Malpuech, G.

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

Mandehgar, M.

Marquardt, F.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Matheny, M. H.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Melloni, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Metelmann, A.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Mikhrin, V. S.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Ming, H.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Miri, M.

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

Miroshnichenko, A. E.

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
[Crossref]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Painter, O.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Petrov, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Poo, Y.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Popovic, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[Crossref]

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Qiu, D.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Raghu, S.

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
[Crossref]

Renner, H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Rivas, J. G.

Ruesink, F.

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

Sasin, M. E.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Sauvan, C.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Seisyan, R. P.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Senellart, P.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Shelykh, I.

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

Shelykh, I. A.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

Soric, J.

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

Sounas, D. L.

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

Symonds, C.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

Talbayev, D.

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Tsai, D. P.

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

Vanwolleghem, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Vasil’ev, A. P.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

Verhagen, E.

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

Voisin, P.

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

Wang, G.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

Wang, J.

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
[Crossref]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Wang, K.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

Wang, L.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

Wang, P.

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Wang, Q. J.

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

Wang, R.

Wang, X.

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Wu, J. W.

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

Wu, P.

Wu, R.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Xiao, M.

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

Xu, Y.

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
[Crossref]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Yang, G.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

Yang, L.

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

Yang, Y.

M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38, 3437–3440 (2013).
[Crossref] [PubMed]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Yao, P.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Yu, S.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Yu, S. F.

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

Yu, Z.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
[Crossref]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

Zhang, D.

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Zhang, H.

Zhang, W. L.

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

Zhang, Y.

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

Zhou, H.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

Zhou, J.

Zhu, L.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

ACS Photonics (1)

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Analytical Biochemistry (1)

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Applied Physics Letters (7)

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
[Crossref]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Laser Photonics Reviews (1)

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Nat. Photonics (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Nature Communications (1)

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

Nature Photonics (2)

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
[Crossref]

Nature Physics (2)

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (1)

Optics Communications (1)

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

Optics Express (2)

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
[Crossref] [PubMed]

Optics Letters (5)

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
[Crossref] [PubMed]

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015).
[Crossref]

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

Phys. Stat. Sol. (a) (1)

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Physical Review A (1)

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
[Crossref]

Physical Review Applied (1)

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

Physical Review B (4)

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
[Crossref]

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Physical Review B 76, 165415 (2007).
[Crossref]

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
[Crossref]

Physical Review Letters (5)

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
[Crossref]

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[Crossref]

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

Scientific Reports (1)

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 (a) Schematic diagram of the proposed MPC structure, formed by alternating magneto-optical active [permittivity ϵ 1 ¯ ] and isotropic dielectric layers [permittivity ϵ 2 ]. The semi-infinite MPC structure with a top magneto-active layer is embedded into a kind of homogeneous background dielectric material with its permittivity ϵ b . (b) Dispersion of bound TPPs at the surface of MPCs. Gray and red lines correspond to the TPPs solutions when the external magnetic field is absent [B = 0T] or present [ B = 0.1 T], respectively. f + and f denote respectively the cutoff frequencies where the forward- and backward-propagating modes vanish, then representing the one-way wave propagation by light blue region. Yellow and white regions correspond to pass-bands and stop-gaps of an infinite MPC. Light lines for the background material are also shown by dotted lines.
Fig. 2
Fig. 2 Steady-state field distribution Hz at a frequency f = 2.8 THz with the applied magnetic field (a) B = 0T; (b) B = 0.1 T, in the absence of the scatterer; (c) B = 0.1 T, when a large PEC obstacle [height 40 μ m and width 8 μ m ] is inserted. The line source at the interface is marked with " " in the figure.
Fig. 3
Fig. 3 Effect of (a) applied magnetic field B and (b) the permittivity ϵ b of the background material on the cutoff frequency f + and f , and the bandwidth Δ f = f + f of one-way wave propagation band. Note that ϵ b = 4 and B = 0.1 T are used in (a) and (b), respectively. Other parameters are the same as Fig. 1.
Fig. 4
Fig. 4 (a) Dispersion for bound (or radiative) TPPs lying outside (inside) the light cone for the background material by tuning the surface terminating layer from σ = 0.8 to σ = 0.1 . (b) Effect of surface terminating layer on the cutoff frequency f + and f , and the bandwidth Δ f = f + f of one-way wave propagation band. Note that ϵ b = 4 and B = 0.1 T are used in (b). Other parameters are the same as Fig. 1.
Fig. 5
Fig. 5 (a) The schematic diagram is the same as Fig. 1(a) except that the top layer of the MPC and the surrounding materials are replaced by the dielectric and metallic material, respectively. (b) Dispersion for TPPs [the red line] consists of radiativesolutions lying inside the light cone for the background material (with permittivity, ϵ e = 16 ). The applied magnetic field B = 0.3 T and the parameter γ for surface terminating layer is set to γ = 0.4 . All other parameters and settings are the same as in Fig. 1.
Fig. 6
Fig. 6 Steady-state field patterns Hz for the finite-size structure consisting of a unmagnetized InSb layer (with thickness a = 28 μ m ) on the surface of a 3-period MPC plus with a dielectric first layer under the back illumination (a) and front illumination (b), when the incident angle θ is chosen to be θ = 17.72 0 . The proposed finite-size structure is embedded into a uniform surrounding medium with permittivity ϵ e = ϵ 2 = 16 . Here f = 2.67 THz is used. Other parametersare identical with those in Fig. 5. In (a), the TPPs are well excited at the interface between non-magnetized InSb and MPCs, exhibiting strong enhancement on the magnetic field by the white color with its magnitude beyond the scope of the colorbar.
Fig. 7
Fig. 7 Nonreciprocal transmittance T through the finite-size structure in Fig. 6.
Fig. 8
Fig. 8 The calculated isolation spectra for positive and negative incident angles when the loss in ML is absent (a) α = 0 , and present (b) α = 0.1 THz.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ϵ ¯ 1 = ( ϵ 1 i Δ 1 0 i Δ 1 ϵ 1 0 0 0 ϵ 1 ) .
M ^ i j = ϵ j 2 Δ j 2 2 ϵ j k x j ( F j * + F i F j * F i * F j F i F j + F i * ) ,
T ^ ( a 0 b 0 ) = e i K Λ ( a 0 b 0 ) .
( a σ b σ ) = P ^ σ 1 ( a 0 b 0 ) .
q b = i k x 1 ϵ b ϵ 1 ϵ 1 2 Δ 1 2 T 12 e 2 i k x 1 σ d 1 + T 11 e i K Λ T 12 e 2 i k x 1 σ d 1 T 11 + e i K Λ k y ϵ b Δ 1 ϵ 1 2 Δ 1 2 , l m o d e s
q b = k y 2 ( ω c ) 2 ϵ b ,
q b = ϵ b ϵ 1 2 Δ 1 2 ( k y Δ 1 + k x 1 ϵ 1 )
f + = 1 2 π [ ω c 2 4 + ϵ ω p 2 ϵ b + ϵ + ω c 2 ] ,
f = 1 2 π [ ω c 2 4 + ϵ ω p 2 ϵ b + ϵ ω c 2 ] .
q b = i k x 2 ϵ b ϵ 2 T 12 e 2 i k x 2 γ d 2 + T 11 e i K Λ T 12 e 2 i k x 2 γ d 2 T 11 + e i K Λ ,

Metrics