1. Introduction

Asymmetric light transmission devices, such as optical diodes [1–9], have attracted tremendous attention for their capability of directing light propagation in a one-way manner. Considerable efforts have been made to achieve asymmetric optical transmission by breaking time-reversal symmetry with non-reciprocal components, such as magneto-optical materials [1–5], or nonlinear materials [6–9]. Alternatively, asymmetric optical transmission can also be achieved by breaking spatial symmetry with artificial structures made of reciprocal materials, for example, asymmetric double gratings [10,11], asymmetric metal films [12], photonic crystals(PCs) [13,14], chiral metamaterials [15–17], zero refractive index materials [18], and graphene [19]. In recent years, research into unidirectional propagation and transmission of light has been reinvigorated due to the boom of topological photonics which enables the design of UDT devices based on topological edge states. Robust unidirectional propagation has been achieved in various topological photonic structures including topological PCs [20], PC heterostructures [21], photonic Wey1 materials [22], Su–Schrieffer–Heegermodel [23], Dirac PCs [24] and so on. Despite these impressive achievements, to the best our knowledge, most UDTs are optimized for transmission along a certain direction, i.e., UDTs are unilateral.

With the progress of optical communication and information processing, more complicated optical circuits and components with special functions are desired. For example, a bilateral UDT device has at least two UDTs with opposite transmission directions which perform separately at two different frequencies, i.e., if it has left-to-right unidirectional transmission for one operating frequency, it has another one-way transmission from right to left for another operating frequency. This function is suitable in near field detection for extracting the signal light from the pump light. It is also able to separate the output light with different frequencies in a multi-frequency laser. In this work, a bilateral UDT device is numerically demonstrated by exciting two different types of resonances in a grating and PC hybrid structure. Grating-based UDT designs have been studied for many years [10–11,14,25–27]. The common principle is directionally sensitive transmission and reflection for high-order diffractions which make it possible to generate different total transmittances under opposite incidences. As mentioned before, most of these grating-based UDT designs have only one UDT mechanism and transmit light only under one incident direction. Although some asymmetric transmissions have been reported, their transmittances and the transmittance differences are not enough to realize a bilateral UDT [26,27]. Here, we introduce a PC with a defect layer. This all-dielectric design avoids metallic losses and achieves high transmission. The sharp transmission peak of the defect mode improves the transmittance contrast ratio and enables the optimization of bilateral UDTs. Our design, featuring small dimensions, compact structure, and tunable operation wavelengths, has potential to be integrated to optical circuits. For example, a similar optical design with a different function has been successfully realized in an on-chip integrated photonic circuit [28].

2. Bilateral UDT device design

As illustrated in Fig. 1(a), the proposed bilateral UDT device consists of a one-dimensional (1D) PC and a 1D dielectric grating. The 1D PC is an N-layer (here N = 19) structure consisting of alternating Si and SiO₂ layers with a SiO₂ defect layer sandwiched at its center. The thicknesses of the Si layer, the SiO₂ layer, and the defect layer in the PC are h₁, h₂, and L, respectively. The 1D Si grating is attached at one end of the PC with its strips parallel to the PC's surface. The period, width, and thickness of the grating strips are represented by P, W and H, respectively. For simplicity, the filling factor of the grating is fixed to 0.5 (W = P/2) throughout this paper. The refractive indices of SiO₂ and Si are set to 1.46 and 2.82, respectively [29]. In this paper, all calculations are performed by a commercial software, FDTD Solutions.

 

Fig. 1. (a) Three-dimensional illustration of the designed bilateral UDT structure which consists of a one-dimensional PC with a defect and a Si grating attached at one end of the PC. (b)The transmission spectra of the designed bilateral UDT structure for opposite incident directions, where the resonant peaks marked by “A” and “B” are selected to demonstrate the UDTs with opposite transmission directions at different operation frequencies. In the calculations, the transmittance is defined as the ratio of output power integrated over all directions to the incident power. (c)A schematic illustration of the bilateral UDT, where the LI and RI represent the incidences from the PC side and grating side of the structure, respectively. The blue and red arrows indicate the incident(outgoing)waves with the wavelengths at peaks A and B in (b). (d) The transmission energy distribution along the diffraction angle in the far field for forward direction of the two UDTs.

Download Full Size | PDF

In our design, one UDT is a direct consequence of the grating, while the additional UDT is obtained by exciting a defect mode resonance inside the PC. As a defect mode can only exist in a band gap [30], we first design and demonstrate a band gap by choosing suitable PC parameters. Considering practical applications of optical communications, we set h₁ and h₂ to 0.685 µm and 1.290 µm, respectively, realizing a band gap from 1.47 µm to 1.59 µm within the optical communication band. As shown in the inset of Fig. 1(b), the blue solid curve and the red dashed curve represent the transmission spectra of the PC without (L = 1.290 µm) and with (L = 2.105 µm) a defect layer, respectively. All transmittance curves in this paper are calculated as the ratio of output power integrated over all directions to the incident power. The transmission spectrum of the PC without a defect exhibits a wide band gap with zero transmittance. When a defect layer is introduced, a sharp transmission peak with > 90% transmittance appears at a resonant wavelength of 1.536 µm, corresponding to the defect mode of the PC.

Calculated transmission spectra of the whole structure under normal incidence and near the PC's band gap (1.46 µm - 1.60 µm) are shown in Fig. 1(b), where right incidence (RI) is the incidence from the grating side and left incidence (LI) is the incidence from the PC side. In our calculations, the structural parameters P and H are optimized to 1.60 µm and 0.73 µm, respectively. The detail of the optimization process will be addressed in sections 3 and 4. The electric field of the incident plane wave is polarized along the grating strips. Some apparent resonances with greatly enhanced transmittance (T) are excited under both incident directions. Because the resonant wavelengths are different for the two incident directions, the whole structure can function as a UDT device at each resonant wavelength. For example, in Fig. 1(b) the resonant transmission peak A (T = 0.90) for RI is centered at a wavelength of 1.522 µm, while the transmittance for LI at the same wavelength is near zero (T = 1.25×10⁻⁴) due to no resonance. This indicates a highly efficient UDT device with its transmission from right to left. Similarly, the resonant transmission peak B (T = 0.946) for LI is centered at a wavelength of 1.536µm, while the transmittance for RI at the same wavelength is near zero (T = 8.36×10⁻⁴). Thus, another highly efficient UDT device with an opposite transmission direction is obtained. The transmission difference (T₁ – T₂), transmittance contrast ratio (T₁/T₂), and isolation degree (10log(1/T₂)), can reach 90%, 100, and 20, respectively, where T₁ and T₂ are the transmittances for forward and backward incident directions for a given wavelength. The transmission property of the whole bilateral UDT device is illustrated in Fig. 1(c). When light from a dual-wavelength light source is incident from the left side, only one wavelength can be transmitted. In contrast, if it is incident from the right side, only the other wavelength can be transmitted.

Obviously, this structure is a reciprocal system. This means that the propagation direction of light transmitted through the UDTs must deviate from the direction normal to the exit surface as indicated in Fig. 1(c). Otherwise, normally incident light from the reversed direction would also be transmitted. To clarify transmission directions, we calculated far-field energy distributions by performing a Fourier transform on electromagnetic field distributions across exit surfaces. As shown in Fig. 1(d), for both UDTs (at wavelengths of 1.522 µm and 1.536 µm), their transmission directions are along the ± 1st diffraction orders of the grating. This confirms that, similar to most other UDTs in a reciprocal system, the UDTs are obtained through the multiple-channels effect [31]: a designed system has multiple propagating channels for a pair of opposite incidences. Although light propagation through every channel is reversible, the transmittance of the opposite incident directions may not be equivalent if they utilize different propagation channels.

To further understand the bilateral UDT of the designed structure, electric field distributions for RI and LI are plotted separately for each of the two device resonant wavelengths. Figures 2(a) and 2(b) show the electric field intensity distributions for one period of the structure at the resonant wavelength of 1.522 µm, where the red arrows indicate the incident directions and the red lines trace the boundaries of the PC and the grating strip. For RI [Fig. 2(a)], the electric field intensity inside the PC is much stronger than that of the incident wave, confirming the existence of resonance. Furthermore, the transmitted wave on the left side of Fig. 2(a) is in the form of an interference pattern and the overall intensity is comparable to that of the incident light, indicating a relatively high transmittance. In contrast, when the wave is incident from the left side [Fig. 2(b)], no resonance occurs inside the structure. The wave cannot enter the PC or reach the grating because the incident wavelength is within the band gap of the PC. As a result, the intensity distribution on the right side is almost zero, indicating a near-zero transmittance.

 

Fig. 2. The bilateral UDT of the designed structure: (a) and (b) are the electric field intensity distributions for one period of the structure at wavelength of 1.522 µm, where the red arrows indicate the incident directions and the red lines trace the boundaries of the PC and the grating strip. (c) and (d) are the counterparts of (a) and (b) at wavelength of 1.536 µm.

Download Full Size | PDF

Similar electric field intensity distributions are shown in Figs. 2(c) and 2(d) for an incident wavelength of 1.536 µm. For RI, there is no obvious resonance occurring inside the PC and the transmittance is near zero. For LI, however, an apparent resonance is excited and the electric field intensity distribution is centered about the defect center of the PC. This is exactly the resonant behavior of a defect mode. Similar to the wavelength at 1.522µm, when a resonance occurs, the transmittance is greatly enhanced. The overall intensity of the transmitted beam on the right side of Fig. 2(d) is nearly as large as that of the incident beam.

3. Physical mechanisms of UDTs in the structure

In our design, to obtain a unique UDT for each incident direction, we excite two different resonances, each occurring under only one incident direction. The resonance under LI is the defect mode of the PC while under RI it is the grating guided mode resonances (GMRs). In this section, we would like to clarify the mechanisms of the resonances and why they are excited only under one incident direction.

The first mechanism we use to design bilateral UDTs is the defect mode resonance of the PC. As shown in the inset of Fig. 1(b), a defect mode gives rise to a resonant transmission peak which is within the band gap of a PC. A defect layer behaves as a cavity resonator, i.e., when the wave vector component normal to the surface of the defect layer is such that the resonant condition is satisfied, the incident beam will be tunneled to the other side [30]. If the grating is attached at one end of the PC, no matter which side the incident beam comes from, when it reaches the grating, the beam energy will be distributed between the transmission orders and the reflection orders. This distribution is only related to the transmission diffraction efficiency, t_n, and reflection diffraction efficiency, r_n, of the n^th diffraction order. However, the interaction of the beam with the defect layer will depend on whether the beam is diffracted before or after it reaches the defect layer. If a beam is normally incident from the grating side (RI), a portion of the transmitted wave energy will be diffracted to high diffraction orders (n ≥ 1). The wave vector component normal to the surface of the defect layer becomes smaller for higher diffraction orders due to the change in propagation direction. Hence, at the defect mode resonant wavelength, only the 0th transmission order has a wave vector component that meets the original resonant condition and can pass through the PC structure. In contrast, if a beam is normally incident from the PC side (LI), at the defect mode resonant wavelength, almost all energy can transmit through the PC and then reach the grating where it is then diffracted. In this scenario, all transmission orders reach the opposite side of the bilateral UDT. For reflection orders, only the 0th order can reflect and escape from PC side. Thus, when a beam is incident from the PC side, all energy will transmit to the outgoing side except the 0th reflection order. To summarize, for LI, the final transmittance of the whole structure is the sum of the transmission orders and the high diffraction orders of the reflection, ${\textrm{T}_{\textrm{LI}}} = \mathop \sum \nolimits_{ - \textrm{n}}^\textrm{n} {\textrm{t}_\textrm{n}} + \mathop \sum \nolimits_{ - \textrm{n}}^\textrm{n} {\textrm{r}_\textrm{n}} - {\textrm{r}_0}$. For RI, only the 0thdiffraction order can pass through the whole structure, ${\textrm{T}_{\textrm{RI}}} = {\textrm{t}_0}$. Clearly, the addition of a grating enables asymmetric transmittances between the two opposite incident directions at the defect mode resonant wavelength.

Grating parameter optimization is made such that the transmittance under RI (T_RI) becomes zero, resulting in asymmetric transmission at the defect mode to UDT. Here, we take advantage of the thickness of dielectric gratings, which plays a crucial role on the diffraction efficiency of each order [32]. When all energy remains in the 0th transmission order, ${\textrm{T}_{\textrm{LI}}} = {\textrm{t}_0} = {\textrm{T}_{\textrm{RI}}}$, the transmittance is the same for both incident directions. In contrast, if all energy is distributed to high diffraction orders, ${\textrm{t}_0} = {\textrm{r}_0} = 0$, the final transmittance for RI incidence will be zero and UDT appears. To demonstrate these properties, we calculated the transmittances of the whole structure as functions of the grating thickness H for the opposite incident directions at the resonant wavelength of the defect mode, as shown in Fig. 3(a). The period of the grating is set to 1.60 µm and the length of the defect layer set to 2.105 µm, corresponding to the resonant wavelength of 1.536 µm. The black solid curve and red dashed curve represent the LI and RI transmittance, respectively. The two transmittance curves differ for most of the grating thicknesses. Therefore, the transmission under LI and RI is asymmetric. When the grating thickness is 0.267 µm, however, the transmittances for the two incident directions are equivalent, suggesting all light energy occupies the 0th transmission order. To verify this, we calculated the far-field transmission energy distribution for both LI and RI as shown in Fig. 3(b). As we expect, all transmitted energy is concentrated to the 0th transmission order because the PC does not affect the propagation direction of the incident beam. Equivalent far-field energy distributions can also be found at H = 0 µm which simply states that no grating is added to the PC. The parameters at H₂ (H = 0.73 µm) are selected as the structural parameters of our design in Fig. 1. As demonstrated in Fig. 1(d), all transmitted energy resides in the ± 1st diffraction orders, resulting in zero RI transmittance and allowing UDT.

 

Fig. 3. (a) The transmittances as functions of the grating thickness for the opposite incident directions at a wavelength of 1.536 µm, where P = 1.6 µm, W = 0.8 µm, h₁ = 0.685 µm, h₂ = 1.290 µm, and L = 2.105 µm. (b) Far-field diffraction energy distributions for LI and RI when the grating thickness is set to H₁= 0.267 µm.

Download Full Size | PDF

The other resonant mechanism we use to design bilateral UDTs is grating GMRs [33,34]. With grating GMRs, strong transmission occurs at certain wavelengths due to the resonant coupling between the grating-diffracted incident beam and the guided modes of a planar waveguide [33]. In our structure, a PC slab rather than a conventional dielectric substrate serves as the planar waveguide layer. To excite a GMR, it is required that the propagation constant β of the excited guided mode is matched by that of the incident light [34]. Under RI, the incident beam is first diffracted by the grating. High diffraction orders carry on tangential propagation constants which may match the propagation constants of guided modes leading to the excitation of GMRs. In contrast, under LI, when the incident wavelength is within the band gap of the PC, the beam cannot reach the grating. Therefore, GMRs under LI cannot be excited and the transmittance is certainly zero.

The defect layer of the PC also affects grating GMRs. Figure 4 gives the transmission spectra and electric field intensity distribution for the whole structure with (L = 2.105 µm) and without (L = 1.290 µm) a defect layer under RI. In our calculations, the period and the thickness of the grating are set to be P = 1.60 µm and H = 0.73 µm. Apparently, for the structure without a defect layer, there are regular GMRs that appear in the transmission spectrum. When a defect layer is introduced into the PC, the resonant peaks still exist, but are irregularly red-shifted. When a defect layer is introduced, the refractive index distribution of the planar waveguide is modified. As a result, the GMR positions shift accordingly to meet the wave vector matching condition. For our structure, the defect layer increases the optical thickness of the wave guide such that all the resonant modes are red-shifted. By analyzing the electric field intensity distribution for the first three resonant modes shown in Fig. 4(b), we see that the defect layer has a greater impact on the shift of the even modes. Electric field intensity distributions of the resonant peaks are similar for the structures with and without a defect layer. For even modes, there is a local maximum of resonant electric field at the center of the PC where the defect layer is located, while for odd modes there is a local minimum at the center of the PC. As a result, the shifts of the even modes are more pronounced than those of the odd modes.

 

Fig. 4. (a) The transmission spectra of the whole structure with a defect (L = 2.105 µm) and without a defect (L = 1.290 µm). (b) The electric field intensity distributions of the guided mode resonances inside the structure with a defect (L = 2.105 µm) and without a defect (L = 1.290 µm) layer.

Download Full Size | PDF

In summary, defect mode resonances and grating GMRs exist in the hybrid structure. Grating GMRs can only be excited under RI while defect mode resonances can be excited both under RI and LI. Defect mode resonances under RI are weaker than those under LI because only the 0th transmission order of the grating exists under RI. To obtain bilateral UDTs, the defect mode resonance under RI is suppressed by selecting a suitable grating thickness in our design. Thus, bilateral UDT behavior is realized by limiting each incident direction to a single type of resonance.

4. Wavelength tunability of the bilateral UDT

Because UDTs towards opposite directions are based on two resonance mechanisms in this design, their operation wavelengths can be tuned individually. Transmission spectra for different grating periods (P) under the two opposite incident directions, LI and RI, are shown in Figs. 5(a) and 5(b), respectively. In our calculations, the width of the grating strip (W) varies with the change of P to maintain a constant filling factor, W/P = 0.5. The thickness of the grating (H) is set to 0.73 µm and the length of the defect layer (L) is set to 2.105 µm. As the periodicity increases, the resonant transmission peaks for LI remain unchanged while those for RI are red-shifted. Because of the decrease of the grating vector 2π/P, the resonant wavelengths for all GMRs must increase accordingly to satisfy the wave vector matching condition [31]. In contrast, because the positions of defect modes are only related to the length of a defect layer, the increase of period does not change its resonant position. The red dashed line in Fig. 5(b) represents the position of the defect mode excited under LI, corresponding to the position of the UDT under LI. If we select the GMR m = 1 as the UDT for the opposite transmission, its wavelength can be tuned by changing the grating period. Hence, the wavelength interval between the two UDTs with opposite transmission directions is tunable.

 

Fig. 5. The transmission spectra for different grating period P under LI (a) and RI (b), where L = 2.105 µm, H = 0.73 µm, and the dashed line in (b) represents the wavelength where the defect mode is excited. The transmission spectra for different defect length L under LI (c) and RI (d), where P = 1.6 µm, W = 0.8 µm, H = 0.73 µm, and the red dashed lines in (b) represent the wavelengths where the defect modes are excited.

Download Full Size | PDF

Transmission spectra for different lengths of the defect layer (L) under the two opposite incidences, LI and RI, are shown in Figs. 5(c) and 5(d), respectively. The grating parameters are set to P = 1.6 µm, W = 0.8 µm, and H = 0.73 µm. Apparently, the position of the defect mode and GMR modes are both dependent on the length of the defect layer. However, the length of the defect layer affects the position of the defect mode more dramatically than the positions of the GMRs. If we select mode m = 1 under RI as one UDT, for different lengths of the defect layer, the position of this UDT remains nearly unchanged. In contrast, the position of the LI UDT is very sensitive to the length of the defect layer. Therefore, the wavelength interval between the two UDTs are tunable by changing the length of the defect layer. In design, to obtain UDT, the resonant position of the defect mode should avoid the resonant positions of GMRs. In a special case, if the defect mode resonance is not suppressed for RI, the two types of resonances can be simultaneously excited at a same wavelength. In this scenario, the transmission spectrum will present a Fano resonance shape which arises because of the coupling of the two resonances.

5. Bilateral UDT coupler for optical fibers

At last, we would like to demonstrate a direct application of the bilateral UDT, i.e., a bilateral UDT coupler for optical fibers as illustrated in Fig. 6(a). This bilateral UDT system may be an alternative to dichroic mirrors in photo luminescent sensing. The coupler is inserted between the facets of two optical fibers. The solid arrows represent incident beams with the two UDT operation wavelengths given by the red and blue arrows. θ₁ and θ₂ indicate the diffraction angles of UDTs. The dashed arrows represent the transmitted light propagating inside the fibers, each of them can only be transmitted along one propagating direction. In practice, considering a conventional multimode fiber with NA = 0.22 (maximum incident angle θ_max = 12.7°), we increase the period of the diffraction grating to P = 7.50 µm and the width of the grating strip to W = 3.75 µm to reduce the diffraction angle of UDTs so that the transmission energy can be efficiently coupled into this optical fiber. Additionally, to offset the resonant wavelengths of the defect mode and grating GMRs, the length of the defect layer and the thickness of the grating are set to L = 2.00 µm and H = 0.41 µm. The thicknesses of the Si and SiO₂ layers of the PC remain unchanged. Transmission spectra of the bilateral UDT coupler for opposite incident directions are shown in Fig. 6(b). Two UDTs at wavelengths of 1.505 µm and 1.495 µm are realized for LI and RI, respectively. For each UDT, the transmission ratio is greater than 10 which is enough for most photoelectric detections. To investigate transmission directions, far-field diffraction energy distributions for the coupler are calculated and shown in the insets of Fig. 6(b). The transmission energy is mainly concentrated into the ± 1st orders, which are around ± 11.5° for LI at the wavelength of 1.505 µm and are around ± 11.6°for RI at the wavelength of 1.495 µm. Both transmission directions fall within the acceptance angle of the fiber. It is noteworthy that, this UDT coupler is anticipated to selectively convert fundamental mode to higher-order modes. This mode conversion is useful in spatial-division multiplexing [35–36]. While for the inversed incident direction, the coupler can only convert higher-order modes back to fundamental mode for the same wavelength.

 

Fig. 6. An application example of the bilateral UDT: (a) Propagation and transmission of the incident beams with two different operating frequencies in an optical fiber with a bilateral UDT coupler. (b) The transmission spectra for opposite incidences and their far-field diffraction energy distribution for the forward transmission of the bilateral UDT coupler, where P = 7.5 µm, W = 3.75 µm, L = 2.00 µm, H = 0.41 µm, h₁ = 0.685 µm and h₂ = 1.290 µm.

Download Full Size | PDF

6. Conclusions

We demonstrated bilateral UDTs with opposite transmission directions in one hybrid structure consisting of a dielectric grating and a PC with a defect. The unique performance is contributed by defect mode resonances and grating GMRs. By elaborately selecting structural parameters of the structure, the two resonances can be separately tuned to control operation wavelengths as well as wavelength intervals. The performance of UDTs under two incident directions are excellent, providing high transmission difference, high transmittance contrast ratio, and large isolation degree to satisfy the criteria of a UDT device such as a bilateral UDT coupler for optical fibers.