Topological edge state assisted dynamically tunable microwave propagations in photonic crystals

Topological photonics has emerged as a cutting-edge and intriguing field that permits electromagnetic waves to transmit with minimal losses even when they come in contact with sharp turns or imperfections or defects. In this study, we validate a strategy to realize dynamically amplitude tunable light propagation in a topological waveguide based on a three-dimensional printed valley Hall photonic crystal structure operating in the microwave frequency region. Here, tunable light propagation is facilitated by inserting an active defect in the form of a semiconductor (silicon) material slab across the domain boundary of the topological waveguide. In this configuration, dynamic variation of transmission amplitude is realized via photoexcitation of the semiconductor defect using an external laser of wavelength, λ∼510 nm. This results in active amplitude tunability of ∼−10 dB in topological wave propagation under a photoexcitation of 100 mW. Our demonstrated route can lead to the design of dynamically controlled topological photonic devices such as optical modulators, switches, optical buffers, etc which are important for the development of 6G communication systems.


Introduction
The development of novel optical frameworks that can be utilized to manipulate light is a significant area of research in photonics. In the past few decades, many artificially engineered materials such as photonic crystals (PhCs) [1,2], metamaterials [3], and plasmonic systems [4,5] served an important role in the development of photonic devices. Nevertheless, more substantial technologies that are impervious to perturbations, flaws, and disorders are being sought after by contemporary scientific advancements. Fortunately, the discovery of topological photonics has led to radical changes in the field of photonics that act as a major foundation for these investigations and continues to expand as a source of novel ideas for developing photonic devices including defect immune unidirectional propagation [6], beam splitters [7,8], filters [9,10], non-linear devices [11,12], and so on [13,14]. The topological PhCs (TPCs) enter the photonic world by analogy with the time reversal breaking features associated with the quantum Hall effect [15], and additionally, the discovery of the valley degrees of freedom renders it attractive for innumerable applications across all frequency regimes [16,17]. In general, the valley-dependent topological edge states are generated by breaking the mirror symmetry of the periodic structure formed by 2D-honey comb lattices which are confined at the boundaries between two bulk PhC with opposite valley-Chern indices [18,19]. Moreover, these kinds of valley-dependent edge states do not demand the spin-orbit interactions in the presence of an external field that offers excellent performance for ubiquitous applications in the field of photonics such as robust light-transmission devices [20][21][22], time-delay lines [23], dispersion-engineering devices [24], and sensors [25] across the electromagnetic (EM) spectrum.
The optical behavior of the majority of TPC structures are restricted due to the passive and static setups, where the properties of light propagation cannot be adjusted actively once the device has been fabricated. Therefore, the dynamically tunable topological TPC structures are highly desirable to realize reconfigurable, self-adaptive, and multi-functional photonic devices. Although dynamic tunability has been proposed in 1D and 2D TPC structures based on thermal tuning [26], mechanical tuning [27], optical tuning [28][29][30] as well as electrical tuning [31] for acoustic, terahertz, and communication wavelengths, it is still challenging to achieve amplitude tunable topological photonic devices especially when the devices are composed of metal rods. Therefore, in this work, we experimentally demonstrate a technique of dynamic tunability of EM wave propagation through a TPC structure that would be useful to realize modulators, beam splitters, and many other photonic devices in the microwave regime. Here, the topological edge states are examined by calculating the dispersion bands of the proposed structure. Then, we study a passive tuning of the EM waves by varying the height of an inserted intrinsic semiconductor (Si) slab at the middle of the domain boundary (DB). In addition, we experimentally observe the linking between the exact photo excitation location and the transmission spectra for a specific pump power. Finally, we numerically and experimentally demonstrate the amplitude modification of the propagating waves corresponding to different pump powers.

Design of metal based valley PhCs (VPCs)
The design of the proposed topological waveguide is depicted in figure 1(a). The PhC adopts a honeycomb lattice with the unit cell dimension a = 14.5 mm. The unit cell of the proposed design, as illustrated by the green dash line in figure 1(a), comprises two metal (Al) rods of distinct diameters d A = 0.42a and d B = 0.137a, respectively. The DB between two distinct types of VPCs (i.e. VPC-A and VPC-B) is represented by the zigzag-shaped black dash line that serves as a topological channel for the wave propagations. The light waves propagate along the x-direction while the electric field is directed along the z-axis for the transverse magnetic mode analysis. The photonic bands are calculated for a unit cell comprised of two rods by employing the plane wave methods. The first two bands for the lowest transverse mode are presented in figures 1(b) and (c), where figure 1(b) shows the band structure for d A = d B when a graphene-like Dirac point exists near the K or K ′ valley point. Then, the band gap is created by opening these first two lowest bands i.e. breaking the degeneracy near K or K ′ valley in the presence of structural asymmetry. The presence of the asymmetry breaks the mirror symmetry in the structure i.e. the C 6 rotation symmetry is converted to C 3 symmetry [32]. Here, this structural asymmetry is introduced by differing the diameter of one rod within a unit cell and which is designated by ∆d = d A − d B . The band diagram for the non-zero values of the asymmetry parameter is shown in figure 1(c), where the shaded dark portion in between two bands signify the photonic band gap of ∼1.3 GHz. Next, we calculate the dispersion band diagrams of a supercell composed of ten-unit cells extended in both the +y and −y directions as shown in figure 1(d). The grey-shaded regions signify the bulk bands while the two red lines within the bandgap (white region) denote the valley-dependent edge states. Note that the valleys are positioned significantly below the air light line (yellow shaded region). As a consequence, surface modes in the vicinity of Dirac points can find support within the surface-wave PhC [33]. These edge states arise in the presence of the DB which is constructed with two opposite valley Chern index VPCs meanwhile VPC-A has valley Chern index C v < 0 and the same for VPC-B is C v > 0 [34]. Amongst these two edge states, only one can transmit in the forward (K ′ valley-locked) or backward (K valley-locked) direction depending on the valley dependence [10,34]. The edge state creation is important for the topological study because it confirms that the proposed design is topologically protected according to the bulk-edge correspondence theory [35,36].

Optimization
In this section, we describe an optimization approach for tuning the amplitude of EM wave propagation through topological waveguides by altering the height of an Si material inserted as a defect at the DB. In our study, the TPC design is composed of aluminum (Al) rods having a conductivity of σ = 3.72 × 10 7 S m −1 whereas the background material is air. The height of each Al rod in the proposed TPC is 7.5 mm. An Si block having an electrical conductivity of 0.05 S m −1 and a band gap of 1.14 eV is placed in the middle of the DB to control the EM wave propagation. We purposefully change the height of the semiconductor material, h from 5 mm to 9 mm while the width along the y-axis (w Si = 12.5 mm) and thickness (t Si = 0.5 mm) remain fixed throughout this investigation. Here, we use commercially available CST Microwave Studio software to design and calculate the transmission spectrum of the TPC structure.   semiconductor material block is gradually increased, as indicated by a black-shaded arrow. A maximum transmission drop of ∼ −11 dB is obtained for h = 9 mm. Additionally, the E z -field configurations corresponding to the absence and presence of the defect material are shown in figures 2(b)-(e) at 7.25 GHz. The EM field profiles clearly indicate that as we gradually increase the height (h), the field intensity at the output terminal reduces, but the EM wave's propagation remains restricted within the DB only. When the height of the defect material is approximately equal to the height of the constituent rods the amplitude modulation is minimal due to the localization of the edge state in the interface against defects even though the DB is completely covered by the defect material. The intensity of the transmission spectra further reduces as h is increased and after reaching a certain limit of h propagation stops adjacent to the defect region. This reduction in the field intensity is obtained because the no longer proposed TPC completely provides topological protection to the EM wave propagation against the defect material. Since the topologically protected edge states are formed by the virtue of slow adiabatic phase transition near the interface, they are only to a certain extent immune to defects. Therefore, the amplitude inflection is greater when the height of the defect material is higher than the height of the constituent rods. The electric field distribution in figures 2(c)-(e) confirms that the field intensity at the input end is greater than that at the output end as h increases. It is noteworthy to mention that a significant amount of field bypasses the defect material when the height of defect semiconductor is comparable to the height of the constituent rods. The electric field distribution in the output end further reduces with increase in the height of the defect material. Thus, passively tunable topological light wave propagation can be achieved in this design by simply altering the height of a defect state at the channel. Passive tuning has limitations in many practical applications, hence in the next section, we demonstrate a novel dynamic tuning technique that is accomplished by photodoping the silicon defect using a continuous wave (CW) pump laser.

Dynamic amplitude modification of transmission
The active tuning of topological propagation via a photodoped semiconductor (Si) material is demonstrated in figure 3(a). For our experimental investigations, we employ a CW laser for the photoexcitation of the defect material placed in the DB. The wavelength of the pump laser is λ = 510 nm (E = 2.43 eV) while the radius of the circular spot is 1.5 mm with an area of illumination of ∼ 7 mm 2 . We shine the external laser at several positions on the Si block to obtain the most effective location of photodoped material that can offer the utmost amplitude variation of the EM wave for a fixed pump power. A three-dimensional zoomed view of the TPC around photodoped material is represented on the right side of figure 3(a) where the circles with different colors signify their respective pump positions (or photo doping positions). The experimental setup of the fabricated TPC sample is demonstrated in figure 3(b). We use a two-port vector network analyzer coupled with two probe antennas (transmitter and receiver) for transmitting and receiving the EM waves propagated through the DB ( figure 3(b)). The coupling path of the EM waves from one rod to the other within the DB is illustrated by a yellow zigzag shaded line with red arrows. As the spot size of the laser beam is much smaller compared to the dimensions of the Si defect, that resulted in local changes in the conductivity due to the limited area of photoexcitation of the Si block. The maximum tuning of the transmission amplitude of the order of ∼ −10 dB is obtained when we shine the laser light at position 2 with a pump power of 100 mW mm −2 as depicted in figure 4(b) (red color line). On the other hand, we do not observe any significant changes in transmissions in comparison to the no excitation situation when the laser light shines at position 4. It is noticeable that the location of optical excitation at the defect material is vital for achieving effective variation in topological transmissions, particularly with regard to the dynamic tuning of EM waves which takes place through altering the local conductivity of the photodoped material.
Based on the position-dependent photoexcitation of defect materials, we extend our study towards the dynamical tuning of EM wave propagation with a fixed pump power of 100 mW mm −2 while fixing the photo doping at location 2, see figure 3(a) . Figures 4(a) and (b) represent the simulated and experimentally measured transmissions with different optical pump powers, hence different photo doping. In the absence of a defect, high transmission of~0 dB is achieved in the topological waveguide which is denoted by the blue dash line in figure 4(a) while transmission of ∼ −3.2 dB is obtained experimentally as shown by the solid blue line in figure 4(b). It can be noted that the obtained transmissions in the experiment are little less than the numerically simulated results. These discrepancies could be because of several loss factors, such as losses in the coaxial cables, materials impurities, or even due to fabrication uncertainties. In figure 4, the cyan dash line shows the transmissions in the presence of a defect made of an Si (i.e. without any photodoping). It is noteworthy to mention that we have chosen a semiconductor defect having a height of 8 mm and a thickness of 0.5 mm so that it can fully cover the DB, hence the path of the topological wave propagation. As evidenced by figure 4(b), an initial drop in transmission amplitude of ∼ −5 dB is experimentally observed compared to the transmission amplitude in the absence of Si material. Further tunability of the transmission amplitude is obtained when the defect is photodoped through an external laser. Here, we achieve a maximum tuning of the transmission amplitude of −9 dB with a lasing power of 100 mW mm −2 . This variation of the transmission amplitude with the pump can be attributed to the increase of photoexcited free carriers or in other words due to the attenuation of the EM wave within the DB. When photoexcitation energy (E > E g (Si) = 1.14 eV) is irradiated onto the Si defect, free charge carriers are generated due to the excitation of the valance band electrons. It should be noted that the excited charge carriers are created over a thin layer (~1 µm) on the Si substrate as well as in a smaller area depending upon the intensity and spot size of the irradiated laser light [29]. This localized excitation of the photoelectrons leads to an increase in the number of photoexcited charge carriers of the photodoped layer of the Si block. As a result, the transmission amplitude is attenuated due to the absorption of the microwave photons by the photoexcited charge carriers and is further enhanced with increasing laser pump power. The associated numerical simulations are executed by creating a very thin layer of photodoped Si on top of the Si defect and setting the appropriate conductivity values of the photodoping [37]. Figure 4(a) represents the simulated transmission spectra associated with different conductivities. This can be further understood from the corresponding |E z | field distributions represented in figures 4(c)-(e). From the figures, it is clearly observed that the EM waves are confined at the zigzag interface with or without the defect block and the tuning of the transmission amplitudes is confirmed by the diminishing field intensity at the output end of the topological waveguide. It is noteworthy to mention that the fields are well confined within the domain boundaries which indeed evidences the topological protection features that only allow propagation through the DB. Therefore, the demonstrated concept is relatively less cumbersome and cost-effective which can facilitate the development of dynamically controllable topological wave propagations with enormous potential in realizing futuristic photonic devices involving topological photonics.
In summary, we experimentally demonstrate a dynamically tunable topological waveguide by inserting a photo-doped semiconductor (Si) defect. In this semiconductor hybridized TPC waveguide, transmission amplitude is passively tuned from 0 dB to −11 dB by gradually changing the height of the semiconducting defect placed in the DB as a process of optimizing the defect geometry. Further, a dynamical controlling of transmitted amplitude of ∼ −10 dB is realized via photodoping the silicon defect by employing an external pump laser (λ ∼ 510 nm). Such dynamic tunability is replicated in numerical studies by creating a thin (∼0.1 µm) photoconductive Si layer on the Si defect. Such dynamic tuning of the transmission amplitude can be attributed to the enhancement of the free charge carriers with the laser pump, and topologically protected wave propagation is confirmed from the observations of field confinements within the DB. We believe that the integration of amplitude manipulation of propagating waves within PhC in the microwave domain opens a wide array of possibilities for improving communication, sensing, imaging, quantum information processing and various other applications with dynamic functionalities.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).