A novel 2D-PhC based ring resonator design with flexible structural defects for CWDM applications

In this article, a chain-shaped photonic crystal-based ring resonator (PhCRR), which can function as a channel drop filter (CDF), is designed using two-dimensional photonic crystals. Silicon rods with a refractive index of 3.44 are chosen, and they are perforated in the air with a refractive index of 1 for the PhCRR layout design. Silicon material is selected for realizing the PhCRR-based channel drop filter because it exhibits nearly zero absorption in the C-band (1530–1565 nm) spectral region. The PhCRR structure is established within two-dimensional hexagonal lattices. Transmission efficiency, quality factor, and sensitivity are critical parameters in the design of optical components. Our proposed ring resonator achieves a transmission efficiency of 99.7% with a quality factor of 4550 at a wavelength of 1551 nm. To analyze the drop filter’s functionality, we calculate the electric field distribution of two-dimensional photonic crystals at 1551 nm and 1553 nm. We employ the FDTD numerical analyser to extract simulation results, and the plane wave expansion solver method is used to estimate the photonic band gap of the designed resonator. The chain-shaped photonic crystal-based ring resonator is designed to operate in the third optical window wavelength, which offers very low loss (less than 0.2 dB). The proposed PhCRR is designed to operate within the conventional band range of 1530 to 1565 nm and can be used for various applications such as tunable add/drop multiplexing, optical filters, signal routing and switching in CWDM applications, free space communication systems, and photonic integrated circuits.


Introduction
The encroachment in light technology outperforms all other fields because of its miniature structure, little power utilization, extensive bandwidth, and trimness [1].In modern years, due to flexibility in design and miniaturized layout much curiosity developed among researchers for manipulative optical devices and circuits using photonic crystals [2].The optical filter is one of the necessary building blocks for reconfigurable OADMs [3], optical modulators [4], fibers [5], and photonic integrated circuits(PICs) [6].Substantial improvement has been made to optical filter based devices in the areas of compactness, high spectral selectivity, fast switching, and low-power switching [7].A photonic crystal (PhC) with a photonic band gap is a capable candidate for constructing devices that can operate over a wide range of wavelengths [8].Because of its compactness and flexible design parameters, nowadays realization of ring resonators using photonic crystal (PhC) structure has been gaining importance [9].Photonic crystal cavities have unique properties, such as their ability to confine light and trap particular wavelengths strongly by which a high Q-factor can be achieved [10].This motivates the researchers to propose structures based on PhC.Photonic crystal based ring resonator usually consists of two straight waveguides known as bus waveguide and drop waveguide along with a ring resonator sandwiched among those waveguides as in figure 1(a) [11].PhCRR finds its role in numerous applications such as filters [12], wavelength selectors [13], logic gates realization [14], multiplexers [15], routers [16], and demultiplexers etc [17].Some special types of resonators are also reported by various researchers.Without affecting the model's broad applicability, the sidewall grating, or top grating-based Photonic Crystal Ring Resonator configuration has been reported by Brunetti et al [18].According to their report, they were able to attain a Q factor of more than 10 10 at 1.55 μm for a Si 3 N 4 PhCRR with a top grating and a footprint of 4 mm 2 .Kaikai et al [19] realized a 720 million intrinsic Q resonator with corresponding 258 kHz intrinsic and 386 kHz loaded linewidths which can finally be used as a nonlinear resonator.Also, they demonstrated SBS lasing with a 380 μW threshold power.Photonic crystal based ring resonator is proposed as optical filters when the light signal propagating in the bus waveguide drops to the dropping waveguide at a specific wavelength known as the resonant wavelength.The resonant wavelength of the PhCRR can be varied by changing the resonator ring's core section radius, refractive index, shape & dimensions [20].The ring in the resonator can be designed using any shape like quasi square [21], plus shaped [22], hexagon [23], rectangular [24], diamond [25], square [26], circular [27], dual curve [28], modified hexagonal [29], X-shaped [30], line defect cavity [31], etc.The existing PhCRR structures which are designed offers very lowquality factor of less than 1000 and conduction efficiencies of around 80%-90% [32].We designed a four-port photonic crystal based ring resonator in which the resonator is premeditated in chain shape.From the literature survey, it is evident that enhanced quality factors and maximum efficiency can only be obtained for complex structured rings [33].As expected, the proposed chain shaped PhCRR offered excellent transmission efficiency and quality factor.In this attempt, we have also analysed the performance of the designed chain shaped PhCRR for different rod radius with various operating wavelengths.
This paper is organized as follows: section 2 discusses the mathematical modelling used for designing the proposed PhCRR.We deliberated the proposed structure design & working mechanism in section 3.By accomplishing several numerical analysis, the efficiency and Q factor of the proposed structure is determined and compared with other literature in section 4, and finally, section 5 concludes the research article.

Mathematical modelling
Maxwell's equation is considered for describing the performance of light in the photonic crystals.This will serve as the foundation for a series of equations whose solutions can be roughly determined using the plane wave expansion approach.The photonic crystal community frequently uses this plane wave expansion approach to determine the band structure of particular photonic crystal geometrics.The plane-wave expansion method can be considerably streamlined for two-dimensional photonic crystals.This is related to the statistic that eigenstates in two-dimensional systems can be distinguished as transverse electric (TE) and transverse magnetic (TM) polarized.In general, for lattices of high-dielectric-index rods in a low-index background, the creation of band gaps for TM modes is more resilient than that for TE modes, as compared with dispersion relations for TM and TE modes.
These equations further helped in explaining how light behaved in a given structure that was dominated by the transverse electric (TE) and transverse magnetic (TM) polarisation.When the free charges and current are absent, then the Maxwell's equation can be written as follows The constitutive relations are taken as follows, We get a relation that, Assume that the Maxwell equations enforce a field pattern that ensues to differ sinusoidal with the time, and the time dependence of electric and magnetic fields is [34] = where ω refers to the angular frequency.The above-mentioned equation is the harmonic solutions of Maxwell's equation and is called harmonic modes.For steady state condition, Maxwell equations can be written as follows

Photonic crystal resonator design
The devised chain shaped photonic crystal ring resonator with silicon rods that are embedded in an air medium.
For effortless fabrication and to avoid the scattering & transmission loss of signal in a guided medium, the rodsbased arrangement is preferred.The band gap-map technique is employed for choosing the design parameters for our structure.A band gap map is a visualization of a crystal's Photonic band gap that changes one or more of the crystal's parameters.The gap map technique was used to get design parameters such as the rod radius 'r' and the lattice constant 'a'.The proposed layout is designed with silicon rods with a refractive index of 3.44 embedded in an air background having a refractive index of 1 arranged in two dimensional hexagonal patterns.The letter 'a' denotes the lattice constant, which is the space among two adjoining rods and for our structure, we have chosen 'a' is of 0.9 μm.Silicon is used in the design for the reason that it affords large PBG at expedient geometrical factors such as lattice constant (a) and rod radius (r).The initial crystal arrangement is revealed in figure 2. By removing the silicon rods the line defects are created and thereby the necessitated waveguides are formed in two dimensional crystal structure as shown in figure 3. Line defects are preferred for creating the bus and drop waveguides and point defects are employed for constructing ring resonator as it offers low loss and miniaturized size for the devices [35].The photonic bandgap of the devised structure is extracted, and its band structure is shown in figure 2(b).Bus waveguide, drop waveguide and chain shaped resonant ring positioned among the waveguide are the three self-possessed parts of the proposed PhCRR based drop filter.The designed resonator consists of four ports, in which A and B are input ports whereas C and D are output ports used for frontward and rearward dropping.We detached the thirty silicon rods in the central point of the layout for designing the chain shaped resonant ring.The rod radius is 0.29 micrometre which is r = 0.29 * a. Dielectric rods have the refractive index same as the preliminary arrangement, which is 3.44.The graphic arrangement of the chain shaped ring resonator is given in figure 3.At resonance conditions, the wavelength will be coupled into a dropping waveguide from the bus waveguide and flow through any one of the output ports (C or D).The efficiency of the designed PhCRR is identified by observing the power values at ports B, C, and D correspondingly.

Results and discussions
Two dimensional finite difference time domain numerical analyser (Opti-FDTD) is used to simulate the designed PhCRR structure.The most common approach used for solving challenging wave equations like Maxwell's equations is the Opti-FDTD method.It serves as the design formula for all electrical engineering technology.Perfectly matched layers have been used as boundary conditions in FDTD computations that have been researched and applied in 2D and 3D planar PhC waveguide structures.It is a robust, fully integrated, user-friendly tool that can be used to design many advanced photonic components.To terminate the computational regions and prevent back reflections from the border, a perfectly matched layer(PML) is used as an absorbing boundary condition around the structure.The vertical input plane is also placed at z-position with Gaussian modulated continuous wave.The waveguide channel is defined to be material with a refractive index of 3.44 or permittivity of 11.8336 and the default wafer material is air with refractive index or permittivity 1.The mesh delta size is 0.1 μm ×0.1 μm.The simulation is done for 10000 time steps.For our design perfectly matched layers (PML) condition is also used for calculating accurate results.The electric field pattern of the chain shaped Photonic Crystal Ring Resonator is made known in figure 4. Figure 4(a) shows optical wave propagation for wavelength 1551 nm.From the output field pattern, we infer that the optical signal inflowing through port A is propagating from the bus waveguide into the designed chain shaped ring resonator and reaches port C only when the wavelength is 1551 nm.We can also perceive that no output signal is reaching port D at this particular wavelength.For all other wavelengths except this 1551 nm, the optical signal will pass through from port A and it only reaches port B at the other end of the bus waveguide without any dropping.At this particular wavelength, our chain shaped ring resonator produces a transmission efficiency of 99.7% with a Q factor of about 4550 and a 3dB bandwidth of 0.3 nm.The optical signal electric field pattern for other wavelengths (1553 nm is shown in figure 4(b)) within the designed chain shaped PhCRR is observed in figure 4.
Figure 4(a) reveals the dropping mechanism of the designed PhCRR.At the resonating wavelength of 1551 nm, the optical signal from the bus waveguide (port A) enters into the dropping waveguide (port C) through the chain shaped ring and its output pattern is shown in figure 4(a).At 1553 nm the optical signal will propagate from port A to port B without dropping into the designed chain shaped ring.Dropping of the optical signal doesn't happen because the central wavelength and drop wavelengths of the layout do not concur with each other and its output pattern is depicted in figure 4(b).In this article, the main properties of the designed PhCRR  namely normalized transmission, transmission efficiency & quality factor are investigated using 2D-Finite Difference Time Domain (FDTD) numerical analyser.From our simulation, we obtained the full width half maximum value as 0.341 nm for our proposed structure and the dropping wavelength is 1551 nm.By substituting the obtained values in the Q factor equation, we get the Q factor as 4550.
By varying the structural parameters such as refractive index and rod radius we can alter the performance of the designed chain shaped photonic crystal based ring resonator.From figure 5 we deliberate that as the radius of the rods increases by keeping all other structural parameters fixed, the transmission efficiency of the proposed chain shaped PhCRR decreases with respect to operating wavelength.When the radius of the rod is small, we have achieved a higher transmission efficiency of around 99.7% at an operating wavelength of 1551 nm.
The performance of the proposed chain shaped PhCRR is analysed for various rod radius with different operating wavelengths and the obtained normalized transmission values are displayed.Figure 6 reveals the output spectrum of the designed chain shaped PhCRR at various port points.At the operating wavelength of 1551 nm, the optical signal from port A will drop through the designed chain ring resonator into port C and hence we achieved a maximum transmission efficiency of around 99.7% at this point.For our designed structure, 100% efficiency is not achieved due to radiation loss which is unavoidable and may lead to non-zero reflection in devices.For the same operating wavelength, the optical signal doesn't reach port B and hence we achieved 0% transmission efficiency for port B. For the designed chain shaped PhCRR, there is no backward flow of optical signal from port A, B, C to port D and hence always the transmission efficiency of port D is nearer to 0%.Table 1 provides a clear view of Q-factor & TE of different shaped ring resonator based filters.The designed chain shaped ring resonator is compared with different shaped ring resonators and it is inferred that our work provides higher Q-factor & transmission efficiency than other PhCRRs reported.Micro-fabrication techniques like electron-beam lithography (EBL) and focused ion-beam etching methods are used for the fabrication of 2D photonic crystal structures.Due to its deep etching with the aid of extremely durable masks and its best resolution of roughly 1 nm, electron beam lithography (EBL) has emerged as the preferred fabrication technique for 2D PC-based devices and components [36].

Conclusion
We proposed a two dimensional Photonic crystal based chain shaped ring resonator that offered maximum transmission efficiency and quality factor as compared with the existing photonic crystal based ring resonators.The ring resonator is designed with silicon rods that are embedded in an air medium operating with TE mode light signals.Numerical analysis is done with the help of the FDTD method.As compared with other shaped rings like hexagon, square and circular, our chain shaped ring offered sky-scraping performance.The simulation showed very attractive results such as a transmission efficiency of around 99.7% and a quality factor of about 4550 at a wavelength of 1551 nm.We have also investigated the performance of the proposed ring resonator for various rod radius.It is identified that when the radius of the rod increases the transmission efficiency of the resonator decreases.The proposed ring resonator can be utilized as an elementary module in the design of Photonic integrated circuits (PIC) and also in CWDM applications.

Figure 1 .
Figure 1.Schematic of the basic ring resonator structure with an input port and 3 output ports.

Figure 2 .
Figure 2. (a) Periodic structure of crystal arrangement without flexible structural defects and (b) Photonic band gap of the proposed structure.

Figure 3 .
Figure 3. Schematic image of the chain shaped PhCRR and its refractive index profile.

Figure 4 .
Figure 4. Electric field distribution.(a) Schematic image of the wavelength distribution of PhCRR.(b) Electric field distribution pattern of chain shaped PhCRR resonating at 1551 nm wavelength and (c) 1553 nm.

Figure 6 .
Figure 6.Normalised transmission spectra of the designed chain shaped PhCRR at various port points for 1551 nm wavelength.

Table 1 .
Comparison of proposed chain shaped PhCRR with different reported PhCRR structures.