1 Introduction

Photonic crystals (PCs) are nano-structured materials in which the periodic variation of the material dielectric constant results in a photonic band gap (PBG) [1]. This kind of structure provides the method to control photons or in general, electromagnetic waves in the dielectric medium. Photons with wavelengths or energies in this gap cannot travel through the crystal. By introducing point and line defects in these structures, the periodicity and thus the completeness of the band gap are disturbed and the propagation of light can be localized in the PBG region. Utilizing the photonic band gap effect, a lot of active and passive optical devices based on photonic crystals are designed, which may eventually pave the way for photonic integrated circuits (PICs) [2] and wavelength-division multiplexing (WDM) optical communication systems [3]. Photonic crystal (PC)-based optical devices have attracted greater interest due to their compactness (because photonic crystal-based devices can be designed in the range of nanometre), speed of operation and long life [4, 5].

Channel add/drop filters are very important components that can be utilized not only as multichannel multiplexers/demultiplexers (Mux/Demux) and optical add/drop modules (OADMs) for wavelength-division multiplexing (WDM) systems, but also as optical sensors, etc. In these components, it is important to access the signal on one particular channel without disturbing the signals on the other channels.

Photonic crystal ring resonators (PCRR) are common structures for designing optical channel drop filters [12]. PCRR can be used for realizing optical switches, optical sensors, optical demultiplexers and ring laser cavity [6]. The ring dimensions and crystal parameters play an important role in the resonance behaviour of a ring resonator. Two waveguide types are mainly used as platforms for building ring resonator. These types of waveguides have advantages such as low propagation loss, low coupling loss and low dispersion. Dielectric constant of the inner rods and coupling rods are suitable parameters for the tuning of the filter [7, 8]. Higher-order filters, consisting of multiple cascaded resonators, act as a demultiplexer. Demultiplexer is a device that is used to separate one signal into several stream of signal, and it is mostly used in telecommunication to carry the signal over the long distance WDM applications [3].

The optical devices are designed generally for wavelength-division multiplexing (WDM) range [9,10,11,12,13,14,15,16,17], which is enhanced to better bandwidth utilization capacity. Multiple channels with different wavelengths of information carried over a fibre are termed as WDM. The types of WDM techniques are coarse wavelength-division multiplexing (CWDM) [12] and dense wavelength-division multiplexing (DWDM). CWDM is a standardized WDM technology that uses up to 20 different wavelengths for data transmission over a single fibre. CWDM follows ITU-T recommendation G 695 and G 694.2. It uses the spectrum of 1271–1611 nm with 20-nm wavelength spacing and provides 18-nm wavelength channel. Because of the coarse granularity, strict tuning of wavelength is not required for CWDM. In DWDM [18,19,20,21], the spectral channel width is very small that is < 1 nm with few hundreds of channels reported within the range of 1525–1565 nm. The wider channel spacing leads to significant reduction in the manufacturing cost of optical components, when compared with those used in DWDM technology. When one considers its expanded transmission capacity, low component cost, design simplicity and reduced operational cost, CWDM is an optimum choice in lowering capital expenditure.

In the literature, several topologies have been proposed for designing photonic crystal CDFs: by utilizing the resonant coupling between micro-cavity modes produced by point defects and waveguide modes created by line defects [22, 23] or by the non-resonant coupling between two parallel photonic crystal waveguides placed in proximity [24, 25]. Photonic crystal ring resonator (PCRR) is another popular device used for designing channel drop filters. The concept of PCRR was introduced for the first time by Kim et al. [26], where they proposed and demonstrated a two-dimensional photonic crystal (2D-PC) laser based on the hexagonal waveguide ring resonator. Compared to point-defect cavities, ring resonators offer scalability in size, adaptability in structure design because of vast design parameters and flexibility in mode design due to their multi-mode nature. Recently, several types of CDF based on 2D-PCRR have been proposed using square PCRR [27], hexagonal PCRR [28], circular PCRR [29], X-shaped PCRR [30] and elliptical PCRR [31].

In this paper, three-port channel drop filter (CDF) using quasi-square PCRR is proposed whose corresponding parameters, namely, transmission efficiency, dropping efficiency, quality factor and resonant wavelength, are evaluated. Simultaneously, different optimization techniques, like changing the radius of the coupling rods and scattering rods, refractive index of the rods and shapes of the scattering rods, are applied in a structure. An optimum CDF structure is obtained, and then CDF is extended for demultiplexer by having three different channels. Dielectric constant of the inner rods and coupling rods is suitable parameters for the tuning of the filter [7, 8]; in this work, we change the radius of the inner rods for tuning the filter. In this attempt, the transmission efficiency is enhanced and the crosstalk is minimized. The PWE [32] is a popular method used to calculate the band gap of the structure which is used for calculating the PBG without introducing any defects. The normalized transmission spectra and resonance of the demultiplexer is obtained by using FDTD [33] method.

2 Design of single-ring channel drop filter

The proposed structure is contrived on the square lattice system by the silicon rods (pillars of RI = 3.42) built with the air as background index of 1. The lattice constant (distance between the two adjacent pillars) or lattice parameter of the rods is 540 nm, and the pillar radius is 0.19a (a = lattice constant). The number of rods in X and Z directions is 20 and 19, respectively. The band diagram in Fig. 1 gives the propagation modes of the structure without defects; it has PBG for transverse electric (TE) modes whose electric field is parallel to the rod axis. The PC structure has a PBG for TE ranges from 0.2627 to 0.4453 a/\(\lambda \) whose corresponding wavelength accounts from 1212 to 1981 nm. The CDF is designed for a 1550-nm optical wavelength, which shows less attenuation [17]. When the defects (point and line) are created in the structure, the band gap is broken so that electromagnetic waves pass through the photonic band gap region which is essential for complete signal transfer from the bus waveguide to drop waveguide through the ring resonator at resonant wavelength.

Fig. 1
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Band diagram of the structure

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The proposed channel drop filter is composed of three parts: two line defects as the bus waveguide (the upper one) and drop waveguide (the lower one) and a resonant ring located between the waveguides. Also it has three ports, among them port A and B are input and output transmission terminals, respectively, whereas port C is a dropping terminal. In general, the resonators are formed by removing the rods in the middle of the layout. Ring resonator is called as coupling element. The four rods placed at the corner of the ring resonator are called scatters/scattering rods. These scattering rods have a greater impact on the performance of the device. They can improve the spectral selectivity, drop efficiency and suppress the counter propagating modes [35, 36]. The normalized transmission spectra and resonance wavelengths for different refractive index are obtained using two-dimensional finite-difference time-domain (FDTD) method. The schematic diagram of the ring resonator-based channel drop filter is shown in Fig. 2.

Fig. 2
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Schematic layout of ring resonator-based CDF

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At resonance, the wavelength is coupled into the ring resonator from the bus waveguide and it exits through the output port C. The coupling and dropping efficiencies are detected by monitoring the power at ports B and C, respectively. A continuous wave signal is applied as the input at port A, and the normalized transmission power spectrum is obtained at ports B and C. Figure 3 shows the normalized transmission spectra of PCRR. The resonant wavelength of the proposed structure is obtained at 1550 nm.

Fig. 3
figure 3

Normalized transmission spectra of the CDF at ports B, C and D, respectively

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As shown in Fig. 3, all the power in the bus waveguide is extracted by using resonant tunnelling process [37] and well transferred into port C through the resonant ring.

Figure 4a represents the electric field pattern of PCRR-based channel drop filter at OFF resonance, i.e. 1500 nm. At resonant wavelength \(\lambda \) = 1550 nm, the electric field at the bus waveguide is fully coupled into the ring and reached the output port C as shown in Fig. 4b. Further, it is also investigated that the resonant wavelength and other functional parameters of the filter will be shifted to longer wavelength while increasing the rods radius and vice versa. By utilizing the aforementioned principle, the proposed structure is extended for demultiplexing applications which is discussed in the next section.

Fig. 4
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Electric field distribution of 2D PCRR-based CDF a at 1500 nm (OFF resonance), b at 1550 nm (ON resonance)

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Fig. 5
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Schematic of the optimized structure-1 with different radii

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Fig. 6
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Normalized transmission spectra for different radii of a coupling rods, b scattered rods

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2.1 Optimization of the CDF structure

2.1.1 Changing radii of scattering rods and coupling rods

One of the most important features of any filter is tunability. To improve the dropping efficiency of the designed CDF, investigate parameters which affect the characteristics of the filter. First of all, we change the radius of three coupling rods from 0.08 to 0.12 nm as shown in Fig. 5. This leads to shift of resonating wavelength to higher values as shown in Fig. 6a. In similar way, the radius of four scattered rods is changed from 0.08 to 0.12 nm as shown in Fig. 6b. It is obvious that resonating wavelength increases as radius of scattered rods increases. The output responses have been summarized as shown in Tables 1, 2.

Table 1 Resonant wavelength, dropping efficiency and quality factor of the proposed CDF at different coupling rod radii
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Table 2 Resonant wavelength, dropping efficiency and quality factor of the proposed CDF at different scattered rod radii
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Fig. 7
figure 7

Schematic of the optimized structure-2 with different refractive index

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Fig. 8
figure 8

Normalized transmission spectra for different refractive index of a coupling rods, b scattered rod

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It is clear from Tables 1, 2 that the output response of the CDF is a function of the radius of the coupling and scatter rods. As we changed the rod’s radius, there was a shift in the resonating wavelength. This affects the dropping efficiency of the filter structure. It can be observed from the Tables 1, 2 that the optimum value of the coupling and scattered rod radius is obtained at \(0.1\,{\upmu }\hbox {m}\) with a dropping efficiency 85% at a 1550-nm resonant wavelength. As we reduce the rod’s radius by 0.01 up to \(0.08\,{\upmu }\hbox {m}\), there is resonant shift of 3 nm. Likewise, the same occurs as we increase the rod’s radius by 0.01 up to \(0.12\,{\upmu }\hbox {m}\); there is also a resonant shift of 3–5 nm. As we further increase or decrease the coupling and scattered rod radius, its dropping efficiency and quality factor may be affected by changing its values [34].

2.1.2 Changing refractive index of scattering rods and coupling rods:

In this section, we investigate an another parameter which affects the characteristic of the filter. Changing the refractive index of the coupling rods and scattering rods also plays an important role in the performance of the CDF structure. The scattering rods are assigned different refractive index in the ‘optimized structure-2’ as shown in Fig. 7. As a result, the position and width of the photonic gap change and new opportunities of photon management are created. By changing the refractive index of three coupling rods from 3.42 to 3.46, this leads to shift of resonant wavelength to higher values as shown in Fig. 8a. In similar way, the refractive index of four scattered rods is changed from 3.42 to 3.46 as shown in Fig. 8b. It is obvious that resonant wavelength increases as refractive index of scattered rods increases. The output responses have been summarized as shown in Tables 3, 4.

Table 3 Resonant wavelength, dropping efficiency and quality factor of the proposed CDF at different refractive index of coupling rod
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Table 4 Resonant wavelength, dropping efficiency and quality factor of the proposed CDF at different refractive index of scattered rod
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As we changed the coupling and scattered rod’s refractive index, there was a shift in the resonating wavelength. This affects the dropping efficiency of the filter structure. It can be observed from Tables 3, 4 that the optimum value of the coupling and scattered rod refractive index is obtained at 3.42 with a dropping efficiency 85% at a 1550-nm resonant wavelength. As we increase the rod’s refractive index by 0.02, there is resonant shift of around 5 nm.

Fig. 9
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Schematic of the optimized structure-3 with different shapes of scattered rods

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Fig. 10
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Normalized transmission spectra for different elliptical scattered rods

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2.1.3 Changing scattered rod radius as elliptical

To improve the dropping efficiency of the designed CDF, the design parameters are further investigated. This time, the four circular scattered rods are replaced by four elliptical rods, which is a unique concept for improving the dropping efficiency. It has been observed that as the radius of the scattered rod is increased along the semi-major axis, there is an improvement in the dropping efficiency of the designed CDF. This is due to a reduction in the back reflection at corners and support to confine the signal in the ring resonator, which improves the dropping efficiency. Here, for scattered rod analysis, the circular rods with an optimized value of radius \(0.1\,{\upmu }\hbox {m}\) is changed into an elliptical shape by increasing the radius along the semi-major axis to 0.15, 0.20 and \(0.25\,{\upmu }\hbox {m}\), while semi-minor axis is kept as the optimum radius of a circular rod at \(0.1\,{\upmu }\hbox {m}\). The above discussion is shown in Fig. 9, and the normalized transmission spectra are shown in Fig. 10. The resonant wavelength, dropping efficiency and quality factor with the parameters of elliptical scattered rods are tabulated in Table 5

Table 5 Resonant wavelength, dropping efficiency and quality factor while varying the shape of the scatter rods
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It is clearly observed from Table 5 that the dropping efficiency increases when the size of the semi-major axis increases. Analysis shows that as the semi-major axis increases, the dropping efficiency increases. The dropping efficiency increases from 82 to 94%, and the quality factor is simultaneously increased with the size of the semi-major axis of the elliptical scattered rods.

2.1.4 Quantitative measurements

Different optimization techniques are applied to the PCRR-based CDF structure to improve the dropping efficiency and quality factor. The optimized structures are denoted as ‘optimized structure-1’, ‘optimized structure-2’ and ‘optimized structure-3’. The gradual improvements in the dropping efficiency and quality factor have been summarized in Table 6.

Table 6 Resonant wavelength, dropping efficiency and quality factor for different optimization techniques
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Fig. 11
figure 11

a Schematic diagram of photonic crystal ring resonator-based demultiplexer b its index distribution

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From Table 6, optimized structure-3 gives better dropping efficiency and quality factor. So, use this structure as CDF in demultiplexer for the next section.

3 PCRR-based demultiplexer

The proposed PCRR-based CDF structure is extended for demultiplexing application by increasing the total number of rods and by having three different rod radii in a structure. Typically, the resonant wavelength of the structure is altered by changing the lattice constant, radius of the rod and refractive index. According to the results shown above, we can design a multi-CDF to simultaneously drop various wavelength channels from a single multi-wavelength source using the resonant tunnelling process. To illustrate this concept, three parallel cascaded ring resonators are horizontally coupled to a bus waveguide. The device consists of one bus waveguide and three drop waveguides with three ring resonators of different inner rod radius. We can tune the desired wavelength by varying the inner rod radius. It is clear that resonant wavelength shifts towards the higher wavelength region by increasing the rod radius.

Fig. 12
figure 12

Normalized transmission spectra of the multi-CDF (demultiplexer) at ports C, D and E, respectively

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Table 7 Simulation results of PCRR-based demultiplexer
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Fig. 13
figure 13

Electric field pattern of PCRR-based Demux a OFF resonance at 1500 nm. b ON resonance for the rod radius 80 nm at 1524 nm. c ON resonance for the rod radius 90  nm at 1544 nm and d ON resonance for the rod radius 100 nm at 1565 nm

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The proposed PCRR-based demultiplexer consists of 60 \(\times \) 19 square lattices with circular rod, and its index distribution is shown in Fig. 11a, b. As the designated wavelength is dropped by varying the inner rods radius of the resonator. The first PCRR is having the rod radius of 80 nm, the second one is having 90 nm, and the third one is having 100 nm. The top of the waveguide is called as bus waveguide, and bottom of the waveguide is called as dropping waveguide. The bus and dropping waveguides are formed by introducing line defects. The incident port and exit ports are labelled as A, B, C, D and E, respectively.

As the change in rod radius will change the resonant wavelength, the different resonant wavelengths are dropped at its designated port. At resonance, the wavelength is coupled into the ring resonator from the bus waveguide and exits through any one of the output port C, D and E. The coupling and dropping efficiencies are detected by monitoring the power at ports B, C, D and E, respectively. Broadband light is inserted into the bus, and resonant wavelengths specific to each ring resonator are individually demultiplexed into separate drop waveguides. By reversing the input and output roles, the proposed design can also act as a multiplexer to combine various optical wavelength signals into a single bus waveguide.

4 Results and discussion

The transmission spectra for the proposed structure at ports C, D and E are displayed in Fig. 12. The increase in inner rod radius causes resonant wavelengths to shift towards longer wavelengths, and a decrease in inner rod radius causes a shift towards shorter wavelengths. On the other words, by increasing (decreasing) the inner rod radius, a red shift (blue shift) in resonant wavelength occurs. Resonance properties can be precisely tuned to selected specific wavelengths by modulating the lattice constant or by further tuning such as the radius of the rods. The performance parameters for the three channels are listed in Table 7.

From Table 7, it is observed that resonant wavelength is shifted into the higher wavelength while increasing the inner rod radius. Around 20-nm resonant wavelength shifts are attained for every 10 nm rod radius increment.

Our proposed demultiplexer has met the spectrum range and wavelength spacing of ITU-T recommendation G 695 and G 694.2. So, the filter is used for CWDM application.

Figure 13a represents the electric field pattern of PCRR-based demultiplexer at OFF resonance (1500 nm), and Fig. 13b–d represents the electric field pattern at ON resonance for the rod radius of 80, 90 and 100 nm are 1524, 1544 and 1565 nm, respectively. The 20-nm channel spacing is obtained by having rods with 10 nm of radius difference. At resonant wavelengths, \(\lambda \) = 1524, 1544 and 1565 nm, the electric field of the bus waveguide is fully coupled into the ring resonator and reached the output ports C, D and E, whereas at OFF resonance \(\lambda \) = 1500 nm, the signal directly reaches the port B.

The biggest challenge in designing CWDM demultiplexer is to obtain the low crosstalk. Crosstalk of the designed PCRR-based three-channel demultiplexer varies over the range from − 11.54 to − 24.22 dB as shown in Table 8.

The quality factor (Q) characterizes the resolution of wavelength selecting and that can be calculated as

$$\begin{aligned} {Q}=\lambda _{0}/\Delta \lambda \end{aligned}$$
(1)

where \(\lambda _{0}\) and \(\Delta \lambda \) are central wavelength and full width at half power of output and bandwidth, respectively.

Table 8 Crosstalk of three-channel demultiplexer
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5 Conclusion

A channel drop filter based on two-dimensional photonic crystal ring resonator (PCRR) is proposed and investigated through 2D FDTD method. It is extended to drop three different channels by changing the radius of the inner rods in each ring resonator that acts as a demultiplexer. The designed structure drops three different channels which are 1524, 1544 and 1565 nm, which is used in coarse wavelength-division multiplexing (CWDM) systems. One of the salient features of this device is that by changing the radius of the rods, the desired wavelength of output power and quality factor can be obtained.