1 Introduction

In recent years, numerous researches on optical devices have been investigated based on photonic crystals. The photonic crystals are periodic structures of the alternating layers of materials with different refractive indices (Joannopoulos et al. 2007; Dutta and Pal 2013). Various optical sensors can be implemented using photonic crystal structures. The photonic crystals have properties that enable them to measure very small parameters, including an ultra-high optical limitation, light control in a small area, production with CMOS technology, integration capability of an optical chip, etc. (Olyaee and Najafgholinezhad 2013a; Olyaee and Dehghani 2013).

Photonic crystal sensors are different in application, structure, size of measurement area, and sensing mechanism (Olyaee and Najafgholinezhad 2013a; Olyaee and Dehghani 2013; Coscelli et al. 2010; Lee and Fauchet 2007; Olyaee and Naraghi 2013; Olyaee and Mohebzadeh-Bahabady 2014; Olyaee et al. 2014; Olyaee and Najafgholinezhad 2013b; Hsiao and Lee 2011; Li et al. 2011; Li and Lee 2011; Zhang and Qiu 2005; Qiang and Zhou 2007). So far, several photonic crystal sensors have been provided, one of which is biosensor (Derbali et al. 2011). Proposed biosensors have been used to detect different biological molecules and bio-materials such as antibodies, virus, bacterial cells, toxins, DNA molecules, proteins, etc. The photonic crystal structures such as photonic crystal waveguides (PCWs), photonic crystal fibers (PCFs), photonic crystal micro- and nano-cavities, and photonic crystal ring resonators (PCRRs) can also be used in photonic crystal biosensors.

Photonic crystal sensing mechanism is similar in most sensors. In these sensors, the effective refractive index of holes in sensing area is changed by the activation of sensing processes (for example, binding an analyte to the sensing hole). The effective refractive index variation causes a change in one of the characteristics of the transmission spectrum. In general, there are two methods for bio-sensing mechanisms based on the change of effective refractive index: resonant wavelength shift (RWS) scheme and intensity variation (IV) scheme (Chao and Guo 2006). In these two methods, the amount of resonance wavelength shifts and intensity variations of the transmission spectrum are respectively used to measure the presence of analytes. In RWS method, a wide range is measurable. Narrow full width at half maximum (FWHM) and higher quality factor are important for increasing the accuracy of RWS-based sensors. Using this scheme, the tiny shift in effective refractive index cannot be often determined. IV method has high accuracy and requires simple apparatus. But, in this scheme, a narrow range of wavelength shift is measured. A broader FWHM will be desirable in this case, because at smaller slope values, a finer calibration can be achieved.

Comparing with other types of photonic crystal resonators, PCRR reveals high quality and high sensitivity in biosensing applications (Hsiao and Lee 2009; Sharma and Sharan 2014). Some biosensors based on hexagonal PCRR have been designed and presented (Hsiao and Lee 2010; Li et al. 2011; Ho et al. 2012). The hexagonal ring resonators can be formed by removing the air holes. In 2010, the biochemical sensor based on the single hexagonal PCRR was designed (Hsiao and Lee 2010). Then, a biosensor has been demonstrated by using dual nano-ring resonators (Hsiao and Lee 2011). Also, Ho et al. reported the design of triple nano-ring resonators to be used as a biosensor (Ho et al. 2012). Size of hexagonal ring resonator in all the presented biosensors has been equal to five air holes (approximately equal to \(3\,\upmu \hbox {m}\)).

Recently, a diamond-shaped PCRR biosensor has been designed (Olyaee and Mohebzadeh-Bahabady 2014). The ring resonator and two waveguides were formed by reducing the radius of air holes. Size of the diameter of nano-ring resonator was \(1.1\,\upmu \hbox {m}\). The quality factor and sensitivity were respectively obtained as 3,700 and 3.0 nm/fg. In this sensor, sensing mechanism was based on RWS method.

In this paper, a novel biosensor based on the photonic crystal nano-ring resonator is proposed. This biosensor includes a ring resonator and two waveguides. The ring resonator is shaped by consecutive curves. The sensing mechanism of this biosensor is based on the IV scheme.

2 Designing photonic crystal biosensor

The geometry of presented photonic crystal is a square of silicon with an array of hexagonal lattice of holes. The silicon plate thickness is 220 nm from a silicon-on-insulator wafer. The holes with 120 nm radius are created on the silicon slab with the effective refractive index of 2.825. In this structure, holes are filled with the air molecules that have the refractive index of 1. In the hexagonal lattice of air holes, distance between the centers of two adjacent air holes is equal to 410 nm. Some holes are removed to make the layout of biosensor. The biosensor layout contains a ring resonator and two waveguides. The ring resonator is formed by two consecutive curves. The two waveguides are placed at the bottom and top of the ring resonator. The wave enters through the bottom waveguide, the resonance occurs in the ring resonator, and the wave is transmitted from bottom to top waveguides. Finally, wave leaves the top waveguide and is detected by the time monitor.

The preliminary layout of the biosensor based on photonic crystal nano-ring resonator is shown in Fig. 1. The vertical, horizontal, and coupling distances are marked on this figure. These parameters were studied for the optimal design of the structure. The horizontal distance was equal to the number of rows of air holes between the two curves. The vertical distance meant that the right curve (curve 2) was several rows higher than the left one (curve 1). Also, coupling distance was the number of rows of holes between the waveguides and ring resonator.

For analyzing this biosensor, two-dimensional finite-difference time-domain (2-D FDTD) method and plane-wave expansion (PWE) approach were applied. The 2-D FDTD and PWE methods were used for simulating the propagation of electromagnetism wave and for calculating photonic band gap (PBG) of the periodic structure, respectively. The band diagram of the photonic crystal structure is demonstrated in Fig. 2. The PBG of this structure for TM gap extended from 0.258 to 0.340 eV. The corresponding wavelength range is equal to the wavelengths between 1,205 and 1,640 nm.

Fig. 1
figure 1

The preliminary layout of the biosensor based on photonic crystal nano-ring resonator. The ring resonator is formed by curves 1 and 2. The vertical, horizontal, and coupling distances are marked on this figure

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Fig. 2
figure 2

Band structure of the photonic crystal structure

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Parameters including coupling, vertical, and horizontal distances between the two curves are studied in terms of having the best biosensor performance. In optical sensors, quality factor and sensitivity are two most important parameters. On the other hand, increase of these two features is inconsistent. But, in the biosensor-based IV sensing mechanism, sensitivity is more important comparing to the quality factor. In this study, optimal selection is done in terms of higher sensitivity.

2.1 Coupling distance

The coupling distance is important for efficient transmission between waveguides and ring resonator. Also, it is effective for the sensor sensitivity. By increasing the distance between ring resonator and waveguides, light interaction with analyte in the sensing region is diminished. Thus, intensity of transmission spectra and sensitivity is decreased. Here, three parameters including quality factor, sensitivity, and intensity of the transmission spectrum are important for the sensor performance. Hence, by selecting two rows of air holes as the coupling distance, all three features of the biosensor showed an acceptable value.

2.2 Horizontal distance

The biosensor structure is formed by considering two consecutive curves. To find the best place for making the second curve, the vertical and horizontal distances between the two curves are investigated. In all these cases, the coupling distance is selected as two rows of holes. Initially, two rows of holes are considered for vertical distance, and the horizontal distance between the two curves is investigated. The horizontal distance between the two curves is changed from 1 to 4 rows of holes and, at each stage, the resonance wavelength is obtained. The quality factor and intensity of the resonance wavelength are shown in Fig. 3. The horizontal axis of these graphs is selected based on the number of rows of the holes selected as the horizontal distance.

Fig. 3
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The quality factor and intensity of the resonance wavelength of proposed biosensor with respect to the horizontal distances between the two curves

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2.3 Vertical distance

In this study, the vertical distance between two curves is changed from zero to six rows of holes. The zero vertical distance meant that two curves are aligned in a row, and the one-row vertical distance indicates that curve 2 is one-row above curve 1. In all the cases, coupling and horizontal distances are two rows. The resonance wavelength of each mode is obtained. The quality factor and intensity of the resonance wavelength in all the cases are demonstrated in Fig. 4.

Fig. 4
figure 4

The quality factor and intensity of the resonance wavelength of proposed biosensor as a function of vertical distances between the two curves

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3 Results and discussion

In a sensor with IV sensing mechanism, the amount of intensity change at resonant frequency is measured. So, a higher quality factor is not important. In other words, a lower quality factor leads to the increase of sensitivity. In this study, the structure was simulated so that the biosensor had optimum sensitivity.

In the simulation, for exciting the resonant mode of the ring resonator, a temporal pulse at the input of the waveguide is launched and transmission spectra at the output waveguide are recorded by a time monitor. For coupling distance, two rows of air holes are selected. Also, one row of air holes is selected for horizontal and vertical distances. The designed structure and output transmission spectrum of the ring resonator are shown in Figs. 5 and 6, respectively.

Fig. 5
figure 5

The proposed final structure with optimized parameters. Marked hole is the best sensing hole

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Fig. 6
figure 6

a The resonant wavelengths when the sensing hole has different refractive indices. b The resonant wavelengths in more details. By increasing the refractive index in the sensing hole, intensity of the transmission spectrum is shifted to a higher value

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The sensing mechanism of this biosensor is based on IV scheme. The best sensing hole for binding an analyte is shown in Fig. 5. This hole has more sensitive compared to the others, because it has the stronger light interaction with the analyte. The effective refractive index of the sensing hole is changed in the range of 1.33–1.48. Output transmission spectrum when the sensing hole has different refractive indices, is shown in Fig. 6. As demonstrated in this figure, by increasing the refractive index, intensity was shifted to a higher value. Intensity variations occurred at the wavelength of 1,482.7 nm.

The normalized curve related to the intensity shifts of transmission spectra which is changed by the refractive index variation is shown in Fig. 7. In this curve, the intensity of the transmission spectrum of the refractive index of 1.33 is equal to zero. Figure 7 demonstrates a linear relationship between refractive index and intensity shift. Regression coefficient of the biosensor was about 0.99967 which showed a good linearity relation.

Fig. 7
figure 7

Normalized curve related to the intensity shifts of transmission spectra with respect to the effective refractive index

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In the IV scheme of bio-sensing mechanism, sensitivity can be defined as the ratio of the amount of intensity change to refractive index unit. For calculating the sensitivity of the biosensor, transmission spectra of the refractive indices of 1.33 and 1.45 are studied. The sensing hole is assumed to be filled with water molecules at first. Then, the sensing hole is filled with DNA molecules. For this change in refractive index in the sensing hole, the transmission spectrum shifts are equal to 1.71 units. Therefore, for a unit change in the refractive index of the biosensor, the intensity of transmission spectrum is reduced by 14.26 units.

4 Conclusion

In this paper, a biosensor based on the nano-ring resonator has been formed by two consecutive curves. Three parameters of the structure including coupling, vertical, and horizontal distances have been investigated in terms of having the best biosensor performance. In this biosensor, the sensing mechanism was based on IV scheme. By increasing the refractive index of the sensing hole, the intensity of transmission spectrum was shifted to a higher value. Therefore, for a unit change in the refractive index of the biosensor, intensity of transmission spectrum has been reduced by 14.26 units. The results reveal that the regression coefficient of the biosensor was about 0.99967.