Elongated-Hexagonal Photonic Crystal for Buffering, Sensing, and Modulation

nanomaterials

Article Elongated-Hexagonal Photonic Crystal for Buffering, Sensing, and Modulation

Sayed Elshahat 1,2,3,4 , Israa Abood 3, Zixian Liang 1, Jihong Pei 2 and Zhengbiao Ouyang 3,*

1 Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China; [email protected] (S.E.); [email protected] (Z.L.) 2 College of Electronics and Information Technology, Shenzhen University, Shenzhen 518060, China; [email protected] 3 THz Technical Research Center of Shenzhen University, Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China; [email protected] 4 Physics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt * Correspondence: [email protected]

Abstract: A paradigm for high buffering performance with an essential fulﬁllment for sensing and modulation was set forth. Through substituting the fundamental two rows of air holes in an elongated hexagonal photonic crystal (E-PhC) by one row of the triangular gaps, the EPCW is molded to form an irregular waveguide. By properly adjusting the triangle dimension solitary, we fulﬁlled the lowest favorable value of the physical-size of each stored bit by about 5.5510 µm. Besides, the

EPCW is highly sensitive to refractive index (RI) perturbation attributed to the medium through inﬁltrating the triangular gaps inside the EPCW by microﬂuid with high RI sensitivity of about

Citation: Elshahat, S.; Abood, I.; 379.87 nm/RIU. Furthermore, dynamic modulation can be achieved by applying external voltage Liang, Z.; Pei, J.; Ouyang, Z. and high electro-optical (EO) sensitivity is obtained of about 748.407 nm/RIU. The higher sensitivity Elongated-Hexagonal Photonic is attributable to strong optical conﬁnement in the waveguide region and enhanced light-matter Crystal for Buffering, Sensing, and interaction in the region of the microﬂuid triangular gaps inside the EPCW and conventional gaps Modulation. Nanomaterials 2021, 11, (air holes). The EPCW structure enhances the interaction between the light and the sensing medium. 809. https://doi.org/10.3390/ nano11030809 Keywords: photonic crystal waveguide; optical buffers; sensors; dynamic modulation

Academic Editors: Detlef W. Bahnemann and Iole Venditti 1. Introduction Received: 20 February 2021 Slotted photonic crystal waveguides (SPCWs) with various PCW modalities, have Accepted: 18 March 2021 Published: 22 March 2021 been anticipated theoretically and experimentally demonstrated [1]. They are created by opening a narrow slot or irregular air gaps as a line-defect inside a PCW. Due to the

Publisher’s Note: MDPI stays neutral discontinuity at the interface of silicon slab with high refractive index and air gaps with with regard to jurisdictional claims in low index, the electric/magnetic field in the air gaps with low index is enhanced [2], published maps and institutional affil- with associated optical-buffer enhancement accessible from the PCW [3]. They can be iations. advantageously used in high-sensitivity sensors [4], optical switches [5], and high-speed electro-optical modulators [6], etc. Optical buffers can store data temporally and adjust the timing of optical packets [7]. Optical buffer is a significant component for all-optical communication networks, processors, and optical computers in the future. The unique PCW nanostructure designed is efficient for optical buffering performances [3,8] because Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. of room-temperature operation [9], masterful manipulation of the guided-mode dispersion This article is an open access article relations with a change in subtle structure parameters, and compatibility for on-chip distributed under the terms and integration [10]. conditions of the Creative Commons Besides, by fine-tuning the defects in a PCW or infiltrating appropriate materials, Attribution (CC BY) license (https:// photonic crystal (PhC) devices are truly auspicious for sensing attributable to the bright creativecommons.org/licenses/by/ features like high sensitivity, ultra-compact size, structural design flexibility [11,12], and 4.0/). suitable for massive integration [13]. Particularly, air-gap infiltration with microfluids in

Nanomaterials 2021, 11, 809. https://doi.org/10.3390/nano11030809 https://www.mdpi.com/journal/nanomaterials Nanomaterials 2021, 11, x FOR PEER REVIEW 2 of 11

Nanomaterials 2021, 11, 809 2 of 10

massive integration [13]. Particularly, air-gap infiltration with microfluids in the PCWs has beenthe PCWs suggestively has been demonstrated suggestively [14] demonstrated that can ma [ke14 ]availability that can make variation availability in microfluid variation re- fractivein microfluid index, refractivewhich enhances index, the which dispersi enhanceson and the sensing dispersion properties and sensingof PCWs properties [15]. of PCWsIn [this15]. paper, the proposed structure is based on the merging between hexagonal and squareIn lattices this paper, to produce the proposed an elongated structure hexagonal is based onphotonic the merging crystal between structure hexagonal (E-PhC). Throughand square substituting lattices to producethe central an elongatedtwo rows of hexagonal air holes photonic with one crystal row of structure triangular (E-PhC). gaps, anThrough irregular substituting waveguide the is central designed. two rowsThe tria of airngular holes gaps with inside one row the of proposed triangular structure gaps, an behaveirregular as waveguide microcavities is designed. of a low-refractive-index. The triangular gaps At insidethis point, the proposedevery triangle structure can be behave con- sideredas microcavities a defect and of a every low-refractive-index. defect can be consider At thised point, as a everycavity. triangle Thus, a can sequence be considered of cavi- tiesa defect can couple and every together defect to can form be a considered line of cavities as a cavity.or the defect-cavity Thus, a sequence waveguide. of cavities Firstly, can bycouple properly together adjusting to form the a line triangular of cavities dimension, or the defect-cavity high buffering waveguide. performance Firstly, has by properlybeen attained.adjusting Then, the due triangular to the strong dimension, light confinemen high bufferingt, which performance gives intensification has been attained. to the optical Then, modedue to with the stronga guided-mode light confinement, wavelength, which the gives sensitiv intensificationity to the refractive to the optical index mode(RI) through with a infiltratingguided-mode the wavelength, air gaps by themicrofluid sensitivity was to studied. the refractive Finally, index dyna (RI)mic through modulation infiltrating with measuringthe air gaps electro-optical by microfluid (EO) was sensitivity studied. Finally,based on dynamic the proposed modulation EPCW withcan be measuring achieved byelectro-optical filling the EO-effect (EO) sensitivity polymer based into onthe theair proposedgaps and EPCWholes. To can sum be achieved up, the enhanced by filling structurethe EO-effect is vastly polymer appropriate into the for air optical gaps andbuffering holes. and To sumis completely up, the enhanced possible due structure to the limitedis vastly optimization appropriate process. for optical buffering and is completely possible due to the limited optimization process. 2. Structure Model and Results 2. Structure Model and Results The scrutinized structure is based on the merging between hexagonal and square lat- The scrutinized structure is based on the merging between hexagonal and square tices to produce E-PhC [16]. The constructed structure is the PhC slab of 𝑛 = 3.48with lattices to produce E-PhC [16]. The constructed structure is the PhC slab of n = 3.48 with fixed and large air holes of radius 𝑅 = 0.45𝑎, where 𝑎 is the lattice period. The proposed fixed and large air holes of radius R = 0.45a, where a is the lattice period. The proposed EPCW is created through substituting two rows of fundamental air holes by one row of EPCW is created through substituting two rows of fundamental air holes by one row of equilateral triangular gaps inside the EPCW to form an irregular waveguide. Each triangle 𝑙 has aa sideside lengthlengthl as as shown shown in Figurein Figure1. By 1. properly By properly adjusting adjusting the triangle the triangle dimension dimension solely solelywithout without varying varying the lattice the constants, lattice constants,R and a, high𝑅 and buffering 𝑎, high performance buffering performance with an essential with anperformance essential performance for sensing and for modulationsensing and havemodulation been attained. have been Suppose, attained. for instance,Suppose, that for instance,the dielectric that constantthe dielectric is independent constant is onindependent the Y-axis. on Then the the Y-axis. solutions Then allthe take solutions the form all take the form of either transverse electric (TE) modes with nonzero (𝐻 , 𝐻 , 𝐸 ) or trans- of either transverse electric (TE) modes with nonzero Hx, Hz, Ey or transverse magnetic 𝐻 , 𝐸 , 𝐸 . verse(TM) modesmagnetic with (TM) nonzero modesH withy, Ex ,nonzeroEz . For clarity, firstly, For the clarity, photonic firstly, band the gaps photonic (PBGs) bandhave beengaps simulated(PBGs) have for been TM by simulated the spectral for featuresTM by the of thespectral basic features E-PhC structure of the basic of a siliconE-PhC structureslab at n of= a 3.48siliconand slabR at= 𝑛0.45 =a 3.48as shownand 𝑅 in = the 0.45𝑎 inset as ofshown Figure in2 the. Via inset a fast of Figure Fourier 2. Viatransform a fast Fourier (FFT) algorithm,transform (FFT) the output algorithm, of the the transmission output of the spectrum transmission in the spectrum frequency in thedomain frequency fromthe domain time domainfrom the is time shown domain in Figure is shown2. The in transmission Figure 2. The spectrum transmission has a largespec- trumTM PBG has of a normalizedlarge TM PBG frequency of normalized from ωa/ 2frequencyπc = 0.2485 fromto 0.3805𝜔𝑎/2𝜋𝑐along the propagation= 0.2485 to 0.3805 alongdirection the Γpropagation–X. direction Γ–X.

Figure 1. Schematic diagram of the proposed EPCW structure.

Nanomaterials 2021, 11, 809 3 of 10 Nanomaterials 2021, 11, x FOR PEER REVIEW 3 of 11

FigureFigure 2. 2.The The transmissiontransmission spectrumspectrum of of the the basic basic E-PhC E-PhC slab slab of ofn 𝑛= 3.48 = 3.48 andand R 𝑅= 0.45= 0.45𝑎.a.

TheThe EPCWEPCW hashas aa perfectperfect bufferingbuffering performance performance in in a a wide-range wide-range variation variation of of triangle triangle defectdefect lengthlength l.𝑙. Whilst,Whilst, wewe willwill concernconcern about the variation of of l𝑙 in in thethe rangerange fromfrom 1.461.46𝑎a toto1.54 1.54𝑎a with with an an increment increment of of∆ l𝛥𝑙= 0.02 = 0.02𝑎a for for high high optical optical buffering buffering properties. properties.Figure Figure3 3 explainsexplains thethe variation of of the the group group velocity velocity (𝑣v/𝑐)g/c forfor TM TM guided-mode guided-mode with with the the normal- nor- malizedized frequency frequency 𝑈U == 𝜔𝑎/2𝜋𝑐ωa/2πc =via =𝑎/𝜆 a/ theλ via plane the wave plane expansion wave expansion (PWE) method (PWE) methodthrough throughthe module the moduleBandSOLVE BandSOLVE of RSoft ofsoftware, RSoft software, whereas whereasthe inset thefigure inset shows figure the shows supercell the supercellmodel for model PWE for calculations. PWE calculations. It can be It canseen be from seen Figure from Figure 3a that3a thatthe thegroup group velocity velocity de- decreasescreases from from high high values values until until 𝑙 l = 1.50𝑎1.50 anda and then then starts starts to toincrease increase once once more more with with the thecurve curve moving moving to a to higher a higher frequency frequency area. area. The Thetransmission transmission mechanism mechanism of TM of light TM lightpulse pulseinside inside the proposed the proposed EPCW EPCW can can be beunderstood understood by by the the magnetic magnetic field field (M-field)(M-field) profileprofile shownshown inin Figure3 3b.b. The M-field M-field of of the the transm transmissionission pulse pulse is ishighly highly confined confined around around and andinside inside the thetriangular triangular gaps gaps of ofEPCW EPCW and and diff differenterent from from that that observed inin conventionalconventional PCWs.PCWs. WeWe observe observe spatially spatially light light confinement confinement and and periodic periodic oscillations oscillations in in the the field field profile profile lengthwiselengthwise on on the the propagation propagation path, path, displaying displaying a a strong strong coupling coupling between between the the triangular triangular defectdefect cavitiescavities thatthat formform aa channel channel waveguide. waveguide. TheThe M-fieldM-field profileprofile shows shows the the pulse pulse being being inin periodicperiodic alternatingalternating betweenbetween compressioncompression andand expanding,expanding, inin which which the the hop hop between between Nanomaterials 2021, 11, x FOR PEER REVIEWeach two neighboring spatial compressions is 6a as shown in Figure3b. Wherefore,4 of the11 each two neighboring spatial compressions is 6a as shown in Figure 3b. Wherefore, the EPCWEPCW may may be be usedused toto generategenerate vastlyvastly low-thresholdlow-threshold lasers, lasers, in in optical optical modulators modulators and and can can be used for enhancing dealings between light and sensing media. be used for enhancing dealings between light and sensing media. Combined with the transmission determination in data interconnections, the EPCW is superior for realizing all-optical buffers in practical applications for its compact physical size, owing to its performance of delaying light in optoelectronic devices. The ingoing data into the buffer possesses a categorization of packets (i.e., sequences of bits) with the optical central wavelength 𝜆. The data bit period in each packet is 𝜏 with a base-bandwidth 𝐵 =1/𝜏. The optical data bandwidth is ∆𝜔̀ = 4𝜋 𝐵 [17] in rad/s and can be defined through the normalized bandwidth by ∆𝑈 = (𝑎/2𝜋𝑐)∆𝜔̀ [18]. The key factor for all delay-line optical buffers is the physical size of each stored bit in the buffer 𝐿 = 𝑣 ×𝜏 = 𝑣 ×(2𝑎/c∆𝑈) [17], which is independent of the delay line length. To minimize the physical size of each stored bit or maximize the number of stored bits in the buffer, a low group velocity compatible with wider transmission bandwidth is required.

The simulation data in Figure 3 is presented in Table 1 for clarity. The vital wave- 1.55 μm 1 μm length can be scrambled to be via contraction the lattice period a from to Figure 3. (a) Group velocity vg/c for TM guided-mode with the normalized frequency U = ωa/2πc = a/λ at Figure 3. (a) Group velocity (𝑣the/𝑐) values for TM according guided-mode to withTable the 1. normalized It is obvious frequency from 𝑈them = that𝜔𝑎/2𝜋𝑐 the optimum =at 𝑎/𝜆 different case of the valuesdifferent of 𝑙 values, whereas of l ,the whereas inset proposedfigure the inset shows figure EPCW the shows supercell is at the 𝑙 supercell model = 1.50𝑎 for model whichPWE forcalculations; shows PWE calculations; a wider (b) the bandwidth M-field (b) the M-fieldprofile of aboutof profile the trans-56.6128 of the nm missiontransmission pulse at pulse 𝑙 at = l 1.50𝑎.= 1.50 a. with 𝑣 = 0.0654c within ±10% variation of 𝑣 corresponding to the lowest 𝐿 = 5.5510 μm. Consequently, in that case for storing 1 bit, a storage length of 5.5510 μm is required. In comparison with other previous structures, for example in the case of photonic crystal coupled-cavity of micro-optical buffer, the lowest physical size of each stored bit 𝐿 reached 16.33 μm [18]. After a series of modification in silicon-polymer photonic-crystal coupled-cavity waveguide 𝐿 was 7.97 μm [19], and by introducing air holes in W2 PCW 𝐿 was 10.85 μm [15]. Mainly for all new-generation communication systems and optical signal processing, high bit rates are needed with a small storage length. The EPCW is a potential candidate for all the requirements of optical-signal processing. Thus, we can say that introducing triangular defects in EPCW possesses an advantage for enhancing the coupling between the defects to enlarge bandwidth, group delay, and low 𝐿.

Table 1. EPCW optical buffering properties at different values of triangle-defect side length l.

Parameter (𝒍/𝒂) ∆𝑼 ∆𝝀 𝒂𝒕 𝟏𝟓𝟓𝟎 𝐧𝐦 𝒂(𝛍𝐦) 𝒗𝒈/𝒄 𝑳𝒃𝒊𝒕 (𝛍𝐦) 1.46 0.0113 55.2527 0.4931 0.0887 7.7164 1.48 0.0118 56.3811 0.5011 0.0833 7.1020 1.50 0.0120 56.6128 0.5084 0.0654 5.5510 1.52 0.0118 55.3925 0.5101 0.0702 6.0916 1.54 0.0105 48.6741 0.5173 0.0708 6.9864

3. Refractive-Index Sensing As mentioned above, the EPCW exhibits strong light confinement, which gives intensification to the optical mode with a guided-mode wavelength that is vastly sensitive to refractive index (RI) perturbation attributed to the medium through infiltrating the air holes of EPCW by microfluid. RI sensor was established based on the optimum EPCW of 𝑙 fixed at 1.50𝑎 and for operating at the optical communication wavelength, the lattice constant was selected to be 𝑎 = 0.5084 μm. Figure 4a shows the variation of 𝑣/𝑐 with the operating wavelength due to filling the triangular gaps inside the EPCW by microfluid with changing microfluid refractive index of 𝑛 from 1.00 to 1.10 with an increment of 𝛥𝑛 = 0.01 as shown in Figure 4a, all guide-mode wavelengths are deflected towards the higher wavelength (i.e., redshift) as 𝑛 increases. When 𝑛 changes from 1.00 to 1.10, 𝑣 changes from 0.085𝑐 to 0.110𝑐 with the shifting of the central guide-mode wavelength by nm from 1554 to 1591. In designed sensor devices, sensitivity (S) is the imperative indicator for appraising sensing ability. 𝑆 measures the variation of the guided-mode wavelength ∆𝜆 produced during the change in refractive index ∆𝑛 of the microfluid filled in the triangular gaps inside the EPCW and can be expressed via the

Nanomaterials 2021, 11, 809 4 of 10

Combined with the transmission determination in data interconnections, the EPCW is superior for realizing all-optical buffers in practical applications for its compact physical size, owing to its performance of delaying light in optoelectronic devices. The ingoing data into the buffer possesses a categorization of packets (i.e., sequences of bits) with the optical central wavelength λ0. The data bit period in each packet is τbit with a base- 0 bandwidth Bpacket = 1/τbit. The optical data bandwidth is ∆ω = 4π Bpacket [17] in rad/s 0 and can be deﬁned through the normalized bandwidth by ∆U = (a/2πc)∆ω [18]. The key factor for all delay-line optical buffers is the physical size of each stored bit in the buffer Lbit = vg × τbit = vg × (2a/c∆U) [17], which is independent of the delay line length. To minimize the physical size of each stored bit or maximize the number of stored bits in the buffer, a low group velocity compatible with wider transmission bandwidth is required. The simulation data in Figure3 is presented in Table1 for clarity. The vital wavelength can be scrambled to be 1.55 µm via contraction the lattice period a from 1 µm to the values according to Table1. It is obvious from them that the optimum case of the proposed EPCW is at l = 1.50a which shows a wider bandwidth of about 56.6128 nm with vg = 0.0654c within ±10% variation of vg corresponding to the lowest Lbit = 5.5510 µm.

Table 1. EPCW optical buffering properties at different values of triangle-defect side length l.

¯ Parameter (l/a) ∆U ∆λ at 1550 nm a (µm) vg/c Lbit (µm) 1.46 0.0113 55.2527 0.4931 0.0887 7.7164 1.48 0.0118 56.3811 0.5011 0.0833 7.1020 1.50 0.0120 56.6128 0.5084 0.0654 5.5510 1.52 0.0118 55.3925 0.5101 0.0702 6.0916 1.54 0.0105 48.6741 0.5173 0.0708 6.9864

Consequently, in that case for storing 1 bit, a storage length of 5.5510 µm is required. In comparison with other previous structures, for example in the case of photonic crystal coupled-cavity of micro-optical buffer, the lowest physical size of each stored bit Lbit reached 16.33 µm [18]. After a series of modiﬁcation in silicon-polymer photonic-crystal coupled-cavity waveguide Lbit was 7.97 µm [19], and by introducing air holes in W2 PCW Lbit was 10.85 µm [15]. Mainly for all new-generation communication systems and optical signal processing, high bit rates are needed with a small storage length. The EPCW is a potential candidate for all the requirements of optical-signal processing. Thus, we can say that introducing triangular defects in EPCW possesses an advantage for enhancing the coupling between the defects to enlarge bandwidth, group delay, and low Lbit.

3. Refractive-Index Sensing As mentioned above, the EPCW exhibits strong light confinement, which gives intensification to the optical mode with a guided-mode wavelength that is vastly sensitive to refractive index (RI) perturbation attributed to the medium through infiltrating the air holes of EPCW by microfluid. RI sensor was established based on the optimum EPCW of l fixed at 1.50a and for operating at the optical communication wavelength, the lattice constant was selected to be a = 0.5084 µm. Figure4a shows the variation of vg/c with the operating wavelength due to filling the triangular gaps inside the EPCW by microfluid with changing microfluid refractive index of nm f from 1.00 to 1.10 with an increment of ∆nm f = 0.01 as shown in Figure4a, all guide-mode wavelengths are deflected towards the higher wavelength (i.e., redshift) as nm f increases. When nm f changes from 1.00 to 1.10, vg changes from 0.085c to 0.110c with the shifting of the central guide-mode wavelength by nm from 1554 to 1591. In designed sensor devices, sensitivity (S) is the imperative indicator for appraising sensing ability. S measures the variation of the guided-mode wavelength ∆λ produced during the change in refractive index ∆nm f of the microfluid filled in the Nanomaterials 2021, 11, x FOR PEER REVIEW 5 of 11

relation 𝑆 = ∆𝜆/∆𝑛, by the unit nm/RIU. To distinguish the 𝑆 property of the proposed EPCW. Whereas, each value of 𝑛 has its own curve of 𝑣 variation with wavelength as shown in Figure 4a. The corresponding wavelength to average group velocity within ±10% variation of 𝑣 or 𝑛 and most of the practical applications in this range [20] Nanomaterials 2021, 11, 809 is the guided-mode wavelength. The selected guided-mode wavelengths corresponding5 of 10 to each value 𝑛 is shown in Figure 4b. The simulated data is characterized by the red sphere, and the linear fitting by the blue solid line. From linear fitting, 𝑆, the slope is 379.87 nm/RIU, we accomplished a high value of RI sensitivity in the EPCW as compared triangular gaps inside the EPCW and can be expressed via the relation S = ∆λ/∆nm f , withby the most unit previous nm/RIU. studies To distinguish based on the conventionalS property of PCW the proposed as shown EPCW. in Table Whereas, 2. This high each sensitivity is due to the strong optical confinement and light-matter interaction in the re- value of nm f has its own curve of vg variation with wavelength as shown in Figure4a. The gioncorresponding of the slots, wavelength the EPCW structure to average can group increase velocity the withininteraction±10% regionvariation between of vg lightor ng andand themost sensing of the medium. practical applications in this range [20] is the guided-mode wavelength. The (𝑛 = 𝑐/𝑣 ) selectedThe guided-modegroup indices wavelengths correspondingcan be evaluated to each experimentally value nm f is shownvia Fourier in Figure trans-4b. formThe simulatedspectral interferometry data is characterized as a function by the ofred wavelength sphere, and when the the linear proposed fitting structure by the blue is placedsolid line. in one From arm linear of an fitting,unbalancedS, the Mach–Z slope isehnder 379.87 interferometer nm/RIU, we accomplished[21]. The setups a high for bothvalue measurements of RI sensitivity of the in the transmission EPCW as comparedand group with index most are previousshown in studiesdetail in based [22]. More- on the over,conventional by using PCW an optical as shown network in Table analyzer2. This high(Q7750, sensitivity Advantest), is due the to thetransmission strong optical and groupconfinement index spectra and light-matter can be measured interaction directly in the through region the of the modulation slots, the EPCWphase-shift structure method can accordingincrease the to interaction[23,24]. region between light and the sensing medium.

1600 (a) Linear fit, Slope = 379.87 ± 5.09 (b) 0.12 1590 g/c) 0.08 1580

1570 0.04 nmf =1.00 nmf =1.01 nmf =1.02 nmf =1.03 nmf =1.04 nmf =1.05 1560 Group velocity (v nmf =1.06 nmf =1.07 nmf =1.08 nmf =1.09 nmf =1.10 0.00 wavelength(nm) mode Guided 1550 1520 1540 1560 1580 1600 1620 1.00 1.02 1.04 1.06 1.08 1.10 Wavelength(nm) Refractive index(RIU)

Figure 4. (a) Group velocity vg/c as a function of wavelength due to changing RI of nm f from 1.00 to 1.10 with an increment Figure 4. (a) Group velocity 𝑣/𝑐 as a function of wavelength due to changing RI of 𝑛 from 1.00 to 1.10 with an incre- of ∆n = 0.01, (b) the selected guided mode wavelength for each value of n . ment ofm f 𝛥𝑛 = 0.01, (b) the selected guided mode wavelength for each valuem fof 𝑛. The group indices (n = c/v ) can be evaluated experimentally via Fourier transform Table 2. Comparison of RI sensitivityg ing EPCW with previous studies based on the conventional PCW.spectral interferometry as a function of wavelength when the proposed structure is placed in one arm of an unbalanced Mach–Zehnder interferometer [21]. The setups for both measurements of the transmissionStructure and group index are shown in detail in𝑺 [ 22(nm/RIU)]. Moreover, by using an optical network analyzerEPCW (Q7750, Advantest), the transmission and379.87 group index spectra can be measured directlySDPCW through [15] the modulation phase-shift method 244 according to [23,24]. Nano-slotted micro-ring resonator [25] 100 PCW in SOI [26] 174.8 Table 2. Comparison of RISOI sensitivity ring-shaped in EPCW PCW with [27] previous studies based on the conventional 66 PCW. Ring-shaped PhC [28] 110 Structure S (nm/RIU)

EPCW 379.87 SDPCW [15] 244 Nano-slotted micro-ring resonator [25] 100 PCW in SOI [26] 174.8 SOI ring-shaped PCW [27] 66 Ring-shaped PhC [28] 110

4. Dynamic Modulation and Electro-Optical Sensor It is outstanding to realize that the physical characteristics of transmission required can be controlled through an external command to implement optical buffers applications. Moreover, to understand the dynamic modulation of optical-buffer performances in the proposed EPCW, two electrodes are set on both sides of the optimum EPCW of 𝑙 fixed at 1.50𝑎, and for operating at the optical communication wavelength, the lattice constant was selected to be 𝑎 = 0.5084 μm with R = 0.45𝑎 as shown in Figure 5. Then the electrostatic field lines are parallel to the Z-axis, to allow the largest linear electro-optic coefficient 𝛾 in polystyrene [29]. In this context, our electro-optical (EO) sensor based on the proposed EPCW can be achieved by filling the EO-effect polymer into the air gaps (triangles and holes). Particularly, air holes infiltrated with liquid in PCWs have been significantly investigated and demonstrated [14]. Different microfabrication methods have been applied in the polymer-based micro-optical device technology, including soft-lithography, electron- beam-lithography (EBL) [30], and electron beam etching [31]. The fabrication conditions should be chosen carefully to diminish the fabrication errors of the designed parameters. Consequently, it is essential to use some processes with high accuracies, such as high-

Nanomaterials 2021, 11, 809 resolution lithography and high-quality pattern. Thus, the method of direct writing6 by of 10an electron beam is particularly attractive to obtain high-resolution without using further etching steps or photolithography masks [32,33]. On the other hand, nanoimprint lithography (NIL) can be used to emboss stamps with high aspect ratio lines and rod arrays into proposedthin polymer EPCW, films two directly electrodes and to are transfer set on these both patterns sides of into the optimumseveral materials EPCW [34], of l fixed while atNIL1.50 isa ,regardedand for operating as a developing at the optical technique communication for next-generation wavelength, lithography the lattice because constant of wastheir selected producibility to be aof nano-scale= 0.5084 µfeaturesm with [3R5].= Therefore,0.45a as the shown NIL process in Figure could5. Then be appro- the electrostaticpriate for the field fabrication lines are of parallel polymeric to the PhCZ -axis,structures to allow [36]. the For largest example, linear A silicon/organic electro-optic coefficienthybrid modulatorγ33 in polystyrene integrating [ 29PCW,]. In 75 this nm context, slot, EO our polymer electro-optical infiltration (EO) is experimentally sensor based ondemonstrated the proposed [37] EPCW and can also, be high-speed achieved by sili fillingcon themodulator EO-effect with polymer a low-driving into the air voltage gaps (trianglesbased on anda polymer holes). infiltrated slow-light PCW is demonstrated [6].

FigureFigure 5. SchematicSchematic conformation conformation of the of dynamic the dynamic modulation modulation for the optimum for the EPCW optimum R = EPCW R 0.45𝑎,= 0.45 𝑙a, l == 1.50𝑎1.50a andanda 𝑎= 0.5084= 0.5084. μm µm.

Particularly,By applying air an holes external infiltrated modulation with liquid voltage, in PCWs the polymer have been refractive significantly index investi- will be gatedchanged and based demonstrated on the Pockels [14]. Different effect. The microfabrication variation is subject methods to havethe second-order been applied suscep- in the polymer-based〈〉 micro-optical device technology, including soft-lithography, electron-beam- tibility 𝜒 [38] and can be calculated as ∆𝑛 = − 0.5 𝑛 𝛾𝑉/𝑑, where 𝛾 is the lin- lithography (EBL) [30], and electron beam etching [31]. The fabrication conditions should ear electro-optic coefficient, ∆𝑛 represents the extraordinary refractive index of poly- be chosen carefully to diminish the fabrication errors of the designed parameters. Conse- mer, 𝑉 is the applied modulating voltage, 𝑑 is the distance between the two electrodes, quently, it is essential to use some processes with high accuracies, such as high-resolution where 𝛾 should be by μm/V at the time, 𝑉 by V, and 𝑑 by μm so 𝑉/𝑑 by V/μm. The lithography and high-quality pattern. Thus, the method of direct writing by an electron nonlinear effects can be significantly enhanced in the proposed EPCW with low group beam is particularly attractive to obtain high-resolution without using further etching velocity, which is due to the local density compression of states produced by the slow steps or photolithography masks [32,33]. On the other hand, nanoimprint lithography light. In view of the effect on the second-order susceptibility induced by the nanostruc- (NIL) can be used to emboss stamps with high aspect ratio lines and rod arrays into thin polymer films directly and to transfer these patterns into several materials [34], while NIL is regarded as a developing technique for next-generation lithography because of their producibility of nano-scale features [35]. Therefore, the NIL process could be appropriate

for the fabrication of polymeric PhC structures [36]. For example, A silicon/organic hybrid modulator integrating PCW, 75 nm slot, EO polymer infiltration is experimentally demonstrated [37] and also, high-speed silicon modulator with a low-driving voltage based on a polymer infiltrated slow-light PCW is demonstrated [6]. By applying an external modulation voltage, the polymer refractive index will be changed based on the Pockels effect. The variation is subject to the second-order suscepti- 2 3 bility χ [38] and can be calculated as ∆n = − 0.5 npoly γ33V/d, where γ33 is the linear electro-optic coefficient, ∆npoly represents the extraordinary refractive index of polymer, V is the applied modulating voltage, d is the distance between the two electrodes, where γ33 should be by µm/V at the time, V by V, and d by µm so V/d by V/µm. The nonlinear effects can be significantly enhanced in the proposed EPCW with low group velocity, which is due to the local density compression of states produced by the slow light. In view of the effect on the second-order susceptibility induced by the nanostructure, the effective second-order susceptibility in the EPCW depends on the local field factor f and the polymer 2 2 3 2 bulk susceptibility χbulk [38], thus χpc = f χbulk. In that case, the electro-optic coefficient 3 converts to be γ33 f and the local field factor f is calculated with the group velocity inside bulk pc the bulk polymer substrate νg = c/nploy, and the group velocity in PhC structure νg . q bulk PC The f in EPCW can be calculated as f = νg /νg . The modified index variation can Nanomaterials 2021, 11, 809 7 of 10

3 2 be expressed as [29]: ∆n = np(V) − np = −0.5 np × ng γ33V/d. Then the dynamic modulation in the optimized EPCW with R = 0.45a, l = 1.50a and a = 0.5084 µm is investigated with γ33 = 150 pm/V [6], np = 1.59, ng = 15.29 and d = 12a = 6.1008 µm. By ﬁne-tuning the external modulated voltage on the electrodes, the optical buffering Nanomaterials 2021, 11, x FOR PEERperformance REVIEW and EO sensing are investigated by adjusting V from 0 V to 25 V with8 anof 11

increment of ∆V = 5 V. Figure6a shows the variation of vg/c with the operating wavelength due to different applied modulation voltages based on filling the air gaps (triangles and holes) with the nonlinear optical (NLO) polymer of np = 1.59 at V = 0 V. compares the group velocity (𝑣/𝑐) for TM guided-mode via the normalized frequency As shown in Figure6a, all guide-mode wavelengths are deflected towards the lower 𝑈 = 𝜔𝑎/2𝜋𝑐 =𝑎/𝜆 for 2-D calculations with 𝑛 = 3.2 approximation and 𝑛 = wavelength (i.e., blueshift) as the n (V) decreases due to increasing the applied modulated 3.48 for the optimum case of thep proposed EPCW at 𝑙 = 1.50𝑎. Figure 7 shows that for voltage. When V changes from 0 V to 25 V with an increment of ∆V = 5 V, which 𝑛 = 3.48 it possesses a narrow waveband with lower group velocity, on the contrary corresponds to a change in polymer refractive index from 1.59 (0 V) to 1.55316 (25 V) 𝑛 = 3.2 it possesses a wider waveband but with the higher group velocity. The wave- with an increment of ∆np (5 V) = −0.00737, with a shifting of the central guide-mode 0.3396(2𝜋𝑐/𝑎) 0.3573(2𝜋𝑐/𝑎) 𝑛 wavelengthband ranging by nm from from 1818 (0 V) to 1791to (25 V) as shown, under from the Figure ±10%6a. variation By the way, of we for mentioned2-D calculations in the previous of 𝑛 section=3.2, thatcorrespondsS measures tothe wider-bandwidth shift of the guided-mode ∆𝜆 about wavelength 78.3781 nm ∆λwithproduced 𝐿 = during 5.7726 the μm change. Whileas, in refractive for 2-D calculations index, so it canof 𝑛 be called = 3.48 as RI, the sensitivity. waveband At is from 0.3220 (2𝜋𝑐/𝑎) to 0.3340 (2𝜋𝑐/𝑎), which corresponds to narrow-bandwidth ∆𝜆 this time for analyzing the sensitivity (Sv) of the EPCW EO sensor, the shift of the guided- modeabout wavelength 56.6128 nm∆ λwithis observed 𝐿 = 5.5510 as a function μm. It can of thebe seen change that in the the results applied for modulatedthe two cases voltageare approximately∆V and can beequal. expressed The curves as: in the two cases can be explained as: from the common equation (𝑐/𝑛 = 𝜔/𝑘), with the increase of refractive index, the slow light bands, 𝑣 curves move toward∆λ the lowernm frequency∆λ area,∆ nasp k being unchanged.∆np As well, from S = by unit = × , Sv = S × , the theorem of electromagnetic∆V V variation [47]:∆n pa higher∆V refractive-index∆V region would lead to a lower mode frequency. Therefore, the 𝑛 approximation leads to the higher aver- whichage group can be velocity. called the Mostly, voltage the sensitivity. properties Eachof PhC value can ofkeepV andon unchanged,np has its own providing curve ofone variationexpands with or contracts wavelength the as parameters shown in Figure of PCW6a. Thestructures corresponding proportionally. wavelength The tovalue average of the groupoptimum velocity operating is the guided wavelength mode ca wavelength.n be selected The of the selected structure guided-mode by only setting wavelengths the value corresponding to each value of V and n are shown in Figure6b. The simulated data and of 𝑎 without simulation repetition. p the linear fitting are characterized by the spheres and solid lines, respectively.

(a) 0.25 (b) Refractive index(RIU) 1.55 1.56 1.57 1.58 1.59 , 0.20 1820 Linear fit of Δλ with Δnp Slope = 748.407 ± 26.678 g/c) 0.15 1810

0.10 V=0V 1800 V=5V 0.05 V=10V

Group velocity (v V=15V Linear fit of Δλ with ΔV, V=20V 1790 Slope =-1.103 ± 0.03931

V=25V wavelength(nm) mode Guided 0.00 0 5 10 15 20 25 1700 1750 1800 1850 1900 Applied Voltage (V) Wavelength(nm)

Figure 6. (a) The variation of vg/c with the wavelength due to different applied modulation voltages from 0 V to 25 V with Figure 6. (a) The variation of 𝑣/𝑐 with the wavelength due to different applied modulation voltages from 0 V to 25 V anwith increment an increment of ∆V =of 5𝛥𝑉V based = 5V on based ﬁlling on thefilling air gapsthe air (triangles gaps (triangles and holes) and holes) with the with nonlinear the nonlinear optical optical (NLO) (NLO) polymer; poly- (b)mer; the selected(b) the selected guided guided mode wavelengths mode wavelengths corresponding corresponding to each valueto each of valueV and ofn p𝑉. and 𝑛.

From the linear ﬁtting of Figure6b, the voltage sensitivity S , the slope, is 1.103 nm/V. 0.15 neff v Besides, the nbulk RI sensitivity can be calculated as 748.407 nm/RIU. Compared to a lattice- )

/c 0.12 shiftedg resonant microcavity in a triangular lattice PhC slab in [39], Sv is 31.90 nm/V andv corresponds to a refractive index changes ∆n = 0.001 results in a ∆λ = 0.18 nm (RI sensitivity0.09 is ~180 nm/RIU). The slotted PCW-based EO modulator demonstrated by [400.06], where the ∆λ is 0.12 nm as refractive index change of ∆n = 0.001, (RI sensitivity

Group velocity( Group 0.03

0.00 0.32 0.33 0.34 0.35 0.36 Normalized Frequency(a/λ)

Figure 7. Group velocity (𝑣/𝑐) for TM guided mode with the normalized frequency 𝑈 = 𝜔𝑎/2𝜋𝑐 =for 𝑎/𝜆 2-D calculations with 𝑛 = 3.2 approximation and 𝑛 = 3.48 of the optimized mode at 𝑙 = 1.50𝑎.

Nanomaterials 2021, 11, x FOR PEER REVIEW 8 of 11

compares the group velocity (𝑣/𝑐) for TM guided-mode via the normalized frequency 𝑈 = 𝜔𝑎/2𝜋𝑐 =𝑎/𝜆 for 2-D calculations with 𝑛 = 3.2 approximation and 𝑛 = 3.48 for the optimum case of the proposed EPCW at 𝑙 = 1.50𝑎. Figure 7 shows that for 𝑛 = 3.48 it possesses a narrow waveband with lower group velocity, on the contrary 𝑛 = 3.2 it possesses a wider waveband but with the higher group velocity. The wave- Nanomaterials 2021, 11, 809 band ranging from 0.3396(2𝜋𝑐/𝑎) to 0.3573(2𝜋𝑐/𝑎), under the ±10% variation of 𝑛8 offor 10 2-D calculations of 𝑛 =3.2, corresponds to wider-bandwidth ∆𝜆 about 78.3781 nm with 𝐿 = 5.7726 μm. Whileas, for 2-D calculations of 𝑛 = 3.48, the waveband is 0.3220 (2𝜋𝑐/𝑎) 0.3340 (2𝜋𝑐/𝑎) ∆𝜆 fromis ~120 nm/RIU). Also, to polymer-filled PCW, which demonstrated corresponds by to [41 narrow-bandwidth], the operating wave- about 56.6128 nm with 𝐿 = 5.5510 μm. It can be seen that the results for the two cases length changes from 1542.02 nm (0 V) to 1533.31 nm (120 V), ~9 nm/120 V (Sv sensitivity areis onlyapproximately 0.0725 nm/V). equal. The The proposed curves in structure the two cases presented can be in explained this paper as: is from preferable the com- as moncompared equation to the(𝑐/𝑛 previous = 𝜔/𝑘) work., with Thethe increase higher sensitivity of refractive is attributableindex, the slow to strong light bands, optical 𝑣concentration curves move in toward the waveguide the lower region frequency and enhanced area, as light-matter k being unchanged. interaction As in well, the region from theof thetheorem microfluid of electromagnetic triangular gaps variation inside the[47]: EPCW a higher and refractive-index conventional gaps region (air would holes), lead i.e., tothe a EPCWlower mode structure frequency. enhances Therefore, the interaction the 𝑛 between approximation the lightand leads sensing to the medium.higher average groupTo strictly velocity. validate Mostly, the simulationthe properties results, of PhC 3-D can simulations keep on unchanged, are required. providing However, one 3-D expandscalculations or contracts are enormously the parameters time-consuming of PCW structures [23,42]. Fortunately, proportionally. it was The demonstrated value of the optimumthat 2-D calculationsoperating wavelength of PhC structures can be withselected the effectiveof the structure refractive by indexonly settingne f f with the infinite value ofheight 𝑎 without is a good simulation approximation repetition. for 3-D structures, which is frequently treated by researchers and appropriated experimentally [23,43]. The 2-D calculations are generally applied with ne f f = 3.2 [16,43–46] in place of slab bulk refractive index. Figure7 compares the group (a) 0.25 = = velocity vg/c for TM guided-mode(b) via the normalizedRefractive frequency index(RIU)U ωa/2πc a/λ for 2-D calculations with ne f f = 3.2 approximation1.55 1.56 and nbulk 1.57= 3.48 1.58for the 1.59 optimum case Δλ Δ , 0.20 of the proposed EPCW at l = 1.50a.1820 Figure7 shows Linear that for fit ofn bulk with= n3.48p it possesses a Slope = 748.407 ± 26.678 g/c) narrow waveband with lower group velocity, on the contrary n f f = 3.2 it possesses a wider ( ) 0.15 waveband but with the higher group velocity. The waveband ranging from 0.3396 2πc/a to 0.3573(2πc/a), under the ±10% variation1810 of ng for 2-D calculations of ne f f = 3.2, corresponds to wider-bandwidth about 78.3781 nm with Lbit = 5.7726 µm. Whileas, for 0.10 2-D calculations of nbulk = 3.48, the waveband is from 0.3220 (2πc/a) to 0.3340 (2πc/a), 1800 which corresponds toV=0V narrow-bandwidth ∆λ about 56.6128 nm with Lbit = 5.5510 µm. It V=5V 0.05 can be seen that the V=10V results for the two cases are approximately equal. The curves in the

Group velocity (v two cases can be explained V=15V as: from the common equation Linear( cfit/ nof Δλ= withω/ kΔ)V,, with the increase V=20V 1790 of refractive index, the slow light bands, vg curvesSlope move =-1.103 toward ± 0.03931 the lower frequency V=25V wavelength(nm) mode Guided 0.00 0 5 10 15 20 25 1700 1750 1800area, as k 1850being unchanged. 1900 As well, from the theorem of electromagnetic variation [47]: a higher refractive-index region would lead to a lowerApplied mode Voltage frequency. (V) Therefore, the Wavelength(nm) ne f f approximation leads to the higher average group velocity. Mostly, the properties of

Figure 6. (a) The variation ofPhC 𝑣/𝑐 can with keep the on wavelength unchanged, due providing to different one applied expands modulation or contracts voltages the from parameters 0 V to 25 of V PCW with an increment of 𝛥𝑉structures = 5V based on proportionally. filling the air gaps The (triangles value of theandoptimum holes) with operating the nonlinear wavelength optical (NLO) can be poly- selected mer; (b) the selected guided ofmode the wavelengths structure by corresponding only setting theto each value value of a ofwithout 𝑉 and 𝑛 simulation. repetition.

0.15 neff nbulk )

/c 0.12 g v 0.09

0.06

Group velocity( Group 0.03

0.00 0.32 0.33 0.34 0.35 0.36 Normalized Frequency(a/λ) FigureFigure 7. 7. GroupGroup velocity velocity (𝑣/𝑐)vg /forc forTM TMguided guided mode mode with withthe normalized the normalized frequency frequency 𝑈 = 𝜔𝑎/2𝜋𝑐U = ωa/2πc =for 𝑎/𝜆= a 2-D/λ forcalculations 2-D calculations with 𝑛 with =n e3.2 f f =approximation3.2 approximation and 𝑛 and n =bulk 3.48= of3.48 the ofopti- the mizedoptimized mode mode at 𝑙at l = 1.50𝑎= 1.50. a.

5. Conclusions In conclusion, a new type of defect is introduced which is created by substituting the fundamental two rows of air holes by one row of the triangular gaps inside the EPCW to form an irregular waveguide. By properly adjusting the triangle dimension solitarily without varying the lattice constant, R and a, high buffering performance with an essential performance for sensing and modulation have been attained. Lower physical size of 5.5510 µm for each stored bit is achieved. Besides, the EPCW can be used as a RI sensor with a RI sensitivity of 379.87 nm/RIU by ﬁlling the triangular gaps inside the EPCW Nanomaterials 2021, 11, 809 9 of 10

with microfluid for a changing microfluid refractive index of nm f from 1.00 to 1.10 with an increment of ∆nm f = 0.01. We accomplished a high value of RI sensitivity in the EPCW as compared with most of previous studies based on conventional PCWs. Besides, the EPCW was studied as EO voltage sensor by fine-tuning an external modulated voltage V from 0 V to 25 V for the air gaps (triangles and holes) filled with the nonlinear optical (NLO) polymer. The high sensitivity of EO voltage sensor is obtained as 1.103 nm/V, which corresponds to a RI of 748.407 nm/RIU.

Author Contributions: Conceived the idea, performed the simulations and writing—original draft preparation, S.E.; methodology and checked the simulation results, I.A.; writing—review and editing, Z.L., J.P. and Z.O. All authors have read and agreed to the published version of the manuscript. Funding: National Natural Science Foundation of China (Grant No.: 61275043, 61307048, 60877034 and 61605128), GDNSF, China (Grant No.: 2020A1515011154), and SZSF, China (Grant No. JCYJ20190808151017218, 20180123) supported this work. Conflicts of Interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References 1. Di Falco, A.; O’Faolain, L.; Krauss, T. Photonic crystal slotted slab waveguides. Photonics Nanostruct. Fundam. Appl. 2008, 6, 38–41. [CrossRef] 2. Almeida, V.R.; Xu, Q.; Barrios, C.A.; Lipson, M. Guiding and confining light in void nanostructure. Opt. Lett. 2004, 29, 1209–1211. [CrossRef][PubMed] 3. Elshahat, S.; Abood, I.; Liang, Z.; Pei, J.; Ouyang, Z. Sporadic-Slot Photonic-Crystal Waveguide for All-Optical Buffers With Low-Dispersion, Distortion, and Insertion Loss. IEEE Access 2020, 8, 77689–77700. [CrossRef] 4. Xu, P.; Zheng, J.; Zhou, J.; Chen, Y.; Zou, C.; Majumdar, A. Multi-slot photonic crystal cavities for high-sensitivity refractive index sensing. Opt. Express 2019, 27, 3609–3616. [CrossRef][PubMed] 5. Zhao, Q.Z.Q.; Cui, K.C.K.; Feng, X.F.X.; Huang, Y.H.Y.; Li, Y.L.Y.; Zhang, D.Z.D.; Zhang, W.Z.W. Ultra-compact variable optical attenuator based on slow light photonic crystal waveguide. Chin. Opt. Lett. 2013, 11, 31301–31304. [CrossRef] 6. Brosi, J.-M.; Koos, C.; Andreani, L.C.; Waldow, M.; Leuthold, J.; Freude, W. High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide. Opt. Express 2008, 16, 4177–4191. [CrossRef] 7. Rawal, S.; Sinha, R.K.; de La Rue, R.M. Slow light miniature devices with ultra-flattened dispersion in silicon-on-insulator photonic crystal. Opt. Express 2009, 17, 13315–13325. [CrossRef] 8. Wu, H.; Han, S.; Li, F.; Yang, Z. Slow light with high normalized delay-bandwidth product in organic photonic crystal coupled- cavity waveguide. Appl. Opt. 2020, 59, 642–647. [CrossRef] 9. Alaeian, H.; Ritter, R.; Basic, M.; Löw, R.; Pfau, T. Cavity QED based on room temperature atoms interacting with a photonic crystal cavity: A feasibility study. Appl. Phys. A 2020, 126, 25. [CrossRef] 10. Yan, S.; Cheng, Z.; Frandsen, L.H.; Ding, Y.; Zhou, F.; Dong, J.; Zhang, X. Bandwidth-adaptable silicon photonic differentiator employing a slow light effect. Opt. Lett. 2017, 42, 1596–1599. [CrossRef][PubMed] 11. Serna, S.; Colman, P.; Zhang, W.; Le Roux, X.; Caer, C.; Vivien, L.; Cassan, E. Experimental GVD engineering in slow light slot photonic crystal waveguides. Sci. Rep. 2016, 6, 26956. [CrossRef][PubMed] 12. Gao, Y.; Dong, P.; Shi, Y. Suspended slotted photonic crystal cavities for high-sensitivity refractive index sensing. Opt. Express 2020, 28, 12272–12278. [CrossRef][PubMed] 13. Zhang, Y.-N.; Zhao, Y.; Lv, R.-Q. A review for optical sensors based on photonic crystal cavities. Sens. Actuators A Phys. 2015, 233, 374–389. [CrossRef] 14. Scullion, M.G.; Di Falco, A.; Krauss, T.F. Slotted photonic crystal cavities with integrated microfluidics for biosensing applications. Biosens. Bioelectron. 2011, 27, 101–105. [CrossRef] 15. Elshahat, S.; Abood, I.; Liang, Z.; Pei, J.; Ouyang, Z. Dispersion engineering of W2 steeple-house-defect waveguide photonic crystal. Results Phys. 2020, 19, 103547. [CrossRef] 16. Elshahat, S.; Abood, I.; Liang, Z.; Pei, J.; Ouyang, Z. Futuristic elongated-hexagonal photonic crystal waveguide for slow light. Opt. Commun. 2020, 474, 126082. [CrossRef] 17. Long, F.; Tian, H.; Ji, Y. A Study of Dynamic Modulation and Buffer Capability in Low Dispersion Photonic Crystal Waveguides. J. Lightwave Technol. 2010, 28, 1139–1143. [CrossRef] 18. Elshahat, S.; Abood, I.; Khan, K.; Yadav, A.; Ouyang, Z. High-capability micro-optical buffer based on coupled hexagonal cavity in photonic crystal waveguide. Appl. Nanosci. 2019, 9, 1963–1970. [CrossRef] 19. Abood, I.; Elshahat, S.; Ouyang, Z. High buffering capability of silicon-polymer photonic-crystal coupled cavity waveguide. Waves Random Complex Media 2021, 1–16. [CrossRef] 20. Krauss, T.F. Slow light in photonic crystal waveguides. J. Phys. D Appl. Phys. 2007, 40, 2666–2670. [CrossRef] Nanomaterials 2021, 11, 809 10 of 10

21. Gomez-Iglesias, A.; O’Brien, D.; O’Faolain, L.; Miller, A.; Krauss, T.F. Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry. Appl. Phys. Lett. 2007, 90, 261107. [CrossRef] 22. Awan, K.M.; Schulz, S.A.; Liu, D.X.; Dolgaleva, K.; Upham, J.; Boyd, R.W. Post-process wavelength tuning of silicon photonic crystal slow-light waveguides. Opt. Lett. 2015, 40, 1952–1955. [CrossRef] 23. Kubo, S.; Mori, D.; Baba, T. Low-group-velocity and low-dispersion slow light in photonic crystal waveguides. Opt. Lett. 2007, 32, 2981–2983. [CrossRef] 24. Kawasaki, T.; Mori, D.; Baba, T. Experimental observation of slow light in photonic crystal coupled waveguides. Opt. Express 2007, 15, 10274–10281. [CrossRef][PubMed] 25. Yang, D.; Duan, B.; Zhang, X.; Lu, H. Nanoslotted microring resonator for high figure of merit refractive index sensing. Opt. Appl. 2020, 50, 37–47. [CrossRef] 26. García-Rupérez, J.; Toccafondo, V.; Bañuls, M.J.; Castelló, J.G.; Griol, A.; Peransi-Llopis, S.; Maquieira, Á. Label-free antibody detection using band edge fringes in SOI planar photonic crystal waveguides in the slow-light regime. Opt. Express 2010, 18, 24276–24286. [CrossRef][PubMed] 27. Lai, W.-C.; Chakravarty, S.; Zou, Y.; Guo, Y.; Chen, R.T. Slow light enhanced sensitivity of resonance modes in photonic crystal biosensors. Appl. Phys. Lett. 2013, 102, 041111. [CrossRef][PubMed] 28. Pu, M.; Liu, L.; Frandsen, L.H.; Ou, H.; Yvind, K.; Hvam, J.M. Silicon-on-insulator ring-shaped photonic crystal waveguides for refractive index sensing. In Proceedings of the 2010 Conference on Optical Fiber Communication (OFC/NFOEC), Collocated National Fiber Optic Engineers Conference, San Diego, CA, USA, 21–25 March 2010; pp. 1–3. 29. Roussey, M.; Baida, F.I.; Bernal, M.-P. Experimental and theoretical observations of the slow-light effect on a tunable photonic crystal. J. Opt. Soc. Am. B 2007, 24, 1416–1422. [CrossRef] 30. Huang, Y.; Paloczi, G.T.; Yariv, A.; Zhang, C.; Dalton, L.R. Fabrication and Replication of Polymer Integrated Optical Devices Using Electron-Beam Lithography and Soft Lithography. J. Phys. Chem. B 2004, 108, 8606–8613. [CrossRef] 31. Sun, H.; Chen, A.; Olbricht, B.C.; Davies, J.A.; Sullivan, P.A.; Liao, Y.; Dalton, L.R. Direct electron beam writing of electro-optic polymer microring resonators. Opt. Express 2008, 16, 6592–6599. [CrossRef] 32. Rola, K.P.; Zajac, A.; Czajkowski, M.; Fiedot-Tobola, M.; Szpecht, A.; Cybinska, J.; Smiglak, M.; Komorowska, K. Electron Beam Patterning of Polymerizable Ionic Liquid Films for Application in Photonics. Langmuir 2019, 35, 11968–11978. [CrossRef] [PubMed] 33. Abood, I.; Elshahat, S.; Ouyang, Z. High Figure of Merit Optical Buffering in Coupled-Slot Slab Photonic Crystal Waveguide with Ionic Liquid. Nanomaterials 2020, 10, 1742. [CrossRef][PubMed] 34. Heyderman, L.; Ketterer, B.; Bächle, D.; Glaus, F.; Haas, B.; Schift, H.; Vogelsang, K.; Gobrecht, J.; Tiefenauer, L.; Dubochet, O.; et al. High volume fabrication of customised nanopore membrane chips. Microelectron. Eng. 2003, 67–68, 208–213. [CrossRef] 35. Chou, S.Y.; Krauss, P.R.; Zhang, W.; Guo, L.; Zhuang, L. Sub-10 nm imprint lithography and applications. J. Vac. Sci. Technol. B 1997, 15, 2897–2904. [CrossRef] 36. Kee, C.-S.; Han, S.-P.; Yoon, K.B.; Choi, C.-G.; Sung, H.K.; Oh, S.S.; Park, H.Y.; Park, S.; Schift, H. Photonic band gaps and defect modes of polymer photonic crystal slabs. Appl. Phys. Lett. 2005, 86, 051101. [CrossRef] 37. Lin, C.-Y.; Wang, X.; Chakravarty, S.; Lee, B.S.; Lai, W.; Luo, J.; Jen, A.K.-Y.; Chen, R.T. Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement. Appl. Phys. Lett. 2010, 97, 093304. [CrossRef] 38. Razzari, L.; Träger, D.; Astic, M.; Delaye, P.; Frey, R.; Roosen, G.; André, R. Kerr and four-wave mixing spectroscopy at the band edge of one-dimensional photonic crystals. Appl. Phys. Lett. 2005, 86, 231106. [CrossRef] 39. Yang, D.; Tian, H.; Ji, Y. The properties of lattice-shifted microcavity in photonic crystal slab and its applications for electro-optical sensor. Sens. Actuators A Phys. 2011, 171, 146–151. [CrossRef] 40. Wülbern, J.H.; Petrov, A.; Eich, M. Electro-optical modulator in a polymer-infiltrated silicon slotted photonic crystal waveguide heterostructure resonator. Opt. Express 2009, 17, 304–313. [CrossRef] 41. Yan, C.; Li, C.; Wan, Y. Dynamic modulation of wideband slow light with continuous group index in polymer-filled photonic crystal waveguide. Appl. Opt. 2017, 56, 9749. [CrossRef] 42. Qiu, M. Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals. Appl. Phys. Lett. 2002, 81, 1163–1165. [CrossRef] 43. Säynätjoki, A.; Mulot, M.; Ahopelto, J.; Lipsanen, H. Dispersion engineering of photonic crystal waveguides with ring-shaped holes. Opt. Express 2007, 15, 8323–8328. [CrossRef] 44. Maache, M.; Hocini, A.; Khedrouche, D. Geometrically tunable slow light based on a modified photonic crystal waveguide. Chin. J. Phys. 2017, 55, 2318–2324. [CrossRef] 45. Elshahat, S.; Abood, I.; Khan, K.; Yadav, A.; Bibbo, L.; Ouyang, Z. Five-Line Photonic Crystal Waveguide for Optical Buffering and Data Interconnection of Picosecond Pulse. J. Lightwave Technol. 2019, 37, 788–798. [CrossRef] 46. Benisty, H.; Weisbuch, C.; Labilloy, D.; Rattier, M.; Smith, C.; Krauss, T.; de La Rue, R.; Houdré, R.; Oesterle, U.; Jouanin, C.; et al. Optical and confinement properties of two-dimensional photonic crystals. J. Lightwave Technol. 1999, 17, 2063–2077. [CrossRef] 47. Joannopoulos, J.D.; Meade, R.D.; Winn, J.N. Photonic Crystals: Molding the Flow of Light; Princeton University Press: Princeton, NJ, USA, 1995.