nanomaterials

Article Switchable Photonic Nanojet by Electro-Switching Nematic

Bintao Du, Jun Xia *, Jun Wu *, Jian Zhao and Hao Zhang

Joint International Research Laboratory of Information Display and Visualization, School of Electronic Science and Engineering, Southeast University, Nanjing 210096, China; [email protected] (B.D.); [email protected] (J.Z.); [email protected] (H.Z.) * Correspondence: [email protected] (J.X.); [email protected] (J.W.); Tel.: +86-83-79-1911-829 (J.X.)

 Received: 28 November 2018; Accepted: 2 January 2019; Published: 6 January 2019 

Abstract: This paper first presents a switchable photonic nanojet (PNJ) generated by a polystyrene (PS) microsphere immersed in nematic liquid crystals (NLCs). The PNJ is switched by applying external voltage, which originates from the refractive index change in the surrounding medium caused by the field-induced realignment of liquid . By tuning the refractive index of NLCs larger or smaller than that of the PS microsphere, the PNJ can be switched off or on. Moreover, we present an optimization study to seek a better electric energy focusing property of the PNJ. Our results reveal that the switchability of PNJ can be optimized by applying a shorter incident wavelength, a double-layer microsphere, and a PS ellipsoid. The full width at half-maximum (FWHM) generated by the PS ellipsoid is narrower than that generated by the microsphere with a shorter incident wavelength. The intensity contrast of the PS ellipsoid is higher than that of the double-layer microsphere. As a whole, the switchability of PNJ can be best optimized by a PS ellipsoid. This should open the way for the development of integrated photonic devices.

Keywords: micro-optics; photonic nanojet; nanomaterials

1. Introduction Sub-wavelength optical resolution has become essential for various applications, from optical microscopy [1], lithography [2], and spectroscopy [3], to data storage [4]. Obtaining the finest resolution [5,6] has been a hot topic for a long time. However, the conventional objective lens has diffraction-limited optical spots [7]. Much effort has been devoted to finding a new way to focus the light to a small spot beyond the diffraction limit [7,8]. The super-focusing effect of “photonic nanojets (PNJs)” [9–21] produced by a dielectric microsphere or microcylinder emerged as a simple and effective way to break the diffraction limit. The PNJ is a narrow high-intensity light flow generated from the shadow surface of transparent nanoparticles. When a transparent nanoparticle with a dimension larger than the wavelength is illuminated by light, PNJ is created due to interferences between the illuminating field and scattering field. The most striking and distinctive feature of PNJ is the high spatial localization of light field in the transverse direction (relative to the direction of incidence), which, in contrast to the conventional high-NA (numerical aperture) focusing optics, can lead to super-resolution dimensions. Moreover, the maximum intensity of the PNJ can reach several hundred times compared to that of the incident light. These features bring about the potential applications of PNJ for nanoscale processing of materials [22], high-resolution microscopy [23], localized sensing techniques [24], optical data storage [25], optical antennas [26], and so on. It has been suggested that the refractive index contrast between the nanoparticle and its background medium plays an important role in the characters of PNJ [27]. Thus, tuning the refractive index of the background medium by external stimuli becomes a key to manipulating PNJ dynamically.

Nanomaterials 2019, 9, 72; doi:10.3390/nano9010072 www.mdpi.com/journal/nanomaterials Nanomaterials 2019, 9, x FOR PEER REVIEW 2 of 11

It has been suggested that the refractive index contrast between the nanoparticle and its background medium plays an important role in the characters of PNJ [27]. Thus, tuning the refractive index of the background medium by external stimuli becomes a key to manipulating PNJ Nanomaterialsdynamically.2019 Recently,, 9, 72 various kinds of micron-sized optical functional materials and devices using2 of 11 (LC) microdroplets have been proposed [28–32]. Primarily, the generation of a PNJ from Recently,an LC microcylinder various kinds with of micron-sized tangential molecular optical functional alignment materials was theoretically and devices analyzed using liquid by crystalfinite- (LC)difference microdroplets time-domain have (FDTD) been proposed[28]. Later [on,28– direct32]. Primarily, experimental the observation generation ofof aelectrically PNJ from tunable an LC microcylinderPNJ generated withfrom tangentialself-assembled molecular LC microdroplet alignments was was theoretically reported [29]. analyzed Such tunable by finite-difference PNJ was also time-domainachieved by using (FDTD) a shell [28 ].and Later LC core on, architecture direct experimental [30]. Similar observation tunable PNJs of electrically created by tunable a core-shell PNJ generatedmicrocylinder from with self-assembled nematic LCs LC infiltrated microdroplets were waspresented reported in [References29]. Such tunable[31,32]. PNJThese was results also achievedindicate that byusing the LC a shell is a andgood LC choice core architecture for PNJ ma [nipulation30]. Similar due tunable to its PNJs rich created variety by of a molecular core-shell microcylinderalignments. with nematic LCs infiltrated were presented in References [31,32]. These results indicate that theUnlike LC isthe a goodprevious choice studies for PNJ above, manipulation in this pa dueper, to itswe rich present variety a study of molecular on a switchable alignments. PNJ generatedUnlike by the a previous polystyrene studies (PS) above, microsphere in this paper, su werrounded present aby study nematic on a switchableliquid crystals PNJ generated (NLCs). byApplying a polystyrene an electric (PS) microspherefield to the surroundeddevice alters by the nematic directors liquid of crystals LC molecules, (NLCs). Applyingwhich changes an electric the fieldeffective to the refractive device altersindex, the and directors electro-switching of LC molecules, of PNJ which is realized. changes FDTD theeffective simulation refractive and analysis index, andresults electro-switching show that the ofPNJ PNJ can is be realized. switched FDTD on simulationand off by andmodulating analysis resultsthe refractive show that index the of PNJ NLCs can besmaller switched and larger on and than off bythat modulating of the PS microsphere. the refractive Th indexis is the of NLCs first time, smaller to the and best larger of our than knowledge, that of the PSthat microsphere. such a case Thisis reported is the first in the time, literature. to the best Furthermore, of our knowledge, optimization that such PNJ a switching case is reported by different in the literature.methods are Furthermore, studied in optimization an ideal model. PNJ switching The results by differentreveal the methods potential are studiedof micro-sized in an ideal particles model. Theimmersed results in reveal the LCs the potentialto control of light micro-sized beyond particles the diffraction immersed limit. in theThis LCs can to be control of interest light beyondfor several the diffractionapplications, limit. especially This can in beoptoelectronic of interest for devices. several applications, especially in optoelectronic devices.

2. Influence Influence of Surrounding MediumMedium onon PNJPNJ Several calculation methods have theoretically and numerically analyzed electromagnetic fieldfield distribution in the vicinity of a transparenttransparent nanoparticle illuminated by a plane wave [[9,27].9,27]. These calculations show show that that the the background background medium medium surrounding surrounding nanoparticles nanoparticles plays plays a significant a significant role role in inthe the formation formation of ofa PNJ. a PNJ. To To verify verify the the effect effect of of the the surrounding surrounding medium, medium, we we performed FDTD simulations using commercial Lumerical SolutionsSolutions software.software. The schematic schematic diagram diagram of of a aPNJ PNJ pr producedoduced by by a dielectric a dielectric microsphere microsphere is shown is shown in Figure in Figure 1. The1. Thenarrow, narrow, high-intensity high-intensity PNJ PNJ that that emerges emerges from from a dielectric a dielectric microsphere microsphere has has been been found found to to present several keykey properties. properties. First, First, the the maximum maximum intensity intensity of PNJ of is PNJ several is hundredseveral hundred times higher times compared higher tocompared that of theto that incident of the light. incident Second, light. theSecond, full width the full at width half-maximum at half-maximum (FWHM) (FWHM) of PNJ canof PNJ be lesscan thanbe less the than classical the classical diffraction diffraction limit. In limit. our simulation,In our simulation, incident incident beams arebeams linearly are linearly polarized polarized with a wavelengthwith a wavelength of 540 nm, of 540 and nm, a 5 µandm-diameter a 5 μm-diameter barium titanatebarium glasstitanate (BTG) microsphere (BTG) microsphere with a refractive with a indexrefractive of 1.9 index is placed of 1.9 in is aplaced medium in a with medium refractive with indexrefractive of n sindex. of ns.

Figure 1. Schematic diagram of a photonic nanojet (PNJ) produced by a dielectric microsphere. Figure 1. Schematic diagram of a photonic nanojet (PNJ) produced by a dielectric microsphere. Figure2a–d show the intensity distributions of BTG microspheres immersed by different Figure 2a–d show the intensity distributions of BTG microspheres immersed by different surrounding medium for ns = 1.0, 1.33, 1.39, 1.52, respectively. We could see that the PNJ will gradually surrounding medium for ns = 1.0, 1.33, 1.39, 1.52, respectively. We could see that the PNJ will shift from the inside to the outside of microspheres when the surrounding medium refractive index ns increases from 1.0 to 1.52. According to Figure2f, the maximum intensity position of the PNJ increases from 1.9 µm to 3.8 µm as the surrounding refractive index increases. In Figure2e, the FWHMs are 170, 246, 260, and 272 nm corresponding to ns = 1.0, 1.33, 1.39, and 1.52, respectively. It indicates Nanomaterials 2019, 9, x FOR PEER REVIEW 3 of 11 gradually shift from the inside to the outside of microspheres when the surrounding medium refractive index ns increases from 1.0 to 1.52. According to Figure 2f, the maximum intensity position of Nanomaterialsthe PNJ increases2019, 9, 72 from 1.9 μm to 3.8 μm as the surrounding refractive index increases. In3 Figure of 11 2e, the FWHMs are 170, 246, 260, and 272 nm corresponding to ns = 1.0, 1.33, 1.39, and 1.52, respectively.that the FWHM It indicates of the PNJthat monotonicallythe FWHM of increasesthe PNJ monotonically with the growth increases of the refractive with the indexgrowth of of the the refractivesurrounding index medium of the surrounding as well. The medium insets in Figureas well.2e,f The show insets the in evolution Figure 2e,f of the show FWHM the evolution with the of themaximum FWHM with intensity the positionmaximum with intensity ns increasing position from with 1.0 tons 1.52.increasing Evidently, from increasing 1.0 to 1.52.ns results Evidently, in increasingelongated ns PNJ, results accompanied in elongated by decreasedPNJ, accompanied peak intensity by decreased and broadens peak theintensity FWHM. and Figure broadens2 is in the FWHM.agreement Figure with 2 theis in tendency agreement studied with in the previous tendency works, studied which in indicates previous that works, the key which parameter indicates of the that thePNJ key depends parameter significantly of the PNJ on the depends refractive significantl index of they on surrounding the refractive medium. index Therefore, of the surrounding the key to medium.manipulate Therefore, PNJ is tothe find key a materialto manipulate with a PNJ variable is to refractivefind a material index. with a variable refractive index.

Figure 2. Intensity distributions of barium titanate glass (BTG) microspheres immersed in different Figure 2. Intensity distributions of barium titanate glass (BTG) microspheres immersed in different surrounding medium for (a) ns = 1.0, (b) ns = 1.33, (c) ns = 1.39, (d) ns = 1.52. (e) Transverse intensity surrounding medium for (a) ns = 1.0, (b) ns = 1.33, (c) ns = 1.39, (d) ns = 1.52. (e) Transverse intensity profiles for ns = 1.0, 1.33, 1.39, and 1.52 at maximum intensity spots. (f) Longitudinal intensity profiles profiles for ns = 1.0, 1.33, 1.39, and 1.52 at maximum intensity spots. (f) Longitudinal intensity profiles for ns = 1.0, 1.33, 1.39, and 1.52 sliced along Y = 0. The insets of (e,f) correspond to the FWHM and for ns = 1.0, 1.33, 1.39, and 1.52 sliced along Y = 0. The insets of (e,f) correspond to the FWHM and peak peak intensity position as a function of ns. intensity position as a function of ns. 3. Birefringence of Nematic Liquid Crystals (LNCs) 3. Birefringence of Nematic Liquid Crystals (LNCs) Nematic liquid crystals (NLCs) generally have positive optical anisotropy, and the major axis of NLCNematic molecules liquid cancrystals be orientationally (NLCs) generally aligned have into positive the direction optical decidedanisotropy, by the and external the major voltage axis of NLCand molecules confining can surfaces be orientationally [33]. If an external aligned electric into the voltage direction is applied decided to the by NLCsthe external confined voltage by two and confiningsurfaces, surfaces the molecules [33]. If ofan NLCs external tend electric to rotate voltage to the is direction applied to parallel the NLCs to the confined external by electric two surfaces, field. theThe molecules molecules of of NLCs NLCs alsotend return to rotate to the to original the direction configuration parallel once to thethe electric external field electric is switched field. off, The moleculesoriginating of fromNLCs the also restoring return torquesto the original provided configuration by the strong anchoringonce the electric on the confiningfield is switched surface of off,

Nanomaterials 2019, 9, 72 4 of 11 the device. Due to the high birefringence and sensitive response to the external stress, NLCs become a good candidate for PNJ manipulation. The NLC studied in this paper is positive uniaxial. If we denote the crystalline axes by rx, ry, and rz, the refractive indexes are nrx, nry, and nrz, for light polarized along rx, ry, and rz, respectively. As they are positive uniaxial, it can be assumed that nrx = nry = no, nrz = ne, where no is the refractive index along minor axis and ne is that along the major axis. The refractive indexes along the three axles of the NLC can be characterized by [33]: √ √ √ nrx = εrx, nry = εry, nrz = εrz. (1) where εrx and εry are the ordinary dielectric constants and εrz is the extraordinary dielectric constant. According to Maxwell’s equations, Fresnel Equation is given by the next equation.

2 2 2 k kry k rx + + rz = 0. (2) 1 − 1 1 − 1 1 − 1 n2 εrx n2 εry n2 εrz The solution of the Equation (2) is described as: ( n1 = no n = n (θ) = √ none (3) 2 e 2 2 2 2 no sin θ+ne cos θ where θ is the rotation angle between light propagating direction and the NLC molecule. This means that the lightwave traversing through NLC generally possess two refractive indexes. One is no, the other is ne. For light of arbitrary polarizations, or equivalently, an electro-optics crystal of an arbitrary orientation relative to the polarized light propagation, the resulting propagation of polarized light in the crystal is rather complex [34]. We perform the theoretical analysis of light propagation in NLCs by index ellipsoid method for simplicity [34]. For a linearly polarized light, if the angle between the propagating direction k and the NLC molecule is θ, the cross-section of the NLC molecule and the plane perpendicular to k is an ellipse, as shown in Figure3b. According to the index ellipsoid method, the major axis of ellipse equals to the value ne, and the minor axis of ellipse equals to the value no. The lightwave, whose electric field oscillates along ne vector direction, senses a larger refractive index, corresponding to the extraordinary index ne(θ). The lightwave, whose electric field oscillates along no vector direction, senses the ordinary index, which is a constant no. The intensities of the ordinary and extraordinary light are determined by the components of the initial intensity along no vector and ne vector,Nanomaterials respectively. 2019, 9, x FOR PEER REVIEW 5 of 11

Figure 3. (a) Schematic view of the arrangement of nematic liquid crystals (NLC) molecules. (b) Index Figure 3. (a) Schematic view of the arrangement of nematic liquid crystals (NLC) molecules (b) Index ellipsoid method for a polarized incident light passing through a uniaxial crystal. no and ne correspond ellipsoid method for a polarized incident light passing through a uniaxial crystal. no and ne correspond to the refractive indexes for the ordinary and extraordinary components, respectively. (c) Nematic to the refractive indexes for the ordinary and extraordinary components, respectively. (c) Nematic liquid crystal molecule rotating in X–Y plane with incident light polarized along Y axis. liquid crystal molecule rotating in X–Y plane with incident light polarized along Y axis.

4. Materials and Methods To study the switchability of the microsphere though its surrounding medium, we consider a 5- μm-diameter polystyrene (PS) microsphere with a constant refractive index n = 1.62 immersed in the NLCs with a tunable refractive index ns. The NLC is sandwiched between indium tin (ITO) layers. The inner surface of ITO is coated with polyimide and unidirectionally rubbed along Y-axis. The incident plane light is Y-axis polarized, and the wavelength is 540 nm. To study the evolution of PNJ within a sufficient perspective, the whole size of NLCs in this paper is several micrometers away from the PS microsphere, as shown in Figure 4. When a microsphere is immersed in the NLCs, the director field is always distorted even if the surface anchoring of nematic molecules on the particle is weak. Here, unidirectional planar anchoring is assumed for both planar surfaces and PS microsphere. The boundary conditions are met by the creation of two surface defects, called boojums, located at the poles of the microsphere [35,36]. Actually, by contrast to the microsphere body, the light traveling through the poles of the microsphere plays a weak role in PNJ formation. Surface defect is an impact factor on PNJ control, but not a decisive factor any more. It is difficult to simulate a boojums configuration around the PS microsphere, and an ideal model is used in the following simulation. In the ideal model, the boojums configuration and the ITO layer are negligible.

Figure 4. The arrangements of LCs (a) with an external voltage switched off; (b) with an external voltage switched on.

As shown in Figure 4a, in the absence of an external voltage, the major molecular axis of the LC is aligned parallel to the substrates, corresponding to an effective index of 1.75 for extraordinary light. In contrast, when voltage is introduced, the LC molecules start to change their direction towards the X-

Nanomaterials 2019, 9, x FOR PEER REVIEW 5 of 11

Nanomaterials 2019, 9, 72 5 of 11

If the NLC molecules rotate in X–Y plane (as shown in Figure3b), the incident light, which is arbitrary linearly polarized, can be decomposed into two components along ne and no vector respectively. This means that only the light decomposed along ne vector can sense the refractive index change from ne(θ) to no, leading to a low contrast during a tunable process. The light decomposed along no vectorFigure senses 3. (a) Schematic unchanged view refractive of the arrangement index no before of nematic and liquid after tuning,crystals (NLC) which molecules looks like (b background) Index noise.ellipsoid If the incidentmethod for light a polarized is polarized incident along lightn passinge vector through as shown a uniaxial in Figure crystal.3c, n theo and extraordinary ne correspondlight componentto the refractive is maximum, indexes while for the ordinary ordinary and light extraordinary component compon is minimum.ents, respectively. It is the best (c result) Nematic we want. So, anliquid incident crystal light molecule polarized rotating along in XY–Y-axis plane is with chosen incident in this light paper. polarized along Y axis.

4.4. Materials Materials and and Methods Methods ToTo study study the the switchability switchability of of the the microsphere microsphere though though its itssurrounding surrounding medium, medium, we consider we consider a 5- μam-diameter 5-µm-diameter polystyrene polystyrene (PS) (PS)microsphere microsphere with witha constant a constant refractive refractive index indexn = 1.62n =immersed 1.62 immersed in the NLCsin the with NLCs a withtunable a tunable refractive refractive index n indexs. The nNLCs. The is NLCsandwiched is sandwiched between between indium indiumtin (ITO) tin layers. (ITO) Thelayers. inner The surface inner surfaceof ITO ofis ITOcoated is coated with polyimide with polyimide and unidirectionally and unidirectionally rubbed rubbed along along Y-axis.Y-axis. The incidentThe incident plane plane light lightis Y-axis is Y-axis polarized, polarized, and the and wavelength the wavelength is 540 is nm. 540 To nm. study To study the evolution the evolution of PNJ of withinPNJ within a sufficient a sufficient perspective, perspective, the thewhole whole size size of ofNLCs NLCs in inthis this paper paper is is several several micrometers micrometers away away fromfrom the the PS PS microsphere, microsphere, as shown in Figure4 4.. WhenWhen a a microsphere is is immersed in in the the NLCs, NLCs, the the director director field field is always distorted even even if if the surfacesurface anchoring anchoring of nematic nematic molecules molecules on the the particle particle is is weak. weak. Here, Here, unidirectional unidirectional planar planar anchoring anchoring isis assumed assumed for for both both planar surfaces and and PS micr microsphere.osphere. The The boundary boundary conditions conditions are are met met by by the creationcreation ofof twotwo surface surface defects, defects, called called boojums, boojums, located located at the at poles the ofpoles the microsphereof the microsphere [35,36]. Actually,[35,36]. Actually,by contrast by to contrast the microsphere to the body,microsphere the light body traveling, the throughlight traveling the poles through of the microsphere the poles playsof the a microsphereweak role in PNJplays formation. a weak role Surface in PNJ defect formation. is an impact Surface factor defect on PNJis an control, impact but factor not on a decisive PNJ control, factor butany not more. a decisive It is difficult factor to any simulate more. aIt boojums is difficult configuration to simulate arounda boojums the PSconfiguration microsphere, around and an the ideal PS microsphere,model is used and in the an followingideal model simulation. is used in Inthe the following ideal model, simulation. the boojums In the configurationideal model, the and boojums the ITO configurationlayer are negligible. and the ITO layer are negligible.

FigureFigure 4. TheThe arrangements arrangements of of LCs LCs ( (aa)) with with an an external external voltage voltage switched switched off; off; ( (bb)) with with an an external voltage switched on.

AsAs shown shown in Figure 44a,a, inin thethe absenceabsence ofof anan externalexternal voltage,voltage, thethe majormajor molecularmolecular axisaxis ofof thethe LCLC isis alignedaligned parallel parallel to to the the substrates, substrates, corresponding corresponding to toan an effective effective index index of of1.75 1.75 for for extraordinary extraordinary light. light. In contrast,In contrast, when when voltage voltage is introduced, is introduced, the theLC LCmolecules molecules start start to change to change their their direction direction towards towards the theX- X-axis, resulting in a refractive index of 1.52 for extraordinary light. By tuning the effective refractive index larger or smaller than that of the PS microsphere, the PNJ can be switched off and on. Nanomaterials 2019, 9, x FOR PEER REVIEW 6 of 11 axis, resulting in a refractive index of 1.52 for extraordinary light. By tuning the effective refractive index largerNanomaterials or smaller2019, than9, 72 that of the PS microsphere, the PNJ can be switched off and on. 6 of 11

5. Results and Discussion 5. Results and Discussion When ne changes from 1.75 to 1.52, the spatial distribution of PNJ also changes, as shown in Figure 5a,c. FigureWhen 5b,dne changes correspond from to 1.75 the tocross-sections 1.52, the spatial of Figure distribution 5a,c at ofthe PNJ peak also intensity, changes, which as shown are sliced in alongFigure X =5 a,c.8.85 Figure μm. The5b,d longitudinal correspond intensity to the cross-sections graphs shown of Figurein Figure5a,c 5e at is the sliced peak along intensity, Y = 0. which In Figure µ 5f,are the sliced transverse along XFWHM= 8.85 ofm. nanojet The longitudinal is measured intensity to be 600 graphs nm. By shown switching in Figure the5 erefractive is sliced alongindex of extraordinaryY = 0. In Figure light5 f,from the transverse1.75 to 1.52, FWHM the intensity of nanojet at X is = measured8.85 μm changes to be 600 from nm. 1.5 By to switching 42. To study the the refractive index of extraordinary light from 1.75 to 1.52, the intensity at X = 8.85 µm changes from 1.5 switchability of photonic nanojet, it is necessary to define an intensity contrast. The intensity contrast is to 42. To study the switchability of photonic nanojet, it is necessary to define an intensity contrast. given by the ratio between the peak intensity for ne = 1.52 and the intensity at the same position for ne = The intensity contrast is given by the ratio between the peak intensity for n = 1.52 and the intensity 1.75. And the intensity contrast here is 28. Applying an electric field to the devicee adjusts the director of at the same position for ne = 1.75. And the intensity contrast here is 28. Applying an electric field the LCs, which changes the effective refractive index, and the electro-switching of PNJ is realized. to the device adjusts the director of the LCs, which changes the effective refractive index, and the However,electro-switching the cost for of this PNJ switching is realized. of photonic However, nanojet the cost is widening for this switching the FWHM of and photonic reducing nanojet the peak is intensity.widening Based the FWHM on the andapplication reducing of the active peak tuning intensity. in nanophotonics, Based on the application there is a need of active to optimize tuning in the PNJnanophotonics, switchability thereof this is technique. a need to optimizeWe, therefore, the PNJ present switchability an optimization of this technique. study which We, therefore,seeks better electricpresent energy an optimization focusing properties study which of PNJ. seeks better electric energy focusing properties of PNJ.

Figure 5. Intensity distribution of a polystyrene (PS) microsphere immersed by NLCs for (a) ne = 1.75 Figure 5. Intensity distribution of a polystyrene (PS) microsphere immersed by NLCs for (a) ne = 1.75 (c) ne = 1.52. (b,d) Transverse intensity profiles sliced along X = 8.85 µm corresponding to (a,c). (c) ne = 1.52. (b,d) Transverse intensity profiles sliced along X = 8.85 μm corresponding to (a,c). (e) (e) Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. (f) (f) Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = 8.85 µm. Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = 8.85 μm. The same structure but with a shorter incident wavelength of 400 nm is analyzed and discussed first.The In same fact, NLCs structure with but different with incidenta shorter wavelengths incident wavelength have different of 400 birefringence nm is analyzed due to and dispersion. discussed first.However, In fact, theNLCs difference with different of ∆n ( incidentne(θ) − n wavelengo) is onlyths about have 0.05 different here, which birefringence plays a weak due to role dispersion. in the However,switching the of PNJ.difference So, the dispersionof ∆n (ne(θ in) our− no study) is only is negligible. about 0.05 Figure here,6a,c which show theplays spatial a weak distributions role in the switchingof PNJs forof nPNJ.e = 1.75 So, and the 1.52, dispersion respectively. in our Figure study6b,d is are negligible. the corresponding Figure cross6a,c show sections the sliced spatial

Nanomaterials 2019, 9, x FOR PEER REVIEW 7 of 11

Nanomaterials 2019, 9, 72 7 of 11 distributions of PNJs for ne = 1.75 and 1.52, respectively. Figure 6b,d are the corresponding cross sections sliced along X = 9.3 μm. It can be seen that the PS microsphere with 400 nm incident alongwavelengthX = 9.3 providesµm. It can an be FWHM seen that of the480 PSnm, microsphere which is tighter with400 compared nm incident to that wavelength with 540 nm provides incident an FWHMwavelength, of 480 as nm, shown which in Figure is tighter 6f. comparedHowever, tothe that peak with position 540 nm shifts incident from wavelength, 8.85 μm to 9.3 as shownμm when in Figurethe incident6f. However, wavelength the peak decreases position from shifts 540 from nm 8.85 to 400µm nm. to 9.3 Byµ mswitching when the the incident refractive wavelength index of decreasesextraordinary from light 540 nmfrom to 1.75 400 to nm. 1.52, By the switching intensity the at refractiveX = 8.85 μm index changes of extraordinary from 0.3 to 60. light The from intensity 1.75 tocontrast 1.52, the in intensityFigure 6 is at 200,X = obviously 8.85 µm changes stronger from than 0.3 that to 60.shown The in intensity Figure contrast5. The results in Figure showed6 is 200, that obviouslythe switching stronger properties than thatof PNJ shown can inbe Figureoptimized5. The by results tuning showed the wavelength that the switchingof the incident properties light to of a PNJshorter can one. be optimized by tuning the wavelength of the incident light to a shorter one.

FigureFigure 6.6. ((aa)) IntensityIntensity distributiondistribution ofof aa PSPS microsphere with a shorter incident wavelength of 400 nm. for (a) n = 1.75 (c) n = 1.52. (b,d) Transverse intensity profiles sliced along X = 9.3 µm corresponding for (a) nee = 1.75 (c) ne = 1.52. (b,d) Transverse intensity profiles sliced along X = 9.3 μm corresponding to (a,c). (e) Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along to (a,c). (e) Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. (f) Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. (f) Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = X µ 9.3= μ 9.3m. m. Next, we study a microsphere consisting of a BTG spherical core with a refractive index of Next, we study a microsphere consisting of a BTG spherical core with a refractive index of 1.9 1.9 coated with a PS concentric shell. The diameter of the core is 3 µm, and the thickness of the shell coated with a PS concentric shell. The diameter of the core is 3 μm, and the thickness of the shell is 1 is 1 µm, as shown in Figure7. Figure7a,c show the intensity distributions of the coupled core-shell μm, as shown in Figure 7. Figure 7a,c show the intensity distributions of the coupled core-shell microsphere for ne = 1.75 and 1.52, respectively. Figure7b,d correspond to the transverse intensity microsphere for ne = 1.75 and 1.52, respectively. Figure 7b,d correspond to the transverse intensity profiles of Figure7a,c sliced along X = 2.6 µm. Longitudinal intensity graph sliced along Y = 0 is profiles of Figure 7a,c sliced along X = 2.6 μm. Longitudinal intensity graph sliced along Y = 0 is shown in Figure7e. The FWHM for ne = 1.52 in Figure7f is 240 nm. The focusing of the optical shown in Figure 7e. The FWHM for ne = 1.52 in Figure 7f is 240 nm. The focusing of the optical field field by such a coupled core-shell microsphere becomes narrower compared to that generated by a by such a coupled core-shell microsphere becomes narrower compared to that generated by a one- one-layered homogeneous sphere in Figure5 or Figure6. However, the intensities for ne = 1.52 and 1.75 layered homogeneous sphere in Figure 5 or Figure 6. However, the intensities for ne = 1.52 and 1.75 at X = 2.6 µm are 114 and 52, respectively, resulting in a low-intensity contrast of 2.2. So, the coupled core-shell microsphere leads to a narrow FWHM but accompanied with a decreased intensity contrast.

Nanomaterials 2019, 9, x FOR PEER REVIEW 8 of 11 at X = 2.6 μm are 114 and 52, respectively, resulting in a low-intensity contrast of 2.2. So, the coupled Nanomaterials 2019, 9, 72 8 of 11 core-shell microsphere leads to a narrow FWHM but accompanied with a decreased intensity contrast.

Figure 7. (a) Intensity distribution of a coupled core-shell microsphere immersed by NLCs for (a) Figure 7. (a) Intensity distribution of a coupled core-shell microsphere immersed by NLCs for (a) ne = ne = 1.75 (c) ne = 1.52. (b,d) Transverse intensity profiles sliced along X = 2.6 µm corresponding to (a,c). 1.75 (c) ne = 1.52. (b,d) Transverse intensity profiles sliced along X = 2.6 μm corresponding to (a,c). (e) (e) Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. (f) (f) Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = 2.6 µm. Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = 2.6 μm. We further study the spatial distribution of the intensity produced by a spheroid. The corresponding majorWe andfurther minor study diameters the spatial are 5 µdistributionm and 2.5 µ m,of the respectively. intensityFigure produced8a,c show by a the spheroid. intensity The correspondingdistributions ofmajor a spheroid and minor immersed diameters by NLCs are 5 forμmn ande = 1.752.5 μ andm, respectively.ne = 1.52. Figure Figure8b,d 8a,c show show the the intensitytransverse distributions intensity profiles of a spheroid sliced along immersedX = 3.2 byµm. NLCs The intensityfor ne = 1.75 for n ande = 1.52 ne = reaches 1.52. Figure the maximum 8b,d show the42 transverse at X = 3.2 µintensitym, while intensityprofiles sliced for ne =along 1.75 isXonly = 3.2 0.8. μm. The The intensity intensity contrast for n ise about= 1.52 52 reaches and the the maximumFWHM shown 42 at X in = Figure 3.2 μ8m,f is while 300 nm. intensity It turns for out n thate = 1.75 the FWHMis only with0.8. The the oblateintensity spheroid contrast is narrower is about 52 andthan the that FWHM with shown the spherical in Figure one 8f in is Figure 300 nm.5 or It Figure turns6 .out Meanwhile, that the FWHM the intensity with the contrast oblate here spheroid is is highernarrower than than that that in Figures with the5 and spherical7. Therefore, one in the Figure switchable 5 or Figure photonic 6. Meanwhile, nanojet can the be approximatedintensity contrast herewith is high higher efficiency than bythat such in aFigures spheroid. 5 and 7. Therefore, the switchable photonic nanojet can be approximatedThese studies with high reveal efficiency that the switchabilityby such a spheroid. of the PNJ can be optimized by applying a shorter incidentThese wavelength, studies reveal a double-layer that the switchability microsphere orof athe PS PNJ ellipsoid, can be respectively. optimized The by FWHMapplying generated a shorter incidentby the PSwavelength, ellipsoid isa narrowerdouble-layer than microsphere that generated or bya thePS ellipsoid, microsphere respectively. with shorter The incident FWHM generatedwavelength. by the The PS intensity ellipsoid contrast is narrower of such PSthan ellipsoid that generated is also higher by thanthe microsphere that of the double-layer with shorter incidentmicrosphere. wavelength. We conclude The intensity that the contrast switchability of such of PS PNJ ellipsoid can be bestis also optimized higher than by an that ellipsoid of the double- in an ideal model. Although there had been many studies for tuning the PNJ properties using different size, layer microsphere. We conclude that the switchability of PNJ can be best optimized by an ellipsoid material, geometry of spheres or core-shell spheres [37–39], they are an almost passive tunable process. in an ideal model. Although there had been many studies for tuning the PNJ properties using Once the structures are designed and fabricated, their PNJ properties cannot be changed. The main different size, material, geometry of spheres or core-shell spheres [37–39], they are an almost passive difference here is that our method allows for dynamic tunability using electrical control in real time. tunable process. Once the structures are designed and fabricated, their PNJ properties cannot be We pay more attention to the PNJ change for the NLC effective refractive index larger and smaller than changed. The main difference here is that our method allows for dynamic tunability using electrical

Nanomaterials 2019, 9, x FOR PEER REVIEW 9 of 11

Nanomaterialscontrol in real2019 time., 9, 72 We pay more attention to the PNJ change for the NLC effective refractive index9 of 11 larger and smaller than that of the PS microsphere. In practice, natural materials with such thatrelationship of the PS are microsphere. infrequent and In practice, finding naturalother possible materials materials with such is a relationship deserved research are infrequent for further and findingstudy. other possible materials is a deserved research for further study.

Figure 8. (a) Intensity distribution of micron-scale spheroid immersed by NLCs for (a) ne = 1.75 Figure 8. (a) Intensity distribution of micron-scale spheroid immersed by NLCs for (a) ne = 1.75 (c) ne (c) n = 1.52. (b,d) Transverse intensity profiles sliced along X = 3.2 µm corresponding to (a,c). = 1.52.e (b,d) Transverse intensity profiles sliced along X = 3.2 μm corresponding to (a,c). (e) (e) Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. Longitudinal intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along Y = 0. (f) (f) Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = 3.2 µm. Transverse intensity graphs for ne = 1.52 (black curve) and 1.75 (red curve) sliced along X = 3.2 μm. 6. Conclusions 6. Conclusions In this paper, a switchable photonic nanojet achieved by a PS microsphere with NLCs immersed is reported.In this paper, The effectivea switchable refractive photonic index nanojet of NLCs achieved can by be a changedPS microsphere by tuning with the NLCs alignment immersed of theis reported. liquid crystal The effective molecules. refractive Therefore, index of we NLCs are ablecan be to changed switch the by photonictuning the nanojet alignment bytuning of the theliquid surrounding crystal molecules. refractive Therefore, index. Using we are high-resolution able to switch FDTD the simulation,photonic nanojet we indicate by tuning that the photonicsurrounding nanojet refractive is dynamically index. Using switched high-resolution by a PS microsphere FDTD simulation, immersed we indicate in the NLCs.that the Moreover, photonic wenanojet present is dynamically an optimization switched study by which a PS microsphere seeks better electricimmersed energy in the focusing NLCs. Moreover, properties we of thepresent PNJ. Asan optimization a whole, the switchabilitystudy which seeks of the better photonic electric nanojet energy can focusing be best optimizedproperties byof the an ellipsoid.PNJ. As a Suchwhole, a mechanismthe switchability for nanojet of the manipulation photonic nanojet may can open be up best new optimized areas for by a photonic an ellipsoid. device Such with a subwavelengthmechanism for spatialnanojet resolution.manipulation may open up new areas for a photonic device with subwavelength spatial resolution. Author Contributions: Investigation, J.Z.; Resources, H.Z.; Supervision, J.X. and J.W.; Writing-original draft, B.D. Author Contributions: Investigation, J.Z.; Resources, H.Z.; Supervision, J.X. and J.W.; Writing-original draft, B.D. Funding: This research was funded by National Key R&D Program of China, grant number 2017YFB1002900. ConflictsFunding: ofThis Interest: researchThe was authors funded declare by National no conflict Key ofR&D interest. Program of China, grant number 2017YFB1002900. Conflicts of Interest: The authors declare no conflict of interest.

Nanomaterials 2019, 9, 72 10 of 11

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