Recent Advances in Integrated Photonic Jet-Based Photonics
Recent Advances in Integrated Photonic Jet-Based Photonics
Minin, Igor V.;Liu, Cheng-Yang;Geints, Yury E.;Minin, Oleg V.
2020-06-11 00:00:00
hv photonics Review Recent Advances in Integrated Photonic Jet-Based Photonics 1 , 2 , 3 4 1 , 2 Igor V. Minin * , Cheng-Yang Liu , Yury E. Geints and Oleg V. Minin Physical Department, Tomsk State University, 30 Lenin Avenue, 634050 Tomsk, Russia; ovminin@tpu.ru School of Nondestructive Testing, Tomsk Polytechnic University, 36 Lenin Avenue, 634050 Tomsk, Russia Department of Biomedical Engineering, National Yang-Ming University, Taipei City 11221, Taiwan; cyliu66@ym.edu.tw V.E. Zuev Institute of Atmospheric Optics SB RAS, 1 Zuev Square, 634021 Tomsk, Russia; ygeints@iao.ru * Correspondence: IVMinin@tpu.ru Received: 25 April 2020; Accepted: 10 June 2020; Published: 11 June 2020 Abstract: The study of accelerating Airy-family beams has made significant progress, not only in terms of numerical and experimental investigations, but also in conjunction with many potential applications. However, the curvature of such beams (and hence their acceleration) is usually greater than the wavelength. Relatively recently, a new type of localized wave beams with subwavelength curvature, called photonic hooks, was discovered. This paper briefly reviews the substantial literature concerning photonic jet and photonic hook phenomena, based on the photonic jet principle. Meanwhile, the photonic jet ensemble can be produced by optical wave diraction at 2D phase diraction gratings. The guidelines of jets’ ecient manipulation, through the variation of both the shape and spatial period of diraction grating rulings, are considered. Amazingly, the mesoscale dielectric Janus particle, with broken shape or refractive index symmetry, is used to generate the curved photonic jet—a photonic hook—emerging from its shadow-side surface. Using the photonic hook, the resolution of optical scanning systems can be improved to develop optomechanical tweezers for moving nanoparticles, cells, bacteria and viruses along curved paths and around transparent obstacles. These unique properties of photonic jets and hooks combine to aord important applications for low-loss waveguiding, subdiraction-resolution nanopatterning and nanolithography. Keywords: photonic jet; photonic hook; microparticle; cuboid; diraction grating 1. Introduction Nowadays, bending light beams are being intensively investigated for propagation in free space. The most well-known is the Airy beam, which was first predicted by Berry and Balazs in 1979 [1] and experimentally demonstrated by Siviloglou et al. in 2007 [2]. Since that time, dierent types of self-accelerating photonic beams [3–6] have been proposed in a broad range of applied science-related fields, including trapping particles [7], plasma [8], surface plasmon polaritons [9,10], non-lineal optical trapping [11] and electron beam trapping [12]. One of the most important applications of the Airy beams is the development of optical tweezers for moving micron-sized particles along curved paths, which allows one to reduce the light loading on biological tissues. The long-focus Airy beam contains the maximum concentration of the light energy, similar to the focal plane of the Gaussian beam. According to the beam theory [13], the main parameter of such beams is the propagation length along the curved path (acceleration). A common optical scheme for Airy beam formation includes a cylindrical lens and a spatial light modulator (SLM), which operates only at restricted power. The latter is mounted in the front focal plane of the cylindrical lens, while the Airy beam generates in its back focal plane and nearby. The cubic phase modulation of an incident Gaussian beam generated by a modulator Photonics 2020, 7, 41; doi:10.3390/photonics7020041 www.mdpi.com/journal/photonics Photonics 2020, 7, 41 2 of 13 acts as a cubic lens, whereas the curved path is determined by the acceleration rate of the cubic phase change [2]. The Airy laser beams are generated by binary phase diractive optical elements [13]. The phase diraction gratings are used as SLM analogs, which create bending diraction orders [14,15]. The metasurfaces are also used for generating the Airy beams; however, the manufacturing process of the metasurfaces is rather complicated and expensive [16]. The diraction-free pulsed beams in space-time have been the subject of many interesting studies [13]. The lightwave packet becomes a sort of non-paraxial Airy-pulsed beam. Such optical pulsed beams with self-bending parabolic spatial profiles propagate in the forward direction [17]. The acceleration-free Airy wave packet is synthesized by changing its spatiotemporal spectrum. On the other hand, the Bessel beam emitted from expanding circles on the input plane propagates along straight trajectories [18]. In the following studies, it is possible to produce Bessel-like beams along spiral, snake or zigzag trajectories [19–21]. An advantage of the Bessel-like beams is that the convex trajectories are not necessary. Furthermore, abruptly autofocusing beams are generated by Fourier-transforming an apodized Bessel beam [22]. This can be used as a robust photophoretic trap for airborne particles. Three-dimensional manipulation of the trapped particles is experimentally illustrated by applying vortex Bessel-like beams. The trapped particles follow the spiral, parabolic and hyperbolic trajectories along the high-intensity ring of the high-order Bessel beam [23]. The Airy beam innately provides higher contrast and enlarges the field of view. The characteristic asymmetric excitation pattern of the Airy beam can be applied to a step change for light-sheet microscopy [24,25]. It is important that the diameter of the Airy beams is usually several incident wavelengths, equaling the diameter of an optical element which is much larger than the wavelength [13]. Scaling the Airy beam generation from visible light to the terahertz range is not always possible. This is because SLMs cannot operate in the terahertz range, due to the absence of materials with the required modulation [26]. Moreover, the main lobe of a finite energy Airy beam is not observed directly behind the cubic phase element and transition region, where the initial intensity distribution of the incoming beam is transformed into the distinct Airy pattern [27]. With the aim of encouraging photonic study, we summarize the progress made in the photonic area of the jet and hook to-date. The structures of a localized field for a photonic jet and hook dier fundamentally from Airy beams [13]. Moreover, the curvature of the Airy-like beams is determined by a parameter that determines the rate of rise of the cubic phase [13], and is usually greater than several wavelengths. The results and discussions in this paper include the initial identification of the photonic jet and hook for dielectric microparticles, subwavelength curved localized light beams, photonic jet array by diraction grating, experimental observations, and the potential applications. 2. Near-Field Curved Beams It is well known that when diraction arises from the dielectric edge of the Fresnel zone plate, the edge wave has the eikonal approximation (S~Z + X /2Z), where X is the transverse coordinate and Z is the longitudinal coordinate [28]. A solution of the diraction at the edge of the semi-infinite opaque screen is a paraxial two-dimensional light, for which the argument for the complex amplitude function depends on variables (X /Z) [29]. Instead of the Airy beams, the optical beam has a parabolic path y = x , whereas the considered edge beams in the equation propagate along a root-parabolic path y = sqrt(x). Figure 1 shows the full-wave simulation results of the diraction on a rectangular phase plate, under the illumination of a linearly polarized plane wave. It can be seen in Figure 1a that the curvilinear field localization areas arise in the region of the plate edge. As the plate width decreases, these localization regions approach each other. In cases of a small plate width, these optical beams begin to interfere with each other, and form a central classical photonic jet during diraction via a phase step [30,31]. It should be noted that such curved beams can have the self-healing property of the Airy beams, as shown in Figure 1d. Photonics 2020, 7, x FOR PEER REVIEW 3 of 13 Photonics 2020, 7, 41 3 of 13 Figure 1. Full-wave simulation results of the diraction on a rectangular phase plate, with widths of Figure 1. Full-wave simulation results of the diffraction on a rectangular phase plate, with widths of (a) 36 , (b) 24 , (c) 12 , and (d) a rectangular phase plate with defect. (a) 36 λ, (b) 24 λ, (c) 12 λ, and (d) a rectangular phase plate with defect. In this paper, we consider the mesoscale particles for the generation of photonic jets. The Mie In this paper, we consider the mesoscale particles for the generation of photonic jets. The Mie parameter (q = 2r/) is used to determine the particle size. Between the nano-scale optics (q~1) and parameter (q = 2πr/λ) is used to determine the particle size. Between the nano-scale optics (q ~ 1) and traditional optics (q > 100), there is an intermediate range (q~10 : : : 40) of the particle size in particular. traditional optics (q > 100), there is an intermediate range (q ~ 10…40) of the particle size in particular. In the visible light region, this intermediate range matches the micron-sized particles (from several In the visible light region, this intermediate range matches the micron-sized particles (from several micrometers to tens of micrometers). The photonic nanojets (PNJs) are earlier detected by using the micrometers to tens of micrometers). The photonic nanojets (PNJs) are earlier detected by using the particles in this intermediate range [32–34]. The generation of bounded light beams in the near-field particles in this intermediate range [32–34]. The generation of bounded light beams in the near-field is crucial for many applications, for example, for optical memory systems. A subwavelength eect is crucial for many applications, for example, for optical memory systems. A subwavelength effect (PNJ), created by microspheres and microcylinders, can be used in Raman spectroscopy [35] and (PNJ), created by microspheres and microcylinders, can be used in Raman spectroscopy [35] and nanolithography [36]. Moreover, the optical properties of the PNJ can be changed by the interaction nanolithography [36]. Moreover, the optical properties of the PNJ can be changed by the interaction between the nanojet and nanoparticle, and the amplification of back-scattered amplitude from the between the nanojet and nanoparticle, and the amplification of back-scattered amplitude from the microparticle is increased by several orders of magnitude [34]. This opens new perspectives for microparticle is increased by several orders of magnitude [34]. This opens new perspectives for designing sensors of high space resolution, capable of recording objects whose size is hundreds of designing sensors of high space resolution, capable of recording objects whose size is hundreds of times smaller than that of sensors. times smaller than that of sensors. The PNJ phenomenon is very attractive due to the simplicity of its implementation and the The PNJ phenomenon is very attractive due to the simplicity of its implementation and the compact size of the focusing particle. On the other hand, the minimum beam width of the PNJ is about compact size of the focusing particle. On the other hand, the minimum beam width of the PNJ is /3 [34,37,38], where is the wavelength of the incident light. Thus, it is necessary to search for new about λ/3 [34,37,38], where λ is the wavelength of the incident light. Thus, it is necessary to search for methods to further reduce the size of the focal spot of the PNJ. For deep subwavelength-scale focusing, new methods to further reduce the size of the focal spot of the PNJ. For deep subwavelength-scale beyond the solid immersion diraction limit of /2n, a nanohole-structured dielectric microsphere focusing, beyond the solid immersion diffraction limit of λ/2n, a nanohole-structured dielectric was proposed for strong light confinement [39]. The field enhancement is due to the permittivity microsphere was proposed for strong light confinement [39]. The field enhancement is due to the contrast between the nanohole material and the dielectric microparticle material. The proposed permittivity contrast between the nanohole material and the dielectric microparticle material. The mesoscale nanostructured sphere has several unique properties. For example, it could produce a high proposed mesoscale nanostructured sphere has several unique properties. For example, it could optical power and electric field intensity in low-index hole materials (air), whereas this cannot be produce a high optical power and electric field intensity in low-index hole materials (air), whereas achieved through a conventional PNJ produced by spheres, without a nanostructure and with the same this cannot be achieved through a conventional PNJ produced by spheres, without a nanostructure diameter [34]. The incident light wave is confined by the dielectric particle inside the nanohole, even and with the same diameter [34]. The incident light wave is confined by the dielectric particle inside when the hole diameter is deeply sub-wavelength (at least /40). The PNJ resolution near the shadow the nanohole, even when the hole diameter is deeply sub-wavelength (at least λ/40). The PNJ surface of the particle is comparable to the nanohole size (beyond the solid immersion diraction limit). resolution near the shadow surface of the particle is comparable to the nanohole size (beyond the Figure 2 shows the example of field localization in a mesoscale nanohole structured sphere. solid immersion diffraction limit). The manufacturing of a nanohole on the rear surface of a dielectric mesoscale particle allows us to Figure 2 shows the example of field localization in a mesoscale nanohole structured sphere. The compress the field localization characteristic of the PNJ to this nanohole size. The electromagnetic fields manufacturing of a nanohole on the rear surface of a dielectric mesoscale particle allows us to near the edges of the nanohole are large, due to the associated edge singularities. In addition, these compress the field localization characteristic of the PNJ to this nanohole size. The electromagnetic singularities naturally combine energy into all higher-order modes. Because most higher-order modes fields near the edges of the nanohole are large, due to the associated edge singularities. In addition, are evanescent and contribute only to the reactive field of this emitter, they may not propagate in the these singularities naturally combine energy into all higher-order modes. Because most higher-order far field. Therefore, the higher-order modes are present in the near-field of the particle. By designing modes are evanescent and contribute only to the reactive field of this emitter, they may not propagate the nanohole accordingly, it is possible to direct the output power flow near this nanohole to the in the far field. Therefore, the higher-order modes are present in the near-field of the particle. By desired optical beams, i.e., higher-order modes can be used to control the directivity of radiation designing the nanohole accordingly, it is possible to direct the output power flow near this nanohole in the near-field. The mesoscale nanostructured dielectric particles provide better field localization, to the desired optical beams, i.e., higher-order modes can be used to control the directivity of even in the case of the resonant excitation of an ordinary spherical particle, for which the transverse radiation in the near-field. The mesoscale nanostructured dielectric particles provide better field localization, even in the case of the resonant excitation of an ordinary spherical particle, for which the Photonics 2020, 7, 41 4 of 13 Photonics Photonics 2020 2020 , 7 , , x FO 7, x FO R P R P EER EER RE RE VIEW VIEW 4 of 4 of 13 13 size of the radiation localization region can reach /5 with a giant enhancement of the magnetic field trtansvers ransvers ee s s ize o ize o f t f t hh e r e r aa di di at at ion ion loca loca lili zz aa tion reg tion reg ion c ion c aa n re n re ach ach λλ /5 wi /5 wi th th aa gia gia nn t enha t enha ncement ncement of of the the component [40,41]. magnetic magnetic field component [40,41]. field component [40,41]. Figure 2. Field localization by nanostructured spherical particle at d = /15 in (a) zy plane and Figure 2. Field localization by nanostructured spherical particle at d = λ/15 in (a) zy plane and (b) zx plane [36]. Figure 2. Field localization by nanostructured spherical particle at d = λ/15 in (a) zy plane and (b) zx plane [36]. (b) zx plane [36]. 3. Subw 3. Subw avelength avelength Cu Cu rved rved Localized Light B Localized Light B eams eams 3. Subwavelength Curved Localized Light Beams Recently, Recently, a new type of a new type of se se lf-bending lf-bending ligh ligh t beams calle t beams calle dd a phot a phot onic onic hook (P hook (P H) h H) h aa s been report s been report ed ed Recently, a new type of self-bending light beams called a photonic hook (PH) has been reported [42]. [42]. These ph [42]. These ph otonic hooks otonic hooks possess un possess un ique properties ique properties , such , such as extre as extre m m ely ely low c low c uu rv rv ature ature (less than the (less than the These photonic hooks possess unique properties, such as extremely low curvature (less than the emission emiss emiss ion wa ion wa velengt velengt hh ), ), ext ext reme acce reme acce ler ler aa titon, a propa ion, a propa gg at at ion ion lengt lengt hh of sever of sever aa l w l w aa velen velen gg th th s a s a nn d t d t hh e e wavelength), extreme acceleration, a propagation length of several wavelengths and the minimum minimum width of the bea minimum width of the bea m m waist waist [43]. An ord [43]. An ord inar inar yy mesosc mesosc ale ale opti opti cal cal solid-state die solid-state die lectric Jan lectric Jan uu s s width of the beam waist [43]. An ordinary mesoscale optical solid-state dielectric Janus particle part part icle w icle w itih th broken symm broken symm et et ry is ry is used t used t oo generat generat ee the the photonic hook near to its photonic hook near to its shaded shaded surfac surfac e. Using e. Using with broken symmetry is used to generate the photonic hook near to its shaded surface. Using the the photonic hook, one c the photonic hook, one c aa n not only improve the re n not only improve the re solution solution of optical scann of optical scann ing ing sy sy stems, but stems, but also also photonic hook, one can not only improve the resolution of optical scanning systems, but also develop develop develop optomechanic optomechanical t al twweezer eezers for s for moving m moving micr icron-s on-sizized pa ed partrticicleles, cell s, cells,s, ba bacteria a cteria annd vi d viruses, ruses, optomechanical tweezers for moving micron-sized particles, cells, bacteria and viruses, along curved along along curv curveedd p paathths an s and d aaround t round transp ransparent arent ob obststac acleles v s via cont ia contininuous uous-w -wav ave [ e [4444] or p ] or puulslesedd [ [4455] ] paths and around transparent obstacles via continuous-wave [44] or pulsed [45] illumination. At the illu illu m m in in aa tio tio nn . . At the sa At the sa me ti me ti me, the me, the aa pproa pproa ch b ch b aa sed on the sed on the in in tera tera ct ct io io n between n between aa p p la la nn e wa e wa ve a ve a nn d d aa nn same time, the approach based on the interaction between a plane wave and an asymmetric dielectric asymmet asymmetric ric diel dielect ectric ric par particle ticle can can be be sca scaled led t too an another spectrum ran other spectrum rangge. It e. It was exper was experimentally imentally particle can be scaled to another spectrum range. It was experimentally demonstrated in the terahertz dem dem oo nst nst rat rat ee dd in in t t hh ee t t ee rah rah ee rtrt z z ran ran gg e e [4 [4 6] 6] , , in in aco aco uu stst icic s s [4 [4 7] 7] , and , and p p redict redict ee dd fo fo r r su su rfrf ace ace p p lasm lasm oo n [ n [ 44 8], 8], range [46], in acoustics [47], and predicted for surface plasmon [48], recently experimentally confirmed recent recent ly expe ly expe riment riment aa lly lly co co nfirmed nfirmed in in [ [ 44 9] 9] , , as as shown i shown i nn Fig Fig uu re re 3 3 . Th . Th e t e t ime o ime o f t f t hh e e fu fu llll -pha -pha se o se o sci sci llll at at ions ions in [49], as shown in Figure 3. The time of the full-phase oscillations of the optical wave changes of of the opti the opti cal wa cal wa ve cha ve cha nn ges due to the ges due to the asymmetri asymmetri cc sh sh ape of the me ape of the me soscale p soscale p aa rtic rtic le. A le. A s sa result, we a result, we due to the asymmetric shape of the mesoscale particle. As a result, we have a bent output beam of have a bent output beam of light. In particular, this particle shape is first considered in [37], and have a bent output beam of light. In particular, this particle shape is first considered in [37], and light. In particular, this particle shape is first considered in [37], and combines prism refraction with combines prism refra combines prism refra cc tion tion with cube with cube diffract diffract ion. ion. cube diraction. Figure 3. Photonic hook based on Janus particle: (a) THz [44], (b) acoustic [45] and (c) plasmonic [46]. Figure 3. Figure 3. Photo Photo nn ic hook based on Janus parti ic hook based on Janus parti cle: ( cle: ( aa ) THz [44 ) THz [44 ], ( ], ( bb ) acoustic [ ) acoustic [ 45] and ( 45] and ( c) pla c) pla smonic [46]. smonic [46]. Fig Figur Figuurere e 4 sho 4 4 sho shows wws several several s several methods methods fo methods fo for forming r r forming forming photonic phot photonic hoo hooks. onic hoo Ink[ks. I 50 s. I ],nn the [50], the [50], the distortion distortion distortion of the particle’s of the of the part spherical part icle’ icle’ s ssph aberration sph ee ric ric aa l abe l abe was rrat rrat suggested, ion wa ion wa s s s s u via u gge gge placing st st ed, v ed, v a ia p icube-shaped a p lac lac in in g g aa cube cube particle -sh -sh aa ped pa ped pa with a rt rt smaller icle icle wit wit h size h a a sma and sma lle another lle r s r s iz iz ee and r and efractive anot anot her her index r r ee fr fr act inside act ive ive inde the inde spherical x in x in side side t t p hh article, ee s s pp herica herica in or l part lder part ito c ic le, form le, in in orde orde a photonic r t r t oo form form hook. a phot a phot However onic hoo onic hoo , this kk . H . H appr oo wever, wever, oach tis h th is appro not is appro expedient aa cc hh is not is not because expe expe ofdient substantial dient beca beca us us di e of e of culties subst subst in aa nt its nt iaiimplementation. a l l di di ffff icu icu ltlites ies in in it Figur it s imp s imp el4ela e m m shows ent ent aa titon. F the ion. F simulation igure igure 44 aa shows the simulation fo for shows the simulation fo a multifocal curvedr beam r a multifoc a multifoc based al al cu on cu rved bea an rved bea SiO m micr m ba ba s ospher e se d on a d on a en with n SiO SiO 2a microsphe 2 microsphe diameter rof e with a diameter of re with a diameter of 433 (which does 43 not 43 3 3 λ meet λ (wh (wh ithe ch ich does not me mesoscale does not me condition, ee t the mesosc t the mesosc andale cond is ale cond beyond ition, ition, the an range an d d is beyon is beyon of PNJdd existence) the r the r aa nge nge of PNJ ex in of PNJ ex the optical istenc istenc waveb e) e) in the in the and. op By optitadjust cal ical w wa ing avveebthe baand. nd. relative By By adj adj position uuststing ing t th between hee re relat lativiv an ee p p oo os-axis istiitoionn b Gaussian beetw tween een a beam ann of off-f- and axi axis G s a G spherical aauss ussian ian b b particle, eeam am an and itd a isa spherical particle, it is possible to control the beam curvature [51]. A photonic hook, upon asymmetric spherical particle, it is possible to control the beam curvature [51]. A photonic hook, upon asymmetric ill ill umin umin at at ion ion of a of a meso meso sca sca le cyl le cyl inder inder wit wit hh a m a m aa sk sk , i , i s s shown in F shown in F ig ig uu re 4b re 4b [52]. [52]. Fur Fur thermore, the thermore, the double double Photonics 2020, 7, 41 5 of 13 possible to control the beam curvature [51]. A photonic hook, upon asymmetric illumination of a mesoscale cylinder with a mask, is shown in Figure 4b [52]. Furthermore, the double photonic hooks are generated by a specially designed five-layer dielectric cylinder [53]. Furthermore, the dielectric symmetry-broken particles with dierent refractive indexes were proposed and numerically studied for the generation of photonic hooks [54–56] (Figure 4c). At the same time, single plane-wave illumination and twin-ellipse microcylinders were numerically studied to produce twin photonic hooks [57]. In order to dierentiate between cells, a concept for examining the in-vitro biomedical application is proposed, to guide the cells in a curved trajectory [58]. However, this substrate generates its own scattered field, and the field of the photonic hook is destroyed in this geometry due to the interference eect. With the use of the near-field, self-accelerating photon beams of the hook type, it is important to develop methods of control for their parameters, including particles of dierent types and the methods of the photonic hook formation. It is also important to develop a method of property control for generating self-accelerating light beams, and this can be used in dierent scientific and application areas, including portable telecommunication systems. Thus, the change in the curvature (e.g., due to polarization or a dynamic change in the incident radiation and refractive index) provides a control for the beam position in space, its acceleration and self-reconstruction. The main idea of curved photonic flux (photonic hook) generation by means of an index-contrast Janus particle is elucidated in Figure 5. According to previous references [12,13], the optical wave should acquire an asymmetric phase during propagation through a particle for the generating of a photonic hook. It can be achieved in two ways, either by means of a particle with shape asymmetry, or by a particle with built-in refractive index asymmetry (n /n ) [53,55,59], as shown in Figure 5a. 2 3 Thus, the desired phase modulations can be acquired using the gradient distribution of microparticle material, e.g., by merging two materials with dierent optical properties. The detailed analysis of the energy flow structure near a Janus particle shows [59] that the curved photonic jet is formed mainly by the two most intensive optical fluxes (marked S and S in Figure 5c) emerging in the upper and lower 1 2 parts of the particle. Due to wave diraction on rectangular facets, these fluxes are always directed at an angle to each other, and their superposition forms a leaky external optical field in the form of a tilted photonic jet. The optical contrast between the halves of a Janus particle leads to flow imbalance and energy redistribution in favor of the flux passing through the lower refractive index part, according to Snell’s law. As a result, the external photonic jet first acquires a refractive slope towards the exit face of the particle, and then bends due to interference of the fields in two counter-flows. Moreover, depending on the ratio of the Poynting vector flux’s strength, the photonic hook can substantially change its bending angle . The bending angle dependencies of the photonic hook on the index contrast (n /n ) of the Janus particle and its edge inclination angle
are shown in Figure 5d,e. It is 2 3 clearly seen that in both cases there is the specific range of optical contrasts—1.01 < n /n < 1.12—when 2 3 photonic flux bending is most pronounced. The increase of inclination angle
of the secant plane, dividing the Janus particle into two parts, causes the increase of the wave refraction angle at the interface between the parts, thus introducing an imbalance between the light energy fluxes. Mostly, this aects the exit angle of the photonic beam outside the particle, whereas the bending angle of the right arm of the photonic hook is influenced to a lesser extent. The highest degree of photon hook bending is achieved in the case of a bar divided exactly along its diagonal. Photonics 2020, 7, 41 6 of 13 Photonics 2020, 7, x FOR PEER REVIEW 6 of 13 Photonics 2020, 7, x FOR PEER REVIEW 6 of 13 Figure 4. Photonic hook based on Janus particle: (a) cylinder with o-axis Gaussian beam [51], Figure 4. Photonic hook based on Janus particle: (a) cylinder with off-axis Gaussian beam [51], (b) Figure 4. Photonic hook based on Janus particle: (a) cylinder with off-axis Gaussian beam [51], (b) (b) cylinder with partially broken wavefront [52], (c) cylinder with two materials [56]. cylinder with partially broken wavefront [52], (c) cylinder with two materials [56]. cylinder with partially broken wavefront [52], (c) cylinder with two materials [56]. Figure 5. Photonic hook from a Janus slab (L×H = 3.2×3 λ ) exposed to a 500-nm plane wave [59]: (a) Figure 5. Photonic hook from a Janus slab (L H = 3.2 3 ) exposed to a 500-nm plane wave [59]: Figure 5. Photonic hook from a Janus slab (L×H = 3.2×3 λ ) exposed to a 500-nm plane wave [59]: (a) geometrical scheme, (b) intensity map and (c) energy fluxes vector map. Hook angle dependence on (a) geometrical scheme, (b) intensity map and (c) energy fluxes vector map. Hook angle dependence geometrical scheme, (b) intensity map and (c) energy fluxes vector map. Hook angle dependence on (d) optical contrast and (e) slab edge angle. on (d) optical contrast and (e) slab edge angle. (d) optical contrast and (e) slab edge angle. It is interesting to note the following. As was mentioned above, the main PH characteristic It is interesting to note the following. As was mentioned above, the main PH characteristic features are [37,42–46]: (a) the subwavelength radius of curvature, (b) the absence of curved side features are [37,42–46]: (a) the subwavelength radius of curvature, (b) the absence of curved side intensity lobes, and (c) PH emerges near the shadow surface of the mesoscale diffractive optical intensity lobes, and (c) PH emerges near the shadow surface of the mesoscale diffractive optical Photonics 2020, 7, 41 7 of 13 It is interesting to note the following. As was mentioned above, the main PH characteristic features Photonics 2020, 7, x FOR PEER REVIEW 7 of 13 are [37,42–46]: (a) the subwavelength radius of curvature, (b) the absence of curved side intensity lobes, and (c) element. In PH emerges [60]near , the a the uthors di shadow scussed PH surface of ithe n the vi mesoscale sible ba di nd based on ul ractive optical tra- element. thin meta In le[nses. It 60], the must authors be mentioned that the w discussed PH in the visible ave beams co band based nsidered on ultra-thin in [60] do not metalenses. share the i It must ndi be camentioned tive properti that es of a the wave “photonic ho beams consider ok” and meso ed in [scale condit 60] do not shar ions, e a the nd rela indicative te to bea prm operties s of an i of ntermedia a “photonic te type. This t hook” and ype of beam, structurally speaking, is an Airy-like beam, and not a PH. For example, we directly adopted mesoscale conditions, and relate to beams of an intermediate type. This type of beam, structurally Figure 1f from [60], showing the electric field intensity profile under off-axis illumination of the speaking, is an Airy-like beam, and not a PH. For example, we directly adopted Figure 1f from [60], metalens, and processed it as follows. First, this image of intensity spatial distribution was converted showing the electric field intensity profile under o-axis illumination of the metalens, and processed it to the gray-scale, and then digitized by means of OriginPro 2018 (OriginLab Corporation) data as follows. First, this image of intensity spatial distribution was converted to the gray-scale, and then acquisition module. Finally, we picked the horizontal intensity profile at the focal point (y = 200 digitized by means of OriginPro 2018 (OriginLab Corporation) data acquisition module. Finally, we 2 2 pixels) and fitted it with the Ai(-x) function. The results of this fitting procedure are shown in Figure picked the horizontal intensity profile at the focal point (y = 200 pixels) and fitted it with the Ai( x) 6. It is clear that the curved beams considered in [60] resemble closely the classical Airy-type beam function. The results of this fitting procedure are shown in Figure 6. It is clear that the curved beams [40] (at least up to the 6th side lobe), and cannot be attributed to the PH-type beam, because its field considered in [60] resemble closely the classical Airy-type beam [40] (at least up to the 6th side lobe), structure possesses a different spatial dependence and physical nature [37,42–46]. In our opinions, and cannot be attributed to the PH-type beam, because its field structure possesses a dierent spatial the use of the term “photonic hook” in the title and conclusion in [60] strongly misleads the readers. dependence and physical nature [37,42–46]. In our opinions, the use of the term “photonic hook” in the title and conclusion in [60] strongly misleads the readers. Figure 6. Intensity profile fitting results. Adapted from [58]. 4. Photonic Jet Array from Phase Diraction Grating In Sections 2 and 3, we discuss the single photonic jet and hook generated by a single particle. It was shown above that the diraction at the phase step and the formation of both curvilinear localized fields and the photonic jet are interconnected. Consider the problem of optical wave diraction at Figure 6. Intensity profile fitting results. Adapted from [58]. a 2D phase diraction grating, from the viewpoint of a PNJ ensemble formation near the grating 4. Photonic Jet Array from Phase Diffraction Grating output facet. In this section, we would like to discuss the photonic jet array generation, because the photonic jet array has more potential applications in practice. In general, the photonic jet array can be In Sections 2 and 3, we discuss the single photonic jet and hook generated by a single particle. It obtained by particle array. The regular arrangement of transparent particles is analogous to a phase was shown above that the diffraction at the phase step and the formation of both curvilinear localized diraction grating (PDG). Such periodic structure, with alternating refractive indices, is widely used as fields and the photonic jet are interconnected. Consider the problem of optical wave diffraction at a a spectral filter or a beam splitter. We present a complete description of the three types of PDGs for 2D phase diffraction grating, from the viewpoint of a PNJ ensemble formation near the grating output generating a photonic jet array. The three most widely used types of dielectric PDGs are the grooves of facet. In this section, we would like to discuss the photonic jet array generation, because the photonic hemispherical, rectangular and saw-tooth profiles. Figure 7a depicts the schematic diagram of a PDG jet array has more potential applications in practice. In general, the photonic jet array can be obtained for a photonic jet, and the dimensions of the PDGs. The length (L) and width (R) are the dimensional by particle array. The regular arrangement of transparent particles is analogous to a phase diffraction parameters of the photonic jet. The focal length (F) and normalized intensity are the key parameters of grating (PDG). Such periodic structure, with alternating refractive indices, is widely used as a spectral filter or a beam splitter. We present a complete description of the three types of PDGs for generating a photonic jet array. The three most widely used types of dielectric PDGs are the grooves of hemispherical, rectangular and saw-tooth profiles. Figure 7a depicts the schematic diagram of a PDG for a photonic jet, and the dimensions of the PDGs. The length (L) and width (R) are the dimensional Photonics 2020, 7, 41 8 of 13 the photonic jet. Laser beams with the wavelengths 405 nm, 532 nm and 671 nm are incidental from the bottom of the phase diraction grating. The schematic profiles of gratings are shown in Figure 7b–d. Photonics 2020, 7, x FOR PEER REVIEW 8 of 13 All grating profiles are described by the groove distance d and the groove height h. The hemispherical and rectangle profiles have a spatial period P. The saw-tooth profile is determined by the blaze angle the blaze angle α. In Figure 6e–g, we show the Finite-Difference Time-Domain (FDTD) simulations . In Figure 6e–g, we show the Finite-Dierence Time-Domain (FDTD) simulations of power flow of power flow distributions for the PDGs with different groove profiles at a wavelength of 532 nm. distributions for the PDGs with dierent groove profiles at a wavelength of 532 nm. The algorithm and The algorithm and details of FDTD simulations were described in references [59,61,62]. According to details of FDTD simulations were described in references [59,61,62]. According to the physical optics, the physical optics, the mono-layered array of closely packed dielectric particles may be considered the mono-layered array of closely packed dielectric particles may be considered as a phase medium as a phase medium with a periodical refractive index [62–64]. The PDGs of different types can be with a periodical refractive index [62–64]. The PDGs of dierent types can be represented as such a represented as such a medium—the hemispherical grating represents a general-purpose diffraction medium—the hemispherical grating represents a general-purpose diraction grating, the rectangle grating, the rectangle grating provides a method for the application of guided-mode coupling and grating provides a method for the application of guided-mode coupling and optical commutation, optical commutation, and the saw-tooth grating has the enhanced capacity for collecting radiation and the saw-tooth grating has the enhanced capacity for collecting radiation [62–64]. [62–64]. Figure Figure 7. 7. ( (a a) ) Schematic diagra Schematic diagram m of a phase diffraction grat of a phase diraction grating ing for a photonic jet. for a photonic jet. Schematic Schematic profiles o profiles off thr three types of ee types of phase phase diffract diraction ion gratings: ( gratings: (b b)) hemispherical, hemispherical, ( (cc)) rectangle, and ( rectangle, and (d d )) saw- saw-tooth. tooth. FDT FDTD D simulation simulation of of power flow di power flow distributions stributions for for the ph the phase ase diffraction gratings having the grooves diraction gratings having the grooves of (of e) (hemispherical, ( e) hemispherical, f) rectangular, and ( (f) rectangular, and g) (g saw-to ) saw-tooth oth profiles at profiles incident wavele at incident wavelength ngth of 532 nm. of 532 nm. The PDGs were fabricated with a polydimethylsiloxane (PDMS) material. The techniques The PDGs were fabricated with a polydimethylsiloxane (PDMS) material. The techniques of of lithography and replica molding [62,65] were used primarily to fabricate the phase diraction lithography and replica molding [62,65] were used primarily to fabricate the phase diffraction gratings. Figure 8 shows the laser scanning digital microscope (LSDM) images of three types of PDGs. gratings. Figure 8 shows the laser scanning digital microscope (LSDM) images of three types of PDGs. The dimensions of the phase diraction gratings are d = 5 m, h = 3.75 m and p = 12.5 m for the The dimensions of the phase diffraction gratings are d = 5 μm, h = 3.75 μm and p = 12.5 μm for the hemispherical profile, d = 5 m, h = 5 m and p = 7.5 m for the rectangle profile, and d = 5 m, hemispherical profile, d = 5 μm, h = 5 μm and p = 7.5 μm for the rectangle profile, and d = 5 μm, h = h = 2.5 m and = 45 for the saw-tooth profile. It can be observed that the sidewall of the phase 2.5 μm and α = 45 for the saw-tooth profile. It can be observed that the sidewall of the phase diraction gratings is almost vertical. Every dimension of the grating profile, from the top of grating diffraction gratings is almost vertical. Every dimension of the grating profile, from the top of grating to the bottom, is nearly the same. The raw experimental images of power flow distributions for the to the bottom, is nearly the same. The raw experimental images of power flow distributions for the three types of phase diraction gratings, with the grooves of hemispherical, rectangular and saw-tooth three types of phase diffraction gratings, with the grooves of hemispherical, rectangular and saw- profiles at incident wavelengths of 405 nm, 532 nm and 671 nm, are shown in Figure 8. The laser beam tooth profiles at incident wavelengths of 405 nm, 532 nm and 671 nm, are shown in Figure 8. The is incident from the bottom of the grating. The photonic nanojet beam was reconstructed from the laser beam is incident from the bottom of the grating. The photonic nanojet beam was reconstructed collected stack of images by scanning the raw stack of real images along the z axis for all gratings to get from the collected stack of images by scanning the raw stack of real images along the z axis for all the best small spot. The diraction gratings of the considered types can form a photonic nanojet array gratings to get the best small spot. The diffraction gratings of the considered types can form a photonic nanojet array with unique characteristics. Rectangular grooves at the wavelength of 405 nm generate light fluxes with the best spatial localization in the transverse direction (about 0.66 λ), with moderate intensity, but the best spatial localization in the transverse direction is generated by the saw-tooth grating at the wavelengths of 532 nm and 671 nm. The saw-tooth gratings at the designed wavelength generate localized optical fields with the best spatial resolution in the transverse Photonics 2020, 7, 41 9 of 13 with unique characteristics. Rectangular grooves at the wavelength of 405 nm generate light fluxes with the best spatial localization in the transverse direction (about 0.66 ), with moderate intensity, but the best spatial localization in the transverse direction is generated by the saw-tooth grating at the wavelengths of 532 nm and 671 nm. The saw-tooth gratings at the designed wavelength generate Photonics 2020, 7, x FOR PEER REVIEW 9 of 13 localized optical fields with the best spatial resolution in the transverse dimensions, and possesses the highest dimensions, optical intensity and possesses the high . The long photonic est opt nanojet ical int array ensity. The at the lo designed ng photonic wavelength nanojet a ar rra e y formed at the from designed wavelength are formed from the gratings with the rectangle groove shape. On the other the gratings with the rectangle groove shape. On the other hand, the greatest focal distance from the hand, the greatest focal distance from the grating surface and the long photonic nanojet array are grating surface and the long photonic nanojet array are formed by the grating with a hemispherical formed by the grating with a hemispherical profile of grooves. The maximal length (~14.5 λ) of the profile of grooves. The maximal length (~14.5 ) of the photonic nanojet array with the highest optical photonic nanojet array with the highest optical intensity is observed for the grating with the intensity is observed for the grating with the hemispherical groove at the wavelength of 405 nm. hemispherical groove at the wavelength of 405 nm. Figure 8. The raw experimental images of power flow distributions for the three types of phase Figure 8. The raw experimental images of power flow distributions for the three types of phase diraction gratings having grooves with hemispherical (I), rectangular (II) and saw-tooth (III) profiles, diffraction gratings having grooves with hemispherical (I), rectangular (II) and saw-tooth (III) at incident profiles,wavelengths at incident wavel (a)e405 ngths ( nm, a) 405 (b) nm, 532(b nm ) 532 nm and ( and (c) 671 c) 671 nm. nm. InIn t the he bottom, bottom, LSDM images LSDM images of of (I) hemispherical, (II) rectangular and (III) saw-tooth phase diffraction gratings; top view (left side) (I) hemispherical, (II) rectangular and (III) saw-tooth phase diraction gratings; top view (left side) and perspective view (right side) are shown. and perspective view (right side) are shown. A new design of the binary PDG with an embedded pupil opaque mask inside each stripe was A new design of the binary PDG with an embedded pupil opaque mask inside each stripe was proposed in [66]. It was shown that in such a masked phase grating, the spatial resolution of the near- proposed in [66]. It was shown that in such a masked phase grating, the spatial resolution of the field localization can be brought beyond the solid immersion limit (λ/2n). Due to an anomalous near-field localization can be brought beyond the solid immersion limit (/2n). Due to an anomalous apodization effect, the subdiffraction field localization is accompanied by an enhancement of apodization eect, the subdiraction field localization is accompanied by an enhancement of intensity, intensity, as compared to the classical (non-masked) design. The pupil mask rearranges the optical as compared to the classical (non-masked) design. The pupil mask rearranges the optical fluxes within fluxes within the stripes and promotes the Fano resonance’s excitation in the periodic step lattice. The the stripes and promotes the Fano resonance’s excitation in the periodic step lattice. The application of application of this effect in displacement Talbot lithography was discussed in [67]. this eect in displacement Talbot lithography was discussed in [67]. Figure 9 presents the main photonic jet parameters with the highest quality for each considered PDG type [66]. For the synthetic parameter of PNJ spatial localization, we use the jet quality criterion Figure 9 presents the main photonic jet parameters with the highest quality for each considered Q = (ImaxL)/R [40], which combines the three main parameters of a jet (Imax is peak PNJ intensity). PDG type [66]. For the synthetic parameter of PNJ spatial localization, we use the jet quality criterion Obviously, the absolute leader in this competition is the grating with rectangular grooves. However, Q = (I L)/R [40], which combines the three main parameters of a jet (I is peak PNJ intensity). max max other types of diffraction gratings can be interesting for practical needs, e.g., when the most intensive Obviously, the absolute leader in this competition is the grating with rectangular grooves. However, (hemispherical) or the most remote and elongated PNJs (saw-tooth) are required. It is worth noting other types of diraction gratings can be interesting for practical needs, e.g., when the most intensive that the intensity of the photonic jet array for all types of PDG is lower than the typical values for PNJ (hemispherical) or the most remote and elongated PNJs (saw-tooth) are required. It is worth noting produced by a spatially localized microsphere [38]. However, the PDG gives more degrees of Photonics 2020, 7, 41 10 of 13 that the intensity of the photonic jet array for all types of PDG is lower than the typical values for PNJ Photonics 2020, 7, x FOR PEER REVIEW 10 of 13 produced by a spatially localized microsphere [38]. However, the PDG gives more degrees of freedom for manipulating the photonic jet array. The transverse spatial resolution of the PNJ by a PDG is as freedom for manipulating the photonic jet array. The transverse spatial resolution of the PNJ by a good as when done with a microspher or microcylinder. PDG is as good as when done with a microspher or microcylinder. L 98.1 max 43.2 39.7 7.0 6.6 6.4 4.7 4.6 4 3.7 2.1 0.6 0.4 0.3 0.3 0.0 Saw-tooth Rectangle Hemispherical Figure 9. Summary of main PNJ parameters from different PDGs [66]. Figure 9. Summary of main PNJ parameters from dierent PDGs [66]. 5. Conclusions 5. Conclusions Structured dielectric materials that manipulate light in novel ways have many potential Structured dielectric materials that manipulate light in novel ways have many potential applications applications in the electronic industries and telecommunication. The field of the curve and the array in the electronic industries and telecommunication. The field of the curve and the array of photonic jets of photonic jets has been the focus of considerable study. Since the first simulation and experimental has been the focus of considerable study. Since the first simulation and experimental exposition of a exposition of a photonic hook in optics, this field has experienced notable growth, making various photonic hook in optics, this field has experienced notable growth, making various introductions ranging introductions ranging from new theoretical designs of curved beams, to various generation means from new theoretical designs of curved beams, to various generation means and experiments in optics, and experiments in optics, plasmonic and acoustic. The discussions in this paper include a review of plasmonic and acoustic. The discussions in this paper include a review of the initial identification of the initial identification of the PNJ for mesoscale particles, the properties of the photonic jet and hook, the PNJ for mesoscale particles, the properties of the photonic jet and hook, experimental observations, experimental observations, and the PNJ’s array generated by PDGs. The photonic jets demonstrate a and the PNJ’s array generated by PDGs. The photonic jets demonstrate a unique combination of superior unique combination of superior properties, including beam propagation along a curved path, properties, including beam propagation along a curved path, subdiffraction beam width, high peak subdiffraction beam width, high peak intensity, and giant backscattering perturbations for nanoscale intentargets. sity, and Accordingly, the p giant backscatteh rotonic jet an ing perturbd hook po ations forse substa nanosca ntia le ta l promi rgets. sA es wi ccor th rega dingly rds to promoti , the photonic nj g et and current nano-optics, ranging from optical microscopy, to nanomanufacturing processes and hook pose substantial promises with regards to promoting current nano-optics, ranging from optical biophotonics. The experimental verification of the concept of the photonic hook, beyond light and microscopy, to nanomanufacturing processes and biophotonics. The experimental verification of the into surface waves and acoustics, also merits attention. The photonic hook can be generated by a concept of the photonic hook, beyond light and into surface waves and acoustics, also merits attention. compact Janus particle, such as a dielectric cuboid, a cylinder with an off-axis Gaussian beam and The photonic hook can be generated by a compact Janus particle, such as a dielectric cuboid, a cylinder with slab. This simple asymmetric particle functions as an auxiliary structure for subwavelength optical an off-axis Gaussian beam and slab. This simple asymmetric particle functions as an auxiliary structure for micromanipulation. The nanoscale target trapped by the photonic hook can be transported along a subwavelength optical micromanipulation. The nanoscale target trapped by the photonic hook can be curved trajectory. The behavior of the photonic hook and the optical forces provides new applications transported along a curved trajectory. The behavior of the photonic hook and the optical forces provides in optical tweezing and biological nano-manipulation. new applications in optical tweezing and biological nano-manipulation. Author Contributions: Conceptualization, idea, O.V.M. and I.V.M.; software, C.-Y.L., O.V.M., I.V.M. and Y.E.G.; Author formal analysis, Contributions: O.V.M. Conceptualization, and I.V.M.; writing idea, —original draft preparation, O.V.M. and I.V.M.; softwar O.V. e, M. C.-Y and I .L., .V. O.V M.; .M., writing I.V.M. —review and Y .E.G.; formal analysis, O.V.M. and I.V.M.; writing—original draft preparation, O.V.M. and I.V.M.; writing—review and and editing, C.-Y.L., Y.E.G., O.V.M. and I.V.M.; visualization, C.-Y.L., Y.E.G., I.V.M.; supervision, O.V.M. and editing, C.-Y.L., Y.E.G., O.V.M. and I.V.M.; visualization, C.-Y.L., Y.E.G., I.V.M.; supervision, O.V.M. and I.V.M.; I.V.M.; funding acquisition, O.V.M., I.V.M., Y.E.G. and C.-Y.L. All authors have read and agreed to the published funding acquisition, O.V.M., I.V.M., Y.E.G. and C.-Y.L. All authors have read and agreed to the published version version of the manuscript. of the manuscript. PDG jet array parameters Photonics 2020, 7, 41 11 of 13 Funding: This research was funded by Ministry of Science and Technology of Taiwan (MOST 108-2221-E-010-012-MY3, MOST 109-2923-E-010-001-MY2), Yen Tjing Ling Medical Foundation (CI-109-24), Russian Foundation for Basic Research (20-57-S52001), Ministry of Science and Higher Education of the Russian Federation and partially carried out within the framework of the Tomsk Polytechnic and Tomsk State Universities Competitiveness Enhancement Programs, Russia. Conflicts of Interest: The authors declare no conflict of interest. References 1. Berry, M.V.; Balazs, N.L. Nonspreading wave packets. Am. J. Phys. 1979, 47, 264–267. [CrossRef] 2. Siviloglou, G.A.; Broky, J.; Dogariu, A.; Christodoulides, D.N. 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