7300911 ieee journal of selected topics in...

7300911 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 3, MAY/JUNE 2014

Integrated Grating-Nanoslot Probe Tip for Near-FieldSubwavelength Light Confinement and

Fluorescent SensingLingyun Wang, Member, IEEE, Youmin Wang, and Xiaojing Zhang

Abstract—We demonstrate a near-field sub-wavelength lightconfinement probe tip comprised of compact embedded metal-lic focus grating (CEMFG) coupler and photonic crystal (PhC)based λ/4 nano-slot tip, in terms of its far-field radiation directivityand near-field sub-wavelength light enhancement. The embeddedmetallic grating coupler increases the free space coupling at tiltedcoupling angle of 25◦ with over 280 times light intensity enhance-ment for 10 μm coupler size. Further, 20 nm air slot embedded insingle line defect PhC waveguide are designed, using the impedancematching concept of the λ/4 “air rod”, to form the TE mode lightwave resonance right at the probe tip aperture opening. This leadsto the light beam spot size reduction down to λ/20. The near-fieldcenter peak intensity is enhanced by 4.2 times from that of therectangular waveguide input, with the total enhancement factor of1185 from free space laser source intensity. The near-field fluores-cence excitation and detection also demonstrate its single molecularenhanced fluorescence measurement capability.

Index Terms—Metallic grating, λ/4 nano-slot, light confinement,near-field, photonic crystal, single molecule fluorescence detection.

I. INTRODUCTION

N EAR-field subwavelength light confinement probe tip hasbeen applied to overcome the far-field diffraction lim-

ited resolution of the conventional optical confocal microscopysystem. A typical application is near-field scanning optical mi-croscopy (NSOM/SNOM) system that is used in many sub-wavelength imaging applications, such as direct photocurrentmapping of organic solar cells [1], subwavelength optical mi-croscopy for dynamic optical in-vitro observation of biologi-cal sample [2], tip enhanced fluorescence microscopy [3], [4],subwavelength pulsed laser ablation [5], etc. Common NSOM

Manuscript received September 12, 2013; revised January 14, 2014; acceptedJanuary 14, 2014. Date of publication January 17, 2014; date of current versionFebruary 11, 2014. This work was supported by the NSF CAREER Award underGrant 0953311 and the DARPA Young Faculty Award under Grant N66001-10-1-4049.

L. Wang was with the Department of Electrical and Computer Engineering,University of Texas at Austin, Austin, TX 78712 USA. He is now with Printingand Personal System Organization, Hewlett-Packard, Palo Alto, CA 94304 USA(e-mail: [email protected]).

Y. Wang was with the Department of Electrical and Computer Engineer-ing, University of Texas at Austin, Austin, TX 78712 USA. He is nowwith the Himax Display Inc. USA, Campbell, CA 95008 USA (e-mail:[email protected]).

X. Zhang is with the Department of Biomedical Engineering, University ofTexas at Austin, Austin, TX 78712 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTQE.2014.2301232

Fig. 1. Conceptual diagram of subwavelength light confinement probe tipmodular structure. The probe is comprised of PhC nanoresonator tip and theembedded metallic grating coupler. The geometry is only for illustration purposeand is not at scale.

probe tips are made by pulled [6] or chemical etched opticalfiber [7], wet etching silicon (Si) cantilever [8], etc. Due to theevanescent wave based nature of such probes, the subwavelengthaperture size greatly reduces the near-field light intensity dueto the light propagation mode or impedance mismatch betweenthe probe body and the near-field of the probe aperture. Thoughthe surface plasmonic resonance wave by metal coating on suchprobes is commonly used to enhance the localized light inten-sity, such as nano-grating [9], superlens [10], bow-tie [11], [12],dipole antenna [13], etc, the light absorption by metal materialat visible range is a fact that cannot be simply ignored [14].

To solve these problems, we introduce a modular probe tip de-sign approach, as illustrated in Fig. 1, that integrates the CEMFGcoupler and the PhC based λ/4 “air rod” probe tip based onsilicon nitride (Si3N4) waveguide layer stacked on the SiO2substrate. The CEMFG coupler is designed to enhance directivefree space far-field coupling rate without oxide layer thicknessrestriction. The dielectric PhC probe tip avoids the Ohmic lossof the metallic probe tip body at visible light range. Both parts ofthe probe system contribute to the final enhanced near-field lightconfinement intensity from the free space plane wave excitationsource. The first light confinement by the CEMFG part focusesfree space light into the single mode dielectric waveguide. Andthe PhC probe tip utilizes the λ/4 “air rod” subwavelength opti-cal resonance to further enhance the light intensity. For the lightcoupling part, following our initial report in [15], a CEMFGcoupler optimized for 25◦ coupling angle is demonstrated inthis paper to have much higher enhanced free space directivitydue to the shallow light penetration depth for higher coupling

1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

WANG et al.: INTEGRATED GRATING-NANOSLOT PROBE TIP FOR NEAR-FIELD SUBWAVELENGTH LIGHT 7300911

angle. Compared to other kinds of grating couplers, the CEMFGreduces the substrate oxide thickness impact on far-field freespace coupling rate [16], [17]. Though there is still heat ab-sorption problems for the CEMFG coupler, the relative largegrating area can usually dissipate the heat without structuraldamage. For the near-field light confinement probe tip design,we also reported a center placed shrunk air hole based slottedPhC FP nano-resonator for near-field probe tip design by thetotal dielectric material without Ohmic loss, e.g., silicon nitride(Si3N4) [18]. In this paper an improved nano-resonator designby λ/4 “air rod” residing in the optimized PhC single line defect(1 W) waveguide platform is demonstrated to zero the reso-nance gap distance by placing the resonance peak right at the tipexit, and it shows much higher near-field subwavelength lightintensity.

Finally the near-field linearly polarized subwavelength exci-tation and emission detection by the PhC probe tip are analyzedto show that the subwavelength fluorescence signal can be ex-cited in the probe near-field, collected and back converted intothe waveguide travelling mode which can be further spatiallydifferentiated and detected by the CEMFG coupler side for far-field readout.

II. GRATING COUPLER

A. Impact of Etching Depth on Far-Field Directivity

In this research, the grating coupler structure is treated asa radiative optical antenna quantified by its far-field radiationdirectivity and radiation gain with the single mode dielectricwaveguide source excitation [19]. The radiation loss is largelycaused by the absorption or Ohmic loss of the metal materials,Ploss , which cannot be ignored in the electric field calculation.If the impedance mismatch loss is simplified to be zero, theradiation efficiency of an optical antenna is defined in terms offar-field radiation energy Prad [19]

εrad =Prad

Prad + Ploss. (1)

The radiation efficiency only quantifies the total radiationefficiency but not the radiation in certain direction. The totalradiation power, Prad , can be defined as the integration for alldirections of the normalized angular radiation density, Pn (θ,ϕ)[19]

Prad =∫ π

0

∫ 2π

0Pn (θ, ϕ) sin θdϕdθ. (2)

The average angular radiation intensity Pav of an equivalentisotropic radiator can be expressed as [19]

Pav =Prad

4π(3)

that calculates the angular radiation intensity with the same totalradiation power. The directivity of antenna is a dimensionlessparameter that describes the focusing capability of radiationbeam at certain angle at far-field. It is as quoted in the J. D.Kraus’s classic antenna textbook [20], “The directivity D of anantenna is given by the ratio of the maximum radiation intensity(power per unit solid angle) to the average radiation intensity

Fig. 2. 3-D FDTD model of grating coupler design with spherical axis aslabeled. The etched silicon nitride is used as the grating materials in the model.

(averaged over a sphere)”, which refers to the maximum di-rectivity direction at the far-field. For arbitrary direction, theangular directivity D is defined as [19]

D =Pn (θ, ϕ)

Pav= 4π

Pn (θ, ϕ)Prad

. (4)

The gain of the antenna combines both the antenna directivityand the antenna radiation efficiency

G = εradD. (5)

As demonstrated for IR wavelength light coupling [17], ametal grating can be placed on top of the waveguide layer to forma grating coupler on silicon on insulator platform. Another pop-ular grating design uses top etched grooves to form the gratingindex contrast. Both designs need to control the stacked buriedoxide thickness to generate the maximum upward coupling us-ing the constructive interference between wave reflection fromoxide substrate interface and the upward light propagation. Wedemonstrate that besides the oxide layer thickness control, theetching depth also plays an important role to control the direc-tive coupling angle and efficiency for etched grating coupler asshown in Fig. 2.

We have reported the near vertical coupling for the dielectricetched and CEMFG grating coupler designs based on (CAvityModelling Framework) CAMFR [21] and 2-D FDTD methods[15]. The first order grating diffraction equation describes therelationship between the coupling angle and the effective indexof the grating coupler structure

neff = n0 sin θ1 +λ0

Λ(6)

where θ0 is the first order diffraction angle, Λ is the gratingpitch period. For dielectric etched grating coupler the verticalresonance condition can be accurately estimated from the grat-ing etching depth and pitch period using the CAMFR methodto calculate the reflection and out-of-plane coupling resonancecurves. Without considering the vertical Bragg reflector effectof multiple stacked oxide layers, the 3-D far field directivityof the focusing effects grating plane was demonstrated in [15]by forming constructive interference on xy lateral plane of theSi3N4 waveguide layer which can be described by the phase


Fig. 3. The S11 parameter of the 250 nm etching depth (top line) and 110 nmetching depth (bottom line) grating couplers.

matching equation below

qn0 = neff

√x2 + y2 − xn0 sin θ0 , q = 1, 2, 3, ..., (7)

where q is the grating line numbers. It describes a set of ellipsecurves that share a common focal point at (0, 0) on xy plane.At the y = 0 cross line, the pitch period matches that of (6). Itwas found that for Si3N4 waveguide layer thickness of 250 nmby 2-D CAMFR method, the vertical radiation occurs at neff =1.7529 with grating depth of 110 nm. The radiation pattern isalso verified by the 3-D FDTD simulation of the compact focusetched grating coupler with coupler size of 10 μm in y directionand 7 μm in x direction which would fit the approximate coresize of single mode optical fiber at 632.8 nm wavelength forTE0 waveguide excitation source. The dielectric rib waveguidehas cross section length of 500 nm and vertical thickness of250 nm. By only changing the tilted angle θ0 in (7) with the sameeffective index, the light propagation is tilted correspondinglytowards the free space. As it demonstrates in this research thefar-field directivity is also strongly dependent on the etchingdepth control. For non-optimized etching depth, the loss is evenmore due to the mode mismatch between the grating coupler andthe ridged dielectric waveguide taper as shown by the waveguideport reflection coefficient S11 plot in Fig. 3.

The higher of S11 value the more mismatch is between wave-guide and the optical grating structure. Since there is no specialmechanism for blocking the radiation into substrate, almost halfof the light energy is lost into the substrate even for the optimizedetching depth of 110 nm grating coupler design. Based on 3-DFDTD modeling the etching depth also changes the coupling ef-ficiency and beam pattern dramatically. The FDTD simulationof the 80 nm and 250 nm etching depth as shown in Fig. 4 forthe designed effective index neff = 1.7529 with tilted radiationangle of θ0 = 10◦ further confirms that the far-field radiationbeam pattern and peak directivity strongly depend on the gratingetching depth. For 80 nm etching grating coupler, even there isa peak radiation towards free space at angle θ0 = 13◦, the mainlobe is actually pointing towards the substrate direction, whichindicates more light scattering into the substrate than into thefree space direction. For 250 nm etching depth grating coupler,due to the impact of the strong mode mismatch, the far-fielddirectivity is not only reduced to sub 200 level, the direction ofthe radiation peak is also shifted from the original design forθ0 = 10◦ tilted angle.

Fig. 4. Far-field directivity on ϕ = 0◦ plane with main lobe towards substratefor typical non-optimized etching depths. (a) 80 nm etching depth with freespace directivity 280. (b) 250 nm etching depth with free space directivity 90.

TABLE IIMPACT OF ETCHING DEPTH ON FAR-FIELD RADIATION PATTERN

Fig. 5. 3-D illustration of the noble metal compact focus grating on top ofthe SiO2 for interfacing far field free space and Si3 N4 dielectric rib waveguide(geometry not to scale).

However it is very difficult to realize precise etching depthsince the dry etching is essentially a non-stopping layer etchingprocess. To summarize, Table I lists the relationships amongetching depth, far-field directivity and main lobe directivity onϕ = 0◦ plane for the designed neff = 1.7529 and tilted angleθ0 = 10◦.

B. High Tilted Angle CEMFG Coupler Analysis

In order to avoid the oxide thickness control restriction, a bot-tom placed metallic grating coupler was proposed and verifiedby 3-D FDTD model for noble metal of Au and Ag for tilted an-gle of 10◦ as illustrated in Fig. 5 [15]. A metallic grating layer of40 nm is placed on top of the SiO2 layer with duty cycle of 50%,which can be defined by electron beam lithography (EBL) andfabricated by metal lift-off method. Only one EBL alignmentis needed to align the Si3N4 waveguide pattern that is finalizedby dry etching. Similarly the TE0 waveguide excitation sourceis used to calculate the far-field directivity pattern. Si3N4 has


transparent lossless optical properties at 632.8 nm light wave-length with relatively high index (n = 2.02) which will also beutilized in this paper to form the PhC waveguide material.

The purpose of bottom placement of noble metals such as Agand Au is to further enhance the free space light coupling effi-ciency by reducing the light energy loss diffracted with higherorder modes into the SiO2 substrate given by the penetratingproperties of such metals. The top conformal grooves pattern isalso modeled to simulate the uniform conformal Si3N4 deposi-tion. The top Si3N4 conformal grooves do not serve as an activegrating element due to its thin thickness and relative low indexcontrast compared to that of the noble metals.

The grating pitch period is first optimized by 2-D FDTDsimulations with dispersive noble metal optical properties fittedvery accurately by two terms Drude-Lorentz model [15]. Afterthe tilted resonance peak and effective grating index is fixed bythe 2-D metallic grating pitch period, the 3-D compact focusgrating coupler grating curves can be described as

(x − qλn0 sin2 θ0

n2e f f −n2

0 sin2 θ0

)2

(qλn e f f

n2e f f −n2

0 sin2 θ0

)2 +y2

qλ√n2

e f f −n20 sin2 θ0

= 1 (8)

to design the CEMFG coupler. For both Ag and Au metal types,the 3-D FDTE model verifies the accuracy of this design flowfor tilting angle θ0 = 10◦. It demonstrates the enhanced freespace directivity compared to the normal etched dielectric grat-ing coupler type.

In this paper we report the higher tilted angle case for designedangle θ0 = 25◦ for Au grating coupler to further prove this designconcept. In the meanwhile new device performance will also beanalyzed and compared. Equation (6) is only valid by assumingequal effective index in the grating region and the waveguideregion, and it is only fulfilled for shallow gratings less than50 nm [22]. The metal grating grooves in this research only has40 nm thickness which can be regarded as shallow grating. Asit is observed from (8), by finding out the effective index of thegrating coupler at θ0 = 10◦ and simplifying it as a constant for allradiation angles, the optimized grating pitch period for θ0 = 25◦

peak radiation is only related to the designed radiation angle. Bycalculating the model using the updated grating pitch period, the3-D compact metallic focus grating ellipses can also be uniquelyderived for the new 1st order diffraction angle. Thus the effectiveindex of the grating coupler is a very important parameter forgrating coupler design to control main lobe radiation angle.Fig. 6 shows the radiation pattern for θ0 = 25◦ with the exactsame effective index estimation as θ0 = 10◦ for Au gratingcoupler.

The high first order diffraction angle enables longer lightpropagation distance on top of the grating grooves, which ex-plains slightly higher material loss. The total radiation efficiencyonly reduces slightly to 73% for θ0 = 25◦ case, but the freespace directivity is greatly enhanced with strongly suppressedside lobe towards substrate. The side lobe for θ0 = 25◦ casetowards the substrate is only half of the lower diffraction anglecase. And the main lobe towards the free space is enhanced to1200. The side lobe is generated from the light leakage into

Fig. 6. Far-field radiation pattern for first diffraction angle of θ0 = 25◦ forAu grating coupler. (a) 3-D directivity pattern as functions of spherical anglesfor Au grating coupler with peak directivity of 1200. (b) Normalized far-fieldpower radiation pattern as function of θ on ϕ = 0◦ plane.

TABLE IIEMBEDDED METALLIC GRATING COUPLER PERFORMANCE TABLE

substrate and regulated by the metallic grating. The magnitudeof the side lobe is strongly dependent on the penetration depthof the evanescent wave on top of the metal layer. The electricfield of light reaches 1/e of its maximum value on the metalsurface at the penetration depth that is defined as [23]

d(θ0) =λ0

2π√

n2m sin2 θ0 − 1

(9)

where nm is the refraction index of metal, and θ0 is the lightincident angle. As it shows in (9), the penetration depth of lightreduces for higher incident angle, which causes less light pene-tration through metal layer and lowers the side lobe magnitudefor the directivity far-field pattern. Even though most gratingcoupler designs including the one in this contribution choose thenear vertical first order diffraction angle to avoid the possiblesecondary reflection, the proposed embedded metallic gratingdesign has unique advantage of better free space transmissionfor higher radiation angle. The Ag grating design for θ0 = 25◦

with neff = 1.7711 has much higher free space gain as listed inTable II due to its lower light absorption, though the directivityof it has slightly less value as that of the Au one. And the seconddirectivity main lobe of Ag grating coupler with θ0 = 25◦ isonly one third of the θ0 = 10◦ grating coupler.

C. Light Focusing Effects

The previous sections study the light out-coupling from thewaveguide since it is easier to calculate the maximal light cou-pling angle and the far-field free space directivity. To demon-strate the compact focusing effects, it is insightful to calculate


Fig. 7. Plane wave excitation on the Au CEMFG coupler. (a) TE mode exci-tation with tilted poynting vector (θ0 = 10◦) illustrated in 3-D; (b) 2-D surfaceplot of the electric field amplitude on the x = 0 cross plane.

the field intensity inside the dielectric waveguide by externalexcitation of a plane wave source with TE polarization. It isessentially an equivalent problem to calculate light couplingfrom the free space into the dielectric waveguide in terms of thecoupling efficiency based on the reciprocity theorem that hasbeen prove mathematically by using Maxwell’s equations [24].As illustrated in Fig. 7, a plane wave source with Poynting vec-tor of P = − sin θ0 · x − cos θ0 · z covers the whole simulationdomain that contains the grating coupler assuming actual laserbeam spot size is much bigger than the coupler size. For typicallinearly polarized laser source, the focused beam spot size iswell above 700 μm in diameter. A unit |Ey |max = 1 V/m isassumed for the plane wave source. A single mode light withTE0 mode is found to confine and focus on the dielectric ribwaveguide end facet with minimal impedance mismatch. Forthe tilted angle of θ0 = 10◦, the center peak electric componentamplitude of |Ey |max at the waveguide facet at x = 0 enhances15.3 times with that of the plane wave source. In terms of lightintensity, the light intensity enhances 234.09 times of the inci-dent plane wave source. The grating coupler design of θ0 = 25◦

has also been calculated with plane wave source tilted at θ0 =25◦ under the same plane wave intensity to find slightly higher16.8 times enhancement of |Ey |max component. The highertilted angle design as mentioned in last section has higher freespace directivity which also explains the higher focused lightintensity. Table II lists the radiation efficiency, optical antennagain, effective index and designed radiation angle parametersfor comparison purpose.

III. PHOTONIC CRYSTAL-BASED λ/4 NANO-SLOT

Most optical antennas are illuminated from far-field by alight source (especially plane wave source) and the focus size isdiffraction limited, just like the embedded grating coupler designas discussed in last section. The large illumination area causesthe background light contamination that other fancy techniques,

Fig. 8. 3-D model of 1 W PhC waveguide model with half wavelength modetransition adapter with waveguide ports as illustrated.

like Raman scattering enhancement [25], two photon lumines-cence [26] or fluorescent emitters [27], are needed to overcomethe contamination issues. Recently a λ/4 monopole antenna hasbeen modeled and tested in the metal generated plasmonic res-onance waveform as an effective nano light subwavelength fo-cusing probe tip [28]. Though it avoids the background noisecontamination issues by mounting the monopole optical metalantenna on the pulled optical fiber with circular aperture open-ing, the intrinsic low transmission rate by the pulled optical fiberseverely obstructed the final subwavelength localized light in-tensity. The metal structure in the nanometer scale has the lightabsorption that causes heat damage to the probe tip. Moreoverthe probe metal tip is manually fabricated by focused ion beam(FIB) milling which hinders its mass fabrication potential. Inthis section, we study the PhC waveguide made by pure di-electric material to drive the nano slot resonator that has stronglight localization and enhancement in the near-field of the probetip. By considering the light feeding part (PhC waveguide) andthe focus part (nano λ/4 slot resonator) as a whole system, thelight transmission is greatly improved and still in subwavelengthfocusing size in the near-field. The first step is to find the op-timized PhC waveguide with minimal back reflections throughcalculation of scattering parameters. The optimized PhC wave-guide serves as the highly efficient antenna driving light sourcethat there is no place for light in photonic band gap (PBG) toescape except towards the slotted probe tip aperture. Based onthe self-resonance of the slot with λ/4 length, strong resonanceoccurs in the slot region that further enhances the light local-ization intensity and the light throughput at the subwavelengthlevel.

A. Single Line Defect Photonic CrystalWaveguide Optimization

A 250 nm Si3N4 slab thickness is assumed for the FDTDmodel as illustrated in Fig. 8. Two normal dielectric rib waveguides are interfaced on both sides with the PhC waveguideslab. The width of the dielectric waveguide is 500 nm and itconforms with the embedded metallic grating coupler design.Since it is straight single mode waveguide, the loss of the ribwaveguide can be ignored. In order to avoid long adapting lengthof the mode size difference between rib waveguide and that ofthe single line (1 W) PhC waveguide, half wavelength mode


Fig. 9. 1 W PhC waveguide S parameter plot as function of lattice constant abased on FDTD calculation. (a) S11 ; (b) S21 .

Fig. 10. Field distribution and scattering parameters for TE0 waveguide portexcitation at 632.8 nm wavelength. (a) |Ey | distribution surface plots at crosssection planes for 1 W PhC waveguide with lattice constant a = 284 nm onxz center cross plane; (b) on xy center cross plane. (c) S11 as function ofwavelength; (d) S21 as function of wavelength.

adapters are also used on both sides of the PhC waveguide [29].The PhC crystal lattice is set to be triangular with etched airhole radius of 0.3 a. By assuming a single waveguide mode,the transmission and reflection of the structure as a function oflattice constant can be calculated by FDTD model as shown inFig. 9. A waveguide port excitation in TE polarization (with Ey

component only) is set in the rib waveguide on port 1 with totalpower of 1 watts [see Fig. 8(a)]. The optimal lattice constant canbe determined from the scattering parameters of the waveguideports in which the highest the transmission rate corresponds tothe lowest reflection from the excitation port. At lattice constanta = 284 nm, the reflection S11 reaches minimum and the trans-mission S21 reaches maximum indicating the lattice constantvalue for the lowest loss for 1 W PhC waveguide. The peaktransmission rate as indicated by S21 parameter is 92.8% wherethe negligible loss is due to the slight resonance of the trans-mission adapter and the out of plane radiation loss. To furtherprove this, a 3-D FDTD model for lattice constant a = 284 nmcalculates the Ey distribution in the structure at excitation wave-length at 632.8 nm as shown in Fig. 10. The light propagates

along the x direction with no light penetrating the PhC regularlattice area and in the slab vertical direction, light is limitedby the total internal reflection (TIR) which indicates the PhCwaveguide guided mode at 632.8 nm wavelength works underthe light line. The half wavelength mode transition adapter alsochanges the mode size from 500 nm to the 1 W size with min-imal resonance without using longer length adiabatic transitionadapter. The single mode light inside the rib waveguide is kept inboth the input and output direction. Though the PBG is not cal-culated, the time domain calculation that plots the S11 and S21parameters in Fig. 10 indicates the 632.8 nm wavelength locatesin the band gap center. It is observed that the 3 dB transmissionbandwidth in terms of wavelength ranges from 570 to 690 nmfor PhC 1 W waveguide with lattice constant a = 284 nm bythe S21 calculation in Fig. 10(d). It suggests that the proposedPhC 1 W waveguide also supports the light propagation in this3dB wavelength range which also fits the possible fluorescencesignal wavelength for excitation at 632.8 nm. For example, theCy5 fluorophore emission wavelength for 632.8 nm excitation isaround 690 nm. In the biological application part, the detectionscheme by collection nanometer scaled fluorescence emissionis also simulated to assess the performance of the probe.

B. Transmission Line Model of the λ/4 Nano Slot Tip

The λ/4 based resonance devices can be commonly foundin the microwave range for electromagnetic wave impedancematching with maximum power delivery into the load devicelike microwave or RF antennas. A typical transmission linebased impedance matching device is a quarter-wave impedancetransformer. Another λ/4 idea based microwave device is λ/4monopole antenna or slot antenna. The monopole and slot areessentially complementary structure that can be analyzed bysimilar current resonance distribution method. The same λ/4idea can also be used to design the visible light resonators. Inthis section, we propose a λ/4 slot resonator embedded in the1 W PhC waveguide for maximal light energy delivery in thenear-field free space. And due to the boundary condition in theslot, the resonance in a standing wave form is located inside theslot region with light intensity peak near the very end of theprobe aperture tip under ideal impedance matching condition.

Before analyzing the λ/4 slot optical resonator in depth, atransmission line based model calculates the voltage (electricfield) and current distribution in a typical λ/4 impedance trans-former. As illustrated in Fig. 11 in the segment of the trans-mission line input, there is no electromagnetic wave reflectionback at the input point due the impedance match, since the inputimpedance looking into the λ/4 transformer is exactly the sameas the transmission line characteristic impedance. To achievesuch impedance matching condition, there are two conditionsthat need to be met: (1) the length of the matching segment isλ/4 long to cause the light reflected back from load to have 180◦

phase change for each round trip; (2) the impedance of the λ/4transformer, Z1 , is the geometric mean of the load impedanceand the transmission line input impedance [24]. Given by theinput signal from the transmission line with impedance Z0 ex-pressed in harmonic form

Vin = Viejωt−jβz (10)


Fig. 11. Transmission line model. (a) Illustration for the λ/4 impedance trans-former with voltages at each segments as illustrated. (b) voltage and (c) currentamplitude for standing wave in the λ/4 impedance transformer with assumptionof matched condition with Z0 = 50 Ω and ZL = 377 Ω.

where ω is the radian frequency and β = 2π/λ is the wave num-ber, the voltage distribution along the λ/4 line can be describedas

V (z)=Vi

[(ZL/Z1 +1

2

)e−jβz +

(ZL/Z1−1

2

)ejβz

]· ejωt

(11)Equation (11) describes a standing wave distribution along

the λ/4 transformer. As an example the impedances for inputtransmission line and the load are assumed to be Z0 = 50 Ω andZL = 377 Ω with voltage and current distribution amplitudeenvelopes plotted in Fig. 11(b) and (c). For slot waveguideresonator, the near-field free space can be simplified as freespace wave impedance with ZL = 377 Ω, just as most aperturebased antenna structure. The peak voltage amplitude occurs atthe load terminal based on the plot of Fig. 11(b), which alsoindicates the peak electric field locates at the near-field aperturefor aperture type antennas. The same phenomena also happensfor arbitrary combination of Z0 and ZL based on the observationof (11). For instance, as demonstrated in microwave range thestrong electric field near the slot aperture towards free spacecan excite Argon plasma in atmosphere pressure by λ/4 slotwaveguide [30]. The plasma intensity distribution along the slotregion conforms to the electric field distribution. At the end ofthe slot aperture the electric field reaches the highest value.

C. Single Line Defect (1 W) PhC Based λ/4 Nano-SlotTip Analysis

The λ/4 resonance idea can be adapted to design the near-fieldoptical confinement probe. The λ/4 monopole antenna made bymetal at visible range has been realized by FIB etching the metalcoated pulled optical fiber in optical wavelength range just as themonopole radio frequency (RF) antenna [28]. The pulled opticalfiber aperture tip serves as confined light excitation source but inan inefficient manner. There exists strong impedance mismatchbetween the optical fiber travelling mode and the monopoleresonance mode due to the coned optical fiber aperture structure,

Fig. 12. λ/4 nano slot embedded in 1 W PhC waveguide. (a) 3-D model ofthe λ/4 nano slot embedded in 1 W PhC waveguide with waveguide port asillustrated; (b) xy center cross section plane with slot aperture opening and slotwidth as indicated.

which causes much less light transmission efficiency, since theybehave much like two separate systems.

As illustrated in Fig. 12, compared to the microwave coun-terpart made by metal slot, the proposed optical slot is madefrom the pure dielectric material without absorption loss. Theembedding of the nano slot inside the PhC waveguide combinesthe excitation source and the λ/4 slot resonance part as a wholesystem. The 1 W PhC waveguide provides a high insulationplatform for exciting the dielectric slot without mode mismatchrestriction. It also serves as the equivalent ground plane at theinput end of the slot. The boundary condition of continuouselectric displacement field causes the high electric field insidethe air slot for TE polarization waves. The electric field in themetal rod in the RF monopole antenna is distributed on the metalsurface. Instead for optical slot in the proposed structure the elec-tric field locates right inside the so called “air rod” and wavebounces back and force in the similar manner as RF metal rod.The only difference is no Ohmic loss and electric field focusesinside the center of the “air rod” which helps light focused withone single lobe in the center of the probe tip at the near-field.So the proposed λ/4 nano slot embedded with PhC waveguidebehaves similarly as the grounded λ/4 monopole antenna in RFrange.

The transmission line model simplifies the problem into theideal impedance matched scenario. As discussed in the trans-mission line model, the first condition for impedance match atoptical wavelength range is easy to fulfill by just fixing the slotlength in x direction to be λ/4. However the second conditionfor controlling the characteristic impedance Z1 in the slot re-gion is hard to achieve without changing the slot design suchas by adding other delicate tuning elements into the slot region.And in such nanometer scale it is not realistic to put too much


Fig. 13. |Ey |m ax field plots of the λ/4 nano slot embedded in 1 W PhCwaveguide by 3-D FDTD model. (a) |Ey |m ax contour plot on xz center plane.(b) |Ey |m ax contour plot on xy center plane.

extra structure during the fabrication process. In this design wemake a compromise between the ideal impedance match and thesystem complexity to still achieve strong light resonance neartip aperture. Even in non-ideal case, the light also distributesstrongly in the right part of the slot towards the free space load,which is also proved by the number modeling.

In the 3-D FDTD model, as shown in Fig. 13, the struc-ture is excited from single mode waveguide Ey source withwavelength center at 632.8 nm. The rib waveguide, the halfwavelength adapter structure and the 1 W PhC waveguide allhave the same optimized values as the one shown in Fig. 10.The nano slot length is half PhC lattice size (equivalent to λ/4)with arbitrary subwavelength slot width which is only limitedby the fabrication limit. So the typical EBL feature size defini-tion capability limit of 20 nm is chosen as the slot width in themodel. Though the characteristic impedance in the slot regionis not fully satisfied for ideal impedance match, it still presentsthe highest resonance peak at the right part of the slot towardsthe probe tip aperture as predicted by transmission line modeland the close up plot of the Ey field amplitude at the probetip aperture as shown in Fig. 14. The resonance peak can belocated by close up center cross section line plot of Ey fieldas shown in Fig. 15 locating at x = −35 nm which echoesthe discussion of the transmission line model. Compared to thewaveguide excitation source intensity, the enhancement factorof |Ey |max amplitude is 3.6. In the vertical direction, the TIRkeeps the light confined in the vertical direction. The resonancepeak light is confined in the air slot region on the center xylateral plane due to the continuous electric displacement fieldacross the slot/air boundary. Not like the center placed nano slot

Fig. 14. Enlarged |Ey |m ax field plots near nano slot aperture. (a) |Ey |m axcontour plot on xz center plane; (b) on xy center plane. The plots has the sameintensity color bar as that of Fig. 13.

Fig. 15. |Ey |m ax field along the waveguide center line in x direction.(a) |Ey |m ax field in unit of V /m along the x direction for the while calcu-lation domain. (b) |Ey |m ax field in the λ/4 region along the x direction.

Fabry-Perot photonic crystal scanning tip design [18], there isno other resonance points inside the structure except the onenear the probe tip aperture which greatly help reduces the backreflection and enhances the transmission of the probe tip.

It is expected that the near-field light is also confined due tothe aperture beam pattern inside the probe body. Fig. 16 plots the|Ey |max field in 3-D surface form at x = 10 nm yz cross planebased on 3-D FDTD results. There is only one main center lobeat the probe tip aperture center and the beam size in y directionis proportional to that of the slot width. Fig. 16(a) shows the|Ey |2max at the x = 10 nm along y direction. It is found thatthe FWHM of the light beam at x = 10 nm is 32.3 nm whichis only slightly larger than that of the slot width. The beamsize is well below the subwavelength level for λ = 632.8 nm,which is in about λ/20 level. In the vertical direction the beamsize is about λ/3. However compared to the center distributednano resonator [18] and that of the pulled metal coated opticalfiber probe tip, the light intensity is enormously enhanced to be4.2 times higher than that of the waveguide excitation centerintensity as demonstrated in the normalized intensity plot inFig. 16(b).


Fig. 16. |Ey |m ax field at x = 10 nm in near-field for the λ/4 slot PhC probetip. (a) Contour plot at yz center cross plane. (b) Normalized |Ey |2 m ax fieldalong y center line.

IV. TIP ENHANCED SUBWAVELENGTH FLUORESCENCE

Since the very high intensity light can be confined in sub-wavelength scale at the near field of the λ/4 nano slot PhCwaveguide probe tip, it is possible to excite the fluorescencemolecules using extremely focused light at the probe tip. Thusit is meaningful to study the reverse process for subwavelengthlocalized fluorescence light detection by the same probe tip. Asit is observed in Fig. 10(c), the 3 dB transmission window of the1 W PhC waveguide covers the 690 nm fluorescence emissionpeak of Cy5 fluorophore excited by 632.8 nm laser source. It ispossible to reversely transform the polarized fluorescence signalin nanometer scale into the traveling wave of the rib dielectricwaveguide. And such travelling wave continues to propagateback to the compact embedded metallic focus grating couplerregion to further differentiate in free space by far-field imagingmethods [15].

The near-field localized fluorescence light detection by λ/4slot PhC probe tip is almost a reciprocal problem as the lightconfinement process. However it is not exactly a reciprocal onedue to the fact that the wavelength dependent difference betweenthe incident excitation light and the fluorescence light. So a 3-DFDTD model is necessary to assess the fluorescence light detec-tion performance of such a probe tip. In such a numerical modelillustrated in Fig. 17, the probe tip has the has the same struc-tural design as that of Fig. 13, which has 284 nm PhC triangularlattice size, 20 nm slot width and 158.2 nm (∼λ/4) long slotfrom the tip aperture. The PhC has single line defect for maxi-mal light delivery by working in the PGB center for 632.8 nmwavelength. However the structure is illuminated from a wave-guide port source at x = 50 nm with port size plane of 80 nm in

Fig. 17. Reverse detection model for localized and linearly polarized near-field fluorescence signal of wavelength at 690 nm. The fluorescence waveguideport has geometry of 80 nm in y and 250 nm in z direction located at x = 50 nmfrom the probe tip exit in the near-field.

Fig. 18. Ey distribution plots on the xy center cross plane for 690 nm fluores-cence waveguide port excitation at x = 50 nm near-field yz plane. (a) Ey 3-Dsurface plot on center xy cross plane. (b) Close up plot of |Ey | amplitude aroundprobe tip aperture on xy cross plane. (c) S21 of the fluorescence waveguide port(port 2) excitation at x = 50 nm near-field yz plane as a function of wavelengthwith range center at 690 nm. The waveguide port 1 locates at the dielectric ribwaveguide.

y direction and 250 nm in z direction with fluorescence signalat 690 nm wavelength linearly polarized in y direction. Sucha waveguide port size is delicately chosen to model the lightdiffuse size at the x = 50 nm yz cross plane for the light con-finement source from the probe tip at 632.8 nm wavelength.The polarization of the fluorescence signal depends not onlyon the polarization of the excitation source (in this model theexcitation source is linearly polarized in y direction), but alsothe local medium composition. For biological system the con-stituents of the local medium varies for different experimentscenarios. Thus the linearly polarization for the fluorescencesignal is assumed only to simplify the problem. The 3-D surfaceplot of Ey field on xy center cross plane is shown in Fig. 18(a),and the enlarged close up plot around tip aperture is shown in2-D surface plot in Fig. 18(b). Similar to the 632.8 nm


wavelength excitation/illumination field distribution, there isalso light resonance near the probe tip aperture, but at the near-field of the probe tip. And the light is confined in the slot regionwith higher intensity. This demonstrates that higher light in-tensity in the slot region is not strongly wavelength dependent.Instead the light polarization plays a much more important role.Traveling wave in single mode wave form propagates towardsthe rib dielectric waveguide direction. The transmission S21 pa-rameter is also calculated as a function of wavelength with rangecenter at 690 nm in Fig. 18(c). Compared to the S21 at 632.8 nm[see Fig. 10(c)], there is about 3dB drop for fluorescence wave-length at 690 nm. This conforms to the 1 W PhC waveguidedesign. So the fluorescence light transmission drop is largelycaused by the light loss in out of plane radiation form in thePhC waveguide structure.

V. CONCLUSION

A modular near-field light confinement probe tip designapproach is proposed and verified numerically by combiningCEMFG coupler and the λ/4 nano slot resonator embedded insingle line defect (1 W) PhC waveguide. It demonstrates totallight confinement intensity enhancement factor of 1185 withbeam size of λ/20, which are well beyond the transmission rateof the plasmonic based or pulled optical fiber based light con-finement probe tip designs. The latter approaches also comewith Ohmic or heat damaging problem at the tip structure. Theproposed λ/4 probe tip can both excite the Cy5 fluorophoremolecules and detect the linearly polarization kept fluorescencesignal in subwavelength scale. Through the versatile near-fieldand far-field light conversions, such multi-functional monolithicphotonic probe tip system enables a large variety of applicationsin imaging, sensing and nanomanufacturing.

ACKNOWLEDGMENT

This research was performed in the Department of BiomedicalEngineering, Microelectronics Research Center (MRC), TexasAdvanced Computing Center (TACC), and Center for Nano andMolecular Science (CNM) at the University of Texas at Austin.

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Lingyun Wang received the B.S. degree in electron-ics and information system from East China Nor-mal University, Shanghai, China, in 2000, the M.S.degree in electrical engineering from University ofAlaska Fairbanks, Fairbanks AK, USA, in 2002 andthe Ph.D. degree in electrical and computer engineer-ing from University of Texas at Austin, Austin, TX,USA, in 2012. He is currently with the Printing andPersonal System Organization of Hewlett-Packard asMEMS process engineer in Corvallis, OR, USA. Hisresearch interests include antenna, numerical mod-

eling, ionosphere scintillation analysis, nanophotonics, photonic crystal de-vices, nanomaterial processing, and integrated optoelectronics for biomedicalimaging.

Youmin Wang received the B.S. degree in elec-tronics engineering from Shanghai Jiao Tong Uni-versity, China, in 2008. He received the M.S. andPh.D. degrees in electrical and computer engineeringfrom The University of Texas at Austin, TX, USA.He is currently a R&D Engineer at Himax Display,Inc., working on the design and modeling of digitalmicromirror array devices. His research interests in-clude the optical MEMS devices, optical imaging andspectroscopy instrumentation for the medical and bi-ological applications.

Xiaojing Zhang received the Ph.D. degree fromStanford University, CA, USA, in 2004. He was aResearch Scientist at Massachusetts Institute of Tech-nology (MIT), Cambridge, before joining the fac-ulty at University of Texas of Austin in 2005. He iscurrently an associate professor at the University ofTexas of Austin (UT Austin) in the Department ofBiomedical Engineering, with joint affiliations withInstitute for Cellular and Molecular Biology (ICMB),Microelectronics Research Center and Texas Ma-terials Institute. His research focuses on exploring

bio-inspired nanomaterials, scale-dependent biophysics, and nanofabricationtechnology, towards developing new diagnostic devices and methods on prob-ing complex cellular processes and biological networks critical to develop-ment and diseases. Both multi-scale experimental and theoretical approachesare combined to investigate fundamental force, flow and energy processes atthe interface of engineering and biomedicine. In particular, his laboratory isleading the development of integrated photonic microsystems (MEMS, micro-electro-mechanical systems), semiconductor chips and nanotechnologies crit-ical to healthcare, defense and environmental applications. He has publishedmore than 120 peer reviewed papers and proceedings, presented more than 45invited seminars worldwide, and filed over 15 U.S. patents (five patents issued).His research findings have been highlighted in many public media, and werelicensed to two companies: CardioSpectra, Inc., and NanoLite Systems, Inc.He has organized many major conferences in the area of MEMS/BioMEMS,nanotechnologies and biomedical engineering. In addition to being the prin-ciple investigator of many major grants from U.S. federal agencies such asNIH, NSF, and DARPA, he also received many prestigious awards, including:the Wallace H. Coulter Foundation Early Career Award for Translational Re-search in Biomedical Engineering in 2006, the British Council Early CareerRXP Award in 2008, NSF Faculty Early Career Development Program (NSFCAREER) Award in 2009–2014, DARPA Young Faculty Award in 2010, and aninvitee to attend U.S. National Academy of Engineering, Frontiers of Engineer-ing (NAE-FOE) program in 2011, the NAE Frontiers of Engineering Education(NAE FOEE) program in 2012, and subsequently China-America Frontiers ofEngineering Symposium (CAFOE) program in 2013.

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