Pseudo-Surface Wave Resonator and Its Applications

8/12/2019 Pseudo-Surface Wave Resonator and Its Applications

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Pseudo-Surface Wave Resonator and its ApplicationsPuck Ja

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Introduction

Optical dielectric microresonators with circular boundaries that support whispering-gallery mode (WGM)resonance, such as microspheres [1], microdisks [2], and microrings [3], have been widely used in

biological and chemical material sensing applications. The high-quality (Q) resonance established bysuch resonators provides the capability of high-resolution spectroscopy thanks to the narrow resonance

bandwidth and the resulting high signal-to-noise (SNR) ratio. Resonance may be acquired by couplinginterrogation light into a microresonator and then detecting an out-coupled signal. When samples presentin the proximity of the microresonator and interact with the evanescent field of the resonating light, the

change of the resonant spectrum provides a detection signal. Detection limits as low as 1E-7 refractiveindex (RI) for bulk refractive index sensing have been experimentally demonstrated [3, 4], and evenlower limits have been predicted through theoretical analysis [1]. Recently, a new type of WGM ring

resonator formed by a thin-wall capillary has also been proposed [5]. While sample flows through thecapillary bore along the longitudinal axis, it can be detected by the optical ring defined along the inner

circumference of the capillary by coupling the interrogation light transversely. Thus, the inner surfaceserves as the wall of the fluidic channel and the sensing surface simultaneously. Such a design has a greatadvantage by separating the sample flow and optical path, which not only reduces the complexity of the

system design but also makes WGM sensing technology feasible for practical applications.

Since WGM microresonators are most sensitive at the sample-resonator interface due to the exponentialdecay profile of the evanescent field, most commonly proposed sensing schemes for WGM resonators are

based on surface binding events, such as immunoassays or detection of surface adsorption. However, the

sensitivity of this model is limited due to the fact that the evanescent wave accounts for only a smallpercentage of the total resonance field. Most of the resonant light resides inside the resonator body and is

isolated from the sample to be sensed. The already-low sensitivity is further reduced in the case ofgaseous samples since the evanescent field intensity decreases when the refractive index contrast between

the sample and resonator becomes greater. In order to improve sensitivity, work has been done toincrease the evanescent field strength. For example, microspheres with higher radii of curvature,microrings with narrower waveguides [3], microspheres coated with high refractive index materials [6],

and liquid ring resonators [7]have been proposed for improved sensitivity. However, because sensitivityalone does not determine the detection limit, considerations such as the ratio of the sensitivity to the

resolution of the specific interrogation method [8]must also be addressed. For example, the resonancequality or the spectral linewidth needs to be maintained to manifest the full advantage of improvedsensitivity.

Due to the low evanescent field, traditional WGM sensors are not optimized for volume sensing

applications, such as bulk refractive index sensing or absorption spectroscopy. The majority of the WGMresonant light resides inside the resonator body and close to the surface and, hence, cannot interact with

the entire sample, especially the portion of the sample distant from the resonator surface. This problem iseven more pronounced for mid-infrared (MIR) applications because the resonator materials commonlyused in WGM sensors have significant material absorption at those wavelengths. Such excessive losscaused by the resonator body results in poor resonance quality and thus prevents traditional WGM sensors

being used in MIR absorption spectroscopy applications.

Here, an inverse type of optical microresonator, which extends a greater portion of resonant light intothe sample volume, is presented so as to provide improved sensitivity for either surface or volumesensing. In traditional WGM microresonator sensor applications [1-7], a resonator body with optically
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denser material guides the light and establishes the evanescent field outside the body through the propertyof total internal reflection (TIR). In the inverse resonator being described, a curved reflective wall is used

to guide the light inside the sample volume to enable use of the full wave for sensing. In one sense, theinverse resonator may be comprehended as a Fabry-Perot resonator with both ends connected to form aninfinite loop. The circulating light continuously bounces around the circular reflective wall and henceforms a light wave that peaks close to the surface. However, this surface-bound field is not an

evanescent wave but constitutes a full wave going through a continuous reflection. Consequently, thisphenomenon has been termed a pseudo-surface wave (PSW). The pseudo-surface wave goes around thecircular boundary and may form resonance once the phases are matched after each loop.

Since PSW resonance can be formed with any circular reflective wallfor example, the cross section of acylindrical structureone natural application of PSW resonance is the detection of analytes in a sample

passing through a circular tube, such as gas/liquid chromatography columns, fluid/gas transport tubing, oreven factory or laboratory plumbing lines. Bulk refractive index sensing or absorption spectroscopy may

be implemented. Since most of the resonating energy of the PSW mode resides in the sample volumeinstead of sensor device itself, the excessive absorption loss issue at the mid-infrared wavelength is

avoided. The inner surface of a PSW resonator also can be modified and functionalized to provide sensingspecificity; the modified PSW mode can be optimized to have high sensitivity to detect chemically or

physically adsorbed samples on the sensing surface. With improved sensitivity, versatile sensingapplications, convenient fluidics design, and simplified optical interrogation, PSW sensors have great

potential in physical, chemical, and biological sensing applications.

The reflective surface of PSW resonators can be formed by metallic mirrors or dielectric mirrors, such as1D or 2D photonic bandgap (PBG) structures. In this report, a PSW model with a perfect electric

conductor (PEC) wall and 1D photonic bandgap wall will be used for analytical and numerical analysis.After the discussion of theoretical model, several coupling schemes will be discussed. Finally, both the

volume and surface sensitivity of the proposed PSW sensors will be analyzed and compared with those ofother WGM sensors.

Pseudo-surface Mode Resonance

Although the fundamental means for light-guiding in a PSW resonator is quite different from that oftraditional WGM resonators, both be modeled with essentially identical mathematical equations but withdifferent boundary conditions since both are morphological-dependent resonances inside a circular cavity.A two-dimension analysis is performed here for the simplicity and for the direct relation to theapplications with tubular structures. The electric field of a transverse-electric (TE) mode inside a simple

PSW resonator with a reflective wall can be described as

wwm

wsm

zrmnkBH

rmnkJAE

);cos()(

);cos()(

0)1(

0, (1)

where mJ is the Bessel function,)1(

mH is the Hankel function of the first kind, 0k is the free-space wavenumber, wr is the inner radius of the PSW reflective wall, and sn and wn are the refractive indices of

the medium (sample) in the borehole and of the wall, respectively.

The transverse-magnetic (TM) equation may be derived with duality. For a reflector of finiteconductivity, the resonant wavelength can be found by matching the boundary conditions. If perfectelectric conduction is used, the electric field in the wall will be zero, and the resonance mode can be

found simply by solving the roots of the Bessel function. The -th root is used to solve for the resonance


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wavelength of the -th radial mode, which has peaks in the field spatial profile along the radial

direction. As shown inFigure 1,the lowest radial order mode ( =1) has only one energy peak along the

radial direction (solid line in the plot), and its position is close to the reflective wall. For higher radial

modes, multiple spatial energy peaks will be distributed along the radial direction with the largest peaklocated closer to the center of the bore. Therefore, the lowest radial order PSW mode may be modified for

surface sensing application, and higher order modes may be used for volume sensing applications.

The azimuthal mode number, m , indicates the number of periods around the circumference of the PSW

resonator. For example, the125

mTE mode shown inFigure 1 has 25 periods along the inner

circumference and one peak on the radial axis. The spatial distributions of a 2D PSW mode and a WGM

mode are visually similar. According to the ray-tracing model [9], the resonance wavelength cantherefore be approximated by

)2/1/(2 mnr scs (2)

where csr is the caustic radius of the resonant mode.

125

mTE

221

mTE

92

mTE

Figure 1.Spatial distributions of PSW resonance with various radial modes: the radial distribution of the 1st

order mode is shown as a solid line, 2nd

order mode as a dashed line, and 9thorder mode as a dotted line.

The azimuthal distribution images are embedded in the plot, and the mode numbers are labeled.

Volume Sensitivity

Sensitivity is directly related to the resonant energy interacting with the sample medium. Therefore, thevolume (bulk) refractive index sensitivity of the PSW sensor will always be optimized because the total

energy always resides inside the sensing zone and is independent of the radial mode order. However, thelower order mode probes closer to the inner surface, while the higher order mode interrogates the regioncloser to the center of the capillary borehole. If the excited mode can be controlled, volume sensing with


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an adjustable probing depth in the radial direction may be possible. The PSW mode excitation/couplingcontrol will be discussed later.

Although most literature expresses bulk refractive index sensitivity reported as a unit of wavelength shiftper unit refractive index change (e.g., nm/RI), such representation is actually operating wavelength-dependent and hence may not be suitable for absolute performance comparison. Therefore, normalized

volume RI sensitivity (NVS), which is defined as )/( dnd , is used in this comparison. Based on Eq.(2),the NVS of a PSW sensor can be expressed by a simple equation,

NVS = sn/1 , (3)

where sn is the bulk refractive index of the sample in the resonator. Based on this model, the NVS of a

PSW sensor to aqueous and gaseous sample is ~0.75 and ~1.00, respectively. For demonstrationpurposes, these values can also be converted back to the traditionally used units. The bulk RI sensitivity

of a PSW sensor with aqueous sample at 980-, 1310-, and 1550-nm wavelengths would be about 735,983, and 1163 nm/RIU, respectively. All these numbers are consistent with the results directly solved

from Eq.(1) at corresponding wavelengths. The NVS of a PSW and a Fabry-Perot (etalon) sensor are

exactly the same, which is expected since both use their full wave in the volume sensing mode.

Modified PSW Modes

Although the lowest order PSW mode has its spatial peak close to the resonator inner surface, the fieldintensity at the interface is actually zero with a PEC wall, which will provide zero sensitivity on that

surface. However, if we modify the PSW inner surface with certain transparent dielectric coatings, thesensing surface is now moved to the interface of the sample/coating surface. As will be shown, theresonant field at the sensing surface may be adjusted from zero to almost the maximum value, depending

on the coating thickness. Therefore, by using a standoff coating layer, the sensitivity of the surfacesensing mode can be adjusted and optimized. The thickness of the standoff layer should be small enough

so that a full guiding mode cannot be formed in the standoff layer.

The electric field of the TE mode in the modified PSW resonator with a standoff coating layer can bedescribed as

wwm

cscmcm

ssm

z

rmnkHD

rrmnkYCmnkJB

rmnkJA

E

);cos()(

);cos()()cos()(

);cos()(

0)1(

00

0

, (4)

where cn and cw rr are the RI and coating thickness. By specifying the coating properties, the

resonance mode can be solved by matching the boundary conditions at wr and cr . The calculated lowest

order modes of a PSW resonator ( wr = 55 m) filled with aqueous solution (RI = 1.333), coated with

standoff layers (RI = 1.45) of various thicknesses (from 0 to 1 m), and interrogated by a light sourcewith wavelength centered about 980 nm are shown inFigure 2. The distribution of the field intensity

square at the sensing zone is plotted against the relative distance from the sensing surface. The points atthe sensing surface are also marked with crosses. The coating thicknesses are specified in the legend.

Note that the sensing surface for the PSW with and without a standoff layer would be on the sample/PECand sample/dielectric interface, respectively.


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When there is no standoff layer (coating thickness = 0), the field intensity is zero at the sensing surface.As the coating thickness increases, the intensity square at the sensing surface starts to grow and reaches a

local maximum value when the coating thickness is about 400 nm. However, the light intensity at thesensing surface can still be increased with a thicker coating. The global maximum value at a sensing spotis reached with a 510-nm coating. With an even thicker coating, such as 600 nm, the peak intensity canincrease further but the intensity at the sensing surface actually decreases.

rc

rw

Figure 2. PSW field intensity square at a distance relative to the sensing surface. The inner diameter is

55 m and filled with aqueous solution (RI = 1.333).

Surface Sensitivity

Based on reported sensitivity studies of WGM sensors [1, 8], the sensing sensitivity is determined by the

energy fraction,, residing at the sampling volume. This same approach can be used here to analyze and

optimize the surface sensing sensitivity of PSW sensors. By assuming small perturbation ( sa nnn )

caused by a thin uniform layer of analyte deposition (RI = an ), the normalized spectral sensitivity (NSS)

can be estimated as

NSS =snn

(5)

according to Ref.10. When other parameters are held constant, the sensitivity will be proportional to theenergy fraction inside the sensing zone, which is then proportional to the field intensity square at the

sensing surface. Comparing Eq.(3) and Eq.(5),it can be seen that NSS is actually a fraction of NVS,which is the maximum available sensitivity, and the energy fraction in the surface sensing zonedetermines the final sensitivity. The energy fraction residing in the analyte deposition volume can be

found out as:


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dvrEr

rEnLr

dvrEr

dvrEr

V

cac

V

sV

20

220

20

20

)()(

)()2(

)()(

)()(

, (6)

where sV is the volume of the surface sensing zone and L is the PSW mode distributed length in the

longitudinal direction, which will have the same contribution to the numerator and denominator and canbe cancelled out if a uniform deposition is assumed.

In order to validate the linear relationship between surface sensitivity and energy fraction, a

computational study of the sensitivity based on a numerical model of a 110-m PSW resonator modifiedby standoff coating layers of various thicknesses was conducted. The spectral shift due to a uniform 1-nmanalyte deposition (RI = 1.45) and the energy fraction within analyte volume were calculated andcompared at an interrogation wavelength of 980 nm. Excellent linearity between spectral shifts andenergy fractions are shown in the top graph ofFigure 3 with standoff layers of 100, 200, 300, 400, 450,

and 510 nm. The R2 value of the linear fit is ~0.999958. The spectral shift and the surface sensitivityreach an optimal value when a 510-nm standoff layer is coated onto the inner surface as is shown in the

bottom plot ofFigure 3. The peak sensitivity reduces slowly when the coating thickness is off the optimal

case, which provides good tolerance on the coating thickness for the optimal sensitivity.

A uniform 1-nm analyte deposition with RI, an = 1.45, was used as the standard to compute the

normalized surface sensitivity. At this optimal sensitivity, about 122-pm spectral shift or NSS = 1.1E-3was observed with the 1-nm analyte deposition.

Figure 3. (top) PSW mode resonant wavelength shift versus the energy fraction at the analyte depositionlayer. (bottom) Resonant wavelength shift versus the thickness of the standoff layer.

Sensitivity Comparison

Based on these computational data, the surface and volume sensitivity of the PSW mode were compared

with corresponding values from several reported WGM sensing studies. Since the sensitivity of these


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sensing platforms is determined by several parameterssuch as the RI contrast, size of the resonator,polarization mode, the interrogation wavelength, etc.all those parameters will be matched in the

following comparison. WGM sensing platforms such as microspheres [4, 6]and liquid-core optical ringresonators [5]with aqueous samples for biological material sensing are often to be found in the literature.Therefore, the comparison of such sensing scenarios will be the focus here. All the sensitivity data in thefollowing discussion are also listed inTable 1 for quick comparison.

Hanumegowda et al. reported volume sensitivity of an uncoated fused silica microsphere (RI = 1.45) with

a diameter of ~110 m in aqueous solution (RI = 1.333) [4]. The reported bulk RI sensitivity was about

30 nm/RI at wavelength ~980 nm, which can be converted to the normalized value NVS = 0.031. Thecalculated bulk RI sensitivity of a PSW sensor of the same size was approximately NVS = 0.75, which isabout 24-fold over the reported microsphere volume sensitivity.

Surface sensitivity was not reported in Ref.4,so the theoretically calculated data based on the

specification will be used in this comparison. First, a numeric microsphere model was established tomatch the reported bulk RI sensitivity in Ref.4,and then the same model was used to compute surfacesensitivity. The normalized surface sensitivity was used in order to provide fair comparisons among

different wavelengths. By using the standardized 1-nm analyte deposition with n =0.117, the calculatedwavelength shift is about 9 pm (NSS = 7.9E-5). The PSW sensor at exactly the same condition hasdemonstrated 122 pm shift (NSS = 1.1E-3), which was a 14-fold improvement over the uncoatedmicrosphere in terms of surface sensitivity. All computation results of PSW and microsphere sensors arelisted in the 2ndand 3rdcolumn ofTable 1,respectively.

Gaathon et al. have reported a sensitivity improvement scheme for microspheres by coating a thin layer of

high-RI material on the outer surface [6]. A 366-m fluorine-doped silica microsphere (RI = 1.43) coatedwith sub-wavelength polystyrene (RI = 1.57) showed a bulk RI sensitivity improvement of about seven-fold over the uncoated version in their study. An optimal coating thickness of ~340 nm was found for

that specific microsphere at a wavelength of 1310 nm. A numerical microsphere model that matched thedescription was also established. The computed NVS of uncoated and coated microspheres were about0.010 and 0.075, respectively, which confirms the reported seven-fold improvement. By comparison, the

PSW sensor (NVS = 0.75) has an advantage of approximately 75-fold over the uncoated sphere and about10-fold over the coated microsphere in terms of the bulk refractive index sensitivity. The PSW advantageshown in this case is even larger because of the weaker evanescent field produced by the largermicrosphere.

As for surface sensitivity, the PSW sensor has a NSS advantage of about 20-fold over uncoated largersphere. The microsphere coated with an optimized high RI layer does show significant surface sensitivityimprovement. Still, the optimized PSW sensor demonstrated more than a two-fold advantage over thecoated microsphere. The calculated results of uncoated and coated microspheres in Ref [6]are listed in

column 4 and 5 ofTable 1,respectively.

A liquid core optical ring resonator (LCORR) reported in Ref.5 uses the internal surface of a thin-wall

capillary as the sensing surface, which has the same advantage in terms of the simplified fluidics designthat is suggested for the PSW sensor. However, the sensitivity of the LCORR has been low even withhigher order modes because of practical limitations in achievable wall thicknesses. Therefore, PSWsensors can easily demonstrate about 250- and 57-fold sensitivity advantages in the volume and surfacesensing modes, respectively. The calculated sensitivities of LCORR are reported in column 6 ofTable 1.

PSW Uncoated 110-mmicrosphere [4]

Uncoated 366-mmicrosphere [6]

Coated 366-mmicrosphere [6]

LCORR [5]


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Volume (NVS) 0.750 0.031 0.010 0.075 0.003(2

ndorder)

Surface (NSS) 1.1E-3 7.9E-5 5.6E-5 4.7E-4 1.9E-5(2

ndorder)

PSW advantage --

vol: 24xsurf: 14x

vol: 75xsurf: 20x

vol: 10xsurf: 2x

vol: 250surf: 57

Table 1. Sensitivity data and comparison to PSW sensor.

The sensitivity advantage of PSW sensors will be even greater for gaseous phase sensing due to the largerrefractive index contrast between the sample and resonator body. For the volume sensing mode, the NVS

of PSW will actually increase by another 25% (from 0.75 to 1.00), while traditional WGM sensors willlose more than 90% of their already low sensitivity. For the surface sensing mode, the sensitivityadvantage of PSW sensors over traditional WGM sensors is expected to be more pronounced withgaseous sample.

In addition to sensitivity, high-Q resonance is also essential to achieve low detection limits. AlthoughPSW sensors using metallic reflective walls may not have high-Q resonance at optical wavelength, the

ones using dielectric mirrors, such as the hollow core photonic bandgap fiber [11], have the potential to

provide a Q factor of ~1E5 at MIR wavelengths. With certain signal processing techniques, spectralresolution as low as 20 femtometers at 1550 nm has been demonstrated with microring resonators, whichhave a Q factor of only around 2E4 [3]. With high sensitivity and low spectral resolution, the detectionlimit for bulk refractive index sensing as low as 1E-8 would be feasible by PSW sensors with moderate Q

factors.

Coupling Method

The excitation of a specific PSW mode is crucial to provide optimized sensitivity for intended sensing

modes for either volume or surface sensing applications. For volume sensing, the uncoated PSW wouldbe appropriate as the sensitivity is independent of the radial mode order. Different radial order modes,

however, provide different peak sensitivities at different sensing depths within the sensing volume.

Since light propagation inside a PSW resonator is a full wave, specific PSW modes in theory may beexcited by a free-space beam though a large pinhole. However, a wavelength-sized or larger pinholewould introduce excessive out-coupling loss, resulting in low-Q resonance. Therefore, sub-wavelength

pinholes should be used to reduce such loss. As the pinhole becomes smaller, the diffraction effectbecomes significant. Because of the diffraction effect, the in-coupling light start to show a sinc-function-profiled far-field pattern originated from a 1D slot. As the slot length reduces the far-field distributionapproaches to an isotropic pattern. Therefore, the single pinhole excitation has little control on thespecific mode due to the lack of beam directivity control. Since the in-coupling beam has its peak

intensity close to the small transmitted angle, higher order modes tend to be excited with a single pinholewithout regard to the local incident angle. Figure 4 shows an example of a high order PSW mode excited

by a focused Gaussian beam through a sub-wavelength pinhole. The resonator diameter is about 6. The

field distribution shown in the plot is calculated by an open source computation engine, MEEP, which is

based on the finite-difference time-domain (FDTD) method and was developed by MIT. All thesimulated PSW resonances are assumed to have PEC walls unless otherwise specified.


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Figure 4. High order PSW mode excitation with a single pinhole.

In order to provide better mode excitation control, multiple holes will need to be used. When multiple

pinholes are fabricated along the circular circumference of the PSW resonator, the phase relationshipbetween the adjacent pinhole can be specified by the local incident angle of the input beam. Thesemultiple pinholes now work something like an arrayed slot antenna that has beam steering capability andhence enables PSW mode excitation control. Another way to perceive the mode coupling control is to use

the phase-matching condition. The phase velocity of the PSW mode propagating around thecircumference can be matched by an oblique incidence beam through multiple pinholes, as is shown inError! Reference source not found..

d

dkpsw

RI = nwd

Figure 5. Phase relationship between two coupling pinholes.

The phase matching condition is

...2,1,0,2)sin(0 NNdnkdk wdpsw , (7)

where d is the distance between pinholes, wdn is the refractive index of the dielectric substrate of the

reflective wall, and pswk and 0k are the wavenumbers of the PSW mode and free-space input beam,respectively. By specifying the local incident angle,

wd

psw

nk

k

0

1sin with 0N , (8)


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the PSW mode with wavenumber , wpsw rmk / , can be selectively excited. Figure 6Error! Reference

source not found.shows the field distribution of the PSW168TE and

262TE mode excited through 11

pinholes on a resonator with diameter of ~12. The pinhole size is about 0.125, with pinholes separated

by 0.4. The separation distance needs to be less than in order to eliminate counter-propagation andgrating modes. The distance between holes does not need to be uniform since the phase information ismaintained with the incident angle.

Figure 6. Computer simulation of PSW168TE (left) and

262TE (right) mode excited through 11 pinholes.

The incident angles that favorably excite different PSW modes at around a 5-m wavelength are listed inTable 2. Although the theoretically calculated incident angle may optimize the coupling efficiency, thereis quite a large tolerance on the incident angle observed in the simulation results with only 11 pinholes.

The trade-off between mode specificity and input angle tolerance can be controlled with the number of

pinholes. Since a planar surface is assumed in Eq.(8),the phase error due to a curved surface on thePSW resonator needs to be considered when a large number of holes, small radius, or higher degree mode

control is required.

Mode Wavelength (nm) Incident angle (degree) Angular change

TE 68_1 4971.7 36.43 --

TE 62_2 4984.2 32.88 3.55

TE 57_3 5003.0 30.06 2.82

TE 53_4 4990.9 27.69 2.37

Table 2. Incident angles for various PSW mode excitations using multiple pinholes.The fabrication of pinholes on the metallic reflector can be achieved with a laser ablation process. A

nano-second pulsed nitrogen laser has been used to prototype pinholes. Pinholes of several micrometerscan be easily fabricated with manual control. Smaller pinholes may be achieved with higher power,shorter pulse, and a computer-controlled process. Due to the requirement for sub-wavelength pinholes,

the fabrication of PSW sensors for longer wavelengths will easier and more cost effective.

The purpose of using sub-wavelength pinholes is to reduce the coupling loss so that the resonance qualityfactor can be maintained. Based on this objective, a partially removed reflective layer may also be usedto achieve the same purpose. Thinning down a patch of metallic reflector or a section of photonic crystal

wall are two examples of alternative methods to achieve PSW mode coupling.


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Thanks to their low loss materials, hollow-core photonic bandgap (PBG) fibers are good candidates for

high-Q PSW resonators. The coupling port may be formed by partially removing the periodic multi-layerstructure using either chemical etching or laser ablation. The PSW mode resonance and coupling weredemonstrated with a FDTD simulation example. A PSW resonator was formed with a 10 bi-layer PBG

wall and inner diameter of 12. At the coupling port, the PBG wall was partially thinned with only about

four bi-layers remaining. The free space input beam was incident on the coupling port with a local

incident angle matched to the desired PSW mode. Figure 7 shows the simulation results of a PSW163TE

mode excited with specified conditions. The phase matching condition in Eq.(8) is still applied.However, the directivity of transmitted input beam is less well defined than that produced by the multiple

pinholes, and hence the PSW mode excitation is less tightly controlled with this configuration.

Figure 7. Computer simulation of PSW 163TE mode excited through a partially removed PBG wall

Sensor Interrogation

The interrogation methods of PSW sensors are similar to those for traditional WGM sensors. Either anarrow-band tunable light source in conjunction with a wide-band light detector or a wide-band light

source with a narrow-band detector (spectrometer) may be used. In either case, the spectral position ofcertain features in the resonant spectrum is monitored. The direct spectral shift of the spectral feature or

the intensity change due to the spectral shift is tracked and recorded as the sensorgram during the sensingapplication.

Also similar to the WGM sensor, the interrogated PSW signal may be t he through port or the drop

port, to use telecommunication terminology. The through port signal is formed by the interferencebetween the reflected input light and the out-coupling light from the resonator. Spectral dips or nulls willbe formed at the resonant wavelengths. The drop port signal, on the other hand, is simply the leakage ofthe PSW resonant energy and consequently has spectral peaks at the resonance wavelengths. Even using

only a single coupling port, the through and drop port signals may be acquired through same couplingspot but with different light collection angles. However, the exact morphology of the coupling port suchas arrayed pinholes or the defect of a PBG could shift the collection angle. For example, the reflection ofthe input signal from the multiple pinholes is quite different from that reflected with a thinned PBG wall.


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The signal collected around the specular reflection angle can be changed from through port to a mixing ofboth through and drop port depending on the coupling port structure and the collection angle.

FDTD simulation was also used to demonstrate the interrogation of the PSW spectrum. Figure 8 showsthe computed signal spectra acquired at one sampling point outside of the resonator and another oneinside the resonator close to the wall. The top dotted trace is the field spectrum acquired close to the

specular reflection point and exhibiting the features of a through port spectrum, while the bottom solidtrace collected close to the inner wall showed the drop port spectrum with matched peaks. Either thethrough port or the drop port spectrum acquired outside of resonator can be used for sensing applications.

Figure 8. The PSW through port (top trace) and in-cavity (bottom trace) resonant spectra simulated byFDTD method.

Applications

Up to now, our discussion of PSW resonators has concentrated on sensing applications. However, PSWresonators may also be of use as laser cavities. Due to the tunable peak location of the resonant field, thegain medium can either be filled in the borehole or coated on the inner surface of a PSW resonator.Similar to the previously described examples of volume and surface sensing modes, higher order modes

will be suitable for a PSW resonator filled with gain media, and lowest order modes with a standoffcoating layer will be optimal for the resonator with coated gain medium. In addition to using PSW

resonators as miniaturized lasing source, the PSW-based laser cavity also opens up new possibilities forsensing applications. For example, lasing action has been observed by a modified PSW resonator coatedwith a thin layer of amplifying fluorescence polymer (AFP) materials used for explosives detection on top

of the standoff layer. The still-open borehole allows air sample to flow through and interact with theAFP. Since the AFP emission will be quenched in the presence of certain explosives, the nonlinear nature

of the lasing action can be taken advantage of to enhance the sensitivity of the explosive detection.

Volume Sensing Mode

In non-lasing related applications, a PSW resonator can be configured and optimized to operate in the

surface or volume sensing mode as illustrated in above discussion. Here we will use some examples tofurther illustrate potential applications of PSW sensor in the volume and surface sensing mode. Forvolume refractive index sensing applications, the bulk refractive index of the material flowing through the

borehole will be detected. As noted above, it has been theoretically demonstrated that a PSW sensorinherently has the maximum bulk refractive index sensitivity. In addition to direct refractive index


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sensing, other parameters such as temperature, pressure, concentration, etc. also can be in-directlydetected due to their effect on the bulk refractive index.

When a thick layer of transparent dielectric layer is coated on the reflective wall of a PSW resonator, adifferent volume sensing mode with its sensing zone focused inside the coated dielectric layer can beachieved. The coating thickness is significant enough so that the majority of resonant energy resides in

the coated layer. The coating is also admissive to allow analytes to diffuse in and out of the coated layerfrom the vapor or liquid phase sample flow. Polymeric or porous dielectric materials are potential coatingcandidates. Such coatings may provide high sensitivity to a selective group of analytes with or withoutadditional sensitization process. PSW resonators with such thick coating layers may be used as detectorsfor gas/liquid chromatography. Note that this configuration of PSW volume sensor with thick admissivecoating layer is different from the PSW surface sensor with thin coating layer.

PSW resonators also may be used as miniaturized long path-length absorption cells. The high-Qresonance allows the interrogation light interacting with the sample in the borehole a long time to enhancesensitivity. As was mentioned, a PSW resonator provides a unique advantage for the application in the

mid-infrared (MIR) wavelength, where most traditional WGM sensors have not been considered due toexcessive absorption loss from the resonator body. However, only very small amounts of PSW energy

resides inside the resonator body (evanescent field inside the reflective wall) so that the resonance qualityand the sensing performance will not be degraded significantly at MIR wavelengths. Such unique featureenables PSW sensors to be used in this niche application.

Surface Sensing Mode

For surface sensing applications, the modified PSW sensor can provide more than an order of magnitudeof sensitivity improvement over traditional WGM sensors. A thin standoff layer of dielectric coating on

the reflective wall needs to be optimized according to the sensing application so that the maximumsurface sensitivity may be available on the sensing surface. In order to provide sensing specificity, thesensing surface may be sensitized to physically adsorb or chemically bind certain analytes. Immunoassay

in biosensing applications is a typical example of surface sensing.

The inner sensing surface also can be sensitized with different analyte binders or sorbent materials todetect different targets. Multiple pieces of differently sensitized PSW resonators can be connected toachieve multiple target detection or array sensing capabilities. Since the PSW mode spreading width inthe longitudinal direction is around wavelength scale, high throughput screening tests may beimplemented with densely packed PSW sensing. The free-space interrogation scheme also allows

multiple sensing elements to be interrogated simultaneously via imaging techniques, which could providesignificant advantage in an array sensing scheme.

Since the sample flow is confined inside the PSW bore and the optical interrogation is conducted outsideof the PSW wall, the separation of sample path and optical path dramatically reduces the complexity of

system design, which allows the practical implementation of as PSW in sensing devices. There is noadditional need to design the flow channel or near-field optics for optical coupling and sensor

interrogation. Because the PSW excitation is achieved via free-space excitation, disposable sensingelement sand non-contacting sensor interrogation are possible. Such features may be critical in some

biosensing and medical diagnosis applications where contamination would be a great concern.

The advantages of PSW sensors can be summarized as:

1. Optimized sensitivity for either surface or volume sensing mode2. Simplified fluidics and optics design


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3. Array sensing capability4. Free-space coupling5. Low-cost and disposable sensing elements6. Niche sensing applications at longer wavelengths, such as mid-infrared or tera-hertz.

References:

1. Arnold, S., Khoshsima, M., Teraoka, I., Holler, S., and Vollmer, F., "Shift of whispering-gallerymodes in microspheres by protein adsorption," Optics Letters, 28, 272, 2003.

2. Krioukov, E., Klunder, D. J. W., Driessen, A., Greve, J., and Otto, C., "Sensor based on an integratedoptical microcavity," Optics Letters, 27, 512, 2002.

3. Ja, S.-J. Integrated optical microring for high-resolution refractive index and pressure sensingapplications,Proceedings of SPIE, 6538, SPIE Defense and Security Symposium, 2007.

4. Hanumegowda, N., Stica, C., Patel, B., White, I., and Fan, X., "Refractometric sensors based onmicrosphere resonators,"Applied Physics Letters, 87, 201107, 2005.

5. White, I. M., Oveys, H., and Fan, X., "Liquid-core optical ring-resonator sensors," Optics Letters, 31,1319, 2006.

6. Gaathon, O., Culic-Viskota, J., Mihnev, M., Teraoka, I., and Arnolda, S., "Enhancing sensitivity of awhispering gallery mode biosensor by subwavelength confinement,"Applied Physics Letters, 89,223901, 2006.

7. Sumetsky, M., Windeler, R. S., Dulashko, Y., and Fan, X., "Optical liquid ring resonator sensor,"Optics Express, 15, 14376, 2007.

8. White, I. M., and Fan, X., "On the performance quantification of resonant refractive index sensors,"Optics Express, 16, 1020, 2008.

9. Roll, G. and Schweiger, G., "Geometrical optics model of Mie resonances,"J. Opt. Soc. Am. A, 17,1301, 2000.

10.Zhu, H., White, I. M., Suter, J. D., Dale, P. S. and Fan, X., "Analysis of biomolecule detection withoptofluidic ring resonator sensors," Optics Express, 15, 9139, 2007

11.Temelkuran, B., Hart, S. D., Benoit, G., Joannopoulos, J. D., and Fink, Y., "Wavelength-scalablehollow optical fibres with large photonic bandgaps for CO2 laser transmission,"Nature, 420, 650,

2002.

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Pseudo-Surface Wave Resonator and Its Applications

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