Hallynck, Elewout

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Ghent University Academic Bibliography

Photonic crystal biosensingElewout HallynckSupervisor(s): Peter BienstmanI. INTRODUCTIONPhotonic crystals (PhCs) are structures ex-hibiting a periodic variation of the refractiveindex (see Figure 1). Due to this periodicity,light of certain wavelengths will interfere de-structively with itself. We call this property aphotonic band gap (named after a similar phe-nomenon found in electronics: the electronicband gap). The photonic band gap is illustratedin Figure 2.Figure 1. Photonic crystal with periodicity in 2 di-mensions. Also displayed are the two main di-rections of light propagation: ΓM and ΓK.The position and width of this band gap inPhCs strongly depend on the refractive indexof the material in the holes. This fact can beexploited to create a biosensor: when the re-fractive index of the material in the PhC holeschanges (e.g. because of binding between thePhC and the sample) we can measure the shiftof the lower or upper band gap edge of the PhC—————————————————–E. Hallynck is with the Department of In-formation Technology (INTEC), Ghent Uni-versity (UGent), Gent, Belgium. E-mail:Elewout.Hallynck@intec.ugent.be .(see also Figure 2 where the lower band gapedge shifts from λ1 to λ3 and the upper bandgap edge from λ2 to λ4).WavelengthTransmission10WavelengthTransmission10l1 l4 l2l3Figure 2. Transmission as a function of wavelengthin a uniform lossless medium (left) and periodiclossless medium (right).II. INCREASING THE SENSITIVITYIn general, when designing a sensitivebiosensor, one has to make sure there is asmuch interaction as possible between the lightcoupled into the chip and the sample onewishes to analyse - keeping in mind the tech-nological limitations for eventual fabrication.In the case of a PhC biosensor this means thatone wants to concentrate the electric field ofthe light in the holes of the crystal as this iswhere the actual sample to be measured is lo-cated.There are three important guidelines to con-sider when designing a PhC biosensor: (1) theelectric field of the second band mode is muchmore concentrated in the low refractive indexregions compared to the first band mode; (2)the greater the diameter of the PhC holes, themore the field is concentrated in the holes; (3)the ΓM direction is more sensitive than the ΓKdirection. These guidelines are the result oftheoretical considerations and extensive simu-lations using both a plane wave expansion [1]and FDTD [2] method.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450100200300400500600Hole radius (a)Shift (nm/RIU)  GK band 1GM band 1GK band 2GM band 2Figure 3. Silicon photonic crystal membrane (a pho-tonic crystal structure based on refractive indexconfinement in the vertical direction) band gapshift as a function of hole radius for differentcombinations of ΓM, ΓK and lower and upperband gap edge. Thickness of membrane is 0.4times the lattice constant.(1) is a consequence of the variational the-orem [3] which states that a light mode aimsto minimize its electromagnetic energy func-tional. It can do so by concentrating itself inregions of high refractive index and by lower-ing the amount of spatial oscillations while re-maining orthogonal to lower-frequency modes.Because the first mode - at a low frequency - isconcentrated mainly in the high refractive in-dex region, the second mode is forced into thelower refractive index region, at a higher fre-quency.When looking at Figure 3, it can be seen thatthe sensitivity scales with the square of the holeradius. This agrees with what one intuitivelywould conclude since the volume of PhC holesalso scales with the square of the radius.The theoretical explanation behind the thirdguideline is based on field continuity condi-tions.These three guidelines are illustrated in Fig-ure 3.A shift as high as 613 nm/RIU (RefractiveIndex Unit) has been calculated. This shift hasbeen achieved when considering the shift of theupper band gap edge in the ΓM direction in aPhC membrane with a hole radius of 0.42 timesthe lattice constant. This agrees with all threebeforementioned guidelines. The shift can beeven higher when increasing the hole radiusbut due to technological constraints, this is notalways possible.III. COMPARISON WITH OTHERBIOSENSORSHere we make a comparison between sev-eral other photonic biosensors and the struc-ture discussed in this paper. A more exten-sive overview of available biosensors and theircharacteristics can be found in [4].Table 1. Comparison in sensitivity between photoniccrystal biosensor and other biosensors.Biosensor type Sensitivity (nm/RIU)Ring resonator 70Slotted ring resonator 200PhC with resonant defect 200Photonic crystal 613Surface plasmons 630One can see from Table 1 that the PhCbiosensor is only slightly less sensitive than asurface plasmon based biosensor but far moresensitive than ring resonator based ones or aPhC with defect.IV. CONCLUSIONWe have shown that it is possible to design avery sensitive photonic crystal biosensor whenkeeping in mind a few simple design guide-lines. Sensitivities of 613 nm/RIU and moreare possible (depending on technological limi-tations).REFERENCES[1] Steven G. Johnson and J. D. Joannopoulos, Op-tics Express, Vol. 8, No. 3, 173-190, 2001.[2] Ardavan Farjadpour et al, Optics Letters, Vol. 31,No. 20, 2972-2974, 2006.[3] John D. Joannopoulos, Steven G. Johnson,Joshua N. Winn and Robert D. Meade, PhotonicCrystals - Molding the Flow of Light, PrincetonUniversity Press, 2008.[4] Xudong Fan et al, Analytica Chimica Acta 6208-26, 2008.

Photonic crystal biosensing

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Photonic crystal biosensing

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