《电动力学》课程参考文献：Cerenkov Radiation in Photonic Crystals

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REPORTS the position, and t is the time. Bloch waves Cerenkov radiation in photonic rise from the resonance of a planewave source with the photon dispersion relation Cryst (1) Chiyan Luo, Mihai Ibanescu, Steven G. Johnson, where o is the frequency, n is the band index, the wave vector k can include an arbitrary 」D. Joannopoulos reciprocal lattice vector G, and o (k) w (k+ G. The CR consists of modes satis In a conventional material, the coherent Cerenkov radiation due to a moving fying Eq. 1(24), which can be found in k charged particle is associated with a velocity threshold, a forward-pointing adiation cone. and a forward direction of emission We describe different behavior for the Cerenkov radiation in a photonic crystaL. In particular, this A0.5 adiation is intrinsically coupled with transition radiation and is observable without any threshold within one particle-velocity range, we found a radiation pattern with a backward-pointing radiation cone. In another velocity range, backward-propagating Cerenkov radiation can be expected Potential applica tions include velocity-sensitive particle detection and radiation generation at 0.2 selectable frequencies 80.1 When a charged particle travels inside a medi- charge crosses a dielectric boundary or expe- um,it can drive the medium to emit coherent riences an inhomogeneous dielectric environ X electromagnetic energy called Cerenkov radia- ment, and the conventional Cr, in which B 0.5 tion(CR)(). Extensively used in particle de- coherence is preserved throughout the medi- tectors and counters(2), CR in a conventional um. Both effects are incorporated in our ap- material possesses three key characteristics: it proach. However, unlike the Smith-Purcell 3 X occurs only when the particles velocity ex- effect, in which radiation is generated via a ceeds the mediums phase velocity, the energy periodic grating but then propagates through 0 =a/ propagates only in the forward direction, and a uniform medium, this Cr is generated and there is a forward-pointing conical wavefront. propagates within the same crystal in the These characteristics remain qualitatively un- form of Bloch waves. The properties of these -0.5 hanged even in the presence of material dis- Bloch waves can be substantially different 15 persion (3-6). One possible source of unusual from waves in a uniform medium, leading to Kz(2/a) CR is in a medium with simultaneously nega- effects not previously anticipated. In one tive permittivity and permeability, commonly case, we can reverse the overall cone that C known as a negative-index material for its re- encloses all traveling electromagnetic energy versal of Snells law of refraction (7-12), inIn another situation, we demonstrate a back- which CR is predicted to flow backward; i.e., ward-propagating CR behavior reminiscent o033Eo opposite to the particle velocity (7). Another of that predicted in negative-index materials possibility exists near a periodic structure, These are very general results based on direct where simple Bragg scattering of light can give solutions of Maxwells equations and should rise to radiation without any velocity threshold. find applications in particle detection and This was first confirmed by Smith and Purcell wave production techniques 3)in early experiments with electrons travel For simplicity, we focus on a two-dimen ing near the surface of a metallic grating. Cr sional photonic crystal(Fig. 1). Let a charge has since been studied in one-dimensionally q move in the (01) direction of a square periodic multilayer stacks (14, 15), and the lattice of air holes in a dielectric, in the xz Smith-Purcell effect has been extended to near plane, with parameters as specified in the Fig. Fig. 1. Band structure and analysis of cr in a the surface of dielectric structures(16, 17).A 1 legend. Figure 1A shows the calculated tonic crystal.(A) Transverse electric band photonic crystal (18-20), where very complex transverse electric(the electric field in the xz structure of a two-dimensional square lattice of Bragg scattering is possible, presents a rich new plane, appropriate for CR) band structure of air columns in a dielectric dielectric constant e medium for unusual photon phenomena(21- this photonic crystal. We take the particle's lattice period. The crystal structure and the ent particle-velocity regime tric interfaces(Fig. IB, inset). As a reference. nter, and corner of the first Brillouin zone. B) CR in a photonic crystal arises ity(v)of Method of oherent excitation of its eigenmodes this photonic crystal is ve=0. 44c(where c is sects a photonic-crystal dispersion surface. Blu moving the speed of light). The excited radiation can arrows indicate the group velocities of CR transition radiation, which occurs when the be determined by treating the charge as a modes.(C)Method of obtaining CR cone source with space-time dependence 8(r-vr)= shapes. The group velocities for all modes ob- Department of Physics and Center for Materials e, eikr-ik'v, that is, as a superposition of tained in(B)form a contour. a is the cone angle anewaves with different wave vecto es the angle for the overall radiation cone Technology, Cambridge, MA 02139, USA frequencies k. v, where 8 is the Dirac delta ay dashed lines). The angular density of *To whom correspondence should be addressed. E- function, e is the base of the natural loga- the arrows roughly reflects the CR angular rithm, i is the unit of imaginary numbers, ris distribution 17JanUary2003Vol299ScieNcewww.sciencemag.org

Cerenkov Radiation in Photonic Crystals Chiyan Luo, Mihai Ibanescu, Steven G. Johnson, J. D. Joannopoulos* In a conventional material, the coherent Cerenkov radiation due to a moving charged particle is associated with a velocity threshold, a forward-pointing radiation cone, and a forward direction of emission. We describe different behavior for the Cerenkov radiation in a photonic crystal. In particular, this radiation is intrinsically coupled with transition radiation and is observable without any threshold. Within one particle-velocity range, we found a radiation pattern with a backward-pointing radiation cone. In another velocity range, backward-propagating Cerenkov radiation can be expected. Potential applications include velocity-sensitive particle detection and radiation generation at selectable frequencies. When a charged particle travels inside a medium, it can drive the medium to emit coherent electromagnetic energy called Cerenkov radiation (CR) (1). Extensively used in particle detectors and counters (2), CR in a conventional material possesses three key characteristics: it occurs only when the particle’s velocity exceeds the medium’s phase velocity, the energy propagates only in the forward direction, and there is a forward-pointing conical wavefront. These characteristics remain qualitatively unchanged even in the presence of material dispersion (3–6). One possible source of unusual CR is in a medium with simultaneously negative permittivity and permeability, commonly known as a negative-index material for its reversal of Snell’s law of refraction (7–12), in which CR is predicted to flow backward; i.e., opposite to the particle velocity (7). Another possibility exists near a periodic structure, where simple Bragg scattering of light can give rise to radiation without any velocity threshold. This was first confirmed by Smith and Purcell (13) in early experiments with electrons traveling near the surface of a metallic grating. CR has since been studied in one-dimensionally periodic multilayer stacks (14, 15), and the Smith-Purcell effect has been extended to near the surface of dielectric structures (16, 17). A photonic crystal (18–20), where very complex Bragg scattering is possible, presents a rich new medium for unusual photon phenomena (21– 23). We reveal a variety of CR patterns that can occur in a single photonic crystal under different particle-velocity regimes. CR in a photonic crystal arises from a coherent excitation of its eigenmodes by the moving charge. Its origin lies in both the transition radiation, which occurs when the charge crosses a dielectric boundary or experiences an inhomogeneous dielectric environment, and the conventional CR, in which coherence is preserved throughout the medium. Both effects are incorporated in our approach. However, unlike the Smith-Purcell effect, in which radiation is generated via a periodic grating but then propagates through a uniform medium, this CR is generated and propagates within the same crystal in the form of Bloch waves. The properties of these Bloch waves can be substantially different from waves in a uniform medium, leading to effects not previously anticipated. In one case, we can reverse the overall cone that encloses all traveling electromagnetic energy. In another situation, we demonstrate a backward-propagating CR behavior reminiscent of that predicted in negative-index materials. These are very general results based on direct solutions of Maxwell’s equations and should find applications in particle detection and wave production techniques. For simplicity, we focus on a two-dimensional photonic crystal (Fig. 1). Let a charge q move in the (01) direction of a square lattice of air holes in a dielectric, in the xz plane, with parameters as specified in the Fig. 1 legend. Figure 1A shows the calculated transverse electric (the electric field in the xz plane, appropriate for CR) band structure of this photonic crystal. We take the particle’s motion to be in the z direction and consider a path where the particle does not cross dielectric interfaces (Fig. 1B, inset). As a reference, the long-wavelength phase velocity (vc) of this photonic crystal is vc 0.44c (where c is the speed of light). The excited radiation can be determined by treating the charge as a source with space-time dependence (r–vt) k eik r – ik vt , that is, as a superposition of planewaves with different wave vectors k and frequencies k v, where is the Dirac delta function, e is the base of the natural logarithm, i is the unit of imaginary numbers, r is the position, and t is the time. Bloch waves arise from the resonance of a planewave source with the photon dispersion relation n(k) k v (1) where is the frequency, n is the band index, the wave vector k can include an arbitrary reciprocal lattice vector G, and n(k) n(k G). The CR consists of modes satisfying Eq. 1 (24), which can be found in k Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. *To whom correspondence should be addressed. Email: joannop@mit.edu Fig. 1. Band structure and analysis of CR in a photonic crystal. (A) Transverse electric band structure of a two-dimensional square lattice of air columns in a dielectric (dielectric constant ε 12) with column radii r 0.4a, a being the lattice period. The crystal structure and the irreducible Brillouin zone are shown as insets. , X, and M are, respectively, the center, edge center, and corner of the first Brillouin zone. (B) Method of solving Eq. 1 in k space. CR occurs when the kz /v plane (dashed line) intersects a photonic-crystal dispersion surface. Blue arrows indicate the group velocities of CR modes. (C) Method of obtaining CR cone shapes. The group velocities for all modes obtained in (B) form a contour. is the cone angle for the mode with group velocity u, and m gives the angle for the overall radiation cone (gray dashed lines). The angular density of the arrows roughly reflects the CR angular distribution. R EPORTS 368 17 JANUARY 2003 VOL 299 SCIENCE www.sciencemag.org on June 8, 2007 www.sciencemag.org Downloaded from

REPORTS intersecting the plane o= k v with charged particle in the same time. Thus, the possess a backward-pointing overall cone the dispersion surface o= o (k)(Fig. IB). radiation wavefront for each mode lies on a (o >T/2), according to the analysis of Fig The CR behavior in real space, however, "group cone"(3, 6) with its apex on the 1C. This is therefore the reversed-cone re must be obtained from the group velocity u= moving particle and a half-apex angle a, the gime. Such a reversed cone is forbidden by dwak; that is, the gradient vector to a disper- angle between v-H and v. A superposition causality (1) in a uniform passive medium. on surface. which can be shown to be of all group cones gives the overall CR pat- 3)In the - 0. 2csvs-04c regime, all energy transport vector for each mode(25). term, and the maximum angle am of all such the radiation modes in the lowest emission The emission angle is given by the direction as is the half-apex angle for the overall cone. band reside in the region t/a 0 in this regime (where k' is the portional to the distance traveled by the For an electron traveling near a grating sur- Bloch-reduced k in the first Brillouin zone), face, one employs the dispersion relations of the photonic crystal may be regarded as an air along with diffraction to obtain the Smith- effective positive-index medium (22). W A Purcell radiation call this the backward- flux regime In the present photonic crystal, we solved 4) In the v 2 v regime, the solution to Eq 0.2 Eq. 1 using photon bands calculated by I starts from zero frequency, and the group- planewave expansion(27). We focused on velocity g0.1 06 higher-order modes with larger G or in higher now travels faster than all of the excited? bands can be analyzed similarly. Figure 2 modes, and constructive interference is 0.15 06010.2 0.40. 0.8 We see that for v v the familiar CR with a sharp for- -0.4-0.20 tonic band edge are in coexistence with the ward-pointing cone as in a uniform medium uz(c) fast modes. As can be seen from the group is recovered. The angular distribution of ra- velocity contours, in going from v= 0.lc to diation is directly visible (Fig. 3B).When Fig. 2. Calculated CR modes wit v=0.15c. the modes in the forward direction v=0.1c or 0.15c. the radiation is distributed begin to travel slower than the charged par- over a wide range of emission angles without (A)The CR emission band structure ticle(and can even have negative group ve- producing a cone of intensity maxima. For in the first photonic band as a function of locities), eventually producing a contour at = 0.3c or 0.6c, however, the Cr becomes different CR behaviors. (B) The solution k for a v=0. 15c that winds around without enclos- collimated, and a definite emission angle in few vs indicated by the numbers in italics. (c) ing v Because in this band there are some fast both the forward and the backward direction The group velocity contours for the represe modes in the forward direction whose u, ex- for most of the radiation energy can be ob- ative values of v ceeds v, the radiation pattern here should served. In particular, the crystal-induced dis- www.sciencemagorgSciEnceVol29917JanUary2003

space by intersecting the plane k v with the dispersion surface n(k) (Fig. 1B). The CR behavior in real space, however, must be obtained from the group velocity u /k; that is, the gradient vector to a dispersion surface, which can be shown to be the energy transport vector for each mode (25). The emission angle is given by the direction of u. Moreover, the radiation pattern can be deduced from u via the group velocity contour (Fig. 1C). We plot both the charge velocity v and the group velocities u of all the CR modes in a velocity space (26). The magnitude of u is proportional to the distance traveled by the wavefront of the associated photon mode, and the magnitude of v is proportional to the distance traveled by the charged particle in the same time. Thus, the radiation wavefront for each mode lies on a “group cone” (3, 6) with its apex on the moving particle and a half-apex angle , the angle between v u and v. A superposition of all group cones gives the overall CR pattern, and the maximum angle m of all such ’s is the half-apex angle for the overall cone. Propagating Bloch modes can only exist on the rear side of this overall cone, whereas the radiation fields are evanescent on the forward side, and across the overall cone the radiated field amplitude experiences a drop. In the special case of a uniform material, only the G 0 modes are excited and our approach yields the characteristics of conventional CR. For an electron traveling near a grating surface, one employs the dispersion relations of air along with diffraction to obtain the SmithPurcell radiation. In the present photonic crystal, we solved Eq. 1 using photon bands calculated by planewave expansion (27). We focused on the solutions with the lowest frequencies; higher-order modes with larger G or in higher bands can be analyzed similarly. Figure 2 shows the results for the CR emission frequency , wave vector k, and group velocity u. We see that for v vc , the radiation coalesces into Smith-Purcell resonances around G v. For larger v, the resonances merge together to form emission bands outside which CR is inhibited (Fig. 2A). As v increases, k and u within each emission band are strongly influenced by the photonic band structure. We can identify four regimes of the charge velocity (Fig. 2, B and C) with four qualitatively different CR behaviors in a photonic crystal: 1) v 0.1c corresponds to the SmithPurcell regime, in which the CR arises primarily through constructive interference between consecutive unit cells and in the first emission band corresponds to the first resonance near kz 2 /a, where a is the lattice period. The group velocity contour is approximately circular, with radius vc. Because v vc, the overall wavefront will be roughly circular and centered on the slowly moving particle. 2) The regime v 0.15c is unique to the photonic crystal: The first and higher SmithPurcell resonances merge into one band, in which the slow photon modes near the photonic band edge are in coexistence with the fast modes. As can be seen from the group velocity contours, in going from v 0.1c to v 0.15c, the modes in the forward direction begin to travel slower than the charged particle (and can even have negative group velocities), eventually producing a contour at v 0.15c that winds around without enclosing v. Because in this band there are some fast modes in the forward direction whose uz exceeds v, the radiation pattern here should possess a backward-pointing overall cone (m /2), according to the analysis of Fig. 1C. This is therefore the reversed-cone regime. Such a reversed cone is forbidden by causality (1) in a uniform passive medium. 3) In the 0.2c v 0.4c regime, all the radiation modes in the lowest emission band reside in the region /a kz 2 /a with uz 0, which implies that the energy flows opposite to v in this band. The overall cone is now pointing forward and, as described below, the radiation becomes collimated in a backward direction. CR here is strongly similar to the predicted behavior in a negative-index material. However, because k u 0 in this regime (where k is the Bloch-reduced k in the first Brillouin zone), the photonic crystal may be regarded as an effective positive-index medium (22). We call this the backward-flux regime. 4) In the v vc regime, the solution to Eq. 1 starts from zero frequency, and the groupvelocity contour becomes an open-ended curve with positive uz . The charged particle now travels faster than all of the excited modes, and constructive interference is achieved throughout the whole photonic crystal. This behavior is identical to CR in a normal dispersive medium. Hence, this is the normal regime. The CR showed less interesting transitional behavior for intermediate charge velocities between these regimes. For example, when 0.4c v vc , the CR showed a mixture of forward and backward emissions similar to that depicted in Fig. 1C. We confirmed our analysis by performing finite-difference time-domain (FDTD) simulations of radiation for a moving charge in this photonic crystal (28). We reproduce in Fig. 3A the velocity diagrams from Fig. 2C and present the resulting radiation-field simulations in Fig. 3B. To quantitatively demonstrate the backward radiation, we also plot in Fig. 3C the simulated flux through a fixed line perpendicular to v as a function of . At the low velocity, v 0.1c, the radiation shows a Smith-Purcell behavior of near-isotropic wavefront. As the velocity increases to v 0.15c, the overall radiation cone indeed reversed as predicted. Further increasing of v to v 0.3c steers the radiation to the backward direction, and if v is increased to v 0.6c vc the familiar CR with a sharp forward-pointing cone as in a uniform medium is recovered. The angular distribution of radiation is directly visible (Fig. 3B). When v 0.1c or 0.15c, the radiation is distributed over a wide range of emission angles without producing a cone of intensity maxima. For v 0.3c or 0.6c, however, the CR becomes collimated, and a definite emission angle in both the forward and the backward direction for most of the radiation energy can be observed. In particular, the crystal-induced disFig. 2. Calculated CR modes with the lowest frequencies for the photonic crystal of Fig. 1. (A) The CR emission band structure (red region) in the first photonic band as a function of v. Colored vertical lines mark representative vs for different CR behaviors. (B) The solution k for a few vs indicated by the numbers in italics. (C) The group velocity contours for the representative values of v. R EPORTS www.sciencemag.org SCIENCE VOL 299 17 JANUARY 2003 369 on June 8, 2007 www.sciencemag.org Downloaded from

REPORTS persion at v=0.6c becomes so small that a these tails can exhibit a backward radiation centimeter, which should be amenable to strong intensity peak cone is formed and effect as well. rect experimental observation. almost overlaps with the overall cone. a clear The effects presented here can be extend- A number of applications also appear pos distinction between the Cr behaviors for vvs is that for v >vs the measured with little change. As a complete photonic phase-velocity threshold cannot be detected by flux in the z direction is positive over the band gap in three dimensions is not required, conventional CR counters, and currently their emission band, but for v v an electron can emit hundreds sources for frequencies that are otherwise typically have smaller group velocities and of photons per centimeter of its path. Thus, difficult to access. thus form dense forward-pointing cones for the velocities studied here. the emission smaller angles, as first predicted in(6)(for rates correspond to a range starting from coherently driven slow-light media). Here roughly 10 and ranging up to 200 photons per 1.L D. Landau, E M. Liftshitz, L p. Pitaevski, Electro- 0.1c v=0.15c V=0.3c v=0.6c Pergamon, London, 1958). 3. L M. Frank, Nuc Instrum. Methods Phys. Res. Sect. A 248.7(1986 4. G. N. Afanasiev, V. G. Kartavenko, E. N. Magar. 5. T. E. Stevens, I. K Wahlstrand, ]. KuhL R. Merlin, o033Eo Science291.627(2001) 6. I Carusotto, M. Artoni, G.C. L Rocca, F. Bassani, Phys no cone a.>/2 1/2 J. B. Pendry, A. J. Holden, w.J. Stewart, L Youngs, B IEEE Trans. Microwave Theory Tech. 10. D. R. Smith, W.J. Padilla, D. C. Vi Nasser, S.Schultz, Phys. Rev. Lett. 84, 4184(2000 11. R A Shelby, D. R. Smith, S. Schultz, Science 292, 77 13.5.」smth,E 15. B. Lastdrager, A. Tip, J. Verhoeven, Phys. Rev. E 61 5767( Abajo, Phys. Rev. Lett. 82, 2776(1999). 235(2002) 80 S. John, Phys. Rev. Lett. 58, 2486(198 20. ). D. Joannopoulos, R. D. Meade, J. N. winn, Photonic 6020316 oa/2Ic 0a/2c oa/2Tc ca/2c 22 M: Not c. Phbs, e , 62, 10696 (2000: Fig. 3. FDTD simulation results for CR in the photonic crystal of Fig. 1. Each column represents the n Phys. Rev. 865, 201104(R)(2 M os, Appl. Phys. Its for the value of v shown on the top. (A)Overall radiation cone shapes(dashed lines deduced from the group velocity contours in Fig. 2C.(B)Distribution of the radiated magnetic field Lett81.2352(2002) HyBlue, white, and red represent negative, zero, and positive field values, respectively. The color 24. The CR modes are excited with a strengt tional to the density of bles are chosen separately for best illustration in each case. (C) The frequency spectrum of the electromagnetic flux along z through a line perpendicular to v, in arbitrary units(a u. ). Brillouin zone: G=k-k; and e"rnc is the G-Fourier 370 17JanUary2003Vol299ScieNcewww.sciencemag.org

persion at v 0.6c becomes so small that a strong intensity peak cone is formed and almost overlaps with the overall cone. A clear distinction between the CR behaviors for v vc and v vc is that for v vc the measured flux in the z direction is positive over the emission band, but for v vc certain frequency regions appear where the flux can be negative (Fig. 3C). Because positive and negative flux values can occur at the same frequency [e.g., at (a)/(2 c) 0.2], this photonic crystal does not behave as a uniform negative-index medium, as noted before. Another distinction lies in the field pattern and is similar to that reported in (5) at a phonon resonance frequency: The near-static, nonradiating field extends beyond the overall cone when v vc, whereas for v vc, the field outside the cone is strictly zero. These nearstatic fields create an artificial peak around 0 in Fig. 3C for v vc, (as in v 0.1c) which we have verified to reduce to 0 for 0 with increasing computational cell sizes and time steps. Finally, there are highfrequency radiation “tails,” corresponding to higher-order radiation, behind the charge in all cases of Fig. 3B. The higher order modes typically have smaller group velocities and thus form dense forward-pointing cones of smaller angles, as first predicted in (6) (for coherently driven slow-light media). Here these tails can exhibit a backward radiation effect as well. The effects presented here can be extended to three-dimensional photonic crystals with little change. As a complete photonic band gap in three dimensions is not required, the crystal structure can be flexibly chosen. For experimental studies, an appropriate structure that quantitatively approximates our calculations could be a square lattice of air holes perforating a finite-height silicon slab, interacting with fast electrons, and operated near the communication wavelength. The same physics should apply to dielectric-inair–type crystals as well. A practical issue is whether the radiation intensity is sufficiently strong to be observable for small v. Our numerical simulation indicates that, across a bandwidth of around 40%, the average radiation energy is roughly in a ratio of 1:1.5:4: 20 for v/c 0.1, 0.15, 0.3, and 0.6. Furthermore, the radiation intensity at small v may even be much larger than these numbers in narrow bandwidths around specific frequencies, because of the unusual photon density of states in a photonic crystal. In conventional CR, for v vc an electron can emit hundreds of photons per centimeter of its path. Thus, for the velocities studied here, the emission rates correspond to a range starting from roughly 10 and ranging up to 200 photons per centimeter, which should be amenable to direct experimental observation. A number of applications also appear possible. Particles traveling at speeds below the phase-velocity threshold cannot be detected by conventional CR counters, and currently their observation relies on other devices, such as scintillation counters, proportional counters, or cloud chambers. These other devices, however, lack the unique advantages of strong velocity sensitivity and good radiation directionality as in conventional CR (2). With a photonic crystal, one should be able to achieve velocity selectivity and distinctive radiation patterns without any velocity threshold. Moreover, on the high-energy side, CR with a sharp radiation wavefront is possible for particles traveling through an all-air path inside a photonic crystal, allowing complete absence of the impurity scattering and random ionization losses inherent in a dense medium. This should improve the performance of present detectors. Finally, the CR frequency is set by the photonic crystal and is thus selectively scalable beyond optical wavelengths, opening up the possibility of flexible radiation sources for frequencies that are otherwise difficult to access. References and Notes 1. L. D. Landau, E. M. Liftshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, New York, ed. 2, 1984). 2. J. V. Jelly, Cerenkov Radiation and Its Applications (Pergamon, London, 1958). 3. I. M. Frank, Nucl. Instrum. Methods Phys. Res. Sect. A 248, 7 (1986). 4. G. N. Afanasiev, V. G. Kartavenko, E. N. Magar, Physica B 269, 95 (1999). 5. T. E. Stevens, J. K. Wahlstrand, J. Kuhl, R. Merlin, Science 291, 627 (2001). 6. I. Carusotto, M. Artoni, G. C. L. Rocca, F. Bassani, Phys. Rev. Lett. 87, 064801 (2001). 7. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968). 8. J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, Phys. Rev. Lett. 76, 4773 (1996). 9. J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999). 10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. NematNasser, S. Schultz, Phys. Rev. Lett. 84, 4184 (2000). 11. R. A. Shelby, D. R. Smith, S. Schultz, Science 292, 77 (2001). 12. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, Appl. Phys. Lett. 78, 489 (2001). 13. S. J. Smith, E. M. Purcell, Phys. Rev. 92, 1069 (1953). 14. K. F. Casey, C. Yeh, Z. A. Kaprielian, Phys. Rev. 140, B768 (1965). 15. B. Lastdrager, A. Tip, J. Verhoeven, Phys. Rev. E 61, 5767 (2000). 16. F. J. Garcia de Abajo, Phys. Rev. Lett. 82, 2776 (1999). 17. K. Ohtaka, S. Yamaguti, Opt. Quantum Electron. 34, 235 (2002). 18. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987). 19. S. John, Phys. Rev. Lett. 58, 2486 (1987). 20. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, Princeton, NJ, 1995). 21. M. Notomi, Phys. Rev. B 62, 10696 (2000). 22. C. Luo, S. G. Johnson, J. D. Joannopoulos, J. B. Pendry, Phys. Rev. B 65, 201104 (R) (2002). 23. C. Luo, S. G. Johnson, J. D. Joannopoulos, Appl. Phys. Lett. 81, 2352 (2002). 24. The CR modes are excited with a strength proportional to the density of radiation states and qv e*knG, where k is the Bloch-reduced k in the first Brillouin zone; G k – k; and e*knG is the G-Fourier Fig. 3. FDTD simulation results for CR in the photonic crystal of Fig. 1. Each column represents the results for the value of v shown on the top. (A) Overall radiation cone shapes (dashed lines) deduced from the group velocity contours in Fig. 2C. (B) Distribution of the radiated magnetic field Hy. Blue, white, and red represent negative, zero, and positive field values, respectively. The color tables are chosen separately for best illustration in each case. (C) The frequency spectrum of the electromagnetic flux along z through a line perpendicular to v, in arbitrary units (a.u.). R EPORTS 370 17 JANUARY 2003 VOL 299 SCIENCE www.sciencemag.org on June 8, 2007 www.sciencemag.org Downloaded from

REPORTS component of the Bloch electric field, as in E,=2a 28. The simulation uses a thick perfectly Layer 30. M. Koshiba, Y Tsuji, 5. Sasaki, IEEE Microwave Wireless boundary region that overlaps 10 periods of the Components Lett. 11, 152(2001). iv, P. Yeh, Optical Waves in Crystals: Propaga that used in(30) and can 31. Supported in part by NSF's Material tion and Control of Laser Radiation( wiley, New York, contour formed by u is similar to the ray surface e of Naval Research, Multidisciplinary Universit in(29), though it now represents group velocities of tion and whose position depends on time. esearch Initiative program (grant no. N00014-01-1 29. M. Born, E. Wolf, Principles of Optics: Electromagn 27.S. G Johnson, J D Joannopoulos, Opt. Express 8, 173 Light(Cambridge Univ. Press, New York, ed. 7, 1999) 18 October 2002: accepted 5 December 2002 A Reversibly Switching Surface whitin in the range of chemical stability of the Joerg Lahann, Samir Mitragotri, 2 Thanh-Nga Tran SAM(18). In other words, conventional SAMs are too dense to allow conformational Hiroki Kaido, Jagannathan Sundaram,2 Insung S. Choi, ansitions and consequently do not allow for Saskia Hoffer, Gabor A. Somorjai, Robert Langer't witching. To explore SAMs as a model sys- tem for switching, we must establish suffi We report the design of surfaces that exhibit dynamic changes in interfacial cient spatial freedom for each molecule. Once properties, such as wettability, in response to an electrical potential. The change a low-density SAM is created, preferential in wetting behavior was caused by surface-confined, single-layered molecules exposure of either hydrophilic or hydropho- undergoing conformational transitions between a hydrophilic and a moderately bic moieties of the SAM to the surrounding hydrophobic state. Reversible conformational transitions were confirmed at a medium could be exploited for the switching ao molecular level with the use of sum-frequency generation spectroscopy and at a macroscopic level with the use of contact angle measurements. This type of 1 6-Mercapto )hexadecanoic acid (MHA) S surface design enables amplification of molecular-level conformational tran- was chosen as a model molecule because it(1)? itions to macroscopic changes in surface properties without altering the chem- self-assembles on Au(1 11) into a monolayer al identity of the surface. Such reversibly switching surfaces may open pre and (ii) has a hydrophobic chain capped by a viously unknown opportunities in interfacial engineering. hydrophilic carboxylate group, thus poten tially facilitating changes in the overall sur- g Interfacial properties, such as wetting behav- using an active stimulus, such as an electrical face properties. To create a monolayer with ior, are defined by the molecular-level struc- potential, to trigger specific conformational sufficient spacing between the individual ture of the surface(1). Diverse modification transitions(e.g, switching from an all-trans MHA molecules, we used a strategy that g procedures have been used to permanently to a partially gauche oriented conformation; exploits synthesis and self-assembly of a alter wettability(2-4). Control of wettability see Fig. 1). Amplification of conformational MHA derivative with a globular end group, has been recently demonstrated by elegant transitions to macroscopically measurable which results in a SAM that is densely methods including light-induced (5-6) and changes requires synergistic molecular rori- packed with respect to the space-filling end electrochemical surface modifications entations of ordered molecules. In principle, groups but shows low-density packing with p (-10) These systems require chemical reac- this is attainable with a single-molecular lay tions in order to control wettability er, such as a self-assembled monolayer quent cleavage of the space-filling end g We demonstrate an alternative (SAM) of alkanethiolates on gold(15). How- groups establishes a low-density SAM of for dynamically controlling interfa ever, the dense molecular packing in SAMs MHA. The spatial dimensions of the precur- a erties that uses conformational m and the strong interactions between the met sor molecule to be used were adapted to (switching) of surface-confined molecules. ylene groups restrict dynamic molecular mo- match the optimum alkanethiolate density for O Polymers have been shown to undergo con- tions to the outermost atoms(16, 17). All in conformational rearrangements formational reorientations when changed situ evidence so far indicates that applied The equilibrium low-energy conformational from one solvent to another (In) or from one electrical potentials have no effect on long- state of each of the sparsely packed MHA temperature to another (12, 13) because of ohase transitions between a well solvated and a poorly solvated state(14). In contrast, our approach maintains the systems environment unaltered (including solvent, electrolyte con- tent, pH, temperature, and pressure)while Institute of Technology(MIT ) 45 Carleton Street, idge, MA 02139, USA. Department of Chemi- lh Hydrophilic Barbara, CA 93106, USA. Department nistry, University of Califomi group terial Science Division, Lawrence Berkeley Laboratory. *Present address: Depart ydrophoble Gold Electrode ute of Science and Technology, Daejeon 305- ealized representation of the transition between straight(hydrophilic) and bent(hydro- = not shown). The precursor tTo whom correspondence should be addressed. E- MHAE, characterized by a nd group and a thiol head group, was synthesized from maiL: ranger@mit.edu MHA by introducing the(2-chlorop phenylmethyl ester group www.sciencemagorgSciEnceVol29917JanUary2003 371

component of the Bloch electric field, as in Ekn G eknGei(k G) r . 25. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984), chap. 6. 26. The contour formed by u is similar to the ray surface in (29), though it now represents group velocities of different frequencies. 27. S. G. Johnson, J. D. Joannopoulos, Opt. Express 8, 173 (2001). 28. The simulation uses a thick perfectly matched layer boundary region that overlaps 10 periods of the photonic crystal similar to that used in (30) and can absorb the Bloch waves away from a band edge. The moving charge is implemented as a point-like current density that is oriented toward the direction of motion and whose position depends on time. 29. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, New York, ed. 7, 1999). 30. M. Koshiba, Y. Tsuji, S. Sasaki, IEEE Microwave Wireless Components Lett. 11, 152(2001). 31. Supported in part by NSF’s Materials Research Science and Engineering Center program (grant no. DMR-9400334) and the Department of Defense, Of- fice of Naval Research, Multidisciplinary University Research Initiative program (grant no. N00014-01-1- 0803). 18 October 2002; accepted 5 December 2002 A Reversibly Switching Surface Joerg Lahann,1 Samir Mitragotri,2 Thanh-Nga Tran,1 Hiroki Kaido,1 Jagannathan Sundaram,2 Insung S. Choi,1 * Saskia Hoffer,3 Gabor A. Somorjai,3 Robert Langer1 † We report the design of surfaces that exhibit dynamic changes in interfacial properties, such as wettability, in response to an electrical potential. The change in wetting behavior was caused by surface-confined, single-layered molecules undergoing conformational transitions between a hydrophilic and a moderately hydrophobic state. Reversible conformational transitions were confirmed at a molecular level with the use of sum-frequency generation spectroscopy and at a macroscopic level with the use of contact angle measurements. This type of surface design enables amplification of molecular-level conformational transitions to macroscopic changes in surface properties without altering the chemical identity of the surface. Such reversibly switching surfaces may open previously unknown opportunities in interfacial engineering. Interfacial properties, such as wetting behavior, are defined by the molecular-level structure of the surface (1). Diverse modification procedures have been used to permanently alter wettability (2–4). Control of wettability has been recently demonstrated by elegant methods including light-induced (5–6) and electrochemical surface modifications (7–10). These systems require chemical reactions in order to control wettability. We demonstrate an alternative approach for dynamically controlling interfacial properties that uses conformational transitions (switching) of surface-confined molecules. Polymers have been shown to undergo conformational reorientations when changed from one solvent to another (11) or from one temperature to another (12, 13) because of phase transitions between a well solvated and a poorly solvated state (14). In contrast, our approach maintains the system’s environment unaltered (including solvent, electrolyte content, pH, temperature, and pressure) while using an active stimulus, such as an electrical potential, to trigger specific conformational transitions (e.g., switching from an all-trans to a partially gauche oriented conformation; see Fig. 1). Amplification of conformational transitions to macroscopically measurable changes requires synergistic molecular reorientations of ordered molecules. In principle, this is attainable with a single-molecular layer, such as a self-assembled monolayer (SAM) of alkanethiolates on gold (15). However, the dense molecular packing in SAMs and the strong interactions between the methylene groups restrict dynamic molecular motions to the outermost atoms (16, 17). All in situ evidence so far indicates that applied electrical potentials have no effect on longchain alkanethiolate monolayers on gold within the range of chemical stability of the SAM (18). In other words, conventional SAMs are too dense to allow conformational transitions and consequently do not allow for switching. To explore SAMs as a model system for switching, we must establish sufficient spatial freedom for each molecule. Once a low-density SAM is created, preferential exposure of either hydrophilic or hydrophobic moieties of the SAM to the surrounding medium could be exploited for the switching of macroscopic surface properties. (16-Mercapto)hexadecanoic acid (MHA) was chosen as a model molecule because it (i) self-assembles on Au(111) into a monolayer and (ii) has a hydrophobic chain capped by a hydrophilic carboxylate group, thus potentially facilitating changes in the overall surface properties. To create a monolayer with sufficient spacing between the individual MHA molecules, we used a strategy that exploits synthesis and self-assembly of a MHA derivative with a globular end group, which results in a SAM that is densely packed with respect to the space-filling end groups but shows low-density packing with respect to the hydrophobic chains. Subsequent cleavage of the space-filling end groups establishes a low-density SAM of MHA. The spatial dimensions of the precursor molecule to be used were adapted to match the optimum alkanethiolate density for conformational rearrangements. The equilibrium low-energy conformational state of each of the sparsely packed MHA 1 Department of Chemical Engineering, Massachusetts Institute of Technology (MIT ), 45 Carleton Street, Cambridge, MA 02139, USA. 2 Department of Chemical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA. 3 Department of Chemistry, University of California at Berkeley, Material Science Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA. *Present address: Department of Chemistry and School of Molecular Science (BK21), Korean Advanced Institute of Science and Technology, Daejeon 305- 701, Korea. †To whom correspondence should be addressed. Email: rlanger@mit.edu Fig. 1. Idealized representation of the transition between straight (hydrophilic) and bent (hydrophobic) molecular conformations (ions and solvent molecules are not shown). The precursor molecule MHAE, characterized by a bulky end group and a thiol head group, was synthesized from MHA by introducing the (2-chlorophenyl)diphenylmethyl ester group. R EPORTS www.sciencemag.org SCIENCE VOL 299 17 JANUARY 2003 371 on June 8, 2007 www.sciencemag.org Downloaded from

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