Nanocavity plasmonic device for ultrabroadband single molecule ...

Report 2 Downloads 63 Views
April 1, 2009 / Vol. 34, No. 7 / OPTICS LETTERS

1087

Nanocavity plasmonic device for ultrabroadband single molecule sensing Ryan M. Gelfand, Lukas Bruderer, and Hooman Mohseni* Electrical Engineering and Computer Science, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA *Corresponding author: [email protected] Received October 17, 2008; revised January 26, 2009; accepted February 27, 2009; posted March 5, 2009 (Doc. ID 102848); published March 30, 2009

We present a new structure that combines a metal–dielectric–metal sandwich with a periodic structure to form a plasmon polariton photonic crystal. Three-dimensional finite-difference time-domain simulations show a clear bandgap in the terahertz regime. We exploited this property by adding a defect to the crystal, which produces a cavity with a quality factor of 23.3 at a wavelength of 3.45 ␮m. Despite the small Q factor, the ultrasmall sensing volume of 15 zeptoliters produces an extremely large Purcell constant of 4.8⫻ 106. Compared to photonic crystals with similar Purcell constant, the bandwidth is several orders of magnitude larger, or about 7 THz, ensuring high tolerances to manufacturing parameters, and environmental changes, as well as a high specificity owing to the possibility of broadband spectral fingerprint detection. © 2009 Optical Society of America OCIS codes: 250.5403, 160.5298, 040.2235, 140.4780.

Label-free single molecule detection is an exciting avenue of study that will impact many areas of our lives, from explosives detection [1] and security, [2] to helping us discover new drugs [3], to biosensing [4], and detecting cancer in it infant stages [5,6]. To accomplish such a technique, a device must first be fabricated that has high sensitivity and accurate specificity. Optical spectroscopy can potentially address these issues, as well as provide remote sensing capabilities and a fast detection time. Therefore, photonic sensing has become an attractive method for single molecule detection [7]. One of the main issues of sensing larger molecules is that such molecules have a vibrational signature in the mid- and long-IR range; and to have a strong interaction between them and light with such long wavelengths, the light must somehow be compressed much below its diffraction limit. A promising structure that can squeeze light significantly in one dimension is a metal–dielectric– metal (MDM) sandwich with a very thin dielectric layer [8,9], although with no interaction point or resonance effect these structures by themselves would not make for excellent sensors. Photonic crystals (PCs) have many attractive properties, including the ability to dramatically increase the interaction between a small volume and light; however, they rely on extremely high quality 共Q兲 factors to achieve a high interaction coefficient. This high Q factor underscores the need for very narrow spectral linewidth, which in turn reduces the robustness of the device and makes it impossible to obtain enough of a molecule’s spectral fingerprint, preventing reliable detection and high specificity. Also, owing to nanometer limited geometrical tolerances, it is hard to reproduce PCs that match the spectral feature of interest. Similarly tight tolerances to ambient (temperature, concentration, humidity, etc.) changes render these devices difficult to use in the field. Besides PCs, another method currently being looked at as a contender for single molecule detection 0146-9592/09/071087-3/$15.00

is a functionalized metal nanostructured array [10]. These devices are shown to be robust and have a variety of ways of being fabricated [11,12]. By squeezing light into a tight space on the surface of a metal, these plasmonic structures have been used to enhance Raman spectroscopy. However, like a PC, these devices derive their enhanced sensitivity from a tight spectral linewidth. In contrast, our device attains moderately high field intensity enhancements of 104 comparable to typical values for plasmonic nanostructured arrays [13], though sophisticated theoretical structures can attain values as high as 107 at the expense of having extremely narrow bandwidth. The presented device combines MDM structures and a two-dimensional cavity [see Fig. 1(a)] to produce a practical structure that addresses many issues plaguing the aforementioned sensors. We show that our new structure can squeeze light a million times volumetrically, leading to a high Purcell constant comparable to the best reported values by conventional PCs [Fig. 1(b)]. However, the small Q factor of the proposed structure leads to a very wide spectral bandwidth, producing robustness and better specificity as a photonic molecular sensor, while at the same time we can keep the interaction volume small and thus the Purcell factor high. We also show that the main plasmonic mode of the proposed structure has a good coupling to the far field, and hence can be excited by conventional optical devices (e.g., an optical microscope) [Fig. 1(c)]. Before analyzing the nanocavity device, we first had to find its fundamental mode and general photonic band structure. In designing the device we realized that by squeezing light we could increase the effective index of the material, thus slowing it down [14]. However by decreasing the thickness of the dielectric layer, the percent of field energy in the metal increases, thus increasing the loss and decreasing the lifetime. Therefore, higher index dielectrics can increase effective index without a significant reduc© 2009 Optical Society of America

1088

OPTICS LETTERS / Vol. 34, No. 7 / April 1, 2009

Fig. 1. (Color online) (a) Plasmon polariton photonic crystal with 200 nm metal cladding layers sandwiching a 12 nm dielectric layer pierced with an hexagonal lattice of holes, 450 nm in diameter, with a period of 500 nm and a 40 nm diameter central cavity defect hole. (b) Ez mode profile 共87 THz兲 of the center of the cavity at z = 0 nm; the mode is intensely squeezed in and around the defect cavity. (c) Ez intensity along the longitudinal direction of the crystal from the center of the cavity to 200 nm above the crystal. (d) Ez intensity at 500 nm above the top of the crystal shows that a small amount of light emanates from the crystal through the central column.

tion of the lifetime [see Fig. 2(b)]. Therefore we chose a dielectric thickness of 12 nm, although layers as thin as 3 nm have been shown [15], and a high dielectric constant of 9. The gold metal cladding layers were each 200 nm thick, many times larger than the skin depth, so as to minimize the energy loss to the upper surface. When two metal dielectric boundaries are brought close together the modes on each interface start to interact and get coupled. Even at very long wavelengths (away from the plasma frequency) the mode dispersion deviates strongly from the light line for very small gap thicknesses. Depending on the relative phase of the two waves, a symmetric or antisymmetric mode is formed. This research focuses on the antisymmetric mode because of its superior characteristics in propagation distance and dispersion [16]. Bloch boundaries in each lateral direction and an antisymmetric boundary in the z direction reduce the finite-difference time-domain (FDTD) simulation area. The full band plot is shown in [Fig. 2(a)]. The region of the crystal in which we are interested is the bandgap, between 86.6 and 112 THz, or 2.67 to 3.46 ␮m, and because we are working away from the plasmon frequency where the dispersion is flat, each frequency component of any mode launched in the crystal will effectively experience almost the same index [Fig. 2(c)]. This effect is important for sensing molecules where a wide spectral linewidth is preferable. To expand this design as a sensor one needs a detection site, and nanocavities are a natural solution. For our plasmon polariton PC (PPPC) with a defect, a 3D FDTD simulation was used to calculate the wavelength of the resonant modes and the cavity’s Q fac-

Fig. 2. (Color online) (a) 3D FDTD band plot simulation of the PPPC, hole diameter of 450 nm, period of 500 nm, shows a clear bandgap between 86.6 and 112 THz. (b) Graph of the decay time and effective index at 87 THz for various starting permittivities as a function of dielectric thickness. As the thickness of the material decreases the effective index increases, however, the decay time is nearly independent of thickness, so we can choose a thin layer high dielectric material to optimize our device with minimal sacrifice to the lifetime of the photons. (c) Effective index of the MDM slab mode as a function of frequency at a thickness of 12 nm. Away from the plasma frequency the dispersion is flat, so the optical properties of the crystal do not significantly change in our area of interest.

tor. We built our cavity by placing a 40 nm defect hole in a PPPC with a hexagonal array of 450 nm holes and a period of 500 nm. The time evolution of the field is analyzed by first plotting the natural log of the Ez field versus time [Fig. 3(a)]. The peaks are detected and a line is fitted with decay time

Fig. 3. (Color online) (a) Cavity ringdown plot for the fundamental mode, 87 THz, of the crystal showing both the source decay and the mode decay. With a decay time of 42.6 fs the quality factor for the cavity is 23.3. (b) FFT of the fundamental cavity mode showing a spectral line width at FWHM of 7.4 THz. (c) Flat field profile versus time shows a gain of ⬃5500 cm−1 in the dielectric layer that can almost compensate for the total loss, material loss, and leakage of the structure.

April 1, 2009 / Vol. 34, No. 7 / OPTICS LETTERS

␶ = −1 / slope. The Q factor is the angular frequency multiplied by the decay time, Q = ␻*␶. For any optical detection technique to be practical for single molecule detection, the interaction time between the light and the target molecule needs to be long and the spectral linewidth needs to be broad enough to allow for detection of the spectral signatures of the molecules being detected. By exploiting the properties of nanoscale cavities, we have been able to design and simulate a PPPC that can squeeze light in all three dimensions into a small volume facilitating a larger interaction with single molecules. This interaction strength between the light and the cavity can be characterized by Purcell’s constant, 3 Q p=

4␲2 V

ⴱ ␭3 ,

共1兲

where Q is the quality factor of the cavity, V is its volume (1.5⫻ 10−23 m3, or a sensing volume of 15 zeptoliters), and ␭ is its resonant mode 共3.45⫻ 10−6 m兲. A high p, implying an intense interaction between the light inside the cavity and electronic states of the molecules, would be required for any efficient optical sensor [17]. Furthermore a wide spectral linewidth ⌬f is necessary for the operation and robustness of any single molecule sensor to ensure detection within slightly varying conditions such as temperature and cavity geometries. Since ⌬f = f0 / Q, a smaller Q relates to a wider linewidth. This implies that one needs to increase Purcell’s constant without relying on extremely high Q factors to build a practical sensor. To meet these two conditions, V the volume of the cavity must be as small as possible. Our simulation shows a Q factor of 23.3 [Fig. 3(a)] with the fundamental resonant frequency [Fig. 3(b)] of 87 THz. The best PCs at a wavelength of 1.575 ␮m experimentally produce p values of 1.9⫻ 105 with a Q of 4.5⫻ 104 [18]. Theoretical maximums are of the order of 106 – 107 for ultra-high-Q structures with a tight linewidth of hundreds of magahertz [19]. Our device at a wavelength of 3.45 ␮m shows a p value of 4.8⫻ 106 with a ⌬f of 7.4 THz showing that we can squeeze a lot of light, with a broad spectral range, into a small volume. It is these two properties that would suggest this device to be an excellent candidate for a single molecule sensor. Analogously to the sensor this high Purcell constant cavity could be used as a laser if the medium inside can compensate for the high loss introduced by the proximity of the metal cladding layers to the dielectric layer. Simulation shows that a gain material with a gain value of 5500 cm−1 satisfies the lasing condition, and a coherent stabilization of the electromagnetic radiation inside the cavity [see Fig. 3(d)]. Similar to surface plasmon [20] lasers this device would emit light in the terahertz frequency. Another critical feature of this device is that it can be easily coupled to from the outside, a property most useful for building a sensor or a laser. The cavity not only exhibits very intense energy density inside, but

1089

it also shows a column of energy emanating from the center up through the 40 nm diameter defect hole and stays subdiffraction at least 500 nm above the top of the crystal [Fig. 1(d)]. So, theoretically it would be possible to optically pump the microcavity by coupling back through the column thus enabling energy to build up inside. Since the column runs the full length of the device, one could pump from one side and the cavity could emit through the other. This column also allows the passage of media either gaseous or liquid to be passed through the cavity with its contents scanned for certain molecules. We believe that the presented plasmonic nanocavity provides new opportunities to build single molecule detectors and terahertz plasmonic lasers. The applications for plasmon-based sensors and lasers are clearly documented and the same tenets would apply to any PPPC-based device. Investigating the devices based on plasmon polaritons that are capable of producing deep subdiffraction photonic integrated circuits will help give us the versatility we require as devices shrink ever more into the nanoscale world. References 1. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, Semicond. Sci. Technol. 20, S266 (2005). 2. B. Ferguson and X.-C. Zhang, Nature Mater. 1, 26 (2002). 3. L. Ho, M. Pepper, and P. F. Taday, Nat. Photonics 20, 541 (2008). 4. M. Tonouchi, Nat. Photonics 1, 97 (2007). 5. R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, Phys. Med. Biol. 47, 3853 (2002). 6. S. Nakajima, H. Hoshina, M. Yamashita, and C. Otani, Appl. Phys. Lett. 90, 041102 (2007). 7. M. Dragoman and D. Dragoman, Prog. Quantum Electron. 32, 1 (2008). 8. Y. Kurokawa and H. T. Miyazaki, Phys. Rev. B 75, 035411 (2007). 9. G. Veronis and S. Fan, Opt. Express 15, 1211 (2007). 10. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, Nature Mater. 7, 442 (2008). 11. K. Ait-Mansour, A. Buchsbaum, P. Ruffieux, M. Schmid, P. Gröning, P. Varga, R. Fasel, and O. Gröning, Nano Lett. 8, 2035 (2008). 12. J. Henzie, M. H. Lee, and T. W. Odom, Nat. Nanotechnol. 2, 549 (2007). 13. S. Zou and G. C. Schatz, Chem. Phys. Lett. 403, 62 (2005). 14. A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004). 15. H. T. Miyazaki and Y. Kurokawa, Phys. Rev. Lett. 96, 067401 (2006). 16. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton, 2008). 17. T. F. Krauss, Nature Mater. 2, 777 (2003). 18. Y. Akahane, T. Asano, B. Song, and S. Noda, Nature 425, 944 (2003). 19. B. Song, S. Noda, T. Asano, and Y. Akahane, Nature Mater. 4, 207 (2005). 20. N. I. Zheludev, Nat. Photonics 2, 351 (2008).