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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 21 — Oct. 17, 2007
  • pp: 13894–13906

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Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement

T. Xu, X. Jiao, G.-P. Zhang, and S. Blair  »View Author Affiliations


Optics Express, Vol. 15, Issue 21, pp. 13894-13906 (2007)
http://dx.doi.org/10.1364/OE.15.013894


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Abstract

We measure second-harmonic generation from arrays of sub-wavelength apertures in transmission using fundamental input at 800 nm. Lattice arrangements include disordered, Penrose (quasi-periodic or aperiodic), and square (periodic). Strong angular dependence of SHG is observed, with maxima located at angular positions that roughly correspond to incidence angles of extraordinary optical transmission (EOT) for the fundamental. In addition, even at incidence normal to the sample, strong secondary maxima are observed at off-normal scattering angles for the arrangements with higher degree of order. Breaking the inversion symmetry of the aperture allows second harmonic peaks at normal incidence and detection. These measurements help to resolve the role that symmetry plays in second-harmonic generation from arrays of apertures.

© 2007 Optical Society of America

1. Introduction

Extraordinary optical transmission (EOT) through metal films modulated with a 2-D array of sub-wavelength apertures [1

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998). [CrossRef]

] was reported in 1998. There now exists experimental evidence [2

L. Salomon, F. Grillot, A. V. Zayats, and F. Fornel “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001). [CrossRef] [PubMed]

, 3

Y. Liu and S. Blair “Fluorescence enhancement from an array of sub-wavelength metal apertures,” Opt. Lett. 28, 507–509 (2003). [CrossRef] [PubMed]

] that upon the condition of enhanced light transmission, intensity buildup within the apertures occurs. This phenomenon suggests that enhancement of nonlinear processes within the apertures can be obtained. Resonant enhancement of second-harmonic generation (SHG) by a factor of 104 has been demonstrated for a single sub-wavelength aperture surrounded by periodic annular corrugation [4

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi “Enhanced nonlinear optical conversion using periodically nanostructured metal films,” Opt. Lett. 28, 423–425 (2003). [CrossRef] [PubMed]

]. SHG has also been studied in arrays of sub-wavelength apertures of round [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

], triangular [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

], coaxial [6

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood Jr., K. J. Malloy, and S. R. J. Brueck “Second-harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6, 1027–1030 (2006). [CrossRef]

], double-hole [7

A. Lesuffleur, L. K. S. Kumar, and R. Gordon “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006). [CrossRef]

, 8

A. Lesuffleur, L. K. S. Kumar, and R. Gordon “Apex-enhanced second harmonic generation by using double-hole arrays in a gold film,” Phys. Rev. B 75, 045423 (2007). [CrossRef]

], and rectangular [9

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

] shapes, using disordered [10

N. Rakov, F. E. Ramos, and M. Xiao “Strong second-harmonic generation from a thin silver film with randomly distributed small holes,” J. Phys.: Cond. Matter 15, L349–L352 (2003). [CrossRef]

, 5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

] and periodic [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

, 6

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood Jr., K. J. Malloy, and S. R. J. Brueck “Second-harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6, 1027–1030 (2006). [CrossRef]

, 7

A. Lesuffleur, L. K. S. Kumar, and R. Gordon “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006). [CrossRef]

, 9

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

] arrangements. The effect of the symmetry of the aperture has been shown [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

], in that, at normal incidence, apertures with inversion symmetry produce much weaker SH than non-centrosymmetric apertures, while at off-normal incidence, SH can be produced with centrosymmetric apertures [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

, 8

A. Lesuffleur, L. K. S. Kumar, and R. Gordon “Apex-enhanced second harmonic generation by using double-hole arrays in a gold film,” Phys. Rev. B 75, 045423 (2007). [CrossRef]

]. Nevertheless, SHG has been studied at normal incidence where inversion symmetry holds [4

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi “Enhanced nonlinear optical conversion using periodically nanostructured metal films,” Opt. Lett. 28, 423–425 (2003). [CrossRef] [PubMed]

, 9

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

].

Recently, EOT has been observed in quasi-periodic arrangements of sub-wavelength apertures [11

M. Sun, J. Tian, Z.-Y. Li, B.-Y. Cheng, D.-Z. Zhang, A.-Z. Jin, and H.-F. Yang “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chinese Phys. Lett. 23, 486–488 (2006). [CrossRef]

, 12

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature (London) 446, 517–521 (2007). [CrossRef] [PubMed]

, 13

F. Przybilla, C. Genet, and T. W. Ebbesen “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett. 89, 121115 (2006). [CrossRef]

]. While not fundamentally different than EOT in periodic arrangements [14

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” arXiv:cond-mat/0606121v2 (2007).

], the insight gained from the generalization of the phenomenon from periodic to aperiodic [12

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature (London) 446, 517–521 (2007). [CrossRef] [PubMed]

] is expected to yield new applications. We focus here on the effects of aperture symmetry and lattice arrangement on SHG in transmission through sub-wavelength metallic apertures and show that quite different behavior is exhibited in the scattering of the SH signal. In addition, these results help to resolve the role of symmetry in the recent publications on SH in sub-wavelength aperture arrays.

2. Experimental methods

Arrangements of sub-wavelength apertures were produced in 100 nm thick gold films on quartz, using both focused ion beam (FIB) milling and electron beam (e-beam) lithography. Numerous samples were produced via FIB with round apertures of varying sizes and lattice arrangements, but the only sample used in this study is a square lattice of round apertures (see Fig. 5). All other samples were produced with e-beam lithography. Briefly, a 5 nm chromium adhesion layer was sputter deposited onto the quartz substrate, followed by 100 nm of gold and 20 nm of chromium. ZEP520A e-beam resist of about 300 nm thickness was spin coated. Following exposure, the upper chromium layer was dry etched with chlorine, and the e-beam resist removed. The chromium layer served as a hard mask for argon ion milling of the gold. A wet etch removed the upper chromium layer (and likely resulted in some undercut in the underlying chromium adhesion layer). Lattice arrangements in this paper include disordered, square, and Penrose.

The experimental setup is a modification of the one used previously [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

], as shown in Fig. 1. A Ti:Sapphire laser is used at 800 nm wavelength and roughly 30 fs pulse duration. The modified setup allows the rotation of the sample with respect to the incident fundamental beam as well as rotation of the detector around the sample so that the SHG radiation pattern can be measured in transmission. The detector is a blue-sensitized PMT and two spectral filters are used to block the transmitted fundamental at 800 nm and minimize the influence of two-photon luminescence [9

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

]. The angular acceptance of light collection is roughly 1 degree. Lock-in detection is performed by modulating the 86 MHz pulse train at 2 kHz, and average incident power is 75 mW (measured after the chopper).

3. Results

3.1. Disordered lattice

An SEM image of the disordered lattice of round apertures is shown in Fig. 2, along with a scan of the transmission of the fundamental beam and SH output (along the direction of the transmitted fundamental, i.e. γ=θ) versus angle of incidence. As expected due to the inversion symmetry of the aperture, the SH signal is minimum at normal incidence. This is a similar result to that obtained previously [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

].

A double-angle scan for the disordered arrangement of round apertures is shown in Fig. 3. Since the lattice is disordered, the only SH signal observed is along the direction of the fundamental beam. The far-field radiation pattern indicates minimal contribution from two-photon luminescence (which would have a broad angular distribution), and is the result of sources of SH radiation localized at the apertures. For off-normal incidence, the transmitted SH signal increases rapidly due to symmetry breaking at the aperture [15

V. L. Brudny, B. S. Mendoza, and W. L. Mochan “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152–11162 (2000). [CrossRef]

, 5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

]. The SH wavevector satisfies the following momentum-matching condition - k 2ω t = 2k ω t , where t represents transverse components, so that γ= θ.

Symmetry breaking due to off-normal incidence can be understood by considering the distribution of intensity within the aperture as a function of fundamental incidence angle θ for an x'-polarized input field. Calculations were performed using FDTD Solutions (Lumerical Solutions, Inc), the results of which are shown in Fig. 4 for θ = 0°, 30° and 60°. The first row of images shows the x,y and z components of the intensity pattern at normal incidence, at a position 5 nm below the aperture entrance. As expected, there is a reflection symmetry along the y axis. By examining the magnitude of the three orthogonal components, Ex dominates along the x axis, while Ey dominates along the diagonals, suggesting that the local second-harmonic signal arises from the surface χ (2) ⊥⊥⊥ component between gold and air. As shown in cross-section, there are locations where Ez dominates, complicating any detailed microscopic analysis. The aperture symmetry dictates that the effective second-order susceptibility of the aperture χ (2,eff) ttt = 0, where t is a transverse component, such that the local SH sources exactly cancel. As shown in the second row of images, the field distribution throughout the depth of the aperture is non-uniform, with local maxima at the entrance and exit [16

F. Mahdavi, Y. Liu, and S. Blair “Modeling fluorescence enhancement from metallic nanocavities,” Plasmonics 2, 129–141 (2007). [CrossRef]

] (note that Ey is of negligible magnitude in this xz cross section). This asymmetry along the z direction [17

M. D. McMahon, R. Lopez, R. F. Haglund Jr., E. A. Ray, and P. H. Bunton “Second-harmonic generation from an arrays of symmetric gold nanoparticles,” Phys. Rev. B 73, 041401 (2006). [CrossRef]

] allows nonzero effective aperture susceptibilities indexed by zzz,ztt, and tzt = ttz, in principle enabling some SH emission at normal incidence/exit, as exhibited in Fig. 3.

Fig. 1. Experimental setup for second harmonic generation measurements. The output of the Ti:Sapphire laser passes through a neutral density filter and a spectral longpass filter (690 nm) before being focused onto the sample with a 20 μm spot size by a 10 cm focal length lens; all patterned areas were larger than the spot size (the FIB sample is 25 μm by 25 μm and the e-beam samples are 80 μm by 80 μm). Emission from the sample passes through a collection lens of 10 cm focal length, a spectral short-pass filter (450 nm cutoff), a band-pass filter (400 nm center, 40 nm passband), and a 2 mm iris, and is detected with a PMT. As illustrated, θ is positive and γ is negative.
Fig. 2. SEM image of disordered array of round apertures. The apertures are roughly 235 nm by 241 nm in size. The fill fraction is about 4.6% (as calculated by image thresholding and plotting a histogram of the result). Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle (right). Both curves are normalized to their maximum values.
Fig. 3. Second-harmonic output from disordered arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. Second-harmonic intensity is normalized to its’ maximum value.

For off-normal incidence angles, asymmetry in the lateral intensity distribution develops, breaking the symmetry of the aperture, such that χ (2,eff) ttt ≠ 0, where χ (2,eff) xxx is assumed dominant. Note that similar intensity patterns were obtained by asymmetrically placing a point source near a sub-wavelength aperture [18

X. Heng, X. Cui, D. W. Knapp, J. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. Yang “Characterization of light collection through a subwavelength aperture from a point source,” Opt. Express 14, 10410–10425 (2006). [CrossRef] [PubMed]

]. At small incidence angles, the observed increasing SH is initially driven by symmetry breaking, but at larger angles, it is clear that peak intensity increases as well.

3.2. Square lattice

An SEM image of the square lattice of round apertures is shown in Fig. 5. EOT peaks are observed in the transmission of the fundamental beam, but SH output is only observed at angles significantly off-axis. Again, this result is similar to previous measurements [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

] and is due to symmetry breaking by off-axis illumination.

A double-angle scan for the square lattice is shown in Fig. 6. Again, the SH signal is minimum at normal incidence and detection; however, well-defined SH peaks are detected off-axis, indicating that symmetry-breaking also occurs in detection [19

N. I. Zheludev and V. I. Emel’yanov “Phase matched second harmonic generation from nanostructured metallic surfaces,” J. Opt. A: Pure and Appl. Opt. 6, 26–28 (2004). [CrossRef]

, 17

M. D. McMahon, R. Lopez, R. F. Haglund Jr., E. A. Ray, and P. H. Bunton “Second-harmonic generation from an arrays of symmetric gold nanoparticles,” Phys. Rev. B 73, 041401 (2006). [CrossRef]

]. This effect cannot be observed with the disordered lattice as the only SH signal produced is along the direction of the fundamental (i.e. there is no coherent addition of periodic SH sources to produce off-axis beams). Another interesting result is that the peak SH signal is about 25-times greater than for the disordered arrangement.

Fig. 4. Calculated intensity distributions 5 nm below the entrance and in cross section of a 250 nm diameter aperture in 100 nm thick gold under normal illumination at 800 nm (0° plots, top). A 5 nm chromium layer is placed between the gold and substrate, but the diameter is 260 nm assuming 5 nm overetching beneath the gold layer. Cross-section intensity profiles are also shown for 30° and 60° angles of incidence. Aperture geometry illustrated by the semi-transparent overlays.
Fig. 5. SEM image of square lattice of round apertures. Apertures are roughly 240 nm by 285 nm in size, with period 910 nm. The fill fraction is about 6.7%. Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle (right). Both curves are normalized to their maximum values.

The far-field radiation pattern is the result of sources of SH radiation which are periodically arranged. From this observation, the SH wavevector satisfies the following momentum-matching condition:

kt 2ω= 2 ktω+mK
(1)

where K is a reciprocal lattice vector. It is assumed that, at the SH wavelength, there is no coupling between the apertures due to surface waves, as the SPP propagation distance in gold is less than the aperture spacing [5

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

]. If the SH SPP were not negligible, additional phase matching considerations would come into play [20

K. Liu, L. Zhan, Z. Y. Fan, M. Y. Quan, S. Y. Luo, and Y. X. Xia “Enhancement of second-harmonic generation with phase-matching on periodic sub-wavelength structured metal film,” Opt. Commun. 276, 8–13 (2007). [CrossRef]

]. For the square lattice, and assuming that the optical wavevectors have only x̂ and ẑ components, this equation can be written

sin⁡γ= sin⁡θ+m λ 2Λ,
(2)

where Λ is the lattice constant and λ is the fundamental wavelength. As shown in Fig. 6, this equation closely describes the trajectories of the SH peaks.

This simple diffraction model does not, however, explain the absence of the zeroth-order beam; in other words, it does not take into account the symmetry of the aperture. Referring back to Fig. 4 at normal incidence, it is reasonable to approximate the locations of the SH from each aperture as two point sources on opposing side of the aperture (and aligned along the direction of fundamental polarization). Inversion symmetry demands that these two point sources are out of phase. Mathematically, the array of SH source terms can be expressed by

[ comb⁡ ( x+d2Λ)− comb⁡ ( x−d2Λ)] comb⁡ ( yΛ)
(3)
Fig. 6. Second-harmonic output from square arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.

in real space, where d is the aperture diameter. By taking the 2-D Fourier transform (with fx and fy the transverse spatial frequencies), the SH can be expressed in angular space by

comb⁡ ( fxΛ) sin⁡ (π fxd) comb⁡ ( fxΛ),
(4)

where sin γ=λfx /2.

Because of the sin() factor, the SH diffraction pattern has no zeroth order (i.e. where fx = 0). Further, opposing diffraction orders must be out of phase with respect to each other, meaning that if detected symmetrically, they would interfere destructively and cancel. This expression also predicts that for higher diffraction orders, the intensity follows sin2 (πfxd), which has been shown for SH from arrays of symmetric particles [17

M. D. McMahon, R. Lopez, R. F. Haglund Jr., E. A. Ray, and P. H. Bunton “Second-harmonic generation from an arrays of symmetric gold nanoparticles,” Phys. Rev. B 73, 041401 (2006). [CrossRef]

].

In order to obtain a SH signal at normal incidence/detection, the inversion symmetry of the aperture must be broken so as to introduce asymmetry in the local field distribution [21

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007). [CrossRef] [PubMed]

] (a further requirement is that the unit cell must also be non-centrosymmetric [22

B. Lamprecht, A. Leitner, and F. R. Aussenegg “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B 68, 419–423 (1999). [CrossRef]

, 23

A. M. Moran, J. Sung, E. M. Hicks, R. P. van Duyne, and K. G. Spears “Second harmonic excitation spectroscopy of silver nanoparticle arrays,” J. Phys. Chem. B 109, 4501–4506 (2005). [CrossRef]

]). Square arrays of non-centrosymmetric apertures were also fabricated, as shown in Fig. 7, which satisfy these requirements. Also in this figure is a plot of fundamental transmission and SH versus incident angle, which shows that strong SH is obtained at normal incidence where a peak in fundamental transmission (EOT) occurs.

The asymmetry of this aperture shape is exhibited in the intensity distribution upon normal incidence, as shown in Fig. 8, in the xy plane 5 nm below the entrance. Here, the intensity distribution is more complex than for the round aperture, with Ex and Ey components reaching roughly the same magnitudes, even though these magnitudes are less than that obtained for Ex with the round aperture.

The double-angle SH scan for the asymmetric aperture is shown in Fig. 9, where the strong zeroth-order peak is observed at normal incidence. This scan also clearly shows the role of the aperture shape in distributing energy to the diffraction orders.

Fig. 7. Image of asymmetric aperture shape (left). Angles between the three branches are intended to be 90°, 120°, and 150°, clockwise from top. The square array of asymmetric apertures has a pitch of 880 nm and fill fraction of about 3%. Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle (right). Both curves are normalized to their maximum values.
Fig. 8. Calculated intensity distributions 5 nm below the entrance in an asymmetric aperture in 100 nm thick gold under normal illumination at 800 nm. Periodic boundary conditions are used in the calculations to mimic the square lattice. A 5 nm chromium layer is placed between the gold and substrate, overetched beneath the gold layer by 5 nm.

3.3. Penrose lattice

An SEM image of the Penrose lattice with round apertures is shown in Fig. 10. The Penrose tiles are constructed similarly to that used in [13

F. Przybilla, C. Genet, and T. W. Ebbesen “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett. 89, 121115 (2006). [CrossRef]

], with five-fold rotational symmetry. The reciprocal space, with 10-fold rotational symmetry, is also plotted, with peaks indexed by the transverse spatial frequencies fx and fy . Since the reciprocal space is densely packed as compared to that for a square lattice (i.e. there are no primitive vectors), not all peaks are plotted, only those of sufficient magnitude that can be distinctly identified from our measurements.

The same SH measurement has been performed on the Penrose lattice, as shown in Fig. 11. One noticeable feature of this plot is that the SH diffraction orders are more numerous, but significantly weaker, than for the square lattice. This is a direct result of the reciprocal space for the Penrose lattice. Reciprocal vectors along the fx axis are used to plot the trajectories in Fig. 11, which are in good agreement with the measurement.

A Penrose lattice was also fabricated with the same asymmetric aperture shape as used for the square lattice. The measured fundamental transmission and SH for this lattice is shown in Fig. 12, with the full angular scan shown in Fig. 13. A clear zeroth-order SH peak is seen at normal incidence, while many of the diffracted peaks are more clearly defined than with the round aperture.

Fig. 9. Second-harmonic output from square arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.
Fig. 10. Image of Penrose arrangement of round apertures (left). Apertures are roughly 354 nm by 340 nm in size. The fill fraction is about 13%. Calculated reciprocal space (right). The diameter of each peak is indicative of its’ magnitude. The red circles represent the spatial frequencies that are used in the fitting of diffraction orders in the experimental plots, which are fx = 0,1.35,1.65,2.65,2.95, and 4.25 1/μm.
Fig. 11. Second-harmonic output from a Penrose arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.

A recent theoretical paper on EOT in quasi-periodic aperture arrays [14

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” arXiv:cond-mat/0606121v2 (2007).

] has shown that the intensity distribution of incident light is not uniformly distributed at the apertures as it is for a periodic lattice. Because SHG scales as the square of intensity, it is a highly sensitive indicator of this distribution. From the good agreement of the measured SH diffraction pattern to what would be predicted from the reciprocal space (which assumes that the SH intensity from each aperture is equal), it is clear that the hot spots must maintain the same underlying arrangement as the lattice.

4. Discussion and conclusions

We have studied three mechanisms of symmetry-breaking in SHG from arrays of sub-wavelength apertures: off-axis illumination, off-axis detection, and non-centrosymmetric aperture shape. We have also studied the effects of the lattice arrangement, from disordered to periodic.

A simple model of SH emission from centrosymmetric apertures shows why SHG is weak under the conditions of normal incidence and detection, but can be measured under normal incidence and off-axis detection [17

M. D. McMahon, R. Lopez, R. F. Haglund Jr., E. A. Ray, and P. H. Bunton “Second-harmonic generation from an arrays of symmetric gold nanoparticles,” Phys. Rev. B 73, 041401 (2006). [CrossRef]

]. This model also predicts that opposing diffraction orders have opposite signs, and would cancel under symmetric detection, such as collection of SH emission through a high NA objective. Clearly, however, as shown through our asymmetric measurement technique, these orders wouldn’t completely cancel due to other sources of asymmetry.

Fig. 12. Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle for the Penrose arrangement of asymmetric apertures. Both curves are normalized to their maximum values.
Fig. 13. Second-harmonic output from a Penrose arrangement of asymmetric apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.

As we have shown, non-centrosymmetric apertures result in symmetry breaking in the intensity distribution of the fundamental driving field, such that strong SH can be produced under otherwise symmetric conditions. Symmetry breaking is also obtained for a centrosymmetric aperture under off-axis illumination.

Very different behavior in the second harmonic emission pattern is observed as a function of lattice arrangement. The disordered arrangement cannot produce off-axis SH peaks because of the lack of any short or long range periodicity that would allow for coherent addition of local sources in directions off that of the fundamental. The Penrose arrangement is quasi-periodic, allowing this coherent addition to occur, but with weaker diffraction efficiency than obtained for a periodic lattice. Finally, the SH emission pattern closely follows what would be predicted for a Penrose arrangement of SH sources.

The authors thank A. Nahata and A. Agrawal for many useful discussions. This research was sponsored in part by grant ECS 0622225 from the National Science Foundation, and by the Army Research Office. G. P. Zhang was supported by “The Hundred Talent Plan” of the Chinese Academy of Sciences.

References and links

1.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998). [CrossRef]

2.

L. Salomon, F. Grillot, A. V. Zayats, and F. Fornel “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001). [CrossRef] [PubMed]

3.

Y. Liu and S. Blair “Fluorescence enhancement from an array of sub-wavelength metal apertures,” Opt. Lett. 28, 507–509 (2003). [CrossRef] [PubMed]

4.

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi “Enhanced nonlinear optical conversion using periodically nanostructured metal films,” Opt. Lett. 28, 423–425 (2003). [CrossRef] [PubMed]

5.

M. Airola, Y. Liu, and S. Blair “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure and Appl. Opt. 7, S118–S123 (2005). [CrossRef]

6.

W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood Jr., K. J. Malloy, and S. R. J. Brueck “Second-harmonic generation from a nanopatterned isotropic nonlinear material,” Nano Lett. 6, 1027–1030 (2006). [CrossRef]

7.

A. Lesuffleur, L. K. S. Kumar, and R. Gordon “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett. 88, 261104 (2006). [CrossRef]

8.

A. Lesuffleur, L. K. S. Kumar, and R. Gordon “Apex-enhanced second harmonic generation by using double-hole arrays in a gold film,” Phys. Rev. B 75, 045423 (2007). [CrossRef]

9.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). [CrossRef] [PubMed]

10.

N. Rakov, F. E. Ramos, and M. Xiao “Strong second-harmonic generation from a thin silver film with randomly distributed small holes,” J. Phys.: Cond. Matter 15, L349–L352 (2003). [CrossRef]

11.

M. Sun, J. Tian, Z.-Y. Li, B.-Y. Cheng, D.-Z. Zhang, A.-Z. Jin, and H.-F. Yang “The role of periodicity in enhanced transmission through subwavelength hole arrays,” Chinese Phys. Lett. 23, 486–488 (2006). [CrossRef]

12.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature (London) 446, 517–521 (2007). [CrossRef] [PubMed]

13.

F. Przybilla, C. Genet, and T. W. Ebbesen “Enhanced transmission through Penrose subwavelength hole arrays,” Appl. Phys. Lett. 89, 121115 (2006). [CrossRef]

14.

J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno “Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes,” arXiv:cond-mat/0606121v2 (2007).

15.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152–11162 (2000). [CrossRef]

16.

F. Mahdavi, Y. Liu, and S. Blair “Modeling fluorescence enhancement from metallic nanocavities,” Plasmonics 2, 129–141 (2007). [CrossRef]

17.

M. D. McMahon, R. Lopez, R. F. Haglund Jr., E. A. Ray, and P. H. Bunton “Second-harmonic generation from an arrays of symmetric gold nanoparticles,” Phys. Rev. B 73, 041401 (2006). [CrossRef]

18.

X. Heng, X. Cui, D. W. Knapp, J. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. Yang “Characterization of light collection through a subwavelength aperture from a point source,” Opt. Express 14, 10410–10425 (2006). [CrossRef] [PubMed]

19.

N. I. Zheludev and V. I. Emel’yanov “Phase matched second harmonic generation from nanostructured metallic surfaces,” J. Opt. A: Pure and Appl. Opt. 6, 26–28 (2004). [CrossRef]

20.

K. Liu, L. Zhan, Z. Y. Fan, M. Y. Quan, S. Y. Luo, and Y. X. Xia “Enhancement of second-harmonic generation with phase-matching on periodic sub-wavelength structured metal film,” Opt. Commun. 276, 8–13 (2007). [CrossRef]

21.

B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen “Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers,” Nano Lett. 7, 1251–1255 (2007). [CrossRef] [PubMed]

22.

B. Lamprecht, A. Leitner, and F. R. Aussenegg “SHG studies of plasmon dephasing in nanoparticles,” Appl. Phys. B 68, 419–423 (1999). [CrossRef]

23.

A. M. Moran, J. Sung, E. M. Hicks, R. P. van Duyne, and K. G. Spears “Second harmonic excitation spectroscopy of silver nanoparticle arrays,” J. Phys. Chem. B 109, 4501–4506 (2005). [CrossRef]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4350) Nonlinear optics : Nonlinear optics at surfaces
(240.6680) Optics at surfaces : Surface plasmons
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 20, 2007
Revised Manuscript: October 2, 2007
Manuscript Accepted: October 3, 2007
Published: October 8, 2007

Citation
T. Xu, X. Jiao, G.-P. Zhang, and S. Blair, "Second-harmonic emission from sub-wavelength apertures: Effects of aperture symmetry and lattice arrangement," Opt. Express 15, 13894-13906 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13894


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References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391,667-669 (1998). [CrossRef]
  2. L. Salomon, F. Grillot, A. V. Zayats, and F. Fornel "Near-field distribution of optical transmission of periodic subwavelength holes in a metal film," Phys. Rev. Lett. 86,1110-1113 (2001). [CrossRef] [PubMed]
  3. Y. Liu and S. Blair "Fluorescence enhancement from an array of sub-wavelength metal apertures," Opt. Lett. 28,507-509 (2003). [CrossRef] [PubMed]
  4. A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi "Enhanced nonlinear optical conversion using periodically nanostructured metal films," Opt. Lett. 28,423-425 (2003). [CrossRef] [PubMed]
  5. M. Airola, Y. Liu, and S. Blair "Second-harmonic generation from an array of sub-wavelength metal apertures," J. Opt. A: Pure and Appl. Opt. 7,S118-S123 (2005). [CrossRef]
  6. W. Fan, S. Zhang, N. C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, Jr., K. J. Malloy, and S. R. J. Brueck "Second-harmonic generation from a nanopatterned isotropic nonlinear material," Nano Lett. 6,1027-1030 (2006). [CrossRef]
  7. A. Lesuffleur, L. K. S. Kumar, and R. Gordon "Enhanced second harmonic generation from nanoscale doublehole arrays in a gold film," Appl. Phys. Lett. 88,261104 (2006). [CrossRef]
  8. A. Lesuffleur, L. K. S. Kumar, and R. Gordon "Apex-enhanced second harmonic generation by using double-hole arrays in a gold film," Phys. Rev. B 75,045423 (2007). [CrossRef]
  9. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers "Strong modification of the nonlinear optical response of metallic subwavelength hole arrays," Phys. Rev. Lett. 97,146102 (2006). [CrossRef] [PubMed]
  10. N. Rakov, F. E. Ramos, and M. Xiao "Strong second-harmonic generation from a thin silver film with randomly distributed small holes," J. Phys.: Cond. Matter 15,L349-L352 (2003). [CrossRef]
  11. M. Sun, J. Tian, Z.-Y. Li, B.-Y. Cheng, D.-Z. Zhang, A.-Z. Jin, and H.-F. Yang "The role of periodicity in enhanced transmission through subwavelength hole arrays," Chinese Phys. Lett. 23,486-488 (2006). [CrossRef]
  12. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446,517-521 (2007). [CrossRef] [PubMed]
  13. F. Przybilla, C. Genet, and T. W. Ebbesen "Enhanced transmission through Penrose subwavelength hole arrays," Appl. Phys. Lett. 89,121115 (2006). [CrossRef]
  14. J. Bravo-Abad, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, and L. Martin-Moreno "Theory of extraordinary transmission of light through quasiperiodic arrays of subwavelength holes," arXiv:cond-mat/0606121v2 (2007).
  15. V. L. Brudny, B. S. Mendoza, and W. L. Mochan "Second-harmonic generation from spherical particles," Phys. Rev. B 62,11152-11162 (2000). [CrossRef]
  16. F. Mahdavi, Y. Liu, and S. Blair "Modeling fluorescence enhancement from metallic nanocavities," Plasmonics 2, 129-141 (2007). [CrossRef]
  17. M. D. McMahon, R. Lopez, R. F. Haglund, Jr., E. A. Ray, and P. H. Bunton "Second-harmonic generation from an arrays of symmetric gold nanoparticles," Phys. Rev. B 73,041401 (2006). [CrossRef]
  18. X. Heng, X. Cui, D. W. Knapp, J. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. Yang "Characterization of light collection through a subwavelength aperture from a point source," Opt. Express 14,10410-10425 (2006). [CrossRef] [PubMed]
  19. N. I. Zheludev and V. I. Emel’yanov "Phase matched second harmonic generation from nanostructured metallic surfaces," J. Opt. A: Pure and Appl. Opt. 6,26-28 (2004). [CrossRef]
  20. K. Liu, L. Zhan, Z. Y. Fan, M. Y. Quan, S. Y. Luo, and Y. X. Xia "Enhancement of second-harmonic generation with phase-matching on periodic sub-wavelength structured metal film," Opt. Commun. 276,8-13 (2007). [CrossRef]
  21. B. K. Canfield, H. Husu, J. Laukkanen, B. Bai, M. Kuittinen, J. Turunen, and M. Kauranen "Local field asymmetry drives second-harmonic generation in noncentrosymmetric nanodimers," Nano Lett. 7,1251-1255 (2007). [CrossRef] [PubMed]
  22. B. Lamprecht, A. Leitner, and F. R. Aussenegg "SHG studies of plasmon dephasing in nanoparticles," Appl. Phys. B 68,419-423 (1999). [CrossRef]
  23. A.M. Moran, J. Sung, E.M. Hicks, R. P. van Duyne, and K. G. Spears "Second harmonic excitation spectroscopy of silver nanoparticle arrays," J. Phys. Chem. B 109,4501-4506 (2005). [CrossRef]

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