The case for using gap plasmon-polaritons in second-order optical nonlinear processes

doi:10.1364/OE.20.028717

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The case for using gap plasmon-polaritons in second-order optical nonlinear processes

Jacob B. Khurgin and Greg Sun »View Author Affiliations

Optics Express, Vol. 20, Issue 27, pp. 28717-28723 (2012)
http://dx.doi.org/10.1364/OE.20.028717

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– Abstract
1. Introduction
2. Modal overlap and phase matching in MIM waveguides
3. Second order nonlinear processes
4. Summary
– References and links

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Abstract

We show that using metal-insulator-metal (MIM) waveguides to carry out various second-order nonlinear optical processes not only provides highly desired tight optical confinement but also facilitates the phase-matching due to their inherently large anisotropy. This fact allows one to take advantage of otherwise inaccessible large nonlinear susceptibilities of the cubic zinc blende semiconductors. Our efficiency estimates show that since only the longer wavelength infra-red radiation propagates in the surface-plasmon-polariton (SPP) mode, the losses in the metal, while significant, do not preclude development of highly compact nonlinear optical devices on this integration-friendly semiconductor platform.

1. Introduction

Recent years have seen increased (or, more properly, revived) interest in the properties of surface plasmon polaritons (SPP's) [1

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

, 2

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011). [CrossRef] [PubMed]

] existing on the metal/dielectric interfaces or in metal dielectric composites. This interest has been propelled by the fact that in structures incorporating metals the optical fields get confined on sub-wavelength scale and a variety of effects, linear and especially nonlinear, get enhanced. When combined with rapidly improving capabilities of nano-fabrication, plasmonic enhancement carries a promise of on-chip integration of efficient opto-electronic devices, including those using various nonlinear optical effects, such as switches, modulators and optical frequency converter. It is also well known that sub-wavelength confinement in nano-plasmonic structures is always accompanied by substantial losses, associated with field penetrating the metal [3

J. B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96(18), 181102 (2010). [CrossRef]

, 4

F. Wang and Y. R. Shen, “General properties of local Plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006). [CrossRef] [PubMed]

]. For given wavelength these losses cannot be reduced by engineering the shape of plasmonic structures [5

J. B. Khurgin and G. Sun, “Scaling of losses with size and wavelength in nanoplasmonics and metamaterials,” Appl. Phys. Lett. 99(21), 211106 (2011). [CrossRef]

], hence the figure of merit of nonlinear device, loosely defined here as strength of nonlinearity divided by the attenuation coefficient of nonlinear plasmonic devices is not high enough to justify their use in applications that require power efficiency for all intents and purposes, restricting nonlinear plasmonics to sensing. It is the goal of this work to explore whether there are circumstances in which despite being inherent lossy, nonlinear plasmonics can become competitive in terms of efficiency. For that we consider frequency conversion based on second order optical nonlinearity, χ⁽²⁾ since these are the lowest order (i.e. the strongest) nonlinear phenomena, and one can hope that satisfactory frequency conversion efficiency of a few percent per watt can be achieved over the distances less than one absorption length.

As mentioned above, SPP's can be divided into two broad classes: propagating SPP's on the metal/dielectric interface, and localized SPP's in the metal nanoparticles embedded into the dielectrics. The most ubiquitous of χ⁽²⁾ phenomena, second harmonic generation (SHG) has been observed by numerous groups in the media incorporating localized SPP's which may make plasmonic SHG into a diagnostic tool, but the power efficiency of the generation was quite small [6

Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011). [CrossRef] [PubMed]

–10

A. Slablab, L. Le Xuan, M. Zielinski, Y. de Wilde, V. Jacques, D. Chauvat, and J.-F. Roch, “Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres,” Opt. Express 20(1), 220–227 (2012). [CrossRef] [PubMed]

]. This follows from the fact that, as has been known for many decades [11

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968). [CrossRef]

–15

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev. 140(6A), A2020–A2030 (1965). [CrossRef]

], the metals themselves have tiny χ⁽²⁾, mostly due to the quadrupole interaction with the field, so the nonlinear polarization can only come from the surface [16

F. H. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009). [CrossRef]

] or the intrinsic nonlinearity of the surrounding dielectric. Then, first of all, while the fields do get locally enhanced in the vicinity of nanoparticles, the density of nanoparticles must be kept low (to avoid excessive absorption and overheating). Second, SHG is a three-wave process, and its efficiency depends on the overlap between the three interacting vector fields (two for fundamental frequency and one for second harmonic) and the tensor of χ⁽²⁾. This overlap is typically quite small for all geometries. Third, there is no provision for phase-matching. The combination of these three factors makes efficiency of optical nonlinearity using metals negligibly small [17

F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3(12), 1647–1655 (1986). [CrossRef]

] for most applications other than diagnostic, even though the effective nonlinearity per unit volume can be quite high.

This leaves one with propagating SPP’s and there has been an effort to study second-order nonlinearity of metal films early on [18

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974). [CrossRef]

], but, once again due to the inversion symmetry considerations, the strength of the interaction is weak, and, furthermore Kretchman excitation geometry [19

R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005). [CrossRef]

–21

N. B. Grosse, J. Heckmann, and U. Woggon, “Nonlinear Plasmon-Photon Interaction Resolved by k-Space Spectroscopy,” Phys. Rev. Lett. 108(13), 136802 (2012). [CrossRef] [PubMed]

] leads to very short interaction length, meaning that if one uses intrinsic χ⁽²⁾ of the dielectric the efficiency of nonlinear generation will be small. Once the inevitable absorption loss in the metal is accounted for, it appears that propagating SPP's are not capable of facilitating high efficiency χ⁽²⁾ processes, unless (a) the losses are kept to the minimum and (b) SPP offers additional benefits besides improved confinement. In this work we show that gap plasmons [22

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

] in the metal-insulator-metal (MIM) waveguides [23

K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009). [CrossRef]

] offer the added advantage of facilitating phase-matching in the isotropic nonlinear crystals, such as GaAs, and that by using gap plasmons only for the longest wavelength waves one can keep the losses within reasonable limit allowing efficient nonlinear generation.

2. Modal overlap and phase matching in MIM waveguides

Many of the III-V and some of II-VI semiconductors crystallize in the zinc-blend lattice that has no inversion symmetry, allowing for very large χ⁽²⁾, on the order of 100's of pm/V (compared to about 30 for LiNbO₃) [24

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience New York 2003).

], but this lattice is also perfectly isotropic which prevents conventional birefringence phase-matching. While quasi-phase-matching in GaAs has been explored [25

X. Yu, L. Scaccabarozzi, J. S. Harris Jr, P. S. Kuo, and M. M. Fejer, “Efficient continuous wave second harmonic generation pumped at 1.55 μm in quasi-phasematched AlGaAs waveguides,” Opt. Express 13(26), 10742–10748 (2005). [CrossRef]

] its implementation is difficult as in the absence of ferro-electricity the material cannot be poled. In the absence of material birefringence, the artificial waveguide birefringence can be employed using layered structures [26

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, N. Laurent, and J. Nagle, “Phase-matched mid-infrared difference frequency generation in GaAs-based waveguides,” Appl. Phys. Lett. 71(25), 3622–3624 (1997). [CrossRef]

] or slot waveguides [27

J. B. Khurgin, M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Suspended AlGaAs waveguides for tunable difference frequency generation in mid-infrared,” Opt. Lett. 33(24), 2904–2906 (2008). [CrossRef] [PubMed]

], but the fabrication is difficult, and the efficiency is greatly reduced by the fact that it is difficult to achieve good modal overlap between three waves with significantly different wavelengths in the same waveguide. This factor becomes particularly detrimental in the case of nonlinear generation of mid-IR radiation, which is of course the most desirable application of χ⁽²⁾ processes.

Let us consider how employing MIM rather than all-dielectric waveguides can simultaneously provide good modal overlap and phase-matching. Consider the MIM waveguide shown schematically in Fig. 1(a) and consisting of the core layer of GaAs or related zinc blende crystal of thickness d surrounded by metal layers on both sides sitting on top of a wider bandgap dielectric with lower index of refraction. This waveguide is capable of supporting of both TE and TM modes. The TE modes are characterized by the electric field polarized along y-axis,

E_{y} = E_{y 0} \exp (j β_{T E} z) \cos (q_{T E} x)

, inside the core layer and experience cut-off at long wavelength, as can be seen from the dispersion curve for the lowest order TE₀ wave Fig. 1(b). Note that the propagation constant

β_{T E} (ω)

is always smaller than the wave-vector

k_{G a A s} (ω) = n_{G a A s} (ω) \cdot ω / c

of the plane wave propagating in unconstrained GaAs. The dispersion curve for the latter (often referred to as the light line) is also shown in Fig. 1(b) as dashed line, and its deviation from the straight line indicates strong material dispersion impeding phase-matching without the metal. At the same time the lowest order TM₀ wave inside GaAs can be described as

E_{x} = E_{x 0} \exp (j β_{T M} z) \cos h (q_{T M} x)

. In microwave engineering this mode is regularly referred to as transverse-electro-magnetic (TEM) mode, while in optics it is frequently called gap SPP to indicate the fact that this mode does penetrate the metal much more than TE mode. Because of this the propagation constant

β_{T E M} (ω)

is always larger than the wave-vector

k_{G a A s} (ω)

as also shown in Fig. 1(b) and this metal-imposed birefringence can be sufficient to compensate the intrinsic dispersion of GaAs or other non-birefringent nonlinear crystals used as the core layer in the MIM waveguide.

Fig. 1 (a) The lowest order TE and TM modes in MIM waveguide, (b) their dispersion, (c) power densities of fundamental TM and second harmonic TE waves in the MIM waveguide designed for SHG at 775 nm, (d) effective indices, and (e) loss of these modes as a function of waveguide width d.

Let us consider how one can practically take advantage of this phase-matching scheme. First of all the only non-vanishing component of second order susceptibility is

χ_{14}^{(2)}

which requires three interacting fields to be polarized along three crystal axes of zinc blende lattice. Therefore, the propagation direction should be along one of the 110 axes (that happens to take advantage of natural cleavage planes in zinc blende lattice) with metal applied to the sides of the waveguide as shown in Fig. 1(c). To provide vertical confinement the waveguide is grown on top of AlAs cladding layer. The height of the waveguide h is chosen to be fixed and the width d is the adjustable parameter that provides phase-matching.

3. Second order nonlinear processes

For the ubiquitous case of SHG the fundamental wave of frequency ω is then coupled into TEM (gap SPP) mode and the second harmonic frequency 2ω is generated in the TE₀ mode. The field distributions are shown in Fig. 1(c). The phase-matching condition

β_{T E} (2 ω) = 2 β_{T M} (ω)

can also be written as equality of effective indices of refraction,

n_{T E} (2 ω) = β_{T E} (2 ω) \cdot c / 2 ω

and

n_{T M} (ω) = β_{T M} (ω) \cdot c / ω

. As an example we use the fundamental radiation of wavelength

λ_{ω} = 1550

nm and the second harmonic

λ_{2 ω} = 755

nm in the MIM waveguide with Ag side walls, consisting of Al_0.2Ga_0.8As as the core layer of height h = 1µm and width d sitting on top of a AlAs layer of 1µm on a GaAs substrate. The Al_0.2Ga_0.8As core layer is chosen here to avoid optical absorption at λ_2ω = 775nm, and its indices of refraction are n = 3.3 at

λ_{ω} = 1550

nm and n = 3.6 at

λ_{2 ω} = 755

nm. We have numerically calculated the effective indices versus the width d using a FDTD software from Lumerical. The results are shown in Fig. 1(d) and indicate that phase-matching is achieved at d = 0.57µm.

The conversion efficiency of the SHG process depends strongly on the overlap between the fundamental and second harmonic modes and can be found as [24

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience New York 2003).

]

\frac{P_{2 ω}}{P_{ω}} = {(\frac{π l}{λ_{2 ω}})}^{2} d_{14}^{2} S_{e f f}^{- 1} \frac{2 η_{0}}{n_{T M}^{2} (ω) n_{T E} (2 ω)} P_{ω}

(1)

where l is the interaction length,

d_{14} = χ_{14}^{(2)} (2 ω; ω, ω)

is the SHG coefficient, η₀ = 377Ω, and S_eff is the “effective area” of the waveguide defined as

S_{e f f}^{- 1} = \frac{{| \int_{c o r e} E_{2 ω, x} E_{ω, y}^{2} d x d y |}^{2}}{\int {| E_{2 ω}^{} |}^{2} d x d y {(\int {| E_{ω}^{} |}^{2} d x d y)}^{2}}

(2)

where the overlap integral of the field distributions of TE and TM modes in the numerator is taken over the nonlinear core medium only. The interaction length l is of course limited by the large TM mode waveguide loss due to the metal absorption as shown in Fig. 1(e). Note that the TM mode always experiences far larger loss than the TE mode due to field penetrating the metal, and it is the key advantage of our scheme that only the longer wavelength pump propagates in TM mode, which keeps propagation length l_prop to a manageable 23 µm at the phase-matching condition

n_{T M} (ω) = n_{T E} (2 ω) = 3.53

, with the TM mode loss of 1875 dB/cm. Using the numerical field profiles of both TE(2ω) and TM(ω) modes obtained from Lumerical, we have also calculated the effective area of the MIM waveguide to be 1.27 µm² at the phase-matching condition. Using

l = l_{p r o p} (ω) = 23

µm this brings the efficiency of SHG generation to a rather respectable 1.07 × 10⁻² W⁻¹, indicating that high conversion efficiency can be attained with a mode-locked pump.

Of course, SHG by itself is of little practical interest, compared to the difference frequency generation (DFG) capable of converting near IR pumps into the important mid-IR radiation. The DFG efficiency is typically much lower than SHG efficiency, primarily because it is difficult to achieve a good overlap between the relatively short wavelength near IR pumps and long wave-length mid-IR signal. This is where MIM waveguide has distinct advantage as mid-IR TM wave that can be compressed way below diffraction limit without incurring excessive loss. As an example we consider the arrangement shown in Fig. 2(a) in which the TE₀ pump at 1.3 µm and TM signal at 2.0 µm combine in the In_0.2Ga_0.8As MIM waveguide with Ag side walls sitting on top of a GaAs substrate to produce DFG idler at 3.71 µm. The phase-matching condition

β_{T E} (ω_{p}) = β_{T E M} (ω_{s}) + β_{T E M} (ω_{i})

as shown Fig. 2(b) is achieved at d = 0.84 µm when the effective indices of refraction at those wavelengths are

n_{T E}^{(p u m p)} = 3.48

n_{T M}^{(s i g)} = 3.53

, and

n_{T M}^{(i d l)} = 3.37

. The conversion efficiency can be estimated as

\frac{P_{i d l e r}}{P_{s i g n a l}} = {(\frac{π l}{λ_{i d l e r}})}^{2} {(2 d_{14})}^{2} S_{e f f}^{- 1} \frac{2 η_{0}}{n_{T E}^{(p u m p)} n_{T M}^{(s i g)} n_{T M}^{(i d l)}} P_{p u m p}

(3)

where the factor of 2 in the parenthesis indicates that χ⁽²⁾ for DFG is twice that of SHG, and the effective area is

S_{e f f}^{- 1} = \frac{{| \int_{c o r e} E_{p u m p, y} E_{s i g, x} E_{i d l, x} d x d y |}^{2}}{\int {| E |}_{p u m p}^{2} d x d y \int {| E |}_{s i g}^{2} d x d y \int {| E |}_{i d l}^{2} d x d y}

(4)

which is evaluated to be S_eff = 4.78 µm² at phase matching. Since signal and idler get absorbed with loss rate of 1330 dB/cm and 750 dB/cm, respectively, as shown in Fig. 2(c), the effective propagation length is

l = {(1 / l_{p r o p}^{(s i g)} + 1 / l_{p r o p}^{(i d l)})}^{- 1} = 21

µm which brings us to respectable conversion efficiency of about 4.29 × 10⁻⁴ W⁻¹.

Fig. 2 (a) Power densities of TE pump and TM signal and idler waves in the MIM waveguide designed for DFG at 3710 nm, (b) propagation constants, (c) loss of these modes as a function of waveguide width d, (d) power densities of TE pump and TM signal waves in the MIM waveguide designed for degenerate OPG at 3100 nm, (e) effective indices, and (f) loss of these modes as a function of waveguide width d.

DFG is obviously not the best way to obtain mid-IR radiation since it requires two sources – it would be more advantageous to develop an optical parametric generator (OPG) as shown in Fig. 2(d) in which near IR pump at 1.55 µm can produce degenerate signal/idler at 3.1 µm. As one can see from Fig. 2(e) phase-matching is achieved with

n_{T E}^{(p u m p)} = n_{T M}^{(s i g)} = 3.41

when In_0.4Ga_0.6As MIM waveguide width is d = 0.85 µm and the waveguide loss for the signal propagating in TM mode is only 830 dB/cm (propagation length of 52 µm) as shown in Fig. 2(f). The OPG threshold [24

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience New York 2003).

] will occur when the parametric gain overcomes the waveguide loss, or

P_{t h} \approx \frac{n_{T E}^{(p u m p)} {(n_{T M}^{(s i g)})}^{2}}{2 η_{0} {| 2 d_{14} |}^{2}} {(\frac{λ_{s i g}}{π l_{p r o p}^{(s i g)}})}^{2} S_{e f f}

(5)

where S_eff has been defined in Eq. (2) and has been determined to be 4.22 µm². The OPG threshold for our MIM waveguide is about 220 W– such peak powers are attainable from semiconductor mode-locked lasers integrated with power amplifiers [28

K. Kim, S. Lee, and P. Delfyett, “1.4kW high peak power generation from an all semiconductor mode-locked master oscillator power amplifier system based on eXtreme Chirped Pulse Amplification(X-CPA),” Opt. Express 13(12), 4600–4606 (2005). [CrossRef] [PubMed]

] which means that integrated-all-semiconductor parametric source of mid-IR radiation is within the reach.

4. Summary

We have calculated the guided surface plasmon modes of silver nano-scale ridge plasmon waveguides. We find that only one guided plasmon mode is bounded on the top surface of the flat-top metal nano-ride. The nano-ridge plasmon mode is a TEM mode with very small longitudinal electromagnetic field components in the direction of the propagation. We calculated the dispersion of the nano-ridge plasmon mode and its propagation length as a function of the wavelength. We also calculated the figure-of-merit of the nano-ridge mode for different ridge widths. We find that as the nano-ridge width increases, the propagation length always increases, however, the figure of merit increases first as the ridge width increases and then reaches a maximum when the ridge width falls between 100 nm and 200 nm. The nano-ridge waveguide of 100 nm wide has a propagation length of 242.8 µm at an excitation wavelength of 1.55 µm. This propagation length is long enough for building plasmonic circuits. During the process of writing this paper, we have found that a round top single crystal gold nano-ridge waveguide has been fabricated using focused ion beam milling, and the appearance of a nano-ridge plasmon mode was confirmed by the experiment [26

]. Metal nano-ridge surface plasmon waveguides can also be fabricated by metal filling nano-trenches etched in dielectric substrates. We believe the nano-ridge plasmon waveguide can be the building block for making plasmonic integrated circuits for sensor applications.

Acknowledgments

This work was supported by the Air Force Office of Scientific Research, Air Force Research Laboratory and the Air Force Summer Faculty Research Fellowship Program.

References and links

1.	S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
2.	M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011). [CrossRef] [PubMed]
3.	J. B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96(18), 181102 (2010). [CrossRef]
4.	F. Wang and Y. R. Shen, “General properties of local Plasmons in metal nanostructures,” Phys. Rev. Lett. 97(20), 206806 (2006). [CrossRef] [PubMed]
5.	J. B. Khurgin and G. Sun, “Scaling of losses with size and wavelength in nanoplasmonics and metamaterials,” Appl. Phys. Lett. 99(21), 211106 (2011). [CrossRef]
6.	Y. Zhang, N. K. Grady, C. Ayala-Orozco, and N. J. Halas, “Three-dimensional nanostructures as highly efficient generators of second harmonic light,” Nano Lett. 11(12), 5519–5523 (2011). [CrossRef] [PubMed]
7.	N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett. 33(17), 1975–1977 (2008). [CrossRef] [PubMed]
8.	S. Palomba, M. Danckwerts, and L. Novotny, “Nonlinear plasmonics with gold nanoparticle antennas,” J. Opt. A, Pure Appl. Opt. 11(11), 114030 (2009). [CrossRef]
9.	N. I. Zheludev and V. I. Emel’yanov, “Phase matched second harmonic generation from nanostructured metallic surfaces,” J. Opt. A, Pure Appl. Opt. 6(1), 26–28 (2004). [CrossRef]
10.	A. Slablab, L. Le Xuan, M. Zielinski, Y. de Wilde, V. Jacques, D. Chauvat, and J.-F. Roch, “Second-harmonic generation from coupled plasmon modes in a single dimer of gold nanospheres,” Opt. Express 20(1), 220–227 (2012). [CrossRef] [PubMed]
11.	N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968). [CrossRef]
12.	F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965). [CrossRef]
13.	F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14(25), 1029–1031 (1965). [CrossRef]
14.	S. S. Jha, “Nonlinear optical reflection from a metal surface,” Phys. Rev. Lett. 15(9), 412–414 (1965). [CrossRef]
15.	S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev. 140(6A), A2020–A2030 (1965). [CrossRef]
16.	F. H. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009). [CrossRef]
17.	F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3(12), 1647–1655 (1986). [CrossRef]
18.	H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33(26), 1531–1534 (1974). [CrossRef]
19.	R. Naraoka, H. Okawa, K. Hashimoto, and K. Kajikawa, “Surface plasmon resonance enhanced second-harmonic generation in Kretschmann configuration,” Opt. Commun. 248(1-3), 249–256 (2005). [CrossRef]
20.	K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7(2), 254–258 (2007). [CrossRef] [PubMed]
21.	N. B. Grosse, J. Heckmann, and U. Woggon, “Nonlinear Plasmon-Photon Interaction Resolved by k-Space Spectroscopy,” Phys. Rev. Lett. 108(13), 136802 (2012). [CrossRef] [PubMed]
22.	S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]
23.	K.-Y. Jung, F. L. Teixeira, and R. M. Reano, “Surface plasmon coplanar waveguides: Mode characteristics and mode conversion losses,” IEEE Photon. Technol. Lett. 21(10), 630–632 (2009). [CrossRef]
24.	Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience New York 2003).
25.	X. Yu, L. Scaccabarozzi, J. S. Harris Jr, P. S. Kuo, and M. M. Fejer, “Efficient continuous wave second harmonic generation pumped at 1.55 μm in quasi-phasematched AlGaAs waveguides,” Opt. Express 13(26), 10742–10748 (2005). [CrossRef]
26.	A. Fiore, V. Berger, E. Rosencher, P. Bravetti, N. Laurent, and J. Nagle, “Phase-matched mid-infrared difference frequency generation in GaAs-based waveguides,” Appl. Phys. Lett. 71(25), 3622–3624 (1997). [CrossRef]
27.	J. B. Khurgin, M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Suspended AlGaAs waveguides for tunable difference frequency generation in mid-infrared,” Opt. Lett. 33(24), 2904–2906 (2008). [CrossRef] [PubMed]
28.	K. Kim, S. Lee, and P. Delfyett, “1.4kW high peak power generation from an all semiconductor mode-locked master oscillator power amplifier system based on eXtreme Chirped Pulse Amplification(X-CPA),” Opt. Express 13(12), 4600–4606 (2005). [CrossRef] [PubMed]

OCIS Codes
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.4223) Nonlinear optics : Nonlinear wave mixing
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 2, 2012
Revised Manuscript: November 30, 2012
Manuscript Accepted: November 30, 2012
Published: December 10, 2012

Citation
Jacob B. Khurgin and Greg Sun, "The case for using gap plasmon-polaritons in second-order optical nonlinear processes," Opt. Express 20, 28717-28723 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28717

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References

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19(22), 22029–22106 (2011). [CrossRef] [PubMed]
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The case for using gap plasmon-polaritons in second-order optical nonlinear processes

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Abstract

1. Introduction

2. Modal overlap and phase matching in MIM waveguides

3. Second order nonlinear processes

4. Summary

Acknowledgments

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References

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