Toward parametric amplification in plasmonic systems: Second harmonic generation enhanced by surface plasmon polaritons M. Mayy,1 G. Zhu,1 A. D. Webb,1 H. Ferguson,2 T. Norris,2 V. A. Podolskiy,3 and M. A. Noginov1,* 1 Center for Materials Research, Norfolk State University, Norfolk, VA 23504, USA Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 4810, USA 3 Department of Physics and Applied Physics, University of Massachusetts Lowell, Lowell, MA 01854, USA * [email protected] 2
Abstract: Having in mind parametric amplification of surface plasmon polaritons (SPPs) as the final goal, we took the first step and studied in the Kretschmann geometry a simpler nonlinear optical process – second harmonic generation (SHG) enhanced by SPPs propagating at the interface between gold film and 2-methyl-4-nitroaniline (MNA). The experimentally demonstrated SHG efficiency was nearly 106 times larger than the one reported previously in the SPP system with different nonlinear optical material. The experimentally measured nonlinear conversion efficiency is estimated to be sufficient for parametric amplification of surface plasmon polaritons at ultra-short laser pumping. ©201 Optical Society of America OCIS codes: (190.4400) Nonlinear optics, materials; (240.6680) Surface plasmons; (190.4975) Parametric processes; (250.5403) Plasmonics.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
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1. Introduction. Parametric amplification of surface plasmon polaritons: characteristic length scales The research field of plasmonics has received a widespread attention over the past several decades and led to applications ranging from sensing [1,2] and information technology [3] to medical diagnostics and treatment [4]. The two main phenomena studied in plasmonics are localized surface plasmons (SPs, resonant oscillations of free electrons in metallic nanoparticles [5]) and surface plasmon polaritons (SPPs, surface electromagnetic waves propagating along the interface between metal and dielectric [5]). Unfortunately, most plasmonics applications and devices suffer from the common cause – absorption loss in metal [6]. Furthermore, the majority of current plasmonic applications are passive, while future technologies call for active devices and systems with amplification, tunability and nonlinearity [7]. It has been shown theoretically [6,8–11] and experimentally [12–18] that both problems can be solved (at least, in principle) by adding optical gain to a dielectric that is adjacent to metal. However, optical gain required to conquer loss in metal is prohibitively high (in particular, in the visible range of the spectrum). Furthermore, it is an unavoidable source of unwanted spontaneous emission noise, which is detrimental for imaging and information technology applications. Optical parametric amplification (OPA), whose usage in metamaterials has been first discussed in [19], provides viable alternative to conventional optical gain based on population inversion. What makes this process particularly attractive is
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(i) the fact that parametric amplification does not have a quantum defect, which is unavoidable source of heat in gain media based on excited atoms or molecules, (ii) its noise, theoretically, can be smaller than the noise of conventional gain media amplifiers – 3 dB at non-degenerate parametric amplification (without excess noise due to incomplete population inversion) and 0 dB at degenerate parametric amplification, (iii) a possibility of frequency tuning, and (iv) potential of generating entangled SPPs, which can find application in future on-chip quantum information processing [20]. Furthermore, this is probably the only amplification technique capable of preserving quantum information. The efficiency of optical parametric amplification can be evaluated (at good phase matching) as g = κI
(1)
where g is the gain, I is the pumping flux and
κ = 8π 2 d eff2 / λs λi ns ni n p ε 0 c
(2)
is the coupling constant [21]. Here deff is the effective nonlinear coefficient; ns, ni, and np are the indices of refraction at the signal wavelength (λs), idler wavelength (λi), and pumping wavelength (λp), respectively; ε0 is the vacuum permittivity; and c is the speed of light. The value of parametric gain g, estimated at λs≈λi≈1 μm, ns≈ni≈np≈2, Ι = 10 MW/cm2, and deff = 30 pm/V, is equal to ≈7 cm−1. Although this value is much smaller than the one required for compensation of SPP loss in silver in the visible range (~1000 cm−1 [14]) it can be sufficient to conquer propagation loss of long range surface plasmons at the telecom frequency (~1cm−1 [22]). In the calculation above, we used the parameters, which approximately correspond to 2Methyl-4-nitroaniline (MNA) – our material of choice, whose second order nonlinearity, is stronger than that in LiNbO3 (coefficient d11 in MNA exceeds that in LiNbO3 forty-fold [23,24]). The coherence length Lc is an important characteristic of any harmonic generation or parametric amplification process. In a simple case of second harmonic generation (SHG), it can be evaluated as [25] Lc =
λ 4(n2ω − nω )
(3)
,
Where λω is the wavelength at the fundamental frequency ω, and nω and n2ω are the indexes of refraction at the fundamental frequency and the second harmonic frequency, respectively. At characteristic system parameters (n2ω-nω) = 0.05 and λω = 1 μm, the coherence length Lc is equal to ≈5 μm. Although this value is rather small, it is comparable to the propagation length of SPP [14] ω ε ,ε , 3/ 2 ε ,, ε ,, L p = , 1 2 , 1,2 + ,22 c ε1 + ε 2 ε1 ε 2
−1
,
(4)
which would limit the coherence length anyway. Here ε i = ε i, + iε i" is the complex dielectric permittivity of metal (i = 1) and dielectric (i = 2). Assuming that at λ = 1080 nm, ε1’ = −50.2, ε1” = 3.78 (gold [26]), ε2’ = 3.61, and ε2” = 0 (MNA, as discussed below), one estimates Lp = 14.9 μm, which is of the same order of magnitude as Lc. The estimates above show that parametric amplification of SPPs propagating at the interface between gold and MNA is, in principle, possible and worth researching. In this work, as the first step toward this goal, we have studied in the same system a simpler nonlinear optical process – second harmonic generation – and demonstrated its relatively high efficiency and enhancement by SPP.
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Surface plasmon polaritons at the gold/MNA interface were exited in the Kretschmann geometry [5], Fig. 1. MNA is a biaxial organic crystal, whose high indexes of refraction (strongly varying from one literature source to another) are summarized in Table 1. This has determined our choice of the prism material, rutile (TiO2), whose ordinary and extraordinary indexes of refraction, no = 2.48 and ne = 2.74 [30], are even higher than those of MNA. We have deposited gold film on one half of the prism’s hypotenuse face, after which entire face (with and without Au) was covered with MNA, Fig. 1. Correspondingly, optical properties of one half of the sample, with gold film that enabled SPP, could be compared to that of the other half, which did not have gold and did not support SPP. 2. Experiment 2.1 Samples and setup Gold film (40 nm thick) was produced via thermal vapor deposition. To obtain the MNA film, we heated and melted 10 mg of MNA on top of a glass slide at 145C, after which pressed the hypotenuse side of the prism onto the melt for 20 min. The temperature was then slowly lowered, at the cooling rate of 5C/hour, and MNA crystallized. The resulting 23 μm MNA film had yellowish and slightly milky appearance. The polycrystalline sizes, estimated using optical microscope, ranged between 10 μm and 50 μm and were comparable to or larger than the SPP propagation length Lp. The glass slide was then carefully removed and the MNA film remained attached to the prism. In agreement with the literature [23,24], the x-ray diffraction (XRD) measurements [Fig. 2(a)] have shown that the b axis of the monoclinic MNA crystal (which coincides with the optical y axis) was oriented perpendicular to the film. In order to evaluate sustainability of MNA to short-pulsed laser radiation, thin (15 μm) MNA films deposited on glass were exposed to 100 fs pulses of a mode locked Ti:sapphire laser (λ = 800 nm, reperition rate = 250 kHz) and the intensity of the second harmonic radiation has been studied as a function of time, Fig. 2(b). Table 1. Indexes of refraction nx, ny and nz in MNA. λ, nm 1064 633 532 1064 532 1064 532 1064
nx 1.8 2 2.2 1.763 2.291 1.8 2.2 2.093
633 532
2.341 2.484
ny
nz
1.695
Ref. [24] [24] [24] [27] [27] [28] [28] [29]
1.752 1.845
[29] [29]
1.6 1.514 1.843
1.359 1.569
We have found that at the pumping power density equal to 30 GW/cm2, the second harmonic light intensity decreased less than by 1% over 30 min of exposure. This damage resistance is sufficient for table-top experiments and proof of principle demonstrations. In the optical studies, the prism with deposited gold and MNA films was placed on a rotating stage and excited with 5 ns pulses (at λ = 1080 nm) from an optical parametric oscillator (OPO). The optic axis of the rutile prism was perpendicular to the base faces. In most measurements, the incident beam was horizontally polarized (p polarization that was perpendicular to the optic axis – ordinary ray for rutile). Three types of measurements have been performed (as discussed below) on the halves of the hypotenuse side of the prism coated and not coated with gold.
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Fig. 1. Left: Experimental setup. Red rays– fundamental frequency (1080 nm); green rays– SHG frequency (540 nm). Solid rays – horizontal (p) polarization; dashed rays – vertical (s) polarization. Right: Schematic of the gold and MNA layers deposited onto the hypotenuse side of the prism.
Fig. 2. (a) X-ray diffraction (XRD) scan of the deposited MNA film, showing the crystallographic b axis (010) of the monoclinic MNA crystal to be oriented perpendicular to the film. (b) Time dependence of second harmonic generation in thin MNA film exposed to 100 fs laser pulses (peak power density = 30 GW/cm2, repetition rate = 250 kHz, λ = 800 nm).
2.2 Angular reflection profiles The prism was rotated and the angular dependence of reflection R(θ) (in p polarization) has been studied. The signal was detected with Detector 1, which was an integrating sphere connected with an optical fiber bundle to a photomultiplier tube (PMT), Fig. 1. The reflectance, measured on the half of the prism without gold, changed abruptly from low to high at the critical incidence angle θc = 44°, which corresponded to onset of the total internal reflection at the interface between rutile and MNA, Fig. 3(a), trace 1. This critical angle was fitted [Fig. 3(a), trace 3]) by the known theoretical model [5] (see Appendix) using the = 2.48 and the effective index of refraction of ordinary index of refraction of rutile n1080 o MNA n1080 MNA = 1.73 (fitting parameter), which was within the range of values known from the literature, Table 1. An analogous measurement, performed on the half of the prism coated with gold, resulted in the dip at angles θ ranging from 44.7° to 47.8° (measured at half-maximum level), which were slightly larger than θc, Fig. 3(a), trace 2. At closer inspection, one can see that this dip
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has a shoulder at ≈45.3° (arrow I) and a minimum at ≈46.6° (arrow II). The latter minimum is due to SPP propagating at the interface between gold and MNA. Its angular position can be predicted theoretically [5] with fairly high accuracy without use of any additional fitting parameters at the index of refraction of MNA equal to n1080 MNA = 1.73 (same as above) and dielectric permittivity of gold equal to −50.2 (at λ = 1080 nm) [26], compare traces 2 and 4 in Fig. 3(a).
Fig. 3. (a) Angular reflection profiles measured (using Detector 1 in Fig. 1) on the half of the prism without gold (trace 1) and with gold (trace 2). Traces 3 and 4: the corresponding profiles calculated using known formula from Ref [5]. and material parameters described in the text. (b) Traces 1 and 2 are the same as in Fig. 3(a). Dependence of the scattered light intensity (measured with Detector 2) on the incidence angle at the fundamental frequency (trace 3) and the second harmonic frequency (trace 4). The error bars are shown on the right. Arrows I and II point at characteristic peaks, dips, and shoulders discussed in the text.
Although the experimental and the calculated reflectance profiles in Fig. 3(a) had the same angular positions of their characteristic features, the experimental transition from refraction to total internal reflection was not as sharp as the calculated one (traces 1 and 3), and the experimentally measured SPP reflectance dip was much less pronounced than the one predicted by the theory (traces 2 and 4). We attribute this difference to moderate light scattering in the MNA film. (Note that no reflection change at the critical angle or the SPPrelated dip in the reflectance profile have been observed in the case of a much milkier MNA film with shorter transport mean free path.)
2.3 Second harmonic generation scattered from the back side of the prism The laser beam (at λ = 1080 nm) intercepting gold and MNA films deposited onto the hypotenuse side of the prism, produced a bright spot of scattered light (at both fundamental and second harmonic frequencies), which was clearly seen from the back side of the prism. This spot was imaged onto the entrance slit of the monochromator, with a PMT attached to its exit slit. (This detection system is depicted in Fig. 1 as Detector 2.) The intensity of scattered light was studied as the function of the angular position of the prism relative to the pumping beam, Fig. 1. One can see that the scattered light intensity at the fundamental frequency has a maximum at 45.1° (arrow I) and a shoulder at 46.6° (arrow II) – the angles nearly corresponding to the shoulder and the minimum in the SPP reflectance profile, respectively [traces 3 and 2 in Fig. 3(b)]. At the same time, a double-headed band with the peaks at 45.2° and 46.5° (arrows I and II, correspondingly) has been observed in the angular scattering profile at the second harmonic frequency (540 nm), Fig. 3(b), trace 4. Both its maxima nearly coincided with the spectral positions of the minima and maxima of traces 2 and 3 in Fig. 3(b). Note that at pumping density equal to 2 MW/cm2, the second harmonic intensity at the maxima, 45.2° and 46.5°, was nearly thirty-fold stronger than that at the offresonance excitation, 50° (solid line in Fig. 4).
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The results summarized in Fig. 3(b) suggest that SPPs are excited and enhance optical fields at two incidence angles, ≈46.6° and ≈45.2°. While the former one is in a good agreement with theoretical predictions made at plausible system parameters, the origin of the second one is less clear. Formally, SPP excited at the latter incidence angle can be explained assuming that the refraction index of MNA is not 1.73 but 1.71. However, the ground for such assumption is not well justified, and n1080 MNA = 1.71 would not correctly describe the angle of total internal reflection. At λ = 1080 nm, the maximal theoretically predicted SPP enhancement of the fundamental harmonic light intensity, defined as the ratio of |E|2 just above the lower boundary of MNA in the presence of Au film and that in the absence of Au film, is equal to 14.0 (at the optimal thickness of the silver film equal to d = 44.5 nm and optimal incidence angle equal to 46.05°.) This suggests a possibility of nearly 200-fold enhancement of the SHG intensity by surface plasmon polaritons. At the Au film thickness used in our experiments, d = 40 nm, the maximal enhancement of the fundamental harmonic intensity is slightly smaller, 13.5 times.
Fig. 4. Efficiency of second harmonic generation in the Ag/MNA sample calculated based on the fundamental and second harmonic beam intensities at horizontal polarization (solid characters) and vertical polarization (open characters) measured at the incidence angle equal to 45° (squares) and 47° (diamonds). Triangles: efficiency of SHG in bare silver film [31] (open character) and silver film with a monolayer of hemicyanine molecules deposited on top [31] (closed character). Solid line: spectrum of the scattered second harmonic light detected from the back side of the prism (right vertical scale).
2.4 Observation of the second harmonic beams and measurement of the second harmonic efficiency The setup involving Detector 1 (Fig. 1) was also used to study intensities and angular directions of the generated second harmonic beams. In this measurement, optical bundle delivered light to the entrance slit of the monochromator, with the PMT attached to its exit slit. The spectral response of the apparatus was calibrated using the lamp with known emissivity spectrum. The input power was measured with the calibrated powermeter, and the diameter of the pumped spot was measured using the knife edge technique. Experimentally, horizontally polarized (ordinary) beam at λ = 1080 nm was incident onto the hypotenuse side of the prism coated with gold and MNA, at the angle corresponding to excitation of surface plasmon polariton (θ = 45°). It produced two horizontally polarized and two vertically polarized beams at fundamental and second harmonic frequencies, as shown in Fig. 1. As one can see from Fig. 5, depicting angular positions and relative intensities of the four beams measured with the large-area detector (integrating sphere with 1 cm opening), the intensities of polarization-conserving horizontally polarized beams were much larger than those of vertically polarized beams. Expectedly, the intensities of the reflected 1080 nm (540
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nm) beams were linearly (quadraticaly) proportional to the incident light intensity. No vertically polarized, extraordinary, beam at λ = 1080 nm has been produced by the uncoated rutile prism (without Au or MNA). We infer that the vertically polarized beam was generated at the interface between gold film and lightly scattering biaxial MNA film, whose optical axis y was perpendicular to the surface and optical axes x and z of the constituent microcrystallines were randomly oriented in the plane of the interface. This could result in the polarization rotation in MNA and the birefringence in rutile.
Fig. 5. Angular directions and intensities of two horizontally polarized and two vertically polarized outgoing beams at the pumping intensity equal to 2 MW/cm2. Each peak is marked with the corresponding index of refraction, where ‘o’ stands for ordinary beam (horizontal polarization) and ‘e’ stands for extraordinary beam (vertical polarization). Two 1080 nm light intensities are in scale with each other and two 540 nm light intensities are in scale with each other. However, the intensities of the 540 nm beams are not in scale with the intensities of the 1080 nm beams. Dashed line indicates the incidence angle.
By knowing the indexes of refraction of rutile for ordinary and extraordinary rays ( n1080 = 2.47 and ne1080 = 2.73 [30]), we have found that the angles of incidence and reflection o are related to each other via the expression resembling the Snell’s law for refraction, ni sin θ i = nr sin θ r ,
(5)
where indexes i and r stand for ‘incident’ and ‘reflected’, correspondingly. (For polarizationconserving reflection, ni = nr and θi = θr.) At the pumping power density equal to 2 MW/cm2, the intensities of the second harmonics beams were high enough to be seen on a white card with a naked eye. The directions of the generated SHG beams were also governed by Eq. (5), where ordinary and extraordinary indexes of refraction of rutile for outgoing beams corresponded to λ = 540 nm ( no540 = 2.66 and ne540 = 2.97 [30]). Note that the efficiency of the second harmonic generation, calculated [31] as ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 for the fundamental and second harmonic beams at horizontal polarization is reasonably close to that calculated for the fundamental and second harmonic beams at vertical polarization, Fig. 4. This suggests that the horizontally polarized fundamental frequency beam generates horizontally polarized SHG beam and the vertically polarized fundamental frequency beam generates vertically polarized SHG beam. Here Er540 and Er1080 are the amplitudes of electric fields in the outgoing beams at the corresponding wavelengths, and Ei1080 is the amplitude of the electric field in the incident beam. Note that the quantity ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 is the characteristics of the whole device, with inherent radiative and internal losses, angular dependent SPP enhancement, etc., rather than the property of the nonlinear optical material, MNA. (Note that if one will define the efficiency
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of the second harmonic generation as ( Er540 / Ei1080 ) 2 / ( Ei1080 ) 2 , it will be different from
( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 by no more than 20%, since the reflected light intensity (at 1080 nm) is never smaller than 80% of the incident light intensity, Fig. 3.) Analogous measurements with qualitatively similar results have been performed at the incidence angle equal to 47.0°, Fig. 4. The results of the SHG efficiency measurements are summarized in Fig. 4, along with the results of similar experiments reported in the literature [31]. One can see that SHG efficiency in our Au/MNA sample is ~7x105 times larger than that in the system consisting of a glass prism with deposited Ag film and monolayer of hemicyanine molecules, and ~3x107 times larger than that in the silver film without any nonlinear molecules [31]. At the incident light intensity equal to 2 MW/cm2, the SHG yield η = ( Er540 / Er1080 ) 2 in our experiment ranges from 4.8x10−6 (solid square in Fig. 4) to 1.3x10−4 (open diamond in Fig. 4). These values are significantly larger than the one reported in bare metallic split ring nanostructures, η = 3x10−11 at 230 MW/cm2 [32]. (Note that in the historic seminal experiment by Franken et al. [33], the SHG conversion efficiency of a macroscopic quartz crystal was of the order of 10−8 at the pumping density of the order of 102 MW/cm2.) We, thus, infer that in spite of multiple efforts aimed to exploit nonlinearity of constituent components of nanophotonic and plasmonic devises, including metamaterials (see for example, Refs [32, 34–36].), nothing can compare to a highly efficient nonlinear optical material with the record-high χ(2) response, which can be further enhanced by a plasmonic resonance. 3. Summary
To summarize, we have researched 2-methyl-4-nitroaniline (MNA) as a potential nonlinear optical material for parametric amplification of surface plasmon polaritons (SPPs), and studied second harmonic generation (SHG) as the first and easier step. Expectedly, SPP enhancement of the second harmonic generation has been observed experimentally. Thus, in the Kretschmann geometry and at the pumping energy density equal to 2 MW/cm2, SHG light intensity was nearly thirty-fold larger at the SPP resonance angle (46.6°) than that at the offresonance excitation (50°). The maximal SHG efficiency in our sample (defined as ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 ) was equal to 1.7x1017 m2/V2, which is 7x105 times larger than that in the glass prism with deposited Ag film and monolayer of hemicyanine molecules [31] and 2.8x107 times larger than that in the glass prism with bare silver film [31]. Assuming that the experimentally determined SHG efficiency ∝ (ε 0 χ (2) ) 2 ∝ ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 (in our setup, with given material loss and SPP propagation length) is the same as the efficiency of the difference frequency generation (the process, which governs parametric amplification), we have estimated that the pumping power density I ( p ) = ε 0 c( E ( p ) ) 2 , which is required for the generated signal field in the OPA process E ( s out ) to be equal to the input signal field E ( s in ) , is equal to I ( p ) ~25 GW/cm2. Arguably, the latter condition can be regarded as a threshold for parametric amplification. (In the calculation, the output signal field E ( s out ) and the idler field E (i ) were related to the input signal field E ( s in ) and the pumping field E ( p) as ( s out) (2) ( p ) ( i ) ( s in ) (2) 2 ( p) 2 ( s in) ( p) 2 540 1080 2 1080 2 E ∝ ε 0 χ E E ∝ E (ε 0 χ ) ( E ) ∝ E ( E ) [( Er / Er ) / ( Ei ) ] and E (i ) ∝ ε 0 χ (2) E ( p ) E ( s in ) , and the quantity (ε 0 χ (2) ) 2 was substituted with the experimentally
measured ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 .) The required power density of 25 GW/cm2 can be achieved experimentally with an ultrafast (100 fs) Ti:sapphire laser, and it is still below the laser damage threshold for MNA, see Fig. 2(b). This makes parametric amplification of surface plasmon polaritons a realistic task.
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Received 27 Aug 2013; revised 4 Oct 2013; accepted 15 Oct 2013; published 27 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007773 | OPTICS EXPRESS 7781
Appendix
The angular reflectance profiles R(θ) in Fig. 3(a) have been calculated using the formula derived in [5] for a slab with the thickness d and dielectric permittivity ε1, sandwiched between two semi-infinite media with dielectric permittivities ε0 and ε2 (Fig. 6): p 2 012
R= r
Ep = rp E0
2
2
r p + r p exp(2ik z1d ) = 01 p 12p , 1 + r01 r12 exp(2ik z1d )
p is the amplitude reflection coefficient for p polarized light, accounting for where r012
reflection at both interfaces 0-1 and 1-2; Erp and E0p are the electric fields (in p polarization) of the incident and the reflected waves, respectively; rikp =
(k zi ε k − k zk ε i ) (k zi ε k + k zk ε i )
is the amplitude reflection coefficient for p polarized light at the interface between media i and k; εi and εk are the dielectric permittivities of media i and k; 2
ω k zi = ± κ = ± ε i − k x2 , i =0,1,2 c
is the z component of the wavevector in medium i; k x = k phot sin θ 0 is the x component of the wavevector in medium i; ω is the angular frequency; c is the speed of light; θ is the incidence angle; k phot = n0ω / c is the wavenumber for a photon in medium 0; and n0 = ε 0 is the index of refraction of medium 0 (in our study, ε0 corresponded to rutile and was assumed to be purely real). ε2
z
ε1 ε0
x
d
θ Fig. 6. Schematics assumed at calculation of the angular reflectance profile.
Acknowledgments
MM, GZ, ADW and MAN were supported by the NSF PREM grant DMR-1205457, NSF IGERT grant DGE-0966188, and AFOSR grant FA9550-09-1-0456. VAP acknowledges the support from ARO grant W911NF-12-1-0533. TN and HF acknowledge NSF MRSEC grant DMR 1120923, and NSF PREM DMR 1205457. The authors cordially thank Jacob Khurgin for useful discussions and suggestions.
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Received 27 Aug 2013; revised 4 Oct 2013; accepted 15 Oct 2013; published 27 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007773 | OPTICS EXPRESS 7782
Abstract: Having in mind parametric amplification of surface plasmon polaritons (SPPs) as the final goal, we took the first step and studied in the Kretschmann geometry a simpler nonlinear optical process – second harmonic generation (SHG) enhanced by SPPs propagating at the interface between gold film and 2-methyl-4-nitroaniline (MNA). The experimentally demonstrated SHG efficiency was nearly 106 times larger than the one reported previously in the SPP system with different nonlinear optical material. The experimentally measured nonlinear conversion efficiency is estimated to be sufficient for parametric amplification of surface plasmon polaritons at ultra-short laser pumping. ©201 Optical Society of America OCIS codes: (190.4400) Nonlinear optics, materials; (240.6680) Surface plasmons; (190.4975) Parametric processes; (250.5403) Plasmonics.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
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17. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010). 18. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009). 19. A. K. Popov and V. M. Shalaev, “Negative-index metamaterials: second-harmonic generation, Manley–Rowe relations and parametric amplification,” Appl. Phys. B 84(1-2), 131–137 (2006). 20. R. Paschotta, Encyclopedia of laser physics and technology, (Wiley-VCH, 2008). 21. W. Koechner and M. Bass, Solid–State lasers engineering, (Springer–Verlag, 2003). 22. M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8(11), 3998–4001 (2008). 23. G. F. Lipscomb, “An exceptionally large linear electro-optic effect in the organic solid MNA,” J. Chem. Phys. 75(3), 1509 (1981). 24. B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, and J. L. Bernstein, “An organic crystal with an exceptionally large optical second-harmonic coefficient: 2-methyl-4-nitroaniline,” J. Appl. Phys. 50(4), 2523– 2527 (1979). 25. J. Jerphagnon and S. K. Kurtz, “Maker fringes: A detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41(4), 1667–1681 (1970). 26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). 27. S. R. Marder, J. E. Sohn, and G. D. Stucky, eds., “Materials for nonlinear optics: Chemical perspectives,” ACS symposium series no. 455. (American Chemical Society,1991). 28. H. Itoh, K. Hotta, H. Takara, and K. Sasaki, “Frequency doubling of a Nd:YAG laser by a MNA single crystal thin film on a slab-type optical glass waveguide,” Appl. Opt. 25(9), 1491–1494 (1986). 29. G. Zhang and K. Sasaki, “Measuring anisotropic refractive indices and film thicknesses of thin organic crystals using the prism coupling method,” Appl. Opt. 27(7), 1358–1362 (1988). 30. M. W. Ribarsky, “Titanium Oxide” in Handbook of Optical Constants of Solids, edited by E. D. Palik and G. Ghosh, volume 2. (Academic Press, 1998) 31. I. R. Girling, N. A. Cade, P. V. Kolinsky, G. H. Cross, and I. R. Peterson, “Surface plasmon enhanced SHG from a hemicyanine monolayer,” J. Phys. D 19(11), 2065–2075 (1986). 32. 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). 33. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961). 34. D. Cho, W. Wu, F. Wang, X. Zhang, and Y.-R. Shen, “Nonlinear Optics in Metamaterials,” Conference Paper, Laser Science, San Jose, CA USA, October 11–15, 2009. 35. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011). 36. S. Palomba, H. Harutyunyan, J. Renger, R. Quidant, N. F. van Hulst, and L. Novotny, “Nonlinear plasmonics at planar metal surfaces,” Philos Trans A Math Phys Eng Sci 369(1950), 3497–3509 (2011).
1. Introduction. Parametric amplification of surface plasmon polaritons: characteristic length scales The research field of plasmonics has received a widespread attention over the past several decades and led to applications ranging from sensing [1,2] and information technology [3] to medical diagnostics and treatment [4]. The two main phenomena studied in plasmonics are localized surface plasmons (SPs, resonant oscillations of free electrons in metallic nanoparticles [5]) and surface plasmon polaritons (SPPs, surface electromagnetic waves propagating along the interface between metal and dielectric [5]). Unfortunately, most plasmonics applications and devices suffer from the common cause – absorption loss in metal [6]. Furthermore, the majority of current plasmonic applications are passive, while future technologies call for active devices and systems with amplification, tunability and nonlinearity [7]. It has been shown theoretically [6,8–11] and experimentally [12–18] that both problems can be solved (at least, in principle) by adding optical gain to a dielectric that is adjacent to metal. However, optical gain required to conquer loss in metal is prohibitively high (in particular, in the visible range of the spectrum). Furthermore, it is an unavoidable source of unwanted spontaneous emission noise, which is detrimental for imaging and information technology applications. Optical parametric amplification (OPA), whose usage in metamaterials has been first discussed in [19], provides viable alternative to conventional optical gain based on population inversion. What makes this process particularly attractive is
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(i) the fact that parametric amplification does not have a quantum defect, which is unavoidable source of heat in gain media based on excited atoms or molecules, (ii) its noise, theoretically, can be smaller than the noise of conventional gain media amplifiers – 3 dB at non-degenerate parametric amplification (without excess noise due to incomplete population inversion) and 0 dB at degenerate parametric amplification, (iii) a possibility of frequency tuning, and (iv) potential of generating entangled SPPs, which can find application in future on-chip quantum information processing [20]. Furthermore, this is probably the only amplification technique capable of preserving quantum information. The efficiency of optical parametric amplification can be evaluated (at good phase matching) as g = κI
(1)
where g is the gain, I is the pumping flux and
κ = 8π 2 d eff2 / λs λi ns ni n p ε 0 c
(2)
is the coupling constant [21]. Here deff is the effective nonlinear coefficient; ns, ni, and np are the indices of refraction at the signal wavelength (λs), idler wavelength (λi), and pumping wavelength (λp), respectively; ε0 is the vacuum permittivity; and c is the speed of light. The value of parametric gain g, estimated at λs≈λi≈1 μm, ns≈ni≈np≈2, Ι = 10 MW/cm2, and deff = 30 pm/V, is equal to ≈7 cm−1. Although this value is much smaller than the one required for compensation of SPP loss in silver in the visible range (~1000 cm−1 [14]) it can be sufficient to conquer propagation loss of long range surface plasmons at the telecom frequency (~1cm−1 [22]). In the calculation above, we used the parameters, which approximately correspond to 2Methyl-4-nitroaniline (MNA) – our material of choice, whose second order nonlinearity, is stronger than that in LiNbO3 (coefficient d11 in MNA exceeds that in LiNbO3 forty-fold [23,24]). The coherence length Lc is an important characteristic of any harmonic generation or parametric amplification process. In a simple case of second harmonic generation (SHG), it can be evaluated as [25] Lc =
λ 4(n2ω − nω )
(3)
,
Where λω is the wavelength at the fundamental frequency ω, and nω and n2ω are the indexes of refraction at the fundamental frequency and the second harmonic frequency, respectively. At characteristic system parameters (n2ω-nω) = 0.05 and λω = 1 μm, the coherence length Lc is equal to ≈5 μm. Although this value is rather small, it is comparable to the propagation length of SPP [14] ω ε ,ε , 3/ 2 ε ,, ε ,, L p = , 1 2 , 1,2 + ,22 c ε1 + ε 2 ε1 ε 2
−1
,
(4)
which would limit the coherence length anyway. Here ε i = ε i, + iε i" is the complex dielectric permittivity of metal (i = 1) and dielectric (i = 2). Assuming that at λ = 1080 nm, ε1’ = −50.2, ε1” = 3.78 (gold [26]), ε2’ = 3.61, and ε2” = 0 (MNA, as discussed below), one estimates Lp = 14.9 μm, which is of the same order of magnitude as Lc. The estimates above show that parametric amplification of SPPs propagating at the interface between gold and MNA is, in principle, possible and worth researching. In this work, as the first step toward this goal, we have studied in the same system a simpler nonlinear optical process – second harmonic generation – and demonstrated its relatively high efficiency and enhancement by SPP.
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Surface plasmon polaritons at the gold/MNA interface were exited in the Kretschmann geometry [5], Fig. 1. MNA is a biaxial organic crystal, whose high indexes of refraction (strongly varying from one literature source to another) are summarized in Table 1. This has determined our choice of the prism material, rutile (TiO2), whose ordinary and extraordinary indexes of refraction, no = 2.48 and ne = 2.74 [30], are even higher than those of MNA. We have deposited gold film on one half of the prism’s hypotenuse face, after which entire face (with and without Au) was covered with MNA, Fig. 1. Correspondingly, optical properties of one half of the sample, with gold film that enabled SPP, could be compared to that of the other half, which did not have gold and did not support SPP. 2. Experiment 2.1 Samples and setup Gold film (40 nm thick) was produced via thermal vapor deposition. To obtain the MNA film, we heated and melted 10 mg of MNA on top of a glass slide at 145C, after which pressed the hypotenuse side of the prism onto the melt for 20 min. The temperature was then slowly lowered, at the cooling rate of 5C/hour, and MNA crystallized. The resulting 23 μm MNA film had yellowish and slightly milky appearance. The polycrystalline sizes, estimated using optical microscope, ranged between 10 μm and 50 μm and were comparable to or larger than the SPP propagation length Lp. The glass slide was then carefully removed and the MNA film remained attached to the prism. In agreement with the literature [23,24], the x-ray diffraction (XRD) measurements [Fig. 2(a)] have shown that the b axis of the monoclinic MNA crystal (which coincides with the optical y axis) was oriented perpendicular to the film. In order to evaluate sustainability of MNA to short-pulsed laser radiation, thin (15 μm) MNA films deposited on glass were exposed to 100 fs pulses of a mode locked Ti:sapphire laser (λ = 800 nm, reperition rate = 250 kHz) and the intensity of the second harmonic radiation has been studied as a function of time, Fig. 2(b). Table 1. Indexes of refraction nx, ny and nz in MNA. λ, nm 1064 633 532 1064 532 1064 532 1064
nx 1.8 2 2.2 1.763 2.291 1.8 2.2 2.093
633 532
2.341 2.484
ny
nz
1.695
Ref. [24] [24] [24] [27] [27] [28] [28] [29]
1.752 1.845
[29] [29]
1.6 1.514 1.843
1.359 1.569
We have found that at the pumping power density equal to 30 GW/cm2, the second harmonic light intensity decreased less than by 1% over 30 min of exposure. This damage resistance is sufficient for table-top experiments and proof of principle demonstrations. In the optical studies, the prism with deposited gold and MNA films was placed on a rotating stage and excited with 5 ns pulses (at λ = 1080 nm) from an optical parametric oscillator (OPO). The optic axis of the rutile prism was perpendicular to the base faces. In most measurements, the incident beam was horizontally polarized (p polarization that was perpendicular to the optic axis – ordinary ray for rutile). Three types of measurements have been performed (as discussed below) on the halves of the hypotenuse side of the prism coated and not coated with gold.
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Fig. 1. Left: Experimental setup. Red rays– fundamental frequency (1080 nm); green rays– SHG frequency (540 nm). Solid rays – horizontal (p) polarization; dashed rays – vertical (s) polarization. Right: Schematic of the gold and MNA layers deposited onto the hypotenuse side of the prism.
Fig. 2. (a) X-ray diffraction (XRD) scan of the deposited MNA film, showing the crystallographic b axis (010) of the monoclinic MNA crystal to be oriented perpendicular to the film. (b) Time dependence of second harmonic generation in thin MNA film exposed to 100 fs laser pulses (peak power density = 30 GW/cm2, repetition rate = 250 kHz, λ = 800 nm).
2.2 Angular reflection profiles The prism was rotated and the angular dependence of reflection R(θ) (in p polarization) has been studied. The signal was detected with Detector 1, which was an integrating sphere connected with an optical fiber bundle to a photomultiplier tube (PMT), Fig. 1. The reflectance, measured on the half of the prism without gold, changed abruptly from low to high at the critical incidence angle θc = 44°, which corresponded to onset of the total internal reflection at the interface between rutile and MNA, Fig. 3(a), trace 1. This critical angle was fitted [Fig. 3(a), trace 3]) by the known theoretical model [5] (see Appendix) using the = 2.48 and the effective index of refraction of ordinary index of refraction of rutile n1080 o MNA n1080 MNA = 1.73 (fitting parameter), which was within the range of values known from the literature, Table 1. An analogous measurement, performed on the half of the prism coated with gold, resulted in the dip at angles θ ranging from 44.7° to 47.8° (measured at half-maximum level), which were slightly larger than θc, Fig. 3(a), trace 2. At closer inspection, one can see that this dip
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has a shoulder at ≈45.3° (arrow I) and a minimum at ≈46.6° (arrow II). The latter minimum is due to SPP propagating at the interface between gold and MNA. Its angular position can be predicted theoretically [5] with fairly high accuracy without use of any additional fitting parameters at the index of refraction of MNA equal to n1080 MNA = 1.73 (same as above) and dielectric permittivity of gold equal to −50.2 (at λ = 1080 nm) [26], compare traces 2 and 4 in Fig. 3(a).
Fig. 3. (a) Angular reflection profiles measured (using Detector 1 in Fig. 1) on the half of the prism without gold (trace 1) and with gold (trace 2). Traces 3 and 4: the corresponding profiles calculated using known formula from Ref [5]. and material parameters described in the text. (b) Traces 1 and 2 are the same as in Fig. 3(a). Dependence of the scattered light intensity (measured with Detector 2) on the incidence angle at the fundamental frequency (trace 3) and the second harmonic frequency (trace 4). The error bars are shown on the right. Arrows I and II point at characteristic peaks, dips, and shoulders discussed in the text.
Although the experimental and the calculated reflectance profiles in Fig. 3(a) had the same angular positions of their characteristic features, the experimental transition from refraction to total internal reflection was not as sharp as the calculated one (traces 1 and 3), and the experimentally measured SPP reflectance dip was much less pronounced than the one predicted by the theory (traces 2 and 4). We attribute this difference to moderate light scattering in the MNA film. (Note that no reflection change at the critical angle or the SPPrelated dip in the reflectance profile have been observed in the case of a much milkier MNA film with shorter transport mean free path.)
2.3 Second harmonic generation scattered from the back side of the prism The laser beam (at λ = 1080 nm) intercepting gold and MNA films deposited onto the hypotenuse side of the prism, produced a bright spot of scattered light (at both fundamental and second harmonic frequencies), which was clearly seen from the back side of the prism. This spot was imaged onto the entrance slit of the monochromator, with a PMT attached to its exit slit. (This detection system is depicted in Fig. 1 as Detector 2.) The intensity of scattered light was studied as the function of the angular position of the prism relative to the pumping beam, Fig. 1. One can see that the scattered light intensity at the fundamental frequency has a maximum at 45.1° (arrow I) and a shoulder at 46.6° (arrow II) – the angles nearly corresponding to the shoulder and the minimum in the SPP reflectance profile, respectively [traces 3 and 2 in Fig. 3(b)]. At the same time, a double-headed band with the peaks at 45.2° and 46.5° (arrows I and II, correspondingly) has been observed in the angular scattering profile at the second harmonic frequency (540 nm), Fig. 3(b), trace 4. Both its maxima nearly coincided with the spectral positions of the minima and maxima of traces 2 and 3 in Fig. 3(b). Note that at pumping density equal to 2 MW/cm2, the second harmonic intensity at the maxima, 45.2° and 46.5°, was nearly thirty-fold stronger than that at the offresonance excitation, 50° (solid line in Fig. 4).
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The results summarized in Fig. 3(b) suggest that SPPs are excited and enhance optical fields at two incidence angles, ≈46.6° and ≈45.2°. While the former one is in a good agreement with theoretical predictions made at plausible system parameters, the origin of the second one is less clear. Formally, SPP excited at the latter incidence angle can be explained assuming that the refraction index of MNA is not 1.73 but 1.71. However, the ground for such assumption is not well justified, and n1080 MNA = 1.71 would not correctly describe the angle of total internal reflection. At λ = 1080 nm, the maximal theoretically predicted SPP enhancement of the fundamental harmonic light intensity, defined as the ratio of |E|2 just above the lower boundary of MNA in the presence of Au film and that in the absence of Au film, is equal to 14.0 (at the optimal thickness of the silver film equal to d = 44.5 nm and optimal incidence angle equal to 46.05°.) This suggests a possibility of nearly 200-fold enhancement of the SHG intensity by surface plasmon polaritons. At the Au film thickness used in our experiments, d = 40 nm, the maximal enhancement of the fundamental harmonic intensity is slightly smaller, 13.5 times.
Fig. 4. Efficiency of second harmonic generation in the Ag/MNA sample calculated based on the fundamental and second harmonic beam intensities at horizontal polarization (solid characters) and vertical polarization (open characters) measured at the incidence angle equal to 45° (squares) and 47° (diamonds). Triangles: efficiency of SHG in bare silver film [31] (open character) and silver film with a monolayer of hemicyanine molecules deposited on top [31] (closed character). Solid line: spectrum of the scattered second harmonic light detected from the back side of the prism (right vertical scale).
2.4 Observation of the second harmonic beams and measurement of the second harmonic efficiency The setup involving Detector 1 (Fig. 1) was also used to study intensities and angular directions of the generated second harmonic beams. In this measurement, optical bundle delivered light to the entrance slit of the monochromator, with the PMT attached to its exit slit. The spectral response of the apparatus was calibrated using the lamp with known emissivity spectrum. The input power was measured with the calibrated powermeter, and the diameter of the pumped spot was measured using the knife edge technique. Experimentally, horizontally polarized (ordinary) beam at λ = 1080 nm was incident onto the hypotenuse side of the prism coated with gold and MNA, at the angle corresponding to excitation of surface plasmon polariton (θ = 45°). It produced two horizontally polarized and two vertically polarized beams at fundamental and second harmonic frequencies, as shown in Fig. 1. As one can see from Fig. 5, depicting angular positions and relative intensities of the four beams measured with the large-area detector (integrating sphere with 1 cm opening), the intensities of polarization-conserving horizontally polarized beams were much larger than those of vertically polarized beams. Expectedly, the intensities of the reflected 1080 nm (540
#196565 - $15.00 USD (C) 2014 OSA
Received 27 Aug 2013; revised 4 Oct 2013; accepted 15 Oct 2013; published 27 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007773 | OPTICS EXPRESS 7779
nm) beams were linearly (quadraticaly) proportional to the incident light intensity. No vertically polarized, extraordinary, beam at λ = 1080 nm has been produced by the uncoated rutile prism (without Au or MNA). We infer that the vertically polarized beam was generated at the interface between gold film and lightly scattering biaxial MNA film, whose optical axis y was perpendicular to the surface and optical axes x and z of the constituent microcrystallines were randomly oriented in the plane of the interface. This could result in the polarization rotation in MNA and the birefringence in rutile.
Fig. 5. Angular directions and intensities of two horizontally polarized and two vertically polarized outgoing beams at the pumping intensity equal to 2 MW/cm2. Each peak is marked with the corresponding index of refraction, where ‘o’ stands for ordinary beam (horizontal polarization) and ‘e’ stands for extraordinary beam (vertical polarization). Two 1080 nm light intensities are in scale with each other and two 540 nm light intensities are in scale with each other. However, the intensities of the 540 nm beams are not in scale with the intensities of the 1080 nm beams. Dashed line indicates the incidence angle.
By knowing the indexes of refraction of rutile for ordinary and extraordinary rays ( n1080 = 2.47 and ne1080 = 2.73 [30]), we have found that the angles of incidence and reflection o are related to each other via the expression resembling the Snell’s law for refraction, ni sin θ i = nr sin θ r ,
(5)
where indexes i and r stand for ‘incident’ and ‘reflected’, correspondingly. (For polarizationconserving reflection, ni = nr and θi = θr.) At the pumping power density equal to 2 MW/cm2, the intensities of the second harmonics beams were high enough to be seen on a white card with a naked eye. The directions of the generated SHG beams were also governed by Eq. (5), where ordinary and extraordinary indexes of refraction of rutile for outgoing beams corresponded to λ = 540 nm ( no540 = 2.66 and ne540 = 2.97 [30]). Note that the efficiency of the second harmonic generation, calculated [31] as ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 for the fundamental and second harmonic beams at horizontal polarization is reasonably close to that calculated for the fundamental and second harmonic beams at vertical polarization, Fig. 4. This suggests that the horizontally polarized fundamental frequency beam generates horizontally polarized SHG beam and the vertically polarized fundamental frequency beam generates vertically polarized SHG beam. Here Er540 and Er1080 are the amplitudes of electric fields in the outgoing beams at the corresponding wavelengths, and Ei1080 is the amplitude of the electric field in the incident beam. Note that the quantity ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 is the characteristics of the whole device, with inherent radiative and internal losses, angular dependent SPP enhancement, etc., rather than the property of the nonlinear optical material, MNA. (Note that if one will define the efficiency
#196565 - $15.00 USD (C) 2014 OSA
Received 27 Aug 2013; revised 4 Oct 2013; accepted 15 Oct 2013; published 27 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007773 | OPTICS EXPRESS 7780
of the second harmonic generation as ( Er540 / Ei1080 ) 2 / ( Ei1080 ) 2 , it will be different from
( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 by no more than 20%, since the reflected light intensity (at 1080 nm) is never smaller than 80% of the incident light intensity, Fig. 3.) Analogous measurements with qualitatively similar results have been performed at the incidence angle equal to 47.0°, Fig. 4. The results of the SHG efficiency measurements are summarized in Fig. 4, along with the results of similar experiments reported in the literature [31]. One can see that SHG efficiency in our Au/MNA sample is ~7x105 times larger than that in the system consisting of a glass prism with deposited Ag film and monolayer of hemicyanine molecules, and ~3x107 times larger than that in the silver film without any nonlinear molecules [31]. At the incident light intensity equal to 2 MW/cm2, the SHG yield η = ( Er540 / Er1080 ) 2 in our experiment ranges from 4.8x10−6 (solid square in Fig. 4) to 1.3x10−4 (open diamond in Fig. 4). These values are significantly larger than the one reported in bare metallic split ring nanostructures, η = 3x10−11 at 230 MW/cm2 [32]. (Note that in the historic seminal experiment by Franken et al. [33], the SHG conversion efficiency of a macroscopic quartz crystal was of the order of 10−8 at the pumping density of the order of 102 MW/cm2.) We, thus, infer that in spite of multiple efforts aimed to exploit nonlinearity of constituent components of nanophotonic and plasmonic devises, including metamaterials (see for example, Refs [32, 34–36].), nothing can compare to a highly efficient nonlinear optical material with the record-high χ(2) response, which can be further enhanced by a plasmonic resonance. 3. Summary
To summarize, we have researched 2-methyl-4-nitroaniline (MNA) as a potential nonlinear optical material for parametric amplification of surface plasmon polaritons (SPPs), and studied second harmonic generation (SHG) as the first and easier step. Expectedly, SPP enhancement of the second harmonic generation has been observed experimentally. Thus, in the Kretschmann geometry and at the pumping energy density equal to 2 MW/cm2, SHG light intensity was nearly thirty-fold larger at the SPP resonance angle (46.6°) than that at the offresonance excitation (50°). The maximal SHG efficiency in our sample (defined as ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 ) was equal to 1.7x1017 m2/V2, which is 7x105 times larger than that in the glass prism with deposited Ag film and monolayer of hemicyanine molecules [31] and 2.8x107 times larger than that in the glass prism with bare silver film [31]. Assuming that the experimentally determined SHG efficiency ∝ (ε 0 χ (2) ) 2 ∝ ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 (in our setup, with given material loss and SPP propagation length) is the same as the efficiency of the difference frequency generation (the process, which governs parametric amplification), we have estimated that the pumping power density I ( p ) = ε 0 c( E ( p ) ) 2 , which is required for the generated signal field in the OPA process E ( s out ) to be equal to the input signal field E ( s in ) , is equal to I ( p ) ~25 GW/cm2. Arguably, the latter condition can be regarded as a threshold for parametric amplification. (In the calculation, the output signal field E ( s out ) and the idler field E (i ) were related to the input signal field E ( s in ) and the pumping field E ( p) as ( s out) (2) ( p ) ( i ) ( s in ) (2) 2 ( p) 2 ( s in) ( p) 2 540 1080 2 1080 2 E ∝ ε 0 χ E E ∝ E (ε 0 χ ) ( E ) ∝ E ( E ) [( Er / Er ) / ( Ei ) ] and E (i ) ∝ ε 0 χ (2) E ( p ) E ( s in ) , and the quantity (ε 0 χ (2) ) 2 was substituted with the experimentally
measured ( Er540 / Er1080 ) 2 / ( Ei1080 ) 2 .) The required power density of 25 GW/cm2 can be achieved experimentally with an ultrafast (100 fs) Ti:sapphire laser, and it is still below the laser damage threshold for MNA, see Fig. 2(b). This makes parametric amplification of surface plasmon polaritons a realistic task.
#196565 - $15.00 USD (C) 2014 OSA
Received 27 Aug 2013; revised 4 Oct 2013; accepted 15 Oct 2013; published 27 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007773 | OPTICS EXPRESS 7781
Appendix
The angular reflectance profiles R(θ) in Fig. 3(a) have been calculated using the formula derived in [5] for a slab with the thickness d and dielectric permittivity ε1, sandwiched between two semi-infinite media with dielectric permittivities ε0 and ε2 (Fig. 6): p 2 012
R= r
Ep = rp E0
2
2
r p + r p exp(2ik z1d ) = 01 p 12p , 1 + r01 r12 exp(2ik z1d )
p is the amplitude reflection coefficient for p polarized light, accounting for where r012
reflection at both interfaces 0-1 and 1-2; Erp and E0p are the electric fields (in p polarization) of the incident and the reflected waves, respectively; rikp =
(k zi ε k − k zk ε i ) (k zi ε k + k zk ε i )
is the amplitude reflection coefficient for p polarized light at the interface between media i and k; εi and εk are the dielectric permittivities of media i and k; 2
ω k zi = ± κ = ± ε i − k x2 , i =0,1,2 c
is the z component of the wavevector in medium i; k x = k phot sin θ 0 is the x component of the wavevector in medium i; ω is the angular frequency; c is the speed of light; θ is the incidence angle; k phot = n0ω / c is the wavenumber for a photon in medium 0; and n0 = ε 0 is the index of refraction of medium 0 (in our study, ε0 corresponded to rutile and was assumed to be purely real). ε2
z
ε1 ε0
x
d
θ Fig. 6. Schematics assumed at calculation of the angular reflectance profile.
Acknowledgments
MM, GZ, ADW and MAN were supported by the NSF PREM grant DMR-1205457, NSF IGERT grant DGE-0966188, and AFOSR grant FA9550-09-1-0456. VAP acknowledges the support from ARO grant W911NF-12-1-0533. TN and HF acknowledge NSF MRSEC grant DMR 1120923, and NSF PREM DMR 1205457. The authors cordially thank Jacob Khurgin for useful discussions and suggestions.
#196565 - $15.00 USD (C) 2014 OSA
Received 27 Aug 2013; revised 4 Oct 2013; accepted 15 Oct 2013; published 27 Mar 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.007773 | OPTICS EXPRESS 7782
