Local excitation of surface plasmon polaritons by second-harmonic generation in crystalline organic nanofibers

Coherent local excitation of surface plasmon polaritons (SPPs) by second-harmonic generation (SHG) in aligned crystalline organic functionalized para-phenylene nanofibers deposited on a thin silver film is demonstrated. The excited SPPs are characterized using angle-resolved leakage radiation spectroscopy in the excitation wavelength range of 8501325 nm and compared to simulations based on a Green’s function area integral equation method. Both experimental and theoretical results show that the SPP excitation efficiency increases with decreasing wavelength in this wavelength range. This is explained both as a consequence of approaching the peak of the fibers nonlinear response at the wavelength 772 nm, and as a consequence of better coupling to SPPs due to their stronger confinement. © 2012 Optical Society of America OCIS Codes: (190.2620) Harmonic generation and mixing; (190.4350) Nonlinear optics at surfaces; (240.6680) Surface plasmons; (250.5403) Plasmonics; (050.1755) Computational electromagnetic methods. References and links 1. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). 2. I. P. Radko, S. I. Bozhevolnyi, G. Brucoli, L. Martín-Moreno, F. J. García-Vidal, and A. Boltasseva, “Efficiency of local surface plasmon polariton excitation on ridges,” Phys. Rev. B 78(11), 115115 (2008). 3. F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. 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Introduction
Research efforts in the field of plasmonics and in the development of plasmonic circuitry have increased rapidly over the past decade.A prerequisite for major breakthroughs in both areas is the development of active surface plasmon based elements.To facilitate integration of plasmonic circuitry with optical signaling, active elements that can convert optical signals to plasmonic signals and vice versa need to be developed [1].Preferably, surface plasmon polaritons (SPPs) should be excited locally in a well defined part of the plasmonic system.Several ways to achieve this have already been demonstrated including both passive methods like ridge, slit, or grating couplers [2][3][4][5] and active methods based on e.g.four-wave mixing [6] or electrical excitation [7,8].
In this work we demonstrate an alternative method, based on second harmonic generation (SHG) in crystalline organic nanofibers deposited on a thin metal film.This method has the advantage that the generated SPPs are coherent with the excitation light and near-infrared optical signals are converted to SPP signals in the visible range that are easier to detect or convert afterwards.Also, the SPPs excited using this approach have a well defined frequency that is tunable and the method does not require specific angles of incidence of the excitation light to work.Finally, for near-infrared excitation, a considerable part of the generated light is coupled to plasmons, which leaves only a weak background signal at the SH frequency.
SHG in nanowires and cylindrical particles of dielectric, semiconducting or metallic materials has already been studied in great detail [9][10][11][12].Recent developments in organic nanofiber growth techniques have made it possible to produce functionalized organic 1cyano-p-quaterphenylene (CNHP4) crystalline nanofibers with a large second-order optical non-linearity [13].In addition, it has recently been demonstrated that the large second order susceptibility of CNHP4 fibers can be exploited to efficiently generate second-harmonic (SH) radiation [14].Here we demonstrate that it is possible to excite SPPs on an air/silver interface using SHG in CNHP4 fibers and detect the excited SPPs through e.g.leakage radiation spectroscopy.The sub-wavelength dimensions of the nanofibers facilitate direct SHG into SPPs (Fig. 1(a)).In this way, nanofibers can serve as local coherent tunable SPP sources, i.e. within the vertical SPP decay length.Sub-wavelength separation of SH sources from the silver film surface opens an additional channel for SHG, viz., direct SHG into SPP modes (SH-SPP).Therefore, this process is different from the SPP generation by linear polarization sources of illuminated nanofibers that were recently investigated [15].

Theory and modeling
In this section we will theoretically calculate the SH generated power per unit angle in the direction of light propagation in the glass substrate specified by the angle θ (see Fig. 1) when illuminating a single 400 nm wide and 100 nm high CNHP4 nanofiber placed on the air-side of a planar air-silver-glass stack, where the silver film thickness is 40 nm, with a Fundamental Harmonic (FH) normally incident beam.Since the fibers considered in this paper are very long (on the order of 20 µm) it is reasonable in a theoretical calculation to assume that they are infinitely long.Furthermore, similar to the experiment, we will assume that the electric field of the FH beam is polarized perpendicular to the CNHP4 fiber, and that light is propagating in the plane perpendicular to the fiber, i.e. p-polarized light.With these assumptions the theoretical problem reduces to the two-dimensional situation illustrated in Fig. 1(a).Here, it is illustrated that the FH beam (frequency ω) incident on a single CNHP4 fiber results in a left-and a right-propagating SPP (frequency 2ω) due to SHG in the fiber.Due to the finite thickness of the silver film the SH-SPP waves leak into the glass substrate at a characteristic angle, where they can be detected in the far-field.In principle there will also be a SPP excitation at the FH frequency due to scattering of the FH beam off the fiber similar to Ref [15].which is not shown in Fig. 1(a), and which will also not be detected in our experiment considered later since any FH signal is removed by filters.A calculation of the SH power requires several steps [16].The first step is to selfconsistently calculate the FH electric field inside the nanofiber.In this step we will neglect nonlinear effects.From the FH field and a model of the nonlinear properties of the nanofiber we can in the second step obtain the resultant SH polarization current density inside the nanofiber.We can then in a third step once more consider the problem at the SH frequency as a linear problem where the source of the fields is the given SH current density, and once more we need to solve self-consistently for the field inside the nanofiber.In the fourth and final step we can use the calculated SH field and the given SH current density to calculate the radiated SH power per unit angle into the glass substrate as a function of angle.
In the calculations we have set the linear refractive index of the CNHP4 fiber to n CNHP4 = 1.65 for all considered wavelengths similar to our previous work [15] and in agreement with Ref [17].The dielectric constant of silver for different frequencies is obtained via interpolation between the experimentally measured values tabulated in Ref [18].The refractive index of the glass substrate is for all considered wavelengths set to n glass = 1.5.
In the first step we have calculated the total FH electric field using the Green's function area integral equation method (GFAIEM) [19].In this method the total electric field ( ; ) is the dielectric constant of the reference structure without the presence of the nanofiber.The integrand is therefore only non-zero for positions ' r inside the nanofiber.The Green's tensor must satisfy the radiating boundary condition such that it describes wave propagation away from the position ' r .This Green's tensor can be obtained numerically via Sommerfeld integrals using the procedure in Ref [19], while it can be calculated analytically when considering positions in the far-field.
We have solved Eq. ( 1) for a normally incident p-polarized plane wave for each of a range of FH frequencies by discretizing the nanofiber into 80 20 × square-shaped elements, where the electric field is assumed constant within each element.With this assumption and using a point-matching scheme sampling at the center of each cell Eq. ( 1) becomes a linear system of equations for the values of the electric field inside each element of the fiber that can be put on matrix form and solved numerically on a computer.For the coupling from an element i to itself we have applied that for square-shaped elements the integration over the direct (freespace) part of the Green's tensor being highly singular can be re-written as 2 2 (2) where ˆˆˆxx zz = + I is the unit dyadic, and (2) 0 H is the Hankel function of 0 order and 2nd kind.
Once the FH field inside the fiber is known Eq. ( 1) can be applied to straightforwardly calculate the FH field at all other positions, including in the far-field along a direction θ (see Fig. 1), and thus to calculate the FH power per unit angle as a function of the angle θ.This type of results obtained with another but related method was presented in our previous work [15].Here we will make similar angular spectra but for the SH signal.This, however, requires some additional calculation steps.
As a model for the resulting SH polarization inside the CNHP4 fiber we assume that only the FH field component perpendicular to the axis of the CNHP4 fibers (along the molecules) and parallel to the air-silver interface, ( ; ) x FH E r ω , can give rise to a SH polarization, which will be along the same axis, i.e.
[ ] where x is a unit vector along the x-direction (The fibers consist of molecular chain molecules oriented in the direction perpendicular to the long axis of the fibers, i.e. along the x-axis.As reported in [13] the inclination angle of the molecules relative to the x-axis is small and therefore the effect of this small inclination on the susceptibility has been neglected).The corresponding SH polarization current density can be obtained as ( ; ) ( ; ) assuming the implicit time dependence factor exp( ) . Since the radiation from the oscillating SH polarization current density at one position will also contribute to drive the polarization at another position we again need to solve self-consistently for the SH field.In this case the resulting equation for the electric field becomes ( ) This equation is similar to Eq. ( 1) except that the reference field 0 E has been replaced by another term due to the given SH polarization, and it can be solved in the same way as before.
Once the SH field inside the fiber has been calculated by solving Eq. ( 3) self-consistently, this equation can be applied to calculate the SH field at all other positions.
The SH power or Poynting vector flux per unit angle in the far-field is proportional to , where ff refers to the far-field, and r is the distance from the fiber to the considered far-field position r in the glass substrate.In the measurement considered later the SH signal generated by illuminating quartz with the same incident FH beam is used as a reference, and assuming that (2)   χ of quartz is practically wavelength independent for the considered wavelengths the reference SH signal will be proportional to , which is the total resulting field for the reference geometry including also either reflection or is the corresponding transmitted field depending on the position.Thus, we can define a normalized SH power per unit angle as 2 , 4 ( ; ) .
In a first calculation of the normalized SH power per unit angle we have assumed (2) i.e. a (2)   xxx χ with no wavelength dependence, and calculated Eq. ( 4) as a function of angle and FH wavelength (Fig. 2(a)).
where the SPP is phase-matched to propagating waves in the glass substrate.Here we can use / ( 1) , which is the SPP mode index of a SPP propagating along an airsilver interface assuming an infinitely thick silver film.The finite thickness of the silver film mainly affects the imaginary part of the SPP mode index.
The increase in the peak angle seen in Fig. 2(a) with decreasing wavelength is related to an increase in the mode index of the SPP with decreasing wavelength [20,21].This is similar to our previous work [15] except that the peak angular widths can be much broader here since we consider smaller wavelengths.Also notice that for short FH wavelengths approaching 800 nm a significant signal (SH wavelength 400 nm) can also be detected at small angles θ since light can better penetrate through the silver film for these wavelengths.It is clear that for the shorter FH wavelengths the peaks in angular spectra have both larger amplitude and larger width at the same time accounting for a much larger total amount of SH power coupled into SPP waves at short wavelengths compared with the longer wavelengths.This is to a large extent a consequence of SPP waves becoming more and more strongly bound to the air-silver interface with decreasing wavelengths, which increases the SPP excitation from emitters placed very close to the interface.As illustrated in Fig. 1(a) the CNHP4 fiber is located right at the surface, which is the optimum position for coupling to the SPP waves as their field magnitude is largest at the surface.The coupling efficiency will also depend on how strongly the SPP waves are localized near the surface, which can be expressed via the distance, L, into the air-region where the field magnitude has decreased by a factor e, i.e. by the distance given by [20] ( ) where λ SH is the wavelength of the SH signal, which results in L = 117 nm for the SH wavelength 400 nm, and L = 443 nm for the SH wavelength 650 nm.Clearly, the SPP is much more strongly confined for the shorter wavelength.Finally, it may also have an effect that the magnitude of the field 0 ( ; ) FH E r ω will decrease near the air-silver surface for long wavelengths, especially for normally incident light, since the silver properties approach those of a perfect conductor.
The corresponding calculation obtained using a fit to the actual measured (2)   xxx χ of CNHP4 from Ref [14]. is shown in Fig. 2(b).The fit, which allows us to consider longer wavelengths than those covered by the measurements in Ref [14], is given by where we have used A = 16.898,W = 0.31041 and X c = 3.222.The fitting procedure can be justified from the expectation that there will not be additional electronic resonances for the longer wavelengths.Actually, this (2)   xxx χ is the (2)   xxx χ of CNHP4 relative to the (2)  χ of quartz.
However, since (2)   χ of quartz only has a weak dispersion for the considered wavelengths the result in Fig. 2(b) can be considered accurate except for a scaling factor.Since the fitted (2)   xxx χ is a monotonically and rapidly increasing function with decreasing FH wavelengths for the considered spectral range the SH signal at small wavelengths will be even further increased relative to the SH field at longer wavelengths.As a consequence, in Fig. 2(b) the power per unit angle for FH wavelengths longer than 1000 nm is now practically negligible when compared with the shorter wavelengths near 800 nm.
The relative heights of the different spectral features are more easily seen in Fig. 3(a) that shows a 3D plot of the same data as those shown in Fig. 2(b).In Fig. 3(b) and 3(c) we consider a few cross sections of the data in Fig. 3(a) for selected wavelengths of 900 nm, 1000 nm and 1100 nm being normalized for easier comparison.Here we can notice that for the shortest wavelength of 900 nm the SH signal at θ = 0 ͦ is less than a factor of 5 smaller than the peak value of the SPP related peak.For other longer wavelengths the difference is larger.However, since the center peak around θ = 0 ͦ is much broader than the other peaks we can expect that any mechanism that will lead to a broadening of peaks, such as scattering from surface roughness as a result of e.g.having not one but a large number of CNHP4 fibers at the air-silver interface, as is the case in the corresponding experiments considered in this paper, will affect the narrow peaks more.(Another broadening mechanism may come from the measurement where the detector opening is not small enough to resolve peaks as narrow as those found in the theoretical calculation).Such broadening of peaks can easily reverse the situation such that in the end the central peak maximum will be larger than the peak value of the SPP related peaks.
Since we are interested in the excitation of SPP waves at the air-silver interface we may ask how large a fraction of the power coupled into SPP waves propagating along the air-silver interface that leaks into the substrate, where it can be detected as leakage radiation, and how large a fraction that is absorbed in the silver film.From our previous work [15] and Ref [22], we know that the angular width ∆θ FWHM of the SPP related peaks in the angular spectrum for a given wavelength is approximately proportional to the propagation loss, or the imaginary part of the SPP mode index.Since the width of the peaks can easily be 5 times larger for the case of a 40-nm thick silver film compared to the case of a very large silver film thickness with almost no leakage radiation, we can for our theoretical situation safely assume that most of the power coupled into SPP waves at the air-silver interface is coupled out as leakage radiation, and only a small fraction of that power is absorbed in the silver film.Thus, by integrating the angular leakage radiation spectra over the SPP related peaks we will find to a good approximation (accurate within ≈25%) the power that was coupled into the SPP waves at the air-silver interface.

Materials and experimental methods
The sample was a 0.5 mm thick glass substrate (10 mm by 10 mm square) coated on one side with a 40 nm thin film of silver.CNHP4 nanofibers were grown on mica and soft-transferred to the air/silver surface of the sample [23].The average dimensions of the fibers were measured by atomic force microscopy to be approximately 100 nm high, 400 nm wide and 20 µm long.The fibers were aligned along the same direction and had an average spacing between fibers of approximately 5 µm.
As excitation source we used an optical parametric amplifier (OPA) (Light Conversion, TOPAS C) pumped by an amplified femtosecond laser system (Quantronics, Integra C, seeded by a Spectra-Physics Tsunami Ti:Sapphire based oscillator).The OPA delivered ~110 fs pulses, and at a repetition rate of 1 kHz, the average power varied between 20 and 200 mW for wavelengths in the range 850-1350 nm.The power reaching the sample was controlled by neutral density filters and a pair of polarizers, which also defined the polarization of the excitation light to be in the plane scanned by the detector i.e. p-polarized light (any SPPs excited using s-polarized light would primarily propagate and leak out into a plane perpendicular to the plane of the detector and would therefore not be detected).
The experimental set-up used is illustrated in Fig. 1(b).The sample was mounted onto the flat side of a cylindrical prism with an index matching liquid.As illustrated by the insert, the long axis of the fibers was rotated until they were approximately parallel to the symmetry axis of the cylindrical prism, where they generated maximum SHG light using p-polarized incident light (and almost no SHG for s-polarized light).The excitation beam was focused onto the sample by a 300 mm focal length lens placed at a distance of 400 mm from the sample, resulting in a spot size of 0.75 mm (full width at half maximum) at the sample surface, and an average power density of 0.5-1.5 W/cm 2 , which was below the damage threshold of both the CNHP4 fibers and the thin silver film (no damage to the samples was observed).A colored glass filter was inserted right after the lens to remove any SH light generated in the optical components placed before the sample (for wavelengths below 1150nm, a RG715 filter was used while either a RG850 or RG1000 filters were used at longer wavelengths).After the sample additional colored glass filters were placed to remove any residual excitation light as well as any third-harmonic light generated (for wavelengths in the range 850-1125nm GG385, C3C21, C3C23 and BG39 filters were used, while from 1125 to 1325nm GG475, and several KG3 filters were used).The detector was mounted on a rotating arm that was scanned from −90 to + 90 degrees relative to the direction of the excitation light in increments of 0.5 degrees.An iris diaphragm was placed between the sample and the photo multiplier tube (PMT) used as detector, reducing the angular range from which light was collected to 1.7 degrees.The wavelength was scanned from 850 to 1325 nm in steps of 25 nm (at shorter wavelengths two-photon luminescence begins to contribute to the detected signal and at longer wavelengths the sensitivity of the PMT drops rapidly).Each data point was obtained as an average over the signal from 1000 laser pulses using a gated Boxcar integrator (Stanford Research Systems, SR250).
Due to the non-zero second order susceptibility of the CNHP4 fibers (χ (2) max = 2.23 pm/V) [13], external illumination could generate (nonlinear) polarization sources at the SH frequency inside the nanofibers.Due to the small thickness of the fibers compared to the wavelength of the incident light, the fundamental and second harmonic waves do not get significantly out of phase during their propagation through the 100 nm thick fibers.As a consequence, one can assume that phase matching can be achieved throughout the fibers.Because the Ag film was sufficiently thin, generated SPPs (at the SH frequency) could leak out on the opposite side of the film at the angle where phase matching could be achieved between the wavevector of the SPP in the film and light propagating in the glass prism [20].It is important to notice that the relative amount of leakage radiation (compared to absorptive losses) is both wavelength dependent and a function of the thickness of the thin metal film [15,24].This leakage signal, recorded as a function of both angle and excitation wavelength in the range 850-1325 nm, was measured relative to the SHG signal generated in reflection from a quartz crystal wedge mounted in place of the sample, thus yielding a resultant relative signal, which was independent of the absolute laser power, filter transmittance, and detector response.

Experimental results and discussion
The angular distribution of SH radiation detected experimentally around the curved side of the glass prism (Fig. 1(b)) features two side lobes corresponding to generated SPPs, along with a central peak produced by SH light generated in the form of free propagating modes that are partially transmitted through the thin silver film in the forward direction (Fig. 4(a)).Note that only light scattered off an object very near the metal surface, or locally emitted light coming from a position very near the surface, can couple out through the cylindrical prism at angles that are numerically larger than the critical angle of an air-glass interface of approximately 42 degrees (see e.g.Ref [21].).Control measurements on samples with no metal film showed no side lobes, but only a central peak similar to the central peak in Fig. 4(a).In agreement with the theoretical predictions in Sec. 3 the side lobes can be interpreted as SH-SPP radiation leaking out at angles where the SPPs are phase-matched to propagating modes in the glass prism given by Eq. ( 5).The presence of these two leakage peaks therefore demonstrates the feasibility of using the organic nanofibers as coherent local SPP sources at the second-harmonic frequency.The SPP peak at positive angles is slightly larger than that at negative angles.This is because the dipole moments of the CNHP4 molecules are oriented at a small angle relative to the silver surface [13] resulting in slightly different efficiencies of SH-SPP generation in the two directions.All three peaks in Fig. 4(a) increase in amplitude as the wavelength decreases.This is in accordance with the theoretical calculations in Sec. 3 where such an increase could be explained as a combination of better excitation of SPPs and increasing non-linear response of the CNHP4 fibers as the excitation wavelength decreases towards the peak of the fibers nonlinear response at 772 nm [14].One may also note that the amplitude of the SPP leakage peaks relative to the amplitude of the central peak increases as the excitation wavelength increases.This is in agreement with the theoretical calculation in Fig. 3.However, in the theoretical calculation the central was lower than the side lobes for all considered wavelengths, and here this is only the case for excitation wavelengths longer than 1000-1100 nm, whereas at shorter excitation wavelengths the experimentally measured central peak has the largest peak value.This difference can, however, be understood from the fact that the experimentally measured side lobes are broader than the theoretically predicted side lobes, and thus their peak value will be reduced accordingly.
The angular widths (FWHM) of the SPP leakage peaks in Fig. 4(b) vary from 4.6 degrees for illumination wavelength of 1100 nm to 7.5 degrees for 900 nm, and are at least four times broader than theoretically predicted for a single fiber on a smooth silver surface, and even if one takes the limited experimental angular resolution of 1.7 degrees into account the peaks are still broader than predicted by theory.However, the angular width increases as SPP propagation losses increase.Losses can be due to absorption in the metal and leakage radiation through the metal film [24] (included in the theoretical simulations), but scattering due to the surface roughness of the air/silver interface can also contribute to losses [20] and this is not included in the simulations.Therefore, the large measured angular width is likely due to the surface roughness caused by the deposited large irregular array of fibers.The surface roughness due to deposited fibers may also have some influence on the total SHG-to-SPP coupling efficiency.We believe that the limited angular resolution in the experiment only introduce a minor broadening since an averaging of the theoretical results (e.g. Figure 3(c)) over this resolution produces peaks that are flat in the top region approaching a square shape, which is very different from the measured peaks.Hopefully, future experiments on single fibers should be able to further clarify this issue.
Although the efficiency of SPP excitation was largest for short excitation wavelengths where SPP propagation losses are largest, the development of fibers with more red-shifted SHG resonances could make this a viable SPP excitation method further into the (near) infrared.Another option could be to use sum-frequency generation or difference-frequency generation, which are both second-order non-linear processes like SHG, to facilitate local coherent and tunable SPP excitation at longer wavelengths, where propagation losses are lower (e.g.telecom wavelengths).The coupling to SPPs could probably be optimized further by e.g.design of the fiber geometry or by choosing a fiber material with the largest component of the nonlinear susceptibility oriented out of the plane of the metal surface.The later would however require a different excitation geometry, where the fundamental field is not hitting the sample at normal incidence, but instead is incident at an angle.

Conclusions
The angle resolved leakage spectra in Fig. 4 clearly demonstrate that SPP excitation can be achieved through SHG in nanofibers deposited on a smooth metal surface.In addition, the experimental data have been shown to be in agreement with theoretical simulations based on the Green's function area integral equation method.Based on theoretical simulations, two contributions to the observed increasing efficiency of SPP excitation with decreasing wavelength could be identified, namely better coupling to SPP waves due to their stronger confinement, and increasing nonlinear response of the fibers.We have shown that SH-SPP excitation can be achieved over a large spectral range, and that this method offers tunability of the SPP frequency by changing the frequency of the incident light.SPPs excited in this manner will be coherent with the incident light, as SHG is a coherent process.As the fibers supply the optical non-linearity necessary for efficient SHG, SH-SPP excitation will only be possible in very close vicinity of the fibers, which therefore can be used as local SPP sources.Together, this shows the feasibility of using the non-linear polarization generated in the organic fibers as local and coherent SH-SPP sources.Therefore, this method is a promising alternative for creating tunable coherent local SPP sources for e.g.surface plasmon circuitry.

Fig. 1 .
Fig. 1.(a) Light at the second-harmonic frequency, generated inside the CNHP4 nanofibers, couple directly to SPP modes propagating away from the fiber along the silver-air interface.Because of the small thickness of the silver film light coupled to SPPs can leak out into the glass substrate on the opposite side of the silver film.We consider light propagating in the plane perpendicular to the long axis of the fibers that are oriented along the y-axis.(b) Schematic of the experimental setup used: D: Iris diaphragm, L: Lens, F: Colored glass filter, CP: Cylindrical prism, Ag: 40 nm silver layer, ONF: Organic nanofibers, PMT: Photo multiplier tube.The inserts show a zoom on the cylindrical prism with the sample mounted on the flat surface (upper right), and a fluorescence image of the irregular array of deposited fibers (lower left).

Fig. 2 .
Fig. 2. Calculated normalized SH power per unit angle leaking into the quartz substrate (Eq.(4)) when illuminating a CNHP4 fiber of width 400 nm and height 100 nm placed on the airsilver interface of a planar air-(40 nm silver)-quartz stack with a normally incident p-polarized FH plane wave.(a) Assuming a wavelength independent (2) 1 xxx = χ

Fig. 3 .
Fig. 3. (a) Simulated angular spectra of the scattered and SPP leakage radiation upon SHG in a single CHHP4 nanofiber on top of a quartz substrate coated with a 40 nm silver film.(b) Normalized cross sections at three selected wavelengths (c) A zoom on the SPP leakage peaks in the angular range 42-48 degrees.FWHM for each of the three curves are 1.69⁰, 1.05⁰, and 0.70⁰, respectively.

Fig. 4 .
Fig. 4. (a) 3D plot of the relative SHG signal measured as a function of the excitation wavelength and the detection angle.(b) Cross sections of the SPP leakage peaks for a few selected excitation wavelengths.FWHM for each of the three curves are 7.5⁰, 4.9⁰, and 4.6⁰, respectively.