1 Introduction

Generation of high energy electron beams has been significant field of research since last few decades; these energetic beams have several applications in particle physics, material science and medicine. Apart from the conventional accelerators e.g. linear accelerators and RF accelerators, energetic electron beams can also be generated using interaction of high power and ultra-short laser pulses with gas-jet targets. Low intensity pedestal of the laser pulse ionizes the gas and produces plasma, while high intense part of laser pulse interacts with the produced plasma, and generates high amplitude plasma wave that associates with charge separation field. Inherent electric field of the generated plasma wave is termed as wakefield that leads to trap** and acceleration of electrons in laser propagation direction. The concept, popularly known as laser wakefield acceleration (LWFA) (Joshi 2019, Tajima et al. 1979) was proposed by Tajima and Dawson in the year 1979; Later on, it was demonstrated experimentally using femtosecond laser pulses by Faure et al. (2004) in 2004. Recently, Gonsalves et al. (2019) have reported quasi monoenergetic electron bunch of 8 GeV with charge of 320 pC from a table-top setup of laser-plasma accelerator. Various research groups have contributed for better beam quality of electrons using different regimes of acceleration e.g. bubble regime LWFA (Lu et al. 2007, Pukhov et al. 2002) and direct laser acceleration (DLA) (Pukhov et al. 1999). Conceptually, a different approach is also proposed by Gong et al. (2019) in direct laser acceleration of electrons, where a structured hollow core target is used to enhance the longitudinal fields and maintain it over a distance longer than the Rayleigh length by guiding the laser pulse. Electrons are injected by the transverse electric field and accelerated by the laser pulse in the forward direction. Most of the energy is imparted to the electrons by longitudinal laser field and the imparted energies are reflected in the form of super-ponderomotive energies with enhanced collimation in the accelerated electron bunch. Wang et al. (2019) investigated the impact of the ion dynamics on laser-driven electron acceleration in an initially empty channel irradiated by a high intense laser pulse with intensity of the order 1022 W/cm2. Accelerated electrons inside the channel create a quasi-static transverse electric field that leads to gradual expansion of ions within the channel. The ions reduce the role of longitudinal laser electric field, and the transverse electric field becomes the main source of energy for the accelerated electron bunch. Further, the ion dynamics has great impact on the gamma-ray emission in the form of enhanced volumetric distribution with reduction in the total radiated energy.

The LWFA mechanism is applicable for gaseous targets (gas-jets) that generate desired electron beam in single shot experiments. Laser plasma accelerators can become an alternative of the conventional accelerators only when higher repetition rate of energetic electron bunches along with low energy spread, low beam divergence and high current is achieved. To overcome these difficulties solid targets are also used for electron acceleration, but one of the major problems with solid target is the transfer of energy from laser to the over-dense plasma that is created in front of the target. When temperature of over-dense plasma falls in the range of several KeV, the collisional absorption mechanism becomes less efficient at higher temperatures due to scaling of collisional frequency with temperature e.g. \({\nu }_{ei}\propto {T}_{e}^{-3/2}\). Different approaches have been proposed to increase the absorption, among which an efficient one is to use targets with rough surfaces in the form of clusters (Palchan et al. 2007) nanoparticles (Rajeev et al. 2003), and gratings (Kulcsár et al. 2000; Murnane et al. 1993). One approach to increase the accelerated electron beam charge above tens of nC for electron energies in the range of few tens of MeV is to use near critical density plasma (NCD) target (Rosmej et. al. 2019). Rosmej et al. use low density polymer aerogels/foams as target to demonstrate 78 nC bunch charge from highly directional 30 MeV electrons accelerated along the direction of laser propagation. The critical electron density is defined as ncr = m·ωL2/(4πe2), where m and e are the mass of electron at rest and its charge and ωL is the laser frequency. Surface plasma wave (SPW) excitation (Macchi 2018) is another efficient energy transfer mechanism from laser to the charged particles generated during interaction with over-dense plasma target; these electromagnetic modes excite at the sharp material interface having periodic modulation in the form of grating that permits the phase matching with incident laser light (Fedeli 2016; Fedeli, et al. 2016). Longitudinal field component and high phase velocity of the surface wave can accelerate the generated surface electrons to high energies in the range of MeV. Fedeli et al. (2016) have demonstrated experimentally the acceleration of electrons up to a maximum energy of 25 MeV from oblique incidence of laser pulse on grating target. Recent research proved that the structured targets are more efficient than the flat targets in exciting surface plasma waves (Petit, Shen et al. 2021). Recently, Shen et al. (2021) proposed an efficient electron acceleration mechanism termed as peeler acceleration; here laser pulse make parallel incidence to the foil target; simulation results show that the laser pulse peels electrons from the surface and electrons are accelerate by SPW.

In this letter, we present the results of surface plasma wave assisted electron acceleration in the case of grazing incidence of a highly intense, ultra-short and linearly polarized laser pulse on a modulated surface. An optimized grazing angle for laser incidence is proposed using 2D PIC simulations, where peak energy and flux of accelerated electron bunch is improved significantly; which reflects better coupling between the laser and the SP. Flat and grating surfaces have been used previously (Sarma et al. 2022) for electron acceleration with different laser arrangements in terms of large incident angles. In Sect. 2, we discuss the concept and theoretical formulation of surface plasma wave excitation, phase matching condition for efficient energy transfer and electron acceleration. Section 3 describes the simulation set up and laser-plasma parameters used in present set of simulations. Results are analysed in Sect. 4 and conclusions are drawn in last section of the manuscript.

2 Theoretical consideration

Surface plasma waves (SPW) are collective oscillation of electrons at the sharp metal dielectric interface. An efficient coupling of incident Electromagnetic wave with SPW requires phase matching conditions, where frequency of SPW is equal to the laser frequency and surface plasma wave vector is equal to laser wave vector. But, the requirement of phase matching between the SPW and an incident electromagnetic wave (laser) for efficient coupling is not possible at a flat interface (Pitarke et al. 2007). Coupling of laser energy to SPW using a prism (Ono et al. 2012) is an alternative way to overcome the coupling related problem for lower laser intensities. However, this method is not suitable for high laser intensities as the coupling medium will be rapidly ionized by the laser pulse. Whereas, if one uses periodically modulated targets (grating) instead of flat targets (Petit 1980), the phase matching condition gets satisfied.

The dispersion relation of SPW is \({K}_{\text{sp}}=\frac{{\upomega }_{\text{p}}}{c}\sqrt{{\varepsilon }_{1}{\varepsilon }_{2}/{\varepsilon }_{1}+{\varepsilon }_{2}}\), where \({\varepsilon }_{1}\) and \({\varepsilon }_{2}\) are dielectric constants of dielectric and metal respectively, c is the speed of light, \({\omega }_{p}\) and \({K}_{\text{sp}}\) are the frequency and wave number. For metal-vacuum interface \({\varepsilon }_{1}=1, {\varepsilon }_{2}\) = \(1-{\omega }_{p}^{2}/{\omega }^{2}\) that leads to \({K}_{\text{sp}}=\frac{{\omega }_{p}}{c}\sqrt{\frac{{\omega }_{p}^{2}-{\omega }^{2}}{{\omega }_{p}^{2}-2{\omega }^{2}}}\), where ω is laser frequency, \({\omega }_{p} (=\sqrt{4\pi {n}_{e}{e}^{2}/{m}_{e}} )\) is plasma frequency (in CGS). For excitation of surface plasma waves, the phase matching condition should be satisfied i.e. \({\omega }_{sp}=\omega\) and \({\text{K}}_{\text{sp}}={K}_{||}^{L}=\frac{\omega }{c}sin\phi\), where \({K}_{||}^{L}\) is laser wave vector along the target surface and \(\phi\) is the laser incidence angle from target normal. The above phase matching condition can be achieved using metal surfaces with a shallow modulation of period ‘d’. The dispersion relation in this case gets modified as \({K}_{||}^{L}={K}_{\text{sp}}\pm \text{n}\), where period \(q=2\pi /d\) and n is mode number. This leads to \(\pm \text{n}{\uplambda }_{\text{L}}/d=\sqrt{\left(1-\frac{{\omega }_{p}^{2}}{{\omega }^{2}}\right)/\left(2-\frac{{\omega }_{p}^{2}}{{\omega }^{2}}\right)}-\text{sin}\phi\), where \(\lambda\) is laser wavelength, \(d\) is period of grating. For an over-dense plasma (\(\omega \ll {\omega }_{p}\)), if one restricts to the solution with \(n=+1\), the condition for d and \(\phi\) becomes simplified as (Fedeli et al. 2016; Macchi 2018)

$$\frac{{\lambda }_{L}}{d}=1-\text{sin}\phi =1-\text{sin}(90-\theta )$$
(1)

Equation (1) is the condition for resonant excitation of surface plasma wave. Notice that this equation neglects possible relativistic nonlinearities. Thus, Eq. (1) holds good for linear regime but it may not hold good for the nonlinear regime, where the electron dynamics is nonlinear and strongly relativistic. The longitudinal electrostatic field of surface plasma wave is responsible for electron acceleration along the surface of the target.

The basic acceleration process is similar to LWFA; here longitudinal plasma wave has been replaced by a surface plasma wave. The additional difference is that the direction of accelerated electrons is slightly deviated from the target surface to the vacuum side, due to transverse field component of the surface plasma wave, as compared to laser direction in the case of LWFA. It is considered that surface plasmon (SP) is excited by the leading edge of the incident laser pulse. Incident laser and generated SP will have different phase velocities; therefore, a phase difference will be created after both travel some distance along the target surface. Still, SP will sustain for the length less than the dephasing length that is estimated as \({L}_{d}=\lambda /{(\alpha }^{2}+{n}_{c}/{n}_{e})\), where \(\alpha =\frac{\pi }{2}-\theta\). Also, effective spot size of the incident laser on the target surface will be typically of the order of dephasing length. Energy and emission angle of the accelerated electron through SP field is estimated as \({W}_{e}\simeq e{E}_{sp}{\gamma }_{f}^{2}/k\simeq {m}_{e}{c}^{2}{\alpha }_{\text{sp}}\alpha\) and \(\text{tan}{ \phi }_{e}={p}_{x}/{p}_{y}\simeq {\gamma }_{f}^{-1}\), where \({E}_{sp}\) is the amplitude of the longitudinal SP field, \({\gamma }_{f}={(1-{v}_{f}^{2}/{c}^{2})}^{-1/2}\), \(\alpha ={v}_{f}/c\), \({\alpha }_{sp}=e{E}_{\text{ps}}/{m}_{e}\omega c\). This also leads to an acceleration length \({L}_{a}\simeq {W}_{e}/e{E}_{\text{sp}}=(\lambda /\uppi )( {n}_{e}/{n}_{c})\) that is independent of the SP field amplitude. Also, from previously reported experiments (Fedeli et al. 2016), it was confirmed that the acceleration length in case of SP field is limited to the laser spot size. Present mathematical formulations ignore the finite temperature effect, collisional and relativistic nonlinearities that could affect the resonance up to certain level.

3 PIC simulations

Present study is carried out towards the generation of energetic electron bunches with two dimensional (2D) Particle-in-cell (PIC) simulations (Birdsall et al. 1991) using an open source code PICCANTE (Sgattoni et al. 2015). It is observed from initial simulation time steps that, as soon as the laser pulse falls on the grating surface (incidence angles ~  < 10\(^\circ\) there is reflection of the initial part of the laser pulse from the modulated surface (mostly specular, but also scattering due to modulation) and this reflected field travels to open boundaries and undergoes partial reflection. This problem has been resolved by increasing the size of simulation box, so that the artificially reflected fields have to travel with velocity greater than the velocity of main pulse, to reach the main pulse, which is impossible. Size of the simulation box is considered \(80 \mu m\) in X direction and \(90 \mu m\) in Y direction; simulation box is discretized with 7000 cells in X direction and 4000 cells in Y direction that leads to the grid size resolution of 11 nm and 22 nm in X and Y direction respectively. Open boundary conditions are applied for all the directions of the simulation box. A modulated surface or grating target of thickness \(0.8 \mu m\) (x-direction) is placed at the center (x = 0) of simulation box along the y-direction. Electron density is considered as \({n}_{e}=80 {n}_{c}\), where \({n}_{c}=\pi {m}_{e}{c}^{2}/{e}^{2}{\lambda }^{2}\) is the critical density corresponding to the laser wavelength. Macro-particles per cell are chosen as 25 for electrons and 9 for ions respectively. Spatio-temporal field profile is considered as \(E= {E}_{0}{e}^{-{x}^{2}/{r}_{0}^{2}}{e}^{-{t}^{2}/{\tau }_{0}^{2}}{e}^{iky}\widehat{y}\) for present laser pulse, where \({r}_{0}\) is the beam waist size at FWHM and \({\tau }_{0}\) is the pulse duration. Numerical values of laser beam waist and pulse duration are chosen as \(4 \mu m\) and 25 fs respectively, while central wavelength is considered as 800 nm. Laser strength parameter \({(a}_{0})\) is defined as \({a}_{0}=0.85\sqrt{I {\lambda }^{2}/{10}^{18} W {cm}^{-2} {\mu m}^{2}}\) and numerical value for the same is chosen as 5; corresponding peak intensity is estimated to be \({5\times 10}^{19} W/c{m}^{2}\). P-polarized laser pulse is chosen for maximum coupling between laser field and generated SP at grating target. We repeated simulations of ultra-short ultra-intense laser foil interaction (Mandal et al. 2023) carried out using the PIC code EPOCH (Arber et al. 2015) to validate the results of simulation code PICANTE. Further, the experimental parameters of Fedeli et al. (2016) are used to validate PICANTE for the reported simulation setup.

Schematic of the present physical mechanism is shown in Fig. 1, where the laser pulse makes a grazing incidence at an angle \(\phi\) with grating target and its complimentary grazing angle \(\theta ={90}^{^\circ }-\phi\). Laser pulse makes incidence from left \((Y<0)\) to grating surface and SP propagates in the positive Y direction.

Fig. 1
figure 1

Schematic of the laser interaction with grating target at grazing incidence

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4 Results and discussion

Present PIC simulation results discuss SP assisted electron acceleration using ultrashort laser interaction with surface modulated (or grating) target that is required for efficient coupling of incident EM wave to the generated SP. Intensity of laser in our simulation is \(5\times {10}^{19} W/c{m}^{2}\) and the associated electric field is nearly 0.19 TV/cm. Initial plasma density of target is considered as \(80{n}_{c}\) (\({n}_{c}\) is critical density).

As laser pulse make grazing incidence (around \(0 \mu m\) from + Y direction in Fig. 2a) and interacts with target surface, some electrons are pulled out of the target and a coherent structure of electrons appears to form just above the target surface at the back of the laser pulse in between 0 and \(20 \mu m\) in –Y direction (shown in Fig. 2a, 2b). Variation in target density take place from 30\({n}_{c}\) to 140\({n}_{c}\) as interaction process progresses with time; flux of electrons is observed at the back of laser pulse with some ejection angle around \(50 \mu m\) in –Y direction (shown in Fig. 2c). Also, density plots for the interaction process are shown in Fig. 3; where one can see electric charge separation inside the target and just above the surface of the target which prove the excitation of SP and ejection of electrons from vacuum plasma interface. The acceleration mechanism of electrons is similar to the laser wakefield electron acceleration (LWFA), where the laser pulse creates a plasma wave along the direction of laser propagation and co-propagates with it, leading to longer acceleration lengths. However, in the present scenario, the surface plasma wave is assisted by the modulation on the target surface, and is similar to a wakefield parallel to the target surface. Here, the laser is at an angle to target surface hence dephasing length is much smaller as compared to the LWFA. The major difference with respect to LWFA exists in the form of the transverse field component of SP that pushes the electrons on the vacuum side.

Fig. 2
figure 2

Electron density snapshots at different times of simulation at a t = 13 fs b t = 60 fs c t = 160 fs and d t = 190 fs for incidence angle 4°, grating wavelength = 559 nm, grating grow depth = 250 nm

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Fig. 3
figure 3

Zoomed electron density snapshots at different times of simulation at a t = 60 fs and b t = 190 fs for incidence angle 4\(^\circ\), grating wavelength = 559 nm, grating grow depth = 250 nm

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The dephasing length is estimated as \(39.2 \mu m\) for present set of laser-plasma parameters and therefore, SP assisted electron acceleration will take place in the region of dephasing length. At later stage of interaction coherent structure of SP disperses because of the destructive interference between incident laser wave and SP.

Previously, Guang et al. (Hu et al. 2010) reported the enhanced surface acceleration of fast electrons using subwavelength grating targets, which can be applied in the cone-attached ion acceleration and high energy density physics experiments. The fast electron beam emitted along the target surface was enhanced in the maximum energy by more than three times relative to that by using planar target. The total number of the fast electrons ejected from the front surface of grating target was two times higher than that of planar target. The method to enhance the surface acceleration of fast electrons may have several applications such as in ion acceleration and the experiment of high energy density physics.

Figure 4 shows the line out plots of Electric field component (\({E}_{y}\)) parallel to the target surface just above the grating structure. Physically, one can say that these line-outs are electric field amplitude of surface plasma wave and corresponding field gradient is nearly 5 GV/cm that exactly falls in the range of theoretically estimated field gradient using the wavelength of electromagnetic mode just above the vacuum-plasma interface. Electrons injected into surface plasma wave at right phase are accelerated along the surface of the target at the back of laser pulse. This could be the reason for high energy electrons produced in our simulations. Figure 5 shows the phase space plot for fast electrons produced along the direction of SPW (Y-axis) and phase space plot perpendicular to the SPW propagation (X-axis); the Py value confirms the SP assisted flux of accelerated electron bunch at some ejection angles. Electron ejection angle \(\phi =\text{arctan}({p}_{y}/{p}_{x})\) is taken in the range 1° < ϕ < 10° for positive value of momenta \({(p}_{x}>0)\) in transverse direction.

Fig. 4
figure 4

Electric field component at vacuum plasma interface for present laser-target arrangement. a lineout along x = − 0.1, b lineout along x = − 0.2, c lineout along x = − 0.3, d lineout along x = − 0.4

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Fig. 5
figure 5

Phase space plot for electrons along (Y-axis) and perpendicular (X-axis) to SPW at 170 fs

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Therefore, the process of electron acceleration becomes two dimensional and electrons are emitted at an angle with respect to the surface plasma wave propagation. Figure 6 shows the energy spectra corresponding to the accelerated electron bunch from SP field for varying laser incidence angle and the grating period. In case of incidence angle of \(\theta =45^\circ\) and grating period \(d=3.14\lambda\) the maximum electron energy obtained is 15 MeV. For \(\theta =60^\circ\) and \(d=2.00\lambda\), the electron energy goes up to 25 MeV and for \(\theta =75^\circ\) and \(d=1.35\lambda\), the maximum energy decreases to 15 MeV. Simulation results shown in Fig. 6 matches well with the experimental results reported by Fedelli et al. (2016).

Fig. 6
figure 6

Electron energy spectrum at different incidence angles \((\theta )\) and grating periods \((\text{d})\). Here λ is laser wavelength = 800 nm

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Further, the parametric studies are carried out to optimize the laser incidence angle on the grating surface to deduce conditions of maximum energy gain and the ejected electron flux. As the incidence angle increases from 1° to higher value, the electrons maximum energy initially increases and subsequently it starts decreasing, the flux of high energy electrons slightly decreases with increase in maximum energy of electrons.

For grazing incidence angle of less than 10° to the grating surface, electrons of energy almost 2.5 times more than the maximum energy obtained by electrons with laser incidence angles closer to the resonance angle is observed. It is found that 4° grazing incidence angle is optimum and the corresponding maximum energy of electrons is 78 MeV. Electron energy spectrum is shown in Fig. 7 where laser incident angle is varied from θ = 1° to θ = 90° while kee** other laser and target parameters constant. Initially, maximum electron energy gradually increases with the increase in incident angle from θ = 1° to θ = 5° but further increment in incidence angle leads to decrease in the electron energy. Simulation results revealed that θ = 4° is the optimum incident angle to get both the maximum electron energy and higher number of emitted electrons. Acceleration length \({(L}_{a}\simeq ( {n}_{e}/{n}_{c})\) is estimated as \(20 \mu m\) for present set of laser-plasma parameters that leads to the energy gain \({(E}_{g}\simeq \text{e}{E}_{\text{sp}}{ L}_{a})\) in the range (\(\sim 60-70 Me V )\) for observed field gradient \((\sim 5 GV/cm)\) of SP along target surface. Hence, theoretically estimated energy of the SP assisted accelerated electrons lies in the same range as observed from the present PIC simulations.

Fig. 7
figure 7

Electron energy spectrum at 4° angle of incidence and for different grating periods

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Further, following the estimates of Cantono et al. (2018), we estimated our αsp = 3.9 for peak laser intensity of 5 × 1019 W/cm2 and considering same solid target density of 400 nc, we too get γϕ ≈ 20, the maximum energy of accelerated electron comes out to be ≈40 MeV at an angle of incidence ≈ 87° (grazing angle 4\(^\circ\)). However, since we significantly differ in the angle of incidence, where Cantono et al. have reported surface plasmon based electron acceleration at the resonance angle of 30° from target normal, whereas, we report optimum energy at 4° grazing incidence (i.e. 86° from target normal). Hence, the estimates carried out based on Cantono et al. do not match our observations.

Table 1 provides the observed value of the electron energy for varying grazing incidence of the laser pulse. The total charge shown in the Table 1b is calculated by multiplying the total number of accelerated macro-particles in the given energy range with the number of actual electrons per macro-particle. The total number of accelerated macro-particles in the given energy range is dumped by the code, if the particle diagnostics is ON. The total charge calculated in this manner from 2D simulations helps in comparing the simulation results for different angle of incidence and grating parameters, but cannot be used to quantify the actual charge.

Table 1 (a) Laser incidence angle and corresponding maximum electron energy. (b) It shows total electric charge in different energy ranges of electrons (in case of incidence angle \(\theta =4^\circ\))
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Subsequently, the grating period is varied while kee** the angle of incidence to the optimum value of \(4^\circ\) and the variation is electron energy spectrum was studied. It is observed from the simulated energy spectra that no significant change in electron energy spectrum takes place with the change in grating period for the optimum grazing angle.

To further confirm the underlying mechanism of acceleration, we carried out 3D simulation for only the optimum case reported above, which is 4° angle grazing incidence case. The schematic of 3D simulation is shown in Fig. 8 and the 2D slices of density snapshots shown in Fig. 9 (side-view of target) and Fig. 10 (front-view of target). Figure 11 shows the energy spectrum of the accelerated electrons.

Fig. 8
figure 8

Schematic of 3D simulation setup

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Fig. 9
figure 9

Zoomed electron density snapshot in x–y plane (side-view), sliced at the centre of 3D simulation box (z = 0 µm). The electrons seen above the grating lines are the plasma electrons being accelerated. The electron bunches are spaced periodically at grating period leading to plasma wave along y-direction and in the y–z plane

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Fig. 10
figure 10

Zoomed electron density snapshot in y–z plane (front-view), sliced at the centre of 3D simulation box (x = 0.1 µm). The horizontal lines are grating rulings as seen from the front. We see only grating lines, as it is thin slice of electron density averaged over 3 cells along x-direction. The electrons seen above the grating lines are the plasma electrons being accelerated

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Fig. 11
figure 11

The electron energy spectrum of 3D simulation

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It is worth noting here that as we increase the angle of incidence with respect to target normal, most of the laser field will be directed to E⊥ component, and JxB heating should be significant for electrons on the vacuum side of vacuum-plasma interface. For our optimum angle of grazing incidence of 4° (i.e. 86° to target normal), the direction of JxB heated electrons will be inside the target, and even if they are deflected by the transverse field component of SP, they would merge with SP accelerated electrons. Hence, although JxB heating may also be contributing to the electron acceleration at grazing incidence of laser pulse, we do not find any explicit signature of it in our simulations. The higher energy of accelerated electrons could be a combined effect of (SP) wave acceleration, where SP is assisted by the modulation on the target surface, in addition to JxB acceleration. The maximum energy of the accelerated electrons obtained in the case of plane (non-modulated) target interacting with the laser at grazing incidence was not more than 25–30 MeV, which is mostly contributed by JxB mechanism at such high laser intensities. This further confirms that although JxB heating could be providing some contribution in electrons energy, it is the surface plasma wave coupled to the grating modulations, which are creating the electron density ripples at grating wavelength (Fig. 3 of 2D, Fig. 9 of 3D simulation result) leading to an accelerating field similar to wakefield, which is resulting in the higher energy as compared to the unmodulated target.

5 Conclusion

Present PIC simulation results report higher energetic electrons in case of grazing incidence of laser pulse with structured target. Number of the accelerated electrons and maximum attainable energy varies significantly under the variation of the grazing incidence angle. Also, the variation in grating depth is considered which leads to no significant change in electron energy spectrum. Maximum electron energy of 78 MeV is observed in case of incidence angle \(\theta =4^\circ\) which is almost threefold enhancement in the maximum energy for incidence angles closer to the resonance angle. It is clear from the results that the resonant excitation of surface plasma waves at grazing angles is not optimum in the nonlinear regime.