For strong field enhancement of ultrashort light pulses, a 3-D metallic funnel-waveguide is analyzed using the finite-difference time-domain (FDTD) method. Then the maximum intensity enhancement actually developed by the funnel-waveguide upon the injection of femtosecond laser pulses is observed using two-photon luminescence (TPL) microscopy. In addition, the ultrafast dephasing profile of the localized field at the hot spot of the funnel-waveguide is verified through the interferometric autocorrelation of the TPL signal. Finally it is concluded the funnel-waveguide is an effective 3-D nanostructure that is capable of boosting the peak pulse intensity of stronger than 80 TWcm−2 by an enhancement factor of 20 dB without significant degradation of the ultrafast spatiotemporal characteristics of the original pulses.
© 2014 Optical Society of America
Local field enhancement occurring in nanometer-scale structures  has widely been investigated for diverse applications such as surface-enhanced Raman scattering , multi-photon interaction for harmonic generation [3,4] and photoemission or photoluminescence [5–9]. Recently attention is being paid to strong field enhancement of ultrashort light pulses for generation of extreme ultraviolet light in interaction with noble gases [10–16]. This highly nonlinear optical frequency upconversion requires achieving high peak pulse intensities of stronger than 10 TWcm−2 from moderate pulses of ~0.1 TWcm−2 intensity. Such strong field enhancement may be accomplished with V-groove nanostructures [17–19] exploiting the adiabatic slowdown of surface plasmon polaritons, or by adopting nanoantennas [9,20] and tapered slab waveguides [21,22] designed to induce narrowly localized resonance of surface plasmons. Most nanostructures readily fabricated on thin metal films are susceptible to thermal damage [12,23] caused by intense ultrashort pulses. On the other hand, bulk-type nanostructures such as nano-tips [24,25] are capable of providing more robustness to thermal damage, but the resulting hot spot volume tends to reduce due to lower power coupling efficiency to the incident laser field.
In this investigation, we conduct an elaborate evaluation on a 3-D waveguide that was previously designed by the authors for strong field enhancement of femtosecond laser pulses for generation of extreme ultraviolet light [12,13]. The waveguide is fabricated on a thick silver film using the focused ion beam (FIB) process in the form of a single tapered hollow core of funnel shape, through which the incident laser pulse is coupled without significant power loss for strong field enhancement along with high thermal immunity. Here, the dynamic evolution of the field enhancement occurring within the funnel-waveguide is analyzed through finite-difference time-domain (FDTD) simulation. Then, two-photon luminescence (TPL) microscopy [6,9,17,26] is adopted to probe the strong field enhancement actually developed within the hot spot volume of the funnel-waveguide. In addition, the ultrafast spatiotemporal characteristic of the enhanced field is measured using the interferometric autocorrelation (IAC) of the TPL signal. This investigation validates that the funnel-waveguide is an effective 3-D nanostructure capable of boosting the peak pulse intensity of stronger than 80 TWcm−2 by an enhancement factor of 20 dB without significant degradation of the ultrafast temporal characteristics of the original pulses.
2. Strong field enhancement in funnel-waveguide
Figure 1 shows the funnel-waveguide prepared to be tested by TPL microscopy in this investigation. The waveguide is designed so as to compress the incident femtosecond pulse along the tapered hollow core. The cross-section of the hollow core is of elliptical shape and its elliptic ratio of the minor-axis diameter to the major-axis diameter remains constant along the way from the inlet aperture to the exit aperture. The waveguide is fabricated by adopting the focused ion beam (FIB) milling process on a thick Ag layer deposited inside the probing tip of a micro-cantilever commercially available for near-field scanning optical microscopy (NSOM) [13,27]. Details on the fabrication procedure are found in Ref . The geometry of the waveguide is characterized by the four parameters; the minor-axis diameter of the exit aperture (d), the minor-axis diameter of the inlet aperture (b), the elliptic ratio of the cross-section (r = b/a) with a being the major-axis diameter of the inlet aperture, and the waveguide length (h). The geometrical parameters are optimized so as to yield a large hot spot in which the intensity enhancement exceeds 20 dB. Through a series of FDTD simulations (Lumerical solutions, ver. 8.0), the parameters are selected as d = 70 nm, b = 2.2 μm, r = 0.5 and h = 9 μm. The resulting hot spot has a volume of 250 nm × 250 nm × 500 nm in three dimensions with the maximum intensity enhancement factor being ~400 at the center of the hot-spot volume. This waveguide is found almost identical to the previous design explained in Ref , except the exit aperture diameter (d) being reduced to 70 nm from the previous value of 100 nm.
First of all, we calculated the temporal evolution of the field enhancement developed in the designed funnel-waveguide, of which the result is summarized in Fig. 2. In this FDTD calculation, for simulation of the real experimental situation, the incident light was assumed as a femtosecond laser pulse of an 800-nm center wavelength with 12-fs FT-limited pulse duration. The polarization direction of the incident pulse was aligned parallel to the minor-axis of the elliptical cross-section (Fig. 2(a)). The calculation result shows that the propagation of the incident pulse along the waveguide is represented by the fundamental mode that is symmetrical about the minor-axis of the elliptical cross-section. The effective refractive index (neff) of the fundamental mode was also calculated, of which the real part Re(neff) and imaginary part Im(neff) vary along the z-axis of the waveguide (Fig. 2(b)). It is noted that Re(neff) is larger than unity when the incident pulse enters the inlet aperture (z = 9 μm). This indicates that the fundamental mode is a plasmonic mode coupled with surface plasmon polaritons (SPPs). As the fundamental mode propagates further into the waveguide, Re(neff) gradually decreases and eventually crosses the unity line at z = ~3 μm, which implies that the fundamental mode converts to a photonic mode before reaching the exit aperture. The conversion is explained due to the fact that the plasmonic coupling weakens near the exit aperture because the neutralization of electrons through the circumferential silver wall begins to arise in the narrowed polarization gap. Further, as the photonic-converted fundamental mode comes near the exit aperture, Re(neff) reduces drastically while Im(neff) rises up at z = ~1 μm. The increase of Im(neff) infers that the propagation length reduces with increasing energy loss. Eventually, the photonic mode reflects backwards before reaching the exit aperture by the mode cut-off occurring where the cross-section shrinks to a major-axis diameter of less than half the wavelength of the incident laser.
Our FDTD simulation also reveals that the overall behavior of field enhancement within the funnel-waveguide is critically affected by the center wavelength of the excitation laser. For instance, if the center wavelength changes from the current value of 800 nm to a long 1,300 nm wavelength, the design parameters of the funnel-waveguide have to be considerably altered to achieve a similar level of field enhancement. On the other hand, the pulse duration yields no significant effect if it is longer than ~5 fs (see Fig. 5(d)).
A temporal sequence of three snap shots of enhanced intensity distribution is shown in Fig. 2 to illustrate how the fundamental mode of the incident pulse develops as it propagates through the waveguide. In the early period near the inlet aperture, the field enhancement is confined only to the silver wall (Fig. 2(c)). As the incident pulse moves inward further, the plasmonic enhancement extends towards the center of the hollow core (Fig. 2(d)). Finally, near the exit aperture where the fundamental mode turns to a photonic mode and subsequently converges to a hot spot at z = ~0.55 μm, the intensity distribution becomes nearly uniform without significant non-homogeneity across the entire area of the cross-section (Fig. 2(e)). Another fact is that when the fundamental mode is reflected backwards by the mode cut-off, its leading edge is folded with the tailing edge that comes into the hot spot. The result is the constructive interference that increases the enhanced intensity by a factor of 4. In consequence, the intensity enhancement factor in the hot spot reaches 400 with a large 20-dB volume of ~3 × 107 nm3.
The transmittance of the funnel-waveguide is defined as the ratio of P(z)/Pinc wherein Pinc is the incident pulse power while P(z) denotes the pulse power actually propagating along the z-axis from the inlet aperture. For calculation of P(z)/Pinc using the FDTD method, as shown in Fig. 3(a), a straight hollow tube of an elliptical cross-section (260 nm × 520 nm) which is slightly larger than the cross-section of the hot spot was virtually attached to the exit aperture so that the contribution of the mode-cutoff light reflected from near the exit aperture can be eliminated in determining P(z)/Pinc. In addition, a perfectly matched layer (PML) was added to eliminate all the light reaching the exit aperture by absorption. These two virtual modifications allowed us to determine P(z)/Pinc precisely as shown in Fig. 3(b). The computed transmittance P(z)/Pinc reveals that the power coupling efficiency at the hot spot (z = 0.55 μm) turns out to be 53%. This result implies that in consideration of the constructive interference occurring between the leading and trailing edge of the fundamental mode, the pulse power concentrated within the hot spot becomes instantly more than twice the incident power, which is worked out to be 4 × 53% of Pinc. It is necessary to note that at the inlet aperture (z = 9 μm) where the incident pulse enters the waveguide, the transmittance is only ~76%, not 100%, because 24% of the incident light reverses its propagation due to the mode cut-off before reaching the hot spot, escaping the waveguide structure through the inlet aperture. The remaining 23% of the incident light, i.e., 76% at the inlet minus 53% at the hot spot, is lost in the form of absorption and scattering along the hollow core silver surface of the waveguide.
For experimental verification of the strong field enhancement using TPL microscopy, the waveguide is illuminated through the inlet aperture with femtosecond laser pulses. Then, by nonlinear two-photon absorption, frequency-upconverted TPL radiation is generated from the inner silver surface of the hollow core. The TPL signal escaping from the hollow core through the inlet aperture is observed while the waveguide is scanned in steps along the transverse direction as illustrated in Fig. 4(a). The excitation laser pulses are emitted from a Ti:sapphire oscillator (Femtolasers, Femtosource sPro) at a 75-MHz repetition rate with a 100-nm spectral bandwidth about an 800-nm center wavelength. The near infrared (NIR) laser pulses are tightly focused onto the inlet aperture using a focusing lens (8 mm focal length). The group delay dispersion (GDD) is pre-compensated to ~800 fs2 using a pair of chirped mirrors. The pulse duration is maintained at a nearly Fourier-transform-limited (FT-limited) level of 12 fs by use of a wedge pair. The TPL signal is then directed via a dichroic mirror to a photo-multiplier tube (PMT, Hamamatsu, H10721) of 300 - 500 nm detection wavelengths. A spectral filter of a 400 ± 40 nm wavelength transmission band is inserted before the PMT to suppress the noise coming from surroundings as well as the excitation beam. The micro-cantilever structure housing the waveguide is mounted on a 3-axis motorized stage for precise alignment with the aid of a CCD camera installed with a flipping beam splitter.
Figure 4 presents our experiments to monitor the TPL signal by moving the funnel-waveguide in steps along the major-axis direction of the elliptical hollow core in steps of 20 nm. The measured TPL signal was normalized with respect to the reference signal that was obtained from the smooth flat silver surface on the micro-cantilever that houses the funnel-waveguide. The incident average power of the driving laser pulses was set to 15 mW and focused on the inlet aperture with a peak intensity of ~0.05 TW/cm2. As expected, the TPL signal is found polarization-dependent with its maximum reaching 80 (red solid line) when the incident polarization is in parallel with the minor-axis of the inlet aperture. The TPL signal intensity is proportional to the fourth power of field enhancement. Thus, the TPL signal is mainly generated by the high intensity field of the hot spot with insignificant contributions from the remaining surface inside the waveguide. From the measured TPL signal, the intensity enhancement factor α is estimated as [6,9,26]Eq. (1), the ratio of TPLhot/TPLref is obtained from the measured data of Fig. 4(b) as ~80. Besides, <Pref> and <Phot> are taken from the experimental conditions as 15 mW. The excitation laser is assumed to have a circular spot of ~6.5 μm diameter being illuminated through a 1-mm diameter aperture located before the focusing lens. Aref is determined to be ~33.2 μm2 from the focal spot area. And, Ahot is calculated as the effective area of the TPL signal, which is defined as Fig. 2(e), Ahot is obtained as ~1 × 105 nm2. Finally, putting all the computed and measured values of the parameters into Eq. (1) permits determining the value of α to be 165. This measured value is found to be less than the FDTD estimation of ~400 in Fig. 2(e). However, the actual value of α within the hot spot is speculated to be larger than the measured value because the absorption loss of the TPL signal by the inner silver surface of the waveguide, which inevitably occurred during the backward propagation of the TPL signal from the hot spot to the inlet aperture, was not precisely considered due to practical difficulties of estimation. The polarization-dependence of the enhanced field was well verified by the observation that the measured enhancement factor reduces to ~10 when the polarization of the excitation laser is rotated to the direction of the major-axis of the elliptical hollow core.
Figure 4(c) shows how the TPL signal varied as the incident power of the excitation laser was increased from 0 to 140 mW and subsequently decreased back to 0. The TPL signal measured from the inlet aperture yielded a quadratic dependence on the incident power. This observation supports that the measured signal is generated by two-photon absorption. Further, the quadratic dependence was consistently held even when the incident power was increased up to 140 mW, and no significant hysteresis was observed during the two cycles of incident power sweeping shown in the figure. More importantly, no sign of thermal damage due to melting or ablation was detected [9, 28]. The incident power of 140 mW is equivalent to a peak intensity of 0.5 TW/cm2 when focused on the inlet aperture. This infers that the funnel-waveguide is capable of producing intensities of stronger than 80 TW/cm2 in consideration of the intensity enhancement factor obtained from the TPL experiment ( × 165). This experimental observation concludes that the funnel-waveguide offers strong thermal immunity in comparison to the nanostructures fabricated on thin metal layers [12, 14, 23].
3. Ultrafast pulse generation in funnel-waveguide
Characterizing the enhanced field inside the funnel-waveguide requires not only the spatial distribution of the localized hot spot volume but also the temporal shape of the enhanced field within the hot spot. Accordingly, the ultrafast dynamic nature of the enhanced field was examined by experiments together with FDTD calculations. Considering that the incident laser offers a FT-limited pulse duration (ti) of 12 fs at an 800-nm center wavelength, the FDTD calculation shown in Fig. 5(a) indicates that the enhanced field at the hot spot undergoes no significant temporal pulse broadening. The enhanced pulse duration (te) lies in the range of 12.5 – 13 fs near the hot spot (z = ~0.55 μm). In the region away from the maximum field point (z > 0.6 μm), the pulse duration is found increasing rapidly. However, the pulse duration increase is not caused by a prolonged dephasing time but by the overlapping effect of the leading edge of the reflected wave by the mode cut-off with the trailing edge of the forward-moving pulse. The dotted line (blue) indicates the variation of the center wavelength of the propagating pulse that becomes shorter as the pulse propagates towards the exit aperture. The reason is that the mode cut-off wavelength is proportional to the diameter of the tapered hollow core so that longer wavelengths reflect backwards before shorter wavelengths. This spatial wavelength separation reduces the spectral bandwidth of the enhanced field, widening the pulse duration at the hot spot. The center wavelength at the maximum field intensity location (z = 0.55 μm from the exit aperture) is calculated to be 800 nm, which is the same as that of the incident light pulse. The pulse duration of the enhanced field at the hot spot (z = ~0.55 μm) is estimated to be ~12.8 fs (Fig. 5(b)).
In order to measure the actual temporal behavior of the enhanced field near the hot spot, an autocorrelation measuring device of Michelson interferometer type was installed behind the apparatus of TPL measurement of Fig. 4(a). As in the previous TPL experiments, the GDD was minimized using a pair of chirped mirrors and a wedge pair. Subsequently, it was possible to measure the interferometric autocorrelation signal (IAC) of the temporal profile of the incident laser pulse using a two-photon absorption detector with a 1:8 ratio (the dashed line (red) in Fig. 5(c)). The pulse duration (ti) obtained from the IAC signal is measured ~12 fs, which is nearly FT-limited pulse duration in consideration of the spectral bandwidth of the incident laser. As discussed earlier, the TPL signal has a quadratic dependence, which enables the direct detection of the IAC signal via the TPL signal from the PMT in Fig. 4(a). Besides, the TPL signal yields a long decay time, which is not the case for ordinary second harmonic signals. Thus, it was possible to monitor the IAC signal by slowly translating the moving mirror of the interferometer setup (solid blue line in Fig. 5(c)). From the IAC signal of the enhanced field detected by the PMT, the pulse duration (tTPL) was measured to be 13.6 fs which is slightly longer than the FDTD-estimated value of 12.8 fs. The discrepancy may be attributable to the fabrication imperfection of the funnel-waveguide. Besides, the TPL signal experiences absorption loss during its escape from the waveguide backwards through the inlet aperture. Accordingly, the TPL signal generated from the large z partition (z > 0.55 μm) within the hot spot volume contributes more than that of the small z partition (z < 0.55 μm), thereby broadening the pulse duration observed at the inlet aperture even though the actual pulse duration within the hot spot may be shorter than the measured value.
Figure 5(d) presents another FDTD simulation result showing a direct comparison of pulse duration between the incident field and the enhanced field right at the location of the maximum field enhancement. The incident field was assumed as a FT-limited pulse of an 800 nm center wavelength with the pulse duration varying in the range of 3 to 30 fs. Over the entire range of simulation, the computed value of te is found to closely follow the incident laser pulse duration within a single oscillation cycle (t0 = 2.67 fs), even though the relative broadening factor ((te-ti)/t0) appears to be increasing as ti becomes shorter. This simulation result supports that the funnel-waveguide is capable of enhancing the intensity of a few-cycle incident pulse without significant pulse broadening.
Our FDTD simulation performed in this investigation shows that the proposed 3-D metallic funnel-waveguide is an effective nanostructure for strong field enhancement of ultrashort light pulses. The hot spot volume of 20-dB intensity enhancement is estimated to be ~107 nm3 wherein the incident pulse power is concentrated with a 53% power coupling efficiency. The instant peak pulse power is enhanced to be twice the incident laser power due to the constructive interference of the trailing edge of the incoming pulse with its the leading edge reflected backwards by the mode cutoff from the hot spot. Our TPL-exploited experiment confirms that the maximum enhancement factor reaches 165. In addition, the ultrafast dephasing profile of the localized field in the hot spot is identified through the interferometric autocorrelation of the TPL signal. No thermal or ablation damage is seen even for a ~0.5 TWcm−2 incident laser field, which implies that the peak pulse intensity can be enhanced to at least 80 TWcm−2 strong enough to produce extreme ultraviolet light by means of higher harmonic generation.
This work was supported by the National Honor Scientist Research Program from National Research Foundation of the Republic of Korea (NRF).
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