1. Introduction

Materials with a strong power-dependent reflectance or transmittance are key for the development of all-optical applications such as optical signal processing [1], pulse compression [2], passive protective devices [3] and medical image processing [4, 5]. Different types of nonlinear optical (NLO) effects and materials have been used to realize nonlinear reflectors. For instance, the combination of a second harmonic generation (SHG) crystal and a dichroic mirror has been used to demonstrate intra-cavity passive mode-locking operation for picosecond-pulse generation in the visible range [6, 7]. In addition, Bragg-periodic structures comprising semiconductor layers with Kerr nonlinearity in the infrared spectral range have been reported [1, 8]. A common limitation of these approaches is their restrictive wave-vector matching conditions, resulting in a narrow spectral and angular bandwidth. However, little attention has been directed at utilizing the extremely large and ultrafast NLO response of noble metals to develop nonlinear reflectors with broad spectral and angular bandwidth in the visible spectral range.

The NLO response of noble metals is described as a χ⁽¹⁾ process caused by electron and lattice heating [9]. The linear and NLO responses of noble metals are determined by the inherent electronic properties that define their dielectric permittivity. Their electronic properties in the visible spectrum can be divided into two separate mechanisms: interband and intraband transitions. Electronic interband transitions in the visible or ultraviolet (UV) spectral region arise from bound electrons excited from fully occupied electronic states within the d-band, below the Fermi energy level, to the half-filled s-p electronic bands in the conduction band. At lower energies, electronic intraband transitions occur from free electrons stimulated within the conduction band. When a metal film is excited with an ultrafast optical pulse, the absorbed optical field raises the temperature of electron cloud and smears the electronic distribution around the Fermi energy (Fermi-smearing), causing a very strong change of the dielectric permittivity of the metal around the interband transition onset. For all-optical applications in the visible spectrum, Au is an attractive material because its interband transition onset lies around 520 nm [10], causing a very large NLO response across the whole visible spectrum. The nonlinear change of optical path length of an Au thin film has been extracted from pump-probe experiments and shown to be strong, spectrally broad, and ultrafast [11].

In this paper, a novel nonlinear mirror structure comprising only a thick Ag reflector, a first dielectric layer, a 23 nm-thick Au film, and a second dielectric layer on top which will be referred to as a reflection modifier in the following. In this structure the linear absorptance, and consequently the NLO response of the Au thin film can be engineered. As a consequence, the reflectance of the nonlinear mirror can be drastically changed by an optical field through the excitation of the strong thermal nonlinearity of the Au film. Refractive index changes of Au thin film are simulated using the two-temperature model and a physical model that describes the dielectric permittivity. Reflectance changes of the nonlinear mirrors are simulated by a transfer-matrix method with calculated refractive index changes. The nonlinear mirror is designed to maximize reflectance changes. In addition, a figure-of-merit for such a structure is also discussed. This novel nonlinear mirror is a simple structure providing large, ultrafast reflectance changes that are spectrally and angularly broad in the visible spectral range.

2. Experimental method

2A. Fabrication and characterization

All thin films were deposited on VWR Micro Slides glass substrates with a Kurt. J Lesker Axxis electron beam deposition system. Substrates were cleaned ultrasonically in deionized water, acetone and isopropanol for 15 min each. The films were deposited under vacuum at a pressure of 8.6 × 10⁻⁷ Torr (1.1 × 10⁻⁴ Pa) with a rotating sample holder that actively cools the substrates to room temperature. The Ag, Au, and SiO₂ were deposited at a rate of 0.2 nm/s, 0.05 nm/s, and 0.2 nm/s, respectively, monitored by crystal sensors.

The inset of Fig. 1(a) shows a generalized thin film structure of the novel nonlinear mirror. It was fabricated by deposition of the Ag layer onto a glass substrate followed by the deposition of the Au layer sandwiched and protected by thin SiO₂ layers with the following geometry: NLO mirror: Glass/Ag(100 nm) /SiO₂(81 nm)/Au(23 nm)/SiO₂(81 nm).

 

Fig. 1 (a) Comparison of measured (symbols) and simulated (lines) transmittance (T, blue), reflectance (R, green), and absorptance (A, red) spectra in the visible range of the fabricated NLO mirror sample. The inset shows the generalized thin film structure of the NLO mirror. (b) Measured reflectance spectra at varied incidence angles. (c) Absorptance A(j,k) and (d) reflectance R(j,k) at 550 nm of the NLO mirror with different thickness combinations of reflection modifier (j) and cavity (k) layers.

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The layer thicknesses (shown inside the parentheses) were set to optimize the linear spectral and angular bandwidths while maintaining a maximum nonlinear reflectance change. The optimization process will be discussed later. Figure 1(a) shows the comparison between measured values of the transmittance (T), reflectance (R), and absorptance (A) spectra taken by a Shimadzu UV-Vis-NIR scanning spectrophotometer and the simulated spectra using the transfer-matrix method. The good match validates simultaneously the fabrication procedure and the simulation procedure. Spectroscopic ellipsometric (SE) data (J.A. Woollam M-2000UI) were taken on individual films to measure the optical properties of each layer. The refractive indices (N = n + ik) of all films were calculated from SE data imposing Kramers-Kronig consistency to the calculated values. In addition, the spectroscopic ellipsometry also measures the reflectance spectra at varied angles shown in Fig. 1(b) to determine the angular bandwidth of the sample.

The NLO properties of the NLO mirror were characterized by a commercially available white-light continuum (WLC) pump-probe spectroscopy system (Helios, ultrafast system), described in detail in reference [11]. In short, the pump pulse was tuned to a wavelength of 550 nm with a pulse width of 60 fs half-width-1/e (HW 1/e) and a spot size of 347 μm (HW 1/e) at the sample position, measured using a knife-edge scan. The WLC (420 - 950 nm) probe pulse had a spot size of 80 μm (HW 1/e) at the sample position and a low enough fluence to produce no observable NLO response in the sample. The total instrument response time is 150 fs full-width-half-maximum (FWHM). Because the probe spot size is smaller, it is assumed that the probe overlaps with a region of approximately constant peak fluence from the pump. After averaging over one thousand probe pulses at each time delay, the change in optical density (ΔOD(λ, t)) was recorded as a function of wavelength (λ) and delay time (t). The reflectance change spectra (ΔR(λ, t)) of the WLC probe pulses were calculated from measured ΔOD(λ, t) for a variety of pump fluences by $\Delta R\text{(}\lambda \text{,}t\text{)}=R_0(\lambda )\cdot \left({10}^{\Delta OD\text{(}\lambda \text{,}t\text{)}}-1\right)$, where R₀(λ) is the measured linear reflectance spectrum.

3. Results and discussion

3A. Linear optical properties

The inset of Fig. 1(a) shows the structure of the NLO mirror proposed in this paper. The structure can be seen as a Fabry-Perot filter consisting of a central dielectric layer (cavity) sandwiched by two reflectors; the first one is the thick Ag reflector and the second one is the thin Au layer covered by a dielectric layer (reflection modifier) on top.

Figure 1(c) shows a contour plot of absorptance A(j,k) values as a function of the thickness j of the top dielectric layer which is called the reflection modifier, and the thickness k of the dielectric layer sandwiched between the two metal layers and which is referred to as the cavity thickness. The absorptance A(j,k) was simulated using the transfer-matrix method at a wavelength of 550 nm. The structure can provide a wide variation of absorptance values, ranging from 2% to 96%. These variations are periodic with respect to the thicknesses of the reflection modifier and cavity layers, as can be seen from regions [(1,1), (2,1), (3,1), (1,2)] in Fig. 1(c). Not surprisingly, in both directions these regions have a length of 188 nm corresponding to the half-wave optical thickness of SiO₂ at 550 nm [12]. As also indicated in Figs. 1(c) and 1(d), the simulated reflectance is complementary to the absorptance at 550 nm (as expected from the negligible transmittance at this wavelength) and therefore shares the same periodicity.

The dominant contribution to the total absorptance of the mirror (55%) is primarily attributed to the Au thin film (53%), with negligible absorption in its component Ag layer (2%). This is in part because of the electric field distribution imposed by the mirror geometry, and in part because Au is highly absorptive at wavelengths close to the interband transition onset, in the middle of the visible spectral range. On the other hand, the interband transition onset of Ag located in the ultraviolet (UV) spectral range causes light with photon energy far below the onset to be mostly reflected. The SiO₂ films are lossless based on SE data.

To illustrate the proposed approach, the NLO mirror was designed in region (1,1) to have a linear absorptance of 55% and a reflectance of 45% at 550 nm. This choice was arbitrary. However, the criterion for picking up the mirror geometry that optimizes its NLO response will be discussed in detail in the following section. The measured R spectrum in Fig. 1(a) shows the fabricated NLO mirror sample is a long wavelength pass optical filter with a broad spectral bandwidth. In the whole visible spectral range, the R and A spectra are complementary. In addition, the measured R spectrum as a function of angle of incidence in Fig. 1(b) is also shown to be angularly insensitive. Within incidence angles up to 65 degree, the R spectrum barely changes compared to the normal incidence. The linear optical response of the NLO mirror shows both broad spectral and angular bandwidth.

3B. Nonlinear optical properties

The extremely large magnitude of the NLO response in a noble metal thin film is found around wavelengths that are close to the onset of interband transitions and arises from the so-called Fermi smearing process. This process is driven by the rapid heating of electrons upon the absorption of energy from an ultrafast optical pulse. The rise of electronic temperature broadens the electronic distribution around the Fermi energy at the onset of interband transitions, causing a drastic change of the refractive index in the metal. For these reasons, the NLO response of the NLO mirror at visible wavelengths is dominated by the refractive index changes of the Au layer. The contribution of the Ag layer to the overall NLO changes, as described in reference [13], is found to be negligible compared to Au. In addition, various thicknesses of Au films have been studied by transient reflectivity measurements [14] and the results show that the NLO response increases dramatically with decreasing film thickness for thicknesses less than 100 nm.

In the NLO mirror structure, as the linear absorption in the Au thin film is increased, the thermal nonlinearity of this layer is enhanced and consequently the NLO response of the mirror. To illustrate this, we have carried out simulations of the refractive index change on Au using the two-temperature model and a physical model describing the dielectric permittivity as described in detail in reference [11]. In short, the linear absorptance in the Au film is calculated using the transfer-matrix method. The absorbed power is introduced as the source term in the two-temperature model. This model describes the temporal evolution of electron and lattice temperatures as a function of the absorbed power and thermal properties of the electrons and lattice in the metal. The electron temperature derived through this model is used to calculate a temperature-dependent dielectric permittivity function that contains two terms: a first one describing interband transitions using the approximation that electronic transitions occur from a flat d-band to a parabolic conduction band; and a second one describing contributions from intraband transitions by using a Drude function. The refractive index of the metal, before and after optical excitation is taken as the root-square of the calculated dielectric permittivity.

The simulated refractive index changes (ΔN_Au(λ, t_peak) = Δn(λ, t_peak) + iΔk(λ, t_peak)) in the visible spectra are shown in Figs. 2(a) and 2(b) for a 23 nm-thick Au film on a glass substrate (Au Ref) and the same thickness of the Au layer in the NLO mirror structure (as described in Section 2), assuming a pump pulse fluence of 16 J/m² (peak irradiance 13 GW/cm²) at 550 nm. Here, t_peak denotes the delay time of the probe pulse that yields the maximum NLO response in the temporal ranges studied. Note that the peak wavelength of Δn(λ, t_peak) and Δk(λ, t_peak) are always located around the interband transition onset of Au at 520 nm [10]. For the NLO mirror, the peak-to-valley magnitude of Δn and Δk doubles. This is achieved by increasing the linear absorption at 550 nm in the Au thin film from 19% for Au Ref to 53% in the NLO mirror. However, as clearly shown in Figs. 1(c) and (d), an increased linear absorptance also leads to a decreased linear reflectance. Hence, a trade-off exists between the strength of the NLO response of the mirror and its linear reflectance.

 

Fig. 2 Spectral comparison of simulated (a) real and (b) imaginary refractive index changes between the 23 nm-thick Au film inside the NLO mirror (orange lines) and a 23 nm-thick Au film on a glass substrate (Au Ref) (dark yellow symbols). Simulations shown for an incident peak irradiance of 13 GW/cm² at 550 nm. (c) Spectral comparison of simulated $\partial R/\partial n$ and $\partial R/\partial k$ for the same Au containing structures.

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The correspondent reflectance changes as a function of wavelength (λ) and delay time (t) can also be calculated by the following:

Although the reflectance changes ΔR(λ, t) can be calculated exactly and have been used in the optimization process which will be discussed later, developing a simplified analysis is attractive to illustrate the enhancement mechanism of ΔR. For example, the measured ΔR(550 nm, t_peak) increases from −1% for Au Ref to −25% for the NLO mirror both excited by a peak pump irradiance 13 GW/cm² at 550 nm. Hence, the first order approximation to the Taylor expansion of ΔR, Eq. (1), is taken as functions of ΔN_Au and yields the following equation.

In Fig. 2(c), the NLO mirror generally displays higher ∂R/∂n values than the Au Ref in the visible spectral range. For instance, at 550 nm, ∂R/∂n improves from a value of −8 for the Au Ref to a value of −85 for the NLO mirror. Note that the NLO mirror not only doubles the Δn of the Au film due to an increased linear absorptance from 19% for Au Ref to 53% for the NLO mirror, but also introduces a better structural design which improves the sensitivity of R to small changes on the real part of the refractive index of Au. In contrast, the mirror structure reduces the sensitivity of R to changes in the imaginary part of the refractive index of Au; as revealed by the smaller values of ∂R/∂k found for the mirror structure than for Au Ref. As calculated from Eq. (2), ΔR is expected to improve by around 20 times compared to Au Ref. This evaluation was verified by the measured ΔR(550 nm, t_peak), which increases 25 times from Au Ref to the NLO mirror.

It is interesting to note that, spectrally, the maximum magnitude of ∂R/∂n is not at 550 nm, where it reaches a magnitude of −85, but instead at 600 nm, where it reaches a magnitude of −101. This is the case even though the NLO mirror was designed for degenerate pump-probe operation, which means that ΔR(550 nm) was maximized for this geometry, as will be described next. It is to be noted that if the NLO mirror is excited and probed at 600 nm, we would expect a smaller magnitude of ΔR than when excited at 550 nm. This is because the linear absorption at 600 nm is only 31%, much smaller than the 55% obtained at 550 nm. Hence, differences in Δn between excitation at 550 nm and at 600 nm, Δn(550 nm) >> Δn(600 nm), are expected to be more significant than the difference in ∂R/∂n found at these wavelengths.

In addition, note that most ∂R/∂n values in Fig. 2(c) of the NLO mirror are negative with positive Δn values in Fig. 2(b) across the visible spectral range. The total product of ΔR values calculated from Eq. (2) shows that the general characteristic of ΔR is negative. After the NLO mirror is pumped optically, positive Δn values will cause a redistribution of the electric field throughout the structure. These changes in the electric field distribution lead to a larger field within the Au layer, resulting in an increase of absorptance. Since reflectance and absorptance of the NLO mirror are complementary, an increase in absorptance (ΔA) will lead to a decrease in reflectance (ΔR).

In the following section, the optimization process for designing the thickness distribution of the NLO mirror is explained in detail. Although a higher linear absorptance (A) on the NLO mirror leads to stronger NLO changes in the Au layer, the trade-off is that the linear reflectance (R) is also reduced. Arbitrarily, the NLO mirror was set to have a linear absorptance (A) of 55% and a reflectance (R) of 45% at 550 nm. As discussed, the periodicity of R and A on the reflection modifier (j) and cavity (k) thicknesses allows the optimization processes to be conducted only on the region designated (1, 1). Figure 3(a) shows the A(j, k) of the region (1, 1) and a red dashed line indicates all thickness combinations which would fit the design criterion of A(j, k) = 55%. Four different dielectric layer thickness combinations (j, k), a(81, 81), b(116, 98), c(30, 65), and d(156, 94), were picked as examples to illustrate the design process. The units of the thicknesses denoted inside the parenthesis have been dropped for convenience. This process required calculations of ΔR(λ, t_peak) for multiple structures along this line in order to estimate the structure that maximized ΔR(550 nm, t_peak). Figure 3(b) shows the ΔR(λ, t_peak), calculated by Eq. (1) using the values of ΔN_Au(λ, t_peak) shown in Figs. 2(a) and 2(b), at the peak response time, t_peak, for the NLO mirror structures excited at 550 nm. The results show that ΔR(550 nm, t_peak) improves gradually from points d(156, 94) through a(81,81) and starts decreasing from a(81, 81) to c(30, 65). The maximum magnitude of ΔR(550 nm, t_peak) was found to be located at a(81, 81). As expected, the value of ΔR(550 nm, t_peak) was found to be the same in other regions provided that the dielectric thicknesses were increased by half-wave optical thickness of SiO₂ at 550 nm.

 

Fig. 3 (a) Absorptance A(j,k) at 550 nm of the NLO mirror with different thickness combinations of reflection modifier (j) and cavity (k) layers within the region (1,1) defined in Fig. 1(c). The red line represents all thickness combinations leading to A(j,k) = 55%. Points a(81,81), b(116,98), c(30, 65), and d(156,94) represent four different illustrative thickness combinations used for the evaluation of ΔR(λ, t_peak). Numbers inside the parenthesis are thicknesses given in nm. The point a(81,81), highlighted, corresponds to the fabricated NLO mirror. (b) Reflectance changes ΔR of the selected mirror combinations.

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Figure 4(a) shows that angular dependence of ΔR(λ, t_peak) measured in pump-probe experiments conducted on the NLO mirror at a pump irradiance of 15 GW/cm² at 550 nm. Here, t_peak denotes the maximum magnitude of ΔR in the temporal ranges studied. As expected from our simulations, ΔR(λ, t_peak) displays broad spectral and angular bandwidths. For instance, for angles < 20þ it was found that ΔR(λ, t_peak) across the visible spectral range changes by no larger than 7% with respect to data acquired near normal incidence (<5þ).

 

Fig. 4 Reflectance changes (ΔR) of the NLO mirror pumped at 550 nm of (a) spectral spectrum ΔR(λ, t_peak) with respect to different incidence angles of <5þ (purple line), 10þ (orange line), 15þ (pink line) and 20þ (dark blue line); (b) ΔR(λ, t_peak) at the peak response time t_peak, and (c) temporal dependence ΔR(600 nm, t) at probe wavelength 600 nm for different peak pump irradiance 3 (green line), 6 (red line), 9 (blue line), and 15 (dark yellow line) GW/cm²; (c) irradiance dependent reflectance (%) at 550 nm (dark green line and symbol) and 600 nm (dark red line and symbol) by adding linear reflectance R₀(λ) with measured ΔR(λ, t_peak); (d) temporal dependence ΔR(600 nm, t) at probe wavelength 600 nm for different peak pump irradiances

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Figure 4(b) shows the values of ΔR(λ, t_peak) measured for peak pump irradiances of 3, 6, 9, and 15 GW/cm² at 550 nm. For increasing pump irradiance, ΔR(λ, t_peak) spectra consistently displays broad spectral bandwidth characteristics. It was confirmed that the highest irradiance did not damage the sample by acquiring multiple data sets at high and low irradiance levels on the same spot. For potential applications in all-optical devices, it is useful to derive the irradiance evolution of the absolute reflectance calculated by R₀(λ) + ΔR(λ, t_peak), where R₀(λ) is the measured linear reflectance shown in Fig. 1(a). Figure 4(c) shows that the NLO mirror offers a significantly strong reflectance suppression from a reasonably high R₀(λ), such as from 49% to 23% at 550 nm and from 69% to 32% at 600 nm by increasing pump irradiance to 15 GW/cm². Overall, the power dependent reflectance of the NLO mirror can meet multiple engineering requirements in the visible spectral range by having an extremely large magnitude of ΔR, ultrafast response, and fairly broad spectral and angular bandwidths.

Finally, Fig. 4(d) shows the temporal evolution of ΔR(600 nm, t) as a function of the pump irradiances. Here, the peak wavelength has been selected to illustrate the ultrafast temporal evolution of the NLO response of the NLO mirror. For increasing pump irradiances, ΔR(600 nm, t) shows a larger magnitude and a delayed relaxation of the reflectance modulation. A very similar behavior has been reported in single Au films [15, 16], and has been attributed to a change of the electronic specific heat with increased temperature and to a saturation of the electronic occupancy at energies below the interband transition threshold.

4. Conclusion

The linear and nonlinear optical properties of a novel mirror geometry comprised of a 100 nm-thick Ag reflector with a thin 23 nm-thick Au layer sandwiched between two SiO₂ layers were studied. In this structure the linear absorptance, and consequently the NLO response, of the Au thin film can be engineered. Therefore, the nonlinear mirror was designed to maximize reflectance changes by choosing an optimum thickness distribution. The improvement of reflectance changes was observed while comparing the nonlinear mirror with the same thickness Au film on a glass substrate. The significant enhancement was due to a combination of both the increased refractive index change of Au and the increased figure-of-merit derived for these nonlinear mirrors. The reflectance change was increased up to 25 times from a single Au layer to the nonlinear mirror at the wavelength 550 nm. In addition, the reflectance change is ultrafast, spectrally and angularly broad in the visible spectral region. Hence, the nonlinear mirror could be an attractive optical device that meets multiple engineering requirements in the visible spectral range for a variety of all-optical applications.