Voltage-controlled nonlinear optical properties in gold nanofilms via electrothermal effect | Nature Communications

Nature Communications volume 15, Article number: 6372 (2024) Cite this article

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Dynamic control of the optical properties of gold nanostructures is crucial for advancing photonics technologies spanning optical signal processing, on-chip light sources and optical computing. Despite recent advances in tunable plasmons in gold nanostructures, most studies are limited to the linear or static regime, leaving the dynamic manipulation of nonlinear optical properties unexplored. This study demonstrates the voltage-controlled Kerr nonlinear optical response of gold nanofilms via the electrothermal effect. By applying relatively low voltages (~10 V), the nonlinear absorption coefficient and refractive index are reduced by 40.4% and 33.1%, respectively, due to the increased damping coefficient of gold nanofilm. Furthermore, a voltage-controlled all-fiber gold nanofilm saturable absorber is fabricated and used in mode-locked fiber lasers, enabling reversible wavelength-tuning and operation regimes switching (e.g., mode-locking—Q-switched mode-locking). These findings advance the understanding of electrically controlled nonlinear optical responses in gold nanofilms and offer a flexible approach for controlling fiber laser operations.

Gold nanostructures (GNs), such as nanofilms, gratings, nanoparticles, and metamaterials, have been widely exploited in optics because of their unique surface plasmon resonance (SPR) properties. The SPR can strongly enhance linear and nonlinear optical responses around specific wavelengths on demand, leading to the demonstration of unprecedented possibilities for extreme light concentration and manipulation, which makes GNs become excellent platforms for various applications in nonlinear optics1,2,3, quantum optics4,5, nano-optics6 and bio-therapy7,8,9. Recently, various approaches (e.g., electrical, thermal, optical, and mechanical stimulus, etc.) for dynamically controlling the optical properties (linear or nonlinear regime) of gold nanostructures have been developed for advancing photonics technologies10,11,12,13,14,15. Among those approaches, electrical tuning is attractive owing to its easy control, and the corresponding devices can be integrated into optoelectronic devices. Up to now, electrical tuning has been widely investigated for dynamically controlling the optical properties of the gold/dielectric hybrid nanostructures, and has achieved great breakthroughs, such as electrically controlled nonlinear generation of light with plasmonics16,17, resonant plasmonic micro-racetrack modulators with a bandwidth of 176 GHz18. However, the electrical activity of those devices is derived from the dielectric materials rather than the gold itself. It is because the bulk carrier density (nB) is quite large in metals (e.g., gold). To change the surface carrier density (nS) significantly and realize electrical tuning of SPR properties in metals, one needs to achieve very small thickness (t) values (nS = nBt)19,20,21. The difficulty of making continuous metal films with sufficiently small t over a large area prevented the demonstration of electro-optic tunable SPR in metals. Very recently, Maniyara et al. fabricated ultrathin gold films (UTGFs) with a sufficiently low nanometric thickness via a novel deposition technique and further demonstrated the dynamic tuning of optical properties (linear regime) in UTGFs by ion-gel gating. SPR peaks were shifted over hundreds of nanometers and amplitude-modulated by tens of percent through gating using relatively low voltage, which was attributed to the modification of optical damping in UTGFs19.

Despite the electrical gating technique, thermo-optical tuning is another effective and cost-efficient approach for optical modulation. The temperature dependence of gold permittivity has been widely studied22,23,24,25,26. The increase of temperature in GNs results in the change of the temperature-dependent damping constant γ leading to the collateral effect of a change in permittivity Δε, which consequently influences the interaction with light and modifies the optical response of the system27. The thermo-optical dynamics of gold films have undergone detailed study through direct spatiotemporal imaging, which provides valuable insight into the interplay between electrons and phonons in gold24,25. This is important for designing nanoscale thermal management in nano-optoelectronic devices. A large optical modulation of ~30% was demonstrated in 1-nm-thick gold grating by elevating the electron temperature via ultrafast optical pumping22. Although electrical and thermal modulation has shown impressive achievements, the previous studies primarily focused on the modulation of linear optical properties. Whereas, dynamically manipulating Kerr nonlinear optical response of gold nanostructures remains unexplored.

In this paper, we demonstrated the voltage-controlled Kerr nonlinear optical response of gold nanofilms via electrothermal effect. The nonlinear absorption coefficient and the nonlinear refractive index of gold nanofilms were reduced by 40.4% and 33.1%, respectively, through electrical Joule heat with relatively low voltages (~10 V). Furthermore, voltage-controlled all-fiber gold nanofilm saturable absorbers were fabricated and used for constructing a mode-locked fiber laser. By changing the applied voltage, the central wavelength of the mode-locked pulses can be reversibly tuned over ~26 nm. And a reliable switching between continuous-wave mode-locking and Q-switched mode-locking regimes can be achieved by simply changing the applied voltage.

We first illustrate the voltage-controlled linear optical response of the gold nanofilm deposited on quartz. The device was fabricated by the physical vapor deposition method (details in Methods), as shown in Fig. 1a. The physical deposition of a gold film typically follows the Volmer-Weber growth mode due to its weak adhesion with the substrate, resulting in a noncontinuous film with discrete islands and random crevices19,28,29,30,31. The deposition parameters, such as vacuum condition, deposition rate, and substrate temperature, are critical to the surface morphology as well as the optoelectrical properties of the deposited film30,31,32. Moreover, introducing a seed layer (e.g. Cu) is critical for modifying the wetting behaviors of the gold on the substrate and reducing the surface roughness19. We fabricated various thicknesses of gold nanofilms, both unseeded (without Cu seed) and seeded with a Cu seed layer (see Supplementary Fig. 1), the seeded gold nanofilms show smoother surfaces and more homogeneous morphologies. Therefore, to improve the quality of gold nanofilm, a Cu seed layer was introduced in our experiment. In particular, a 1 nm copper seed layer followed by a 15 nm gold layer was deposited on the quartz to form a bilayer nanofilm (hereafter termed as gold nanofilm), with an area of 17 mm × 3.5 mm. The 1 nm copper seed layer forms energetically favorable nucleation sites for the incoming gold atoms, thus facilitating a lower sheet resistance and optical loss of the device19,33,34. Scanning electron microscopy (SEM) image of the gold nanofilm in Fig. 1b shows accretion islands connected to form a semicontinuous network. The root mean square (RMS) roughness (Rq) of the nanofilm was measured to be ~1.08 nm via an atomic force microscope (AFM).

a Schematic of voltage-controlled gold nanofilm deposited on the quartz. b SEM image and c AFM pattern of the gold nanofilm. d Film temperature (Ttemp) as a function of applied voltages (U), inset: heat maps of the nanofilm at 1, 6, and 10 V. e Experimental absorption spectra of the gold nanofilm at different applied voltages. f Relative absorbance change (at 2 μm) as a function of applied voltages. Black dots: experimental data, black circles: FDTD simulation. g FDTD simulated absorption spectra of the gold nanofilm at different applied voltages. Inset: geometrical structure of the gold nanofilm derived from SEM image.

Surface roughness plays a major role in determining the resistivity in ultrathin metal films33. We connected electrodes to the film boundary with silver paste. When a direct current (DC) voltage of 10 V was applied, the seeded gold nanofilm exhibited a higher temperature due to its lower resistivity compared to the unseeded one at equivalent thicknesses (see Supplementary Fig. 2). Besides, the seeded gold nanofilm shows a homogeneous heat distribution, while the unseeded film exhibits local heating near the electrode. This further confirms the critical role of the Cu seed layer in realizing high-quality gold nanofilms. Particularly, the total resistance between two electrodes of the 15 nm seeded gold nanofilm is ~21 Ω. Figure 1d shows the film temperature as a function of the applied voltages. As the applied voltage was increased from 0 to 10 V, the temperature of the nanofilm rose from ~299 to 353 K due to the occurrence of the electrothermal effect induced by electrical Joule heat.

The electrothermal-dependent optical absorption spectra of the 15 nm seeded gold nanofilm (hereafter the gold nanofilm all refers to the 15 nm gold nanofilm seeded with a 1 nm Cu seed layer, unless otherwise specified) were characterized via a UV-vis-NIR spectrophotometer (300 − 2500 nm). As shown in Fig. 1e, the absorption peak of nanofilm was located at ~992 nm, which is attributed to the localized SPR as a signature of the presence of isolated metallic islands35,36,37. The broad plasmon band extends into the infrared region with frequency-independent absorption from ~1700 to 2500 nm38,39, ensuring enhanced light-matter interaction. We note that the intensity and frequency of the absorption peak depend on the size, shape, and density of the islands forming the film40,41,42, which can be easily tuned by adjusting the film thickness (see Supplementary Fig. 6). A thinker film contributes to an increase in grain size and density, consequently leading to a red-shift of the absorption peak. By applying electrical voltage along the nanofilm, a monotonic decrease in absorbance was observed. The relative absorbance change is defined as |Δα | /α0 = | αU − α0 | /α0, where αU and α0 represent the absorbance of the sample with and without applying voltages, respectively, and U represents the applied voltages. It was found that the |Δα | /α0 can be reduced by 5.9% (at 2 μm) as the applied voltage was up to 10 V, as shown in Fig. 1f. To understand the tunable nature of the plasmons, the gold dielectric function was modeled by the temperature-dependent Drude model. As the film temperature increases with applied voltages, the associated increased electron-phonon scattering rate leads to an increase in the Drude damping constant. This results in a significant increase of the imaginary part of gold permittivity, which in turn suppresses the plasmonic resonance23,43,44,45,46. Despite the amplitude modulation in SPR, the resonance peak also blue-shifts to ~968 nm, which is related to the thermal-dependent electron density and effective electron mass (see Supplementary Section IV)23,46. The dependence of the imaginary part of the gold permittivity on temperature is governed by two competing mechanisms23: electron-phonon scattering and changes in the morphology of the gold grains induced by grain boundary movements. As the temperature is elevated from room temperature to 200 °C (473 K), the increasing electron-phonon scattering predominantly influences the gold permittivity and consequently, the optical properties. Above the threshold temperature of 200 °C, the gold grains start to move and merge together, leading to the size and shape change of the gold grains23. However, the highest temperature induced by Joule heating in our experiment (353 K) remains significantly below the threshold temperature for grain boundary movement (473 K)23. As a result, no obvious morphology changes were observed even after applying a voltage up to 10 V (see Supplementary Fig. 9). Therefore, the thermal-induced increase in electron-phonon scattering, and consequently the damping constant, is the dominant factor contributing to the observed effect. To further confirm the temperature-dependent SPR modulation in our case, we simulated the absorption spectra of the gold nanofilm by the 3D FDTD method (Lumerical FDTD Solutions). The morphology of the gold nanofilm was derived from the SEM image, and the results in Fig. 1g show a noticeable resonant mode at the wavelength of ~1060 nm. By adopting the voltage-dependent Drude damping constant in the simulation, we were able to reproduce the tunable SPR intensity of the gold nanofilm. The simulated results were found to agree well with the experimental data, verifying that the SPR absorption of the gold nanofilm could be modified via electrical-induced Joule heating. In previous studies19,22, significant optical modulation was achieved in the ultrathin gold films (thickness of several nm), whereas limited modulation was observed in thicker films (typically ≥ 10 nm). Our system emphasizes the critical role of Joule heating-induced temperature elevation in optical modulation, which mainly depends on the resistance of the film (see Supplementary Fig. 2). In this regard, further improvement of the fabrication method is expected to diminish the resistance of ultrathin gold nanofilms, which may improve the optical modulation capabilities.

Furthermore, the voltage-controlled nonlinear optical response of the gold nanofilm was investigated by the Z-scan measurement, which allows direct characterization of the nonlinear absorption coefficient (β) and nonlinear refractive index (n2)47,48. Both open- and closed-aperture measurements of the gold nanofilm with applying voltages were performed with a 1990 nm femtosecond fiber laser (see Supplementary Section V). Figure 2a shows the normalized open-aperture Z-scan transmission (T) curves of the gold nanofilm under different voltages. Obviously, the transmission increases as the film approaches the focus (z = 0, corresponding to maximum laser intensity), indicating the observation of saturable absorption. This can be attributed to the ground state bleaching of the plasmon, which occurs due to intraband electron excitation49,50. The values of nonlinear absorption coefficients were deduced from the curves by data fitting (Eq. 3, in Methods) and were plotted versus voltages in Fig. 2b (black squares, left axis). A monotonic decrease of the nonlinear absorption coefficient can be observed as the applied voltage increases, which gives a 40.4% reduction of β as the voltage is up to 10 V. The normalized transmittance obtained from the closed-aperture Z-scan measurement is shown in Fig. 2c, which has been divided by the corresponding open-aperture Z-scan transmittance. The peak-valley configuration indicates that the nonlinear refractive index is negative, which results in self-defocusing at high input intensities. The negative n2 reveals that the main contribution is due to the free electrons in sp band51,52. From Fig. 2b (red squares, right axis), we found that the nonlinear refractive index reduces by 33.1% as the applied voltage increases to 10 V. Upon the increase in the applied voltages, the decreased linear absorption of the gold nanofilm leads to a reduction of the local fluctuation of electron density, thus resulting in a decrease in the nonlinear absorption coefficient and the nonlinear refractive index.

a Open-aperture Z-scan data of the gold nanofilm on quartz measured for different applied voltages. Solid lines are theoretical fittings. b Experimental nonlinear absorption coefficients (β, in black, left axis) and nonlinear refractive indexes (n2, in red, right axis) as a function of applied voltage, which are calculated from Z-scan data. c Closed-aperture Z-scan data. d Theoretical calculation of voltage-dependent β (in black, left axis) and n2 (in red, right axis) based on the anharmonic oscillator model. e Nonlinear transmittance (T) at different voltages derived from P-scan measurement. f Modulation depth (ΔT, in black, left axis) and saturation intensity (Isat, in red, right axis) as a function of applied voltage derived from P-scan data. Error bars represent standard deviation.

To quantitatively explain the voltage-dependent nonlinear optical properties of the gold nanofilm, we treat the plasmon in the gold nanofilm as a classical anharmonic oscillator53,54. The third-order Kerr-type nonlinear susceptibility χ(3) of gold can be expressed as54,55

where e is the electron charge, ωp is the plasmon frequency, me is the effective electron mass, \(b={\omega }_{0}^{2}/{d}^{2}\) characterizes the strength of nonlinearity, and d stands for the atomic dimension of gold. The factor \(D(\omega )={\omega }_{0}^{2}-{\omega }^{2}-2i\gamma \omega\) contains the resonance frequency ω0 and the damping constant γ. Evidently, the damping constant γ plays a critical role in determining the behavior of χ(3)3,56. Figure 2d shows the calculated voltage dependence of the nonlinear absorption coefficient and the nonlinear refractive index of the gold nanofilm (for details, see Methods). It can be seen that both β and n2 decrease with the increasing of applied voltages, which agrees well with the experimental results.

The voltage-dependent saturable absorption property of the gold nanofilm was then investigated via the P-scan measurement48,57 (see Supplementary Section V). The measured transmittance as a function of the incident power is shown in Fig. 2e, which was fitted with a two-energy-level model (see Supplementary Section VII). The fitted modulation depth and saturation intensity as functions of the applied voltage are shown in Fig. 2f. As the applied voltage was increased from 0 V to 10 V, the modulation depth ΔT reduced from 4.53% to 3.08%, and the saturation intensity Isat increased from 8 to 9.66 MW/cm2. This is because the increased Joule heating leads to a decrease in linear absorption coefficient (α0) and a stronger electron-phonon scattering. As a result, the modulation depth which is proportional to the linear absorption coefficient (ΔT ∝ α0, see Supplementary Section VII), decreases, while the saturation intensity which is inversely proportional to linear absorption cross-section and relaxation time (Isat = ħω/2σ0τr, where σ0 is linear absorption cross-section and τr is relaxation time), increases. To the best of our knowledge, this is the first demonstration of voltage-controlled nonlinear optical properties in gold nanofilms via electrothermal effect.

Note that the Cu seed layer itself exhibits negligible linear and nonlinear optical responses (see Supplementary Section X), while the observed notable electrothermal optical modulation primarily originates from the gold nanofilm. However, the employing of a (1 − 2 nm) Cu seed layer remains critical for achieving efficient electrothermal modulation, which contributes to a smoother surface, lower resistance, and stronger SPR absorption of the fabricated gold nanofilm.

As has been shown that the voltage-controlled gold nanofilm deposited on quartz manifests significant electrothermal modulation in both linear and nonlinear responses. Utilizing these electrically tunable features, the voltage-controlled all-fiber gold nanofilm saturable absorber (SA) was fabricated and the schematic of the device is shown in Fig. 3a. The 15 nm seeded gold nanofilm was evaporated on the flat surface of the side-polished fiber (SPF) with the same procedure as that for the quartz. Two electrodes were electrically attached at each side of the polished boundary by silver paste.

a All-fiber gold nanofilm SPF SA, total film thickness: ~16 nm (1 nm Cu/15 nm Au), the distance between fiber core boundary and polishing surface: ~2 μm. V+: positive voltage, GND: power ground. b Thulium-doped fiber laser cavity. WDM wavelength-division multiplexing, TDF thulium-doped fiber, ISO isolator, PC polarization controller, OC optical coupler, and DC source direct current source.

The voltage-controlled linear absorption spectra of the gold nanofilm-SPF device were measured by using a super-continuum light source. As illustrated in Fig. 4a, the device shows broadband absorption from 600 nm to 2000 nm owing to the SPR absorption of the gold nanofilm. It is interesting to compare the absorption spectra of the fiber device (Fig. 4a) with that of the normal-incidence case (Fig. 1e). It can be seen that for the fiber device, the interaction below 1750 nm seems to be significantly reduced. This can be understood by considering the wavelength dependence of the mode-field distribution for the fiber device. Specifically, the light interacts with the gold nanofilm via the evanescent field of the guided mode, and the intensity of the electric field at the gold nanofilm is strongly wavelength-dependent, which decreases rapidly with decreasing wavelength. Since the linear absorption (interaction) in evanescent mode is proportional to the integral of the electric field intensity at the film over the film width58, the interaction was significantly reduced for wavelengths below 1750 nm as shown in Fig. 4a. As a DC voltage was applied to the device (in the same direction as the propagating light), the absorbance at longer wavelengths dramatically decreased, which was attributed to the reduction of the SPR absorption of the gold nanofilm with the increase of the applied voltage (shown in Fig. 1e). Moreover, the multiple reflections of light propagation along the polished fiber axis lead to a significant enlargement of the effective interaction area and length59. This results in a remarkable reduction of optical absorption at 2 μm, as depicted in Fig. 4b (black squares), with a decrease of ~36.2% at 10 V. It is worth mentioning that the increase of the overall transmission through the fiber device also contributes to a reduction of the insertion loss of the all-fiber device. Specifically, at 2 μm, the insertion loss was decreased by ~3 dB as the voltage increased to 10 V.

a Linear absorption (α) spectra of the gold nanofilm-SPF device at different applied voltages. b Relative absorbance change (Δα/α0, in black) and insertion loss (in red) as a function of applied voltage. c Nonlinear transmittance (T) of the all-fiber device at different applied voltages. d Modulation depth (ΔT, in black) and saturation intensity (Isat, in red) as a function of applied voltage. Error bars represent standard deviation.

The voltage-controllable saturable absorption of the gold nanofilm-SPF device was characterized by the balanced twin-detector method. As shown in Fig. 4c, d, as the electrical voltage applied to the all-fiber device increases from 0 V to 10 V, the modulation depth gradually decreases from 17.6% to 13.3%, while the saturation intensity increases from 0.29 to 0.5 MW/cm2. This is in accordance with the results obtained from the gold-quartz device. However, more significant modulations were achieved from the all-fiber device owing to the enhanced light-matter interaction.

It is known that the modulation depth and saturation intensity of an SA are critical to pulse shaping dynamics in mode-locking fiber laser systems60,61,62,63,64. To demonstrate the powerful modulation function of the voltage-controlled device, we constructed a thulium-doped mode-locked fiber laser (TDFL), which utilized the gold nanofilm-SPF as an SA (GFSA), as illustrated in Fig. 3b. The mode-locked operation without applied voltages was centered at 1964.9 nm, with a pulse duration of ~482 fs and a signal-to-noise ratio (SNR) of ~64 dB (see Supplementary Fig. 13). The insertion loss of the SA device is ~7.35 dB at 0 V, which includes the saturable (linear) absorption loss α0 and the non-saturable loss αns (see Supplementary Eq. 4). When used in a mode-locked fiber laser, a low non-saturable loss αns and a high saturable absorption loss (or modulation depth) α0 are usually favored65,66. Specifically, a low non-saturable loss can increase the laser slope efficiency65, while a high saturable absorption loss facilitates reliable self-starting of mode-locking and leads to short pulse duration65.

With the other cavity parameters (e.g. pump power and PC state) fixed, we applied voltages to the GFSA device along the fiber axis. Interestingly, an increase in the voltage resulted in a gradual red-shift of the mode-locking wavelength, as shown in Fig. 5a. It is observed that the central wavelength of the mode-locked laser shifted from 1964.9 to 1991.5 nm as the applied voltage increased from 0 to 7 V, which was mainly ascribed to the reduced linear loss of the GFSA at higher voltages. To explain the wavelength-tuning mechanism of the mode-locked fiber laser, we carried out numerical simulations based on a lumped scalar model (for details, see Methods). In the simulation, the linear losses and saturable absorption parameters of the SA at each applied voltage were derived from experimental data (Fig. 4a, d). Figure 5b shows the tunable mode-locked spectra obtained from numerical simulations. The simulated mode-locked wavelength shifts from 1965.76 to 1988.64 nm when the voltage was increased from 0 V to 7 V, which agrees well with the experimental results. Further controlled simulations were conducted which fixed either linear loss or nonlinear saturable absorption. These simulation results reveal that the wavelength tunability results from both the change in linear loss and nonlinear saturable parameters of the GFSA, with the linear loss change emerging as the dominant effect.

a Experimental optical spectra, b numerically simulated optical spectra, and c experimental autocorrelation trace of the mode-locking operation at different applied voltages. Experimentally measured d central wavelength (λcenter), e spectral 3-dB bandwidth (Δλ3-dB), and f pulse duration (Twidth) of the mode-locking pulses as a function of applied voltage.

The mode-locked wavelength can be tuned reversibly, as shown in Fig. 5d (and Supplementary Fig. 14). The stronger intracavity nonlinearity as the voltage increased, contributes to the broadening of the spectral 3-dB bandwidth, as shown in Fig. 5e. Moreover, the pulse width decreased from 482 to 375 fs as the voltage increased from 0 V to 7 V (Fig. 5c, f), which is in accordance with the broadening of the spectral bandwidth. Notably, the mode-locking repetition rate was reduced by ~3 kHz as the voltage was increased to 7 V (see Supplementary Fig. 15). The reduction in repetition rate can be attributed to the red-shift of the mode-locked wavelength, which in turn causes a decrease in the group velocity of the pulse.

A reversible switching between two operation regimes was observed as the voltage was further increased to 8 V. We note that the laser kept operating at the continuous wave mode-locking (CWML) regime when the voltage was below 7 V. However, as the voltage was increased to 8 V, the laser switched to the Q-switched mode-locking (QSML) regime as shown in Fig. 6. The transition can be clearly seen from the measured spectrum shown in Fig. 6a. It was a typical mode-locked soliton spectrum with Kelly sidebands on both sides when the applied voltage was 7 V, and as the voltage was set to 8 V, the measured average spectrum evolved into a bell-shaped profile with a central wavelength of 1965.3 nm. Intriguingly, by switching the applied voltage between 7 V and 8 V, the operation regimes can be switched between CWML and QSML. The operation regime of a mode-locked laser critically depends on the interplay between the gain saturation and the saturable absorption. It has been demonstrated both theoretically60 and experimentally63,64 that by adjusting saturable absorption parameters, it is possible to switch between different pulse operation regimes, such as CWML, Q-switching (QS), and QSML in fiber lasers. The stability criterion for CWML against QSML is given as60,67

where Ep is the intracavity energy, Esat,L is the saturation energy of the gain medium, Esat,A is the saturation energy of the SA, and ΔT is the modulation depth of the SA. Equation 2 indicates that Q-switched instability occurs when the intracavity pulse energy is below the critical value Ep,c = (Esat,LEsat,AΔT)1/2. When the voltage was increased from 7 V to 8 V, both the measured modulation depth and the non-saturable loss decreased, while the saturation energy increased. The operation-regime switching may be attributed to the increasing saturation energy of the saturable absorber, which decreased Ep below the critical value Ep,c.

a Optical spectra of CWML and QSML by driving 7 V/8 V on/off voltage. QSML regime characteristics: b pulse train oscillogram and c radio frequency spectrum at 8 V. d Pulse width (in black, left axis) and repetition rate (in red, right axis) of the Q-switched envelope, and e output power (in red, right axis) and pulse energy (in black, left axis) of the QSML laser as a function of applied voltage.

In the QSML regime, the Q-switched envelope exhibits a 2.56 μs temporal width, which contains a number of ultrashort mode-locked pulses as shown in Fig. 6b. The measured radio frequency (RF) spectrum of the QSML pulses is shown in Fig. 6c. The fundamental frequency peak of the mode-locked pulses was at 24.8 MHz. Multiple sideband frequency components with a frequency interval of 111 kHz can also be observed, which corresponds to the repetition rate of the Q-switched envelope. The QSML sustained as the driving voltage was increased up to 10 V. By changing the voltage from 8 to 10 V, the repetition rate of the Q-switched envelope could be tuned from 111 to 118.5 kHz, and the envelope temporal width reduced from 2.56 to 2.48 μs, as plotted in Fig. 6d, which is typical for the Q-switched behavior. The average output power of the laser also increased by increasing the driving voltage. It can be expected that this flexible voltage-controlled switching is very attractive in nonlinear frequency conversion, precise fabrication, and supercontinuum generation60,68.

In comparison, we also fabricated a voltage-controlled all-fiber 15 nm-thick gold nanofilm SA without a Cu seed layer, which was subsequently inserted into the TDFL as a replacement of the original GFSA. Despite enabling mode-locking and demonstrating wavelength-tunability, this laser with unseeded SA exhibited a narrower tuning range (see Supplementary Fig. 21) compared to the original one implemented with a seeded SA. The limited tuning range can be attributed to the high surface roughness and large resistance of the unseeded gold film. Moreover, a laser with such an unseeded SA tended to undergo unstable operation and it also exhibited no operation-regime switching. Therefore, a gold film at an appropriate thickness (15 nm here) grown with a copper seed layer will be favored to exhibit useful optical modulation. Such films exhibit reduced roughness and resistance, narrow grain-size distribution, and homogeneous morphology30,32, ensuring high Joule heat generation, stable working temperature, and uniform temperature distribution.

Although gold has been demonstrated ultrafast nonlinear optical response24,69,70,71, the response time of the voltage-controlled GFSA was measured to be ~10 s (see Supplementary Fig. 24) due to the slow thermal equilibrium of the electrothermal device72,73. It is useful to compare the performance of several related optical modulators, which utilized acousto-optic (AO), electro-optic (EO), thermo-optic (TO), photothermo-optic (PTO), or electrothermo-optic (ETO) effect (see Supplementary Table 1). The commercial ones, including acousto-optical modulator (AOM) and electro-optical modulator (EOM), exhibit ultrafast response time and high extinction ratios. Although the fiber-coupled AOM and EOM can be easily integrated into fiber optical systems, these devices often require external RF drivers which increases system complexity and cost. Thermo-optical (TO, PTO, ETO) modulators, primarily graphene-based, exhibit strong temperature dependence of optical conductivity and notable thermal effects due to the exceptionally small electronic heat capacity22. This often leads to impressive modulation efficiency (see Supplementary Table 1). However, most of those thermo-optical modulators focused on manipulating the linear optical response, there has been limited exploration into actively controlling nonlinear optical properties, especially for operating at the mid-infrared range (2 μm). In comparison, our voltage-controlled GFSA device offers facile modulation of both linear and nonlinear optical properties, and has the advantage of cost-efficiency, easy fabrication and operation, which allows for easy switching of operation-regime in mode-locked fiber lasers. Moreover, by depositing a gold film onto a microfiber, the response time may be reduced to milliseconds or even tens of microseconds due to the decreased device size and the reduced thermal equilibrium time74,75,76.

We have developed a gold nanofilm device that can actively control its optical response by modifying the damping factor through electrothermal engineering. However, despite the electrothermal effect, other factors such as carrier doping or morphology evolution may also be responsible for such an optical modulation in the gold nanofilm. To confirm that the electrothermal effect is the dominant effect in the optical modification, we applied backward voltages to the nanofilm fiber device. A red-shift of mode-locking wavelength from 1965.4 to 1991.2 nm was also obtained (see Supplementary Section IX), which is quite similar to the forward voltage experiment. It means that the direction of applied voltage has no influence on the mode-locking evolution. To further confirm that the electrothermal effect is the dominant factor for the optical modulation, we performed experiments by directly controlling the temperature of the film without applying any voltages (see Supplementary Section IX). Similar mode-locking evolutions can still be obtained. The reversible manner of mode-locked dynamics can exclude the impact of electrothermal-induced morphology evolution of gold. These results suggest that dissipative heating is the dominant effect, which modifies the linear optical response and saturable absorption properties of the gold nanofilm. Note that the Joule heating would also elevate the temperature of the SPF underneath the gold nanofilm, which would induce the change of optical properties of the optical fiber itself and therefore may contribute to the observed effect. To clarify this point, we inserted an additional bare SPF into the mode-locked fiber laser cavity and changed the temperature of the bare SPF by heating while keeping the temperature (voltage) of the GFSA fixed (see Supplementary Section IX). A negligible mode-locking wavelength shift was observed, which indicates that the temperature-induced optical properties variation of the SPF itself has a negligible impact on the observed electrothermal optical modulation.

Though Maniyara et al. have shown relatively large wavelength tuning (∆λ/λ = 13.6%) and linear transmission modulation (14.4%) in ultrathin gold ribbons by ion-gel gating19, such operations require complicated fabrication techniques which may be particularly challenging to realize in all-fiber systems. Compared with the electrical gating based lithography of ultrathin gold ribbons19 or single-layer nanostructures20, our method is certainly facile and user-friendly in device fabrication and operation. Additionally, by using other metal nanofilms (such as silver and copper) with remarkable SPR properties, good electrically and thermally conductive, comparable or more excellent electrothermal-induced optical modulation may be obtained.

To summarize, we have demonstrated the electrothermal-induced and voltage-controllable Kerr nonlinear optical response of the gold nanofilm device, and show its application in manipulating mode-locking operations. The electrothermal-induced effective modification of the damping factor contributes to dynamically tunable optical nonlinearity in the gold nanofilm, which enables a wide range modulation in the nonlinear absorption coefficient and nonlinear refractive index. We also realized an all-fiber SA device by depositing the gold film on a side-polished fiber, which shows controllable large optical absorption variation (36.2%) and nonlinear modulation depth alteration (4.3%) at a low operation voltage of 10 V. Furthermore, by incorporating this electrically controllable all-fiber SA in a fiber laser cavity, flexible manipulation of the operation states of the mode-locked laser were realized by simply adjusting the applied voltages. This allowed for reversible wavelength-tuning and even switching among operation regimes (e.g., mode-locking—Q-switched mode-locking). This work substantially broadens the research scope of optical nonlinearity in GNs and represents a key technique for electrothermal tunable optical nonlinear processes, which will immediately find enormous applications, particularly in electrically controlled nonlinear optics and optoelectronic information processing in modern photonic waveguide systems.

Voltage-controlled gold nanofilm was fabricated by depositing gold on quartz via the physical vapor deposition (PVD) method. The device actually consists of metallic gold/copper bilayer film. A 1 nm thick copper layer (17 mm × 3.5 mm) was first deposited on the quartz with a deposition rate of 0.6 Å/s as the seed layer. Then, a 15 nm thick gold film was grown on the copper layer with a deposition rate of 0.3 Å/s at a pressure of 1.4 × 10−5 mbar. Two metal wires were bonded to the film boundaries by silver paste to construct an integrated circuit, as shown in Fig. 1a.

Voltage-controllable all-fiber gold nanofilm device was fabricated with a similar process, while the gold was deposited on the flat surface of side polished fiber (SPF). The SPF (purchased from Phoenix Photonics LTD) has a polished length of 17 mm and the distance from the polished surface to the fiber core boundary is about 2 μm. A 1 nm thick copper layer was first deposited on the flat polishing surface of the SPF with a deposition rate of 0.6 Å/s as the seed layer. Then, a 15 nm thick gold film was deposited on the copper layer with a deposition rate of 0.3 Å/s at a pressure of 1.4 × 10−5 mbar. Two metal electrodes were electrically attached at both sides of the polished boundary by silver paste.

We utilized commercially available FDTD Solutions (Lumerical Inc.) to simulate the absorption spectra of the gold nanofilm deposited on the quartz substrate. The geometrical structure of the gold nanofilm was derived from the SEM image, as shown in the inset of Fig. 1g. The optical parameters of the gold nanofilm were determined based on the calculated voltage (temperature)-dependent gold permittivity and the substrate parameters were obtained from the SiO2 of the software. The gold nanofilm was illuminated from the top by the normally incident (backward along the z-axis) plane wave, which is linearly polarized in the x-y plane. The transmitted optical field was recorded by a frequency domain power planar monitor, placed inside the quartz. To reduce the simulation time, periodical boundary conditions were used in the x-y plane simulation area. Perfect matching layers were applied at the top and bottom boundaries of the simulation area to prevent any reflections. The transmittance spectra of the nanofilm were achieved from the transmitted optical field monitor. The absorption spectrum of the film was then calculated as –ln(T)56, where T is the optical transmission through the nanostructure.

The voltage-controlled third-order nonlinear coefficients (β and n2) of gold nanofilm on quartz were characterized using the well-developed Z-scan technique at different applied voltages (see Supplementary Section V). A pulsed fiber laser centered at 1990 nm, with a pulse duration of 150 fs and a repetition rate of 48 MHz was used as the incident laser source. For open-aperture Z-scan experiments, the normalized transmittance T(z) can be theoretically written as47:

where q0 = βI0Leff, Leff = [1–exp(–αL)]/α represents the effective thickness of the sample and α is the linear absorption coefficient, I0 is the peak irradiance at the beam waist, x = z/z0 and z0 = πw02/λ is the Rayleigh range of the Gaussian beam, where w0 denotes the beam waist at the focus and λ is the operating wavelength. The nonlinear coefficients β from 0 to 10 V were fitted to be −10 × 10−5, −9.97 × 10−5, −9.69 × 10−5, −9.3 × 10−5, −8.23 × 10−5, and −5.98 × 10−5 mW−1, respectively.

In the closed-aperture measurements, the variations in the transmission correspond to both nonlinear absorption and nonlinear refraction. Thus, the closed-aperture data must be divided by the open-aperture data to obtain the pure nonlinear refractive index47. Then the theoretical expression of the divided Z-scan data can be fitted with the formula47:

By fitting with the experimental data, the nonlinear refractive indexes from 0 to 10 V were calculated to be −10 × 10−12, −9.88 × 10−12, −9.49 × 10−12, −8.79 × 10−12, −8.07 × 10−12, and −6.73 × 10−12 m2W−1, respectively.

The third-order nonlinear susceptibility of gold was modeled by a classical anharmonic oscillator, where we assumed a centrosymmetric structure of gold and ignored the second-order nonlinearity. The third-order Kerr-type susceptibility of gold can be expressed as Eq. 1. The Z-scan experimental results of the nonlinear refractive index (n2) and nonlinear absorption coefficient (β) were related to the real and imaginary part of χ(3)71,77. By considering the electrothermal-induced damping constant, the analytical solution of voltage-dependent n2 and β can be expressed as:

where ε0 is the permittivity of free space, c is the speed of light, N is the electron density and n0 is the linear refractive index. γ(U) is the voltage-dependent damping constant, where γ0 is a constant for gold.

The fiber laser cavity was constructed using a commercial 1570 nm erbium-doped fiber laser as the pump source, which was launched into the cavity through a 1570/1980 nm wavelength-division multiplexing (WDM). A 0.4 m long thulium-doped fiber (TDF, Nufern, SM-TSF-5/125) served as the gain medium, with group velocity dispersion (GVD) of −20 ps2/km at 1980 nm. To ensure unidirectional light propagation, a polarization-independent isolator (PI-ISO) was added to the cavity. A polarization controller (PC) was used to adjust the polarization state. A 10 dB optical coupler (OC) was adopted to extract 10% of the laser and the rest continued propagating in the cavity. The fiber tails of all components were standard single-mode fiber (SMF 28e) with GVD of −67 ps2/km at 1980 nm. The total length of the ring cavity was ~8.4 m and the net dispersion was calculated to be −0.57 ps2. Finally, our voltage-controlled GFSA was inserted into the cavity where the laser output properties such as optical spectrum, pulse duration and repetition rate were monitored at different applied voltages.

Numerical simulations are based on a lumped scalar model. The pulse propagation in different fiber segments in the cavity is modeled by the nonlinear Schrödinger equation (NLSE)78,79:

where A = A(z, t) is the pulse envelope, z is the propagation coordinate, t is the co-moving time, g is the fiber gain, β2 is the GVD parameter, and γNL is the nonlinear parameter. At 2 μm, β2(SMF) = − 67 ps2/km and γNL(SMF) = 1.1 × 10−3 W−1m−1, and β2(TDF) = − 20 ps2/km and γNL(TDF) = 2.6 × 10−3 W−1m−1. The gain term g is non-zero only in the TDF segment and is modeled as79,80:

where g0 = 14.4 m−1 is the small-signal gain. E = ∫ | A|2dt is the intracavity pulse energy, Esat is the saturation energy of the gain fiber, Ω is the detuned angular frequency, and Ωg corresponds to a 113.89 THz gain bandwidth. The saturable absorption is modeled by a transmittance function which is given as78,79:

where ΔT(U) is the modulation depth of the SA at a certain voltage U, P(t) = |A(z,t)|2 is instantaneous power, and Psat(U) is the saturation power of the SA. Experimentally measured saturable absorption parameters at voltages of 0, 2, 4, and 6 V (Fig. 4d) were used in the numerical simulations, and the corresponding saturable absorption parameters at 1, 3, 5, and 7 V were interpolated. Then the wavelength-dependent linear transmittance of the GFSA (Fig. 4a) at each voltage was implemented in the frequency domain. The simulation used 213 data points, a 200 ps time window, and adaptive spatial steps. The initial field was seeded at the input to the TDF through a (random phase) one photon per mode81.

All data generated in this study are available within the manuscript and the Supplementary Information. Source data are provided with this paper.

The simulation code used in this manuscript is available from the corresponding author upon request.

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This research was supported by the National key research and development program of China (2020YFB1805800 (G.Q. and Z.J.)), National Natural Science Foundation of China (NSFC) (Grant Nos.62090063 (G.Q.), 62075082 (Z.J.), U20A20210 (Z.J.), 61827821 (Z.J.), U22A2085 (G.Q.), 62235014 (F.M.), 62205121 (F.M.)), and the Opened Fund of the State Key Laboratory of Integrated Optoelectronics (G.Q., Z.J. and F.M.).

State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun, 130012, China

Changjian Lv, Fanchao Meng, Linghao Cui, Yadong Jiao, Zhixu Jia, Weiping Qin & Guanshi Qin

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G.Q., F.M., and C.L. conceived the idea and designed the experiments. C.L. built the systems and performed the experiments. F.M. and C.L. developed and performed the numerical simulations. G.Q., F.M., and C.L. performed data analysis, interpretation of the results, and preparation of the manuscript. L.C. and Y.J. assisted in building the systems. Z.J. and W.Q. contributed to data analysis, reviewing, and editing. All authors contributed to data analysis and the preparation of the manuscript.

Correspondence to Fanchao Meng, Zhixu Jia or Guanshi Qin.

The authors declare no competing interests.

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Lv, C., Meng, F., Cui, L. et al. Voltage-controlled nonlinear optical properties in gold nanofilms via electrothermal effect. Nat Commun 15, 6372 (2024). https://doi.org/10.1038/s41467-024-50665-7

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Received: 08 September 2023

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DOI: https://doi.org/10.1038/s41467-024-50665-7

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