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Abstract
Electric-field-induced second harmonic generation (EFISH) as a third order nonlinear process is of high practical interest for the realization of functional nonlinear structures. EFISH in materials with vanishing χ(2) and non-zero χ(3) offers huge potential, e.g., for background-free nonlinear electro-optical sampling. In this work, we have investigated $\textrm{SiO}_{2}$ as a potential EFISH material for such applications using DC-electric fields. We were able to observe significant second harmonic generation (SHG) in comparison to the background SHG signal. The fundamental excitation at 800 nm results in a SHG signal at 400 nm for high applied DC electric fields, which is a clear indication for EFISH. Additionally, we were are able to precisely model the EFISH signal using time-domain simulations. This numerical approach will be of great importance for efficiency enhancement and prove as a valuable tool for future device design.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The EFISH process in materials with zero or negligibly small $\chi ^{(2)}$ due to inversion symmetry [1] offers promising innovative applications in materials that are widely used today, such as $\textrm{Si}$, $\textrm{SiO}_{2}$ or $\textrm{Si}_{3}\textrm{N}_{4}$. EFISH was successfully demonstrated in the GaAs-system for quantum wells as well as surfaces and interfaces [2,3]. EFISH at interfaces was also studied in the silicon material system, in particular at the Si-$\textrm{SiO}_{2}$ interface [4–6] and metal-oxide-silicon structures [7]. Above that, very promising results of photoinduced SHG and all-optical phasematching were demonstrated recently in $\textrm{Si}_{3}\textrm{N}_{4}$ [8,9]. The application of the EFISH process has successfully been demonstrated in silicon device structures like $p-i-n$ junctions [10]. However, the small band gap of silicon ($E_{\textrm{g},\textrm{Si}}= {1.1}\,\textrm{eV}$) limits the usable wavelength range to $\ge {1150}\,\textrm{nm}$ for the SHG signal, leading to the need of a mid-infrared excitation source with $\lambda \ge {2300}\,\textrm{nm}$, which is incompatible with common silicon photonic devices. Therefore, materials with larger band gaps that are compatible with the silicon photonics technology need to be considered. Here, we investigate $\textrm{SiO}_{2}$ as a potential EFISH material. While $\textrm{SiO}_{2}$ has a substantially larger band gap ($E_{\textrm{g},\textrm{SiO}_{2}}\approx {9}\,\textrm{eV}$), its third order nonlinear susceptibility of $\chi ^{(3)}_{\textrm{SiO}_{2}}= 2 \times 10^{-22}\,\textrm{m}^{2}\textrm{V}^{2}$ [11] is much smaller than the $\chi ^{(3)}_{\textrm{Si}}= 2 \times 10^{-19}\,\textrm{m}^{2}\textrm{V}^{2}$ of $\textrm{Si}$ [1,12].
However, the low absorption, the possibility to operate at optical frequencies, higher optical bandwidths combined with low dispersion and better phase matching conditions even compared to established materials for nonlinear optics like $\textrm{LiNbO}_{3}$ still make $\textrm{SiO}_{2}$ an interesting base material for EFISH devices. In spite of these benefits, studies on EFISH in $\textrm{SiO}_{2}$ are scarce with few exceptions such as the early work by Bethea [13].
Today, $\textrm{SiO}_{2}$ in the form of fused silica is widely used in telecommunications for data transmission and allows the realization of active amplifiers or fiber lasers by doping with rare earths. Furthermore it enables applications in nonlinear photonic devices due to its $\chi ^{(3)}$ like third harmonic generation, intensity dependent refractive index, self-focusing, optical Kerr effect and four wave mixing. However, the use of $\textrm{SiO}_{2}$ for parametric processes of lower order is limited due its centrosymmetric nature.
There has been discussion of using this material in combination with the EFISH process for second-order processes in the literature since the 1990s. One prominent example is the method of thermal poling of partially doped quartz glass, where a permanent non-vanishing $\chi ^{(2)}$ can be generated in the centrosymmetric material (see [14], [15], [16]). More recently, high conversion efficiencies were reported using this approach [17]. A review on thermal poling of optical fibers was given by De Lucia and Sazio [18]. However, the high-voltage-induced thermal poling of $\textrm{SiO}_{2}$ leads to a persistent change of $\chi ^{(2)}$ and cannot be used in applications where a fast or dynamic switching is desired. Mukherjee et al. reported time constants for thermal poling up to several 100 seconds [19], rendering this approach useless for fast devices.
Materials like $\textrm{SiO}_{2}$ that have vanishing $\chi ^{(2)}$ and non-zero $\chi ^{(3)}$ offer huge potential as the SHG process can be completely controlled by an external electric field. The fact that SHG is an instantaneous process and the availability of ultrafast fs-Lasers allow, e.g., to exploit this effect for a completely background-free nonlinear electro-optical sampling of ultrafast electrical transients only limited by the pulse-width of the excitation laser. In this work, we investigate the principle feasibility of this concept by applying DC-fields. This can be transferred straightforward to AC-applications by taking into account RC-time constants and proper RF-coupling of the electrical signals.
Here, we will investigate undoped $\textrm{SiO}_{2}$ as a dynamic EFISH material with potentially fast electrical control and describe a method which allows for in-depth numerical analysis of EFISH-based devices based on electromagnetic field simulations. This will allow to optimize such devices in the future.
2. Fabrication
To fabricate the necessary structures on a 1 mm thick uncoated $\lambda /10$ fused silica substrate with 5 mm diameter (Edmund Optics Fused Silica Corning 7980) electron beam lithography (EBL) was employed. Here, the positive resist CSAR 62 is spin-coated with 4000 rpm for 60 s onto the fused silica window and baked at 150 °C for 60 s. In order to mitigate charging effects during lithography caused by the insulating property of fused silica, a thin layer of the conductive protective coating Electra 92 is spin-coated on top of the CSAR 62 with 4000 rpm for 60 s and baked at 90 °C for 120 s. Subsequently, EBL is performed at 25 kV with an area dose of 70 µC cm−2. To prevent fracturing of the finalized gold structures and the ensuing loss of voltage control, all corners in the layout are rounded. The sample is developed in subsequent baths of the developer AR 600-546 for 90 s, the stopper AR 600-60 for 30 s and de-ionized water for 30 s. Electron beam evaporation is used to deposit a 10 nm thin chromium film as adhesion layer followed by a 100 nm thin gold film. The structures are finalized by a lift-off process in the remover AR 300-76 at 80 °C for 5 min. A schematic of the device is shown in Fig. 1(a). Figure 1(b) shows a secondary electron micrograph of a device before bonding. A completed device after bonding is shown in Fig. 1(c). An optical microscope image showing the device under laser excitation is shown in Fig. 1(d).
Fig. 1. (a) Schematic of the EFISH device layout. (b) Secondary electron micrograph of the finished device before bonding. (c) Chip-carrier with bonded device structure. (d) Optical microscope image taken in-situ under 800 nm laser excitation.
3. Theoretical analysis
EFISH is a third order nonlinear process governed by the general third order nonlinear polarization
In this work it is assumed that the third order nonlinear susceptibility is isotropic and independent of location. This simplifies Eq. (2):
As described by Krasnok et al. [20], the overlap integral of multiple electric field distributions at fundamental frequency $\omega$ and SHG frequency $2\omega$ are evaluated, resulting in the effective second order susceptibilityBy dividing the simulation room into areas with six different z-values and calculating $P_{\text {eff}}^{(2)}$ for each individually it is possible to scan the numerically obtained values for $|P_{\text {eff}}^{(2)}|^2$ along the $z$-axis. Comparing this depth profile of the numerically obtained $|P_{\text {eff}}^{(2)}|^2$ with the measured SHG intensity, where the sample position was changed along the z-axis, shows good agreement as can be seen in Fig. 2(c). The differences in the values of $|P_{\text {eff}}^{(2)}|^2$ in Fig. 2(b) and 2(c) are due to the different used integration volumes and the strong localized region of SHG near the surface.
Fig. 2. (a) Static (DC) electric field for an applied voltage of $V= {250}\,\textrm{V}$ between the electrodes. (b) Comparison between numerically obtained values for $|\vec {P}^{(2)}_\text {eff}|^2$ and the measured SHG intensity for different applied DC voltages. (c) Depth profile of the SHG intensity obtained experimentally (red circles) and numerically (solid line).
4. Experimental methods
4.1 EFISH measurements
A customized nonlinear scanning microscope was used for the EFISH measurements, as can be schematically seen in Fig. 3. The microscope consists of a femtosecond oscillator to provide laser pulses with a central wavelength around $ {800}\,\textrm{nm}$ with a pulse duration of about $ {50}\,\textrm{fs}$ and a repetition rate of about $ {80}\,\textrm{MHz}$. The laser pulses are directed to a prism compressor which generates a negative chirp of the laser pulses. It is important that only as much negative chirp is generated as positive chirp is generated by dispersion in the overall system. After the power control unit and a linear polarizer, the laser pulses are focused on the sample by an objective lens with a numerical aperture of NA=0.95. The sample can be moved in all three spatial directions by means of nanopositioners, thus ensuring an excitation area between the DC-electrodes. The SHG signal emitted by the sample is collimated in backscattering geometry by the objective lens and directed to the dichroic short-pass beamsplitter which suppresses the fundamental excitation. For additional suppression a short-pass filter with an optical density of OD=6 at fundamental excitation wavelength is used. A linear polarizer is used for the selection of polarization to be analyzed and the signal is directed to a single-mode fiber coupler. By using a single-mode fiber with a nominal fiber core of about $ {2}\,\mathrm{\mu}\textrm{m}$, a high degree of confocality is achieved within the experimental setup. The $z$-resolution of the optical setup was estimated to $\Delta z_\text {FWHM}\approx {1.6}\,\mathrm{\mu}\textrm{m}$. Finally, the signal is detected via the fiber-optically coupled single-photon counting module (SPCM).
Fig. 3. Experimental setup for EFISH experiments. The fs-oscillator delivers laser pulses with 50 fs duration. For dispersion compensation a pulse compressor is used. An objective lens (NA=0.95) focuses the laser beam onto the sample. The emitted signal passes a dichroic beamsplitter and is coupled into a single-mode optical fiber, providing a confocal filtering. The SHG signal is detected via a single-photon counting module (SPCM). Linear polarizers are used to control the excitation and analyzer polarization. The sample is placed in a dry nitrogen atmosphere to avoid electrical breakdown.
The optical measurements were conducted in dry nitrogen atmosphere. This was required in order to avoid electrical breakdowns between the electrodes in the $\textrm{SiO}_{2}$ which were otherwise observed at the highest voltage of 250 V. During the experiments, the current between the electrodes was monitored and found to be smaller than 10 pA at all times.
5. Experimental results
Figure 4(a) and 4(b) shows the experimentally measured SHG intensity as a function of the laser excitation power for different applied DC voltages. It can be clearly seen that the SHG intensity can be controlled by the externally applied voltage. The continuous lines in Fig. 4(a) represent a parabolic fit to the experimental data.
A double-logarithmic plot of the SHG intensity vs. the excitation power is shown in Fig. 4(b). For voltages larger than 0 V, we observe a power-law dependence. The exponents have been derived from a fitting procedure and were found to be in the range of 0.6 to 1.83. The voltage dependence of the exponents is shown as Fig. S1 in the Supplement 1. An exponent close to two is approached for the highest applied voltage. In fact, a nonlinear behavior is observed: starting from a sub-linear dependence for voltages smaller than 100 V to a super-linear behavior at higher voltages. A nonlinear regime for second-order SHG is reached for the highest electric fields. The reason behind this is not completely clear at this point. If one assumes a constant, i.e., DC-electric field and excitation-power independent $\chi ^{(3)}$, this behavior is not expected. A possible reason is an additional polarization in the $\textrm{SiO}_{2}$ occuring at higher voltages. This explanation seems likely, especially if one considers that the morphological micro-structure of the $\textrm{SiO}_{2}$ is not fully characterized.
Fig. 4. (a) SHG intensity versus excitation power for applied voltages from 0 V to 250 V. (b) Double-logarithmic plot of the SHG intensity vs. the excitation power. (c) Voltage dependence of SHG signal for an excitation power of $P_\text {exc}= {11}\,\mathrm{\mu}\textrm{W}$. (d) Polarization dependence of the SHG signal.
Nevertheless, for the suggested application, e.g., ultrafast electro-optical sampling, this effect is not critical, as it doesn’t affect the background-free generation and detectability of the emitted light at the SHG frequency.
Figure 4(c) shows the SHG intensity for the highest excitation power, i. e., $P_\text {exc}= {11}\,\mathrm{\mu}\textrm{W}$, as a function of the applied DC voltage in the range of 0 V to 250 V. It should be noted that Fig. 4(a) and Fig. 4(c) exhibit slightly different maximum count rates. This is caused by the fact that the measurements could not be recorded at exactly the same position on the microstructure. As the intensity of the nonlinear signal is proportional to the square of the nonlinear polarization, we have:
As shown above, the EFISH contribution to the nonlinear polarization can be computed numerically (see Eq. (5)) and the experimental data can be compared directly to the numerical results. The comparison is shown in Fig. 2(b). The experimental SHG signal shows clear superlinear increase as a function of the applied voltage, as is expected from the parabolic dependence in Eq. (7). However, in the low-voltage region, the experimental results differ from the simulation. For this behavior, two explanations are possible: Firstly, the dark count rate of the used silicon avalanche photodiode, which is in the range of 50 counts/s. Another possible explanation is the presence of surface contributions to the SHG signal. Due to the fact that the experimental curve approximates 40 to 50 counts/s at 0 V, we believe that detector dark counts are the main reason for the low-voltage deviation.
As the applied DC electric field is mainly oriented between the metal electrodes, i. e., the $x$-direction in Fig. 2(a), one expects the resulting SHG light to be linearly polarized along this direction. To check this, we measured the polarization state of the emitted SHG light. The result is shown in Fig. 4(d). Indeed the emitted SHG light is strongly polarized parallel to the direction of the applied DC electric field, thus confirming that the measured signal is indeed EFISH light.
Equations (3) – (5) show that all electric fields $E^\text {DC}(\omega =0), E^{\omega }, E^{2\omega }$ contribute to the resulting EFISH signal in a complex manner. The simulations in Fig. 2(a) and in Fig. S2 (Supplement 1) show that all fields decay into the substrate with different length scales. Therefore, it is not immediately obvious from which regions in the material the nonlinear signal is generated. To probe the depth dependence of the EFISH signal, we have performed a scan along the $z$-axis, i. e., we have used the nonlinear scanning microscope in order to move the focus through the substrate and to record the signal intensity. The results are shown in Fig. 2(c). As expected, the highest SHG intensity is found close to the substrate surface. Towards the bulk of the substrate we observe an exponential decay of the SHG intensity with a characteristic decay length of $\sim {2.5}\,\mathrm{\mu}\textrm{m}$. As can be seen from Fig. S2 in the Supplement 1, the decay lengths for the $E^{\omega }$ and $E^{2\omega }$ fields are much larger so it is reasonable to conclude that the field distribution with the smallest decay length – here $E^\text {DC}$ – dominates the overall behavior. In addition to the experimental data, Fig. 2(c) shows the results for the numerical simulation of the depth profile. Obviously, there is an excellent agreement between the numerical and the experimental data proving the validity of the employed numerical approach which will be a valuable tool in the design of future EFISH-based devices.
6. Summary
In summary, we have demonstrated electric-field induced SHG from $\textrm{SiO}_{2}$-based devices. The chosen technology platform is fully compatible with conventional silicon technology and allows – other than purely silicon-based devices – for the use of typical wavelengths used in silicon photonics. Despite the comparably low $\chi ^{(3)}$ coefficient in this material system, the EFISH signal is easy to detect and could also be used in subsequent devices such as wave guides etc. In addition to the experiments, we have developed a numerical approach that allows reliable and quantitative simulations of EFISH-based devices, which could also be used in other material systems.
Funding
Deutsche Forschungsgemeinschaft (TRR142/2-2021 – Projektnummer 231447078).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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