Passive photonic diodes based on natural van der Waals heterostructures

1 Introduction

Van der Waals heterostructures (vdWHs) [1], [2], [3], composed of stacked atomically thin two-dimensional (2D) crystals, exhibit unprecedented physicochemical properties for exploring new physical or chemical phenomena and intriguing applications ranging from solar cell [4], [ 5], catalysis [6], [ 7] to artificial intelligence devices [8], [ 9]. Bandgap and structure engineering of vdWHs can bring novel functionalities for the optical, electrical, and optoelectronic devices, like modulators [10], [ 11], tunneling transistors [12], filters [13], and light-emitting diodes [14]. Recently, the fabrication of superlattices based on 2D materials through vertical stacking, atomic or molecular embedding, moiré patterning, strain engineering, and lithography has become a strategy to explore new quantum phenomena and further tune the performance of optoelectronic devices [15], [16], [17]. However, vdWHs are usually obtained via mechanical exfoliation and manual restacking process, which is uncertain and challenging due to the need of controlling the crystal arrangement of different crystal lattices and avoiding the introduction of interlayer adsorbates [18]. Franckeite, a naturally occurring heterostructure with superimposed SnS₂-like and PbS-like layers alternately, was found by Velický et al. [19] and Molina-Mendoza et al. [20] in 2017. But even more important, the franckeite is a stable 2D semiconductor with p-type doping and narrow bandgap (<0.7 eV) [20], [ 21]. The spontaneous rippling shows that franckeite breaks the initial lattice symmetry of a single layer and shows structurally anisotropy [22]. All the physicochemical characteristics make franckeite an excellent candidate for high-performance optoelectronic devices [23], [24], [25].

With the development of all-optical networks, all-optical signal processing without passing into the electrical domain becomes more and more important for high-speed and cost-effective characteristics [26]. Photonic diode can realize the one-way transmission of light to prevent the backward transmitted light from causing adverse effects on the light source and the optical path system, which can be used in the fields of optical computing, optical interconnection, laser and so on. To date, different mechanisms and methods such as photonic crystals [27], [ 28], magneto-optical effects [29], liquid crystal heterojunctions [30] and nonlinear optical effects [31], [32], [33], [34] have been proposed to achieve unidirectional light transmission. With the development of low-dimensional (LD) materials, their broadband optical response, tunable absorption, compact structure and ease of preparation provide the possibility for novel all-optical information processing devices [35], [36], [37].

Here, we prepared the layered franckeite by liquid-phase exfoliation (LPE) method. The saturable absorption (SA) characteristics of franckeite were studied through the open aperture (OA) Z-scan experiment, and the nonlinear absorption coefficient of about −1.95 × 10⁻⁴ m/W, saturable intensity of 0.18 kW/cm², and modulation depth of 9.4% were obtained at 1064 nm wavelength. This relatively low-threshold saturable intensity and large modulation depth makes photonic diodes more easily implemented. Ultrafast carrier dynamics characteristic with hundred picoseconds makes franckeite have the potential to contribute to the ultrafast optoelectronic devices. Based on the optical Kerr effect of franckeite, the spatial self-phase modulation (SSPM) effect was measured during the interaction of light-franckeite and the formation of a diffraction ring was observed clearly. Combining with the optical limiting (OL) characteristics of C₆₀, a franckeite/C₆₀-based photonic diode was designed based on the nonlinear optical properties of franckeite to realize nonreciprocal transmission of light, and the nonreciprocity factor was about 2 dB obtained experimentally. Further research found that the nonreciprocal characteristics of the passive photonic diode can be tuned by adjusting the nonlinear parameters, and the SA with low-threshold saturable intensity and large modulation depth can provide more possibilities for the passive photonic diodes.

2 Characterization of layered franckeite

The layered franckeite was prepared from its bulk form by LPE method [21], [ 38]. The franckeite-NMP (N-methyl-2-pyrrolidone) dispersion was suspended on a 1-mm quartz glass plate to prepare a thin film. Scanning electron microscope (SEM) and transmission electron microscopy (TEM) were employed to characterize the morphology. The SEM image in Figure 1A shows that the bulk franckeite has been stripped into flakes. The TEM and corresponding atomic scale high-resolution TEM were also characterized in Figure 1B and C, showing that the observed interdistances of the lattice fringes were found to be 0.33 nm ((100), SnS₂-like) and 0.298 nm ((020), PbS-like). Figure 1D, E, and F show the morphology and thickness information of the layered franckeite film conducted by the atomic force microscopy (AFM) measurement. For precisely analyzing the thickness of franckeite flakes, four different sections were chosen for the measurements, as marked A, B, C, and D in Figure 1D. Figure 1E shows the height difference between the substrate and target sections. The thicknesses of the section A to section D are measured to be about 20.5, 11.3, 7.8 and 6.4 nm, respectively. The statistical analysis of the original height data of AFM shows that the nanoflakes from ∼3 layers (3L) to ∼6L are more widely distributed in the franckeite film (unit cell, H + Q layer, thickness 1.7 nm [20]), as shown in Figure 1F. Raman spectroscopy can clearly show the presence of PbS-like and SnS₂-like compounds, as shown in Figure 1G. The intense, strong peak at about 69 cm⁻¹ corresponds to the acoustic mode of PbS-like [39], [ 40], and the peak at 315 cm⁻¹ corresponds to the A_1g mode of SnS₂-like [41], [ 42]. Other peaks at 122, 190, 253, and the 400–600 cm⁻¹ shoulder are roughly due to the superposition of respective phonon modes of both PbS (including longitudinal optical [LO], 2LO, 3LO modes) and SnS₂ (including the E _g mode and 2nd order effects) [42], [43], [44[42]-[44]]. The linear transmittance spectrum shows the broadband absorption characteristic of franckeite, which verifies its narrow bandgap energy (<0.7 eV) [20], [ 21]. It is worth noting that the transmission spectrum shows a small valley around 1.1 μm wavelength, which is likely related to the superlattice plasma effect introduced by the moiré fringes [24]. Here, we have carried out further research on nonlinear absorption characteristics in the near infrared region to explore its application potential in optoelectronic devices.

Figure 1:

Material characteristics of the layered franckeite.

(A) Scanning electron microscope (SEM) micrograph of layered franckeite after liquid-phase exfoliation (LPE). (B) transmission electron microscopy (TEM) image of layered franckeite. (C) The corresponding atomic scale high-resolution TEM (HRTEM) of an ultrathin franckeite layer. (D) Two-dimensional topographical atomic force microscopy (AFM) image of franckeite film. (E) Height profiles of the sections marked in Figure 1D. (F) Statistical analysis of the AFM raw height data. The inserted numbers prove that the nanoflakes from ∼3 layers (3L) to ∼6L are more widely distributed (unit cell, H + Q layer, thickness 1.7 nm [20]). (G) Raman spectra of layered franckeite. (H) The linear transmittance of layered franckeite shows a small valley around 1.1 μm wavelength.

3 Third-order nonlinear optical characteristics and ultrafast response of franckeite

The OA Z-scan was used to investigate the nonlinear optical characteristics of franckeite [45], [ 46], and the prepared franckeite film was used as the sample. We employed the mode-locked pulse laser with the central wavelength 1064 nm, pulse duration 220 ps, repetition rate 2.8 MHz. Typical OA Z-scan curves are shown in Figure 2A and C. Figure 2B and D are the absorption characteristic curves obtained from the change of z into the change of light intensity. The Z-scan curve of franckeite shows a peak trend and is symmetrical about the laser focus, indicating that the absorption of the material decreases with the increasing light intensity. However, when the transmittance gradually becomes gentle with the increasing light intensity, it indicates that the absorption reaches saturation, which proves that franckeite has SA characteristics. Conversely, the Z-scan curve of C₆₀ is symmetrical about the laser focus and shows a valley trend, that is, the absorption of the material increases with the increasing light intensity (reverse saturable absorption [RSA]), indicating the potential of C₆₀ as an OL material.

Figure 2:

Nonlinear optical characteristics of layered franckeite and C₆₀.

Open aperture (OA) Z-scan curves of (A) franckeite and (C) C₆₀ at 1064 nm wavelength, respectively. The corresponding relationship between transmittance and input intensity of (B) franckeite and (D) C₆₀, respectively.

The optical transmittance of OA Z-scan trace can be fitted by the formula:

β is the nonlinear absorption coefficient, and I ₀ means the focal light intensity of the incident laser. The effective length L eff = [ 1 − e − α 0 L ] α 0 of sample can be obtained by substituting the sample length L and linear absorption coefficient α ₀. z 0 = k ω 0 2 λ is the diffraction length of the beam, and the waist radius ω ₀ of beam focus is about 60 μm measured by the knife edge method.

The relationship between the optical transmittance and the optical intensity can be fitted by the formula:

α _s means the saturable loss or modulation depth and α _ns is the nonsaturable loss, I _s is the saturable optical intensity (for SA) or limiting threshold (for RSA).

By fitting the experimental data, we obtained the SA characteristics of franckeite: the value of the nonlinear absorption coefficient is about −1.95 × 10⁻⁴ m/W, the saturable optical intensity ∼0.18 kW/cm², and the modulation depth of 9.4%. The SA response of franckeite with low-threshold SA and large modulation depth may provide novel nonlinear optical application in near infrared spectral range. Meanwhile, the C₆₀ exhibits excellent OL characteristics with a limiting threshold ∼0.498 kW/cm² and a modulation depth of 9.8%.

Femtosecond transient absorption spectroscopy has the advantages of high time resolution and wide measurement range, which is an effective tool for studying ultrafast dynamic processes of organic or inorganic materials. In the measurement of femtosecond transient absorption spectroscopy, a strong 400 nm wavelength laser is used as the pump light, which is focused into the sample after proper attenuation and polarization direction adjustment. The weaker laser is focused into the nonlinear crystal to generate supercontinuum white light as the signal light and adjusted by the time delay device then focused to the same position of the sample. The time delay device is used to adjust the optical path difference between pump and signal lights, the modulation signal is achieved by white light passing through the sample under different time delays and collected by the line photodiode.

Figure 3 shows the change in optical density of signal light of different wavelengths within a certain delay time after the material is excited, and the positive signal indicates that RSA occurs while the negative signal indicates that SA occurs. The results show that franckeite make a broadband absorption in visible range, especially the ultrafast carrier dynamic processes (about 50–800 ps) generated near ∼500 nm wavelength, which means the complex and competitive absorption process occurs (may including SA caused by ground state bleaching, RSA signal caused by excited state absorption, etc.). Ultrafast carrier dynamics characteristic makes franckeite have the potential to an excellent candidate for ultrafast optoelectronic devices.

Figure 3:

Transient absorption spectroscopy of franckeite. It can be seen that the franckeite make a broadband absorption, especially the multiple ultrafast signals (about 50–800 ps, as shown in the yellow, blue, and green regions) generated near 500 nm wavelength. Color bars indicate changes in optical density.

4 Passive photonic diodes based on nonlinear optical characteristics of franckeite

The nonlinear optical properties of LD materials can be used in photonic applications, such as optical modulators [47], [ 48], isolators [31], and switchers [49] for signal processing, mode-locked lasers for generating ultrashort pulses [50]. By cascading two materials with opposite nonlinear optical behavior in light path, namely introducing nonlinear discontinuities, the axial asymmetry function of the photodiode can be realized. The passive photonic diode was obtained by stacking the franckeite and C₆₀ to achieve the nonreciprocal transmission of light.

In the passive photonic diode structure (as shown in Figure 4), the laser in forward bias passes through SA-RSA films in turn with an overall transmittance increases due to the enhanced transmitted beam of nonlinear part (dark red), which is equivalent to the light-conducting function of the optical diode. Conversely, the total transmittance of the light after passing through the RSA-SA films is reduced in the reverse bias setting, which means the light cutoff function is realized.

Figure 4:

Action of an all-optical diode based on asymmetric nonlinear absorption. Dark red represents nonlinear transmission, light red represents linear transmission.

For an SA nonlinear material, the intensity absorption coefficient is given by [51]:

The generalized pulse propagation equation is obtained as

where z′ is the position coordinate along the axis of propagation in the medium (of length L) and I is I(z′, t).

For RSA material, I ≤ I _s, the nonlinear absorption coefficient can be given by:

β _2PA is the two-photon absorption coefficient. The differential equation describing the optical loss of RSA is given by

For the passive photonics diode, the nonreciprocity factor is defined as:

where T _forward and T _reverse are the nonlinear transmittance values for forward and reverse directions (as shown in Figure 4).

Based on the above theoretical model, combined with the third-order nonlinear optical characteristics of the two nonlinear optical materials, we theoretically and experimentally studied the nonreciprocal optical transmission of the passive photonic diode based on franckeite and C₆₀, as shown in Figure 5. Based on different values of I _s and α _s, we studied the influence of nonlinear parameters on the transmission characteristics of the photonic diode, as shown in Figure 5A and B. In both cases, the transmission is reciprocal when the input intensity is less than 0.1 kW/cm², but at a higher intensity, nonreciprocity is excited and realized to different degrees.

Figure 5:

Nonreciprocal transmission characteristics of the passive photonic diode based on nonlinear optics.

(A) Different values of I _s. (B) Different values of α _s. Nonreciprocal transmission characteristics of the photonic diode based on franckeite/C₆₀ obtained (C) theoretically and (D) experimentally. The nonreciprocity factor ∼2 dB of the passive photonic diode was obtained.

The performance of a nonlinear photonic diode is more affected by the characteristics of SA, the nonreciprocal factor gradually increases with the decrease of I _s or increase of α _s. The results show that SA materials with larger modulation depth and lower saturable intensity will have more potential to develop photonic diodes and even other optoelectronic devices. The prepared franckeite/C₆₀ was placed in forward bias and reverse bias under the same condition, the passive all-optical diode with a nonreciprocity factor of about 2 dB was obtained experimentally (Figure 5D). Combined with ultrafast broadband nonlinear response of franckeite [21], the realization of the franckeite-based passive photonic diode will open up its application potential in photonic and optoelectronic fields in the near-infrared spectral range.

We also verified the photonic diode with the franckeite in solution to realize the nonreciprocal transmission of light [31], [ 33]. The refractive index of franckeite is modulated by the incident light intensity, the change in the refractive index induced by the light field will cause a phase change. That is, the phase of incident laser beam can be modulated by its own intensity when propagating in the nonlinear optical medium, which is known as self-phase modulation (SPM) [51]. The SSPM is an SPM generated on the cross section of the beam, which is used to develop the nonlinear optical characteristics of LD materials [52], [53], [54].

The nonlinear phase change Δ φ ( r ) ≈ Δ φ 0 exp ( − 2 r 2 / ω 2 ) shows Gaussian distribution along the radial direction r for a Gaussian beam, the light is strongest at the center of r = 0 which causes the largest Δφ ₀. If |Δφ ₀| is much larger than 2π, then the center symmetrical peak or valley appears at equal r in the horizontal output power spectrum, thus the projection of the far field appears a ring structure of bright and dark intervals. This is the result of light interference between rings with the same dip angle and different radii (different phases). The number of bright and dark rings is close, and this number is close to the integer of |Δφ ₀|/π. The diameter of the outermost ring is determined by the maximum slope of Δφ(r) at the Gaussian pattern inflection point. In addition, the collapse of diffraction ring (Figure 6A) is mainly caused by the asymmetric thermal convection introduced by gravity during the action. The nonlinear refractive index n ₂ of the natural vdWHs layered franckeite was calculated to be ∼10⁻⁹ m²/W at 1064 nm wavelength [21].

Figure 6:

The experimental results obtained from the franckeite/C₆₀-based nonlinear photonic diode, and the phenomenon of unidirectional diffraction rings excitations.

(A) spatial self-phase modulation (SSPM) experimental device diagrams, the excitation structure from top to bottom are franckeite, C₆₀, franckeite-C₆₀, C₆₀-franckeite, respectively. It can be seen that only the franckeite and franckeite-C₆₀ structures excite the diffraction ring. (B) The transmittance patterns of Gaussian beam through the forward and reverse bias structures under different light intensity. (C) The detailed changes in transmission characteristics of the two structures.

The significant nonlinear optical characteristics of layered franckeite make it have the potential to excite the diffraction rings, but the RSA characteristic of C₆₀ make it have the effect of reducing the light intensity. In Figure 6, the franckeite and C₆₀ dispersions were filled in two closely matched cuvettes to form a mixed structure, which was used as a nonlinear photonic diode to realize the non-reciprocal propagation of light. When the laser passes through the forward bias (franckeite-C₆₀), the diffraction ring will be excited when passing through franckeite dispersion then successively passing through C₆₀, that is to achieve the forward light conduction function (the Gaussian beam evolves into a diffraction ring). It was found that the diffraction ring passes through C₆₀ dispersion with a decrease intensity and an unchange number of rings (Figure 6A). However, when the laser passes through the reverse bias (C₆₀-franckeite), the light intensity is significantly reduced when it first passes through C₆₀, which will lower than the excitation threshold of the nonlinear characteristic of franckeite. Therefore, only a second decrease in light intensity will occur without a diffraction ring generation when franckeite is passed later, that is, the reverse light blocking of the photonic diode is implemented (diffraction rings are not generated and the light intensity is significantly reduced).

Under the same excitation light intensity, the transmittance patterns of Gaussian beam through the forward and reverse bias structures are shown in Figure 6B, and the diffraction ring can be excited under the franckeite-C₆₀ structure, whereas the Gaussian beam still can be obtained under the C₆₀-franckeite structure. The detailed changes in transmission characteristics of the nonlinear photonic diode based on franckeite and C₆₀ are shown in Figure 6C. It is clearly seen that the proposed franckeite/C₆₀ hybrid structure can realize irreversible propagation of light, and the ring number can be modulated by the light intensity, which can be used as nonlinear photonic diodes.

5 Conclusions

In summary, we prepared layered franckeite by LPE method, and studied its nonlinear optical characteristics through Z-scan and SSPM experiments. We have obtained the nonlinear absorption coefficient of about −1.95 × 10⁻⁴ m/W, lower saturable intensity ∼0.18 kW/cm², and large modulation depth of 9.4% of layered franckeite at near infrared spectral range. Ultrafast carrier dynamics characteristic with hundred picoseconds makes franckeite have the potential to contribute to the ultrafast optoelectronic devices. Combined the nonlinear optical characteristics of franckeite with the OL characteristics of C₆₀, the passive photonic diodes have been realized to achieve nonreciprocal transmission of light. By adjusting the nonlinear parameters, the nonreciprocal characteristics of the passive photonic diode can be tuned. Particularly, the low-threshold SA response, outstanding optical Kerr effect and ultrafast response of franckeite may provide some novel nonlinear optical application in the infrared regime. To meet the needs of low power consumption and high performance, franckeite with low nonlinear response threshold is an important candidate for ultrafast optoelectronic devices.