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Abstract
Integrated optical tunable filters are key components for a wide spectrum of applications, including optical communications and interconnects, spectral analysis, and tunable light sources, among others. Compared with their thermo-optic counterparts, integrated acousto-optic (AO) tunable filters provide a unique approach to achieve superior performance, including ultrawide continuous tuning ranges of hundreds of nm, low power consumption of sub-mW and fast tuning speed of sub-µs. Based on suspended one-dimensional (1D) AO waveguides in the collinear configuration, we propose and theoretically investigate an innovative family of integrated AO tunable filters (AOTFs) on thin-film lithium niobate. The AO waveguides perform as tunable wavelength-selective narrow-band polarization rotators, where highly efficient conversion between co-propagating TE0 and TM0 modes is enabled by the torsional acoustic A1 mode, which can be selectively excited by a novel antisymmetric wavefront interdigital transducer. Furthermore, we systematically and quantitatively explore the possibilities of exciting modulated acoustic waves, which contain multiple frequency components, along the AO waveguide to achieve independently reconfigurable multi-band operations, with tunable time-variant spectral shapes. By incorporating a complete set of ultrawide-band polarization-handling components, we have proposed and theoretically investigated several representative monolithic AOTF configurations, featuring different arrangements of single or cascaded identical AO waveguides. One of the present AOTF designs exhibits a theoretical linewidth of ∼8 nm (∼4 nm), a sidelobe suppression ratio of ∼75 dB, and theoretically no excess loss at the center wavelength of 1550 nm (1310 nm), with an ultrawide tuning range of 1.25–1.65 µm (from O-band to L-band), a fast tuning speed of 0.14 µs, and a low power consumption of a few mW.
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1. Introduction
Integrated optical tunable filters (OTFs) [1–3] are one type of the most important reconfigurable integrated photonic devices, which can be widely used in wavelength-division multiplexing (WDM) optical communications, optical interconnects, spectral analysis, and tunable light sources, among others. For example, high-capacity WDM optical communication networks are an indispensable part of the infrastructures for Internet and Internet of things, where tunable filters are the key to realize the flexible reconfiguration of WDM optical networks, including the real-time dynamic optimization of the network structure and the bandwidth allocation. However, integrated thermo-optic tunable filters (TOTFs) [4–8] are generally capable of only 10–20 nm of wavelength tuning ranges, constrained by the operation temperature, which is quite insufficient to cover even a single telecommunication band. In addition, the tuning speed and power consumption of such thermo-optic devices are typically tens of µs and tens of mW, respectively, which pose severe limitations on their real-world applications. As another example, to reveal the diverse molecular fingerprints, typical infrared spectral analysis applications require hundreds or even thousands of nm of wavelength tuning ranges, far exceeding the TOTF capabilities.
Guided-wave acousto-optic (AO) devices provide a unique approach to implement integrated OTFs [9–12], which is to form a reconfigurable waveguide grating by exciting one or more propagating acoustic modes to realize versatile manipulation of optical modes. Because the frequency and power of the acoustic waves can be continuously tuned across wide ranges, the center wavelength of the effective waveguide grating filter has an ultrawide continuous tuning range up to hundreds of nm. More intriguingly, if several propagating acoustic waves of different frequencies are excited simultaneously to form a time-variant synthetic waveguide grating, it is possible to achieve independent reconfigurations of multiple filter bands, with tunable time-variant spectral shapes, which is difficult, if not impossible, to achieve by thermo-optics or other means.
Conventional guided-wave AO devices are typically based on bulk lithium niobate substrates, where surface acoustic waves (SAWs) and diffusion (titanium or proton) waveguides are employed [9,13]. However, such waveguides only support weakly-guided acoustic and optical modes, resulting in low integration density and centimeter-scale device sizes. Recently, thin-film lithium niobate on insulator (LNOI) has emerged [14,15] and attracted extensive attention because of its excellent acousto-optic and piezoelectric properties [16–19]. Furthermore, the nanofabrication processes for LNOI, especially the reactive ion etching (RIE) technology, has also made important breakthroughs [20,21], making LNOI a natural platform for next-generation integrated AO devices. Compared with their conventional counterparts, the new generation of integrated AO devices feature unprecedented compact footprint, strong co-confinement of the acoustic and optical waves and significantly enhanced AO interactions, leading to a variety of pioneering experimental demonstrations [17,22–26]. Especially, in the collinear configuration, suspended one-dimensional (1D) AO waveguides with subwavelength cross-sections have recently been experimentally demonstrated to achieve ∼18% conversion from TE0 mode to TE1 mode [26], with no fundamental obstacles to achieve complete conversion in prospect. The suspension of the thin-film lithium-niobate AO waveguides provides an elegant approach to achieve strong co-confinement of both the acoustic and optical modes.
Here, we propose and theoretically investigate an innovative family of integrated AOTFs with suspended 1D AO waveguides in the collinear configuration on LNOI. The AO waveguides perform as tunable wavelength-selective narrow-band polarization rotators, where highly efficient conversion between co-propagating TE0 and TM0 modes is enabled by the torsional acoustic A1 mode, whose displacement field is antisymmetric with respect to the center of the waveguide cross-section [27]. According to our calculations, this unprecedented AO mode combination (A1/TE0/TM0) leads to stronger AO interactions, hence higher power efficiency, compared with other commonly used combinations. (Here we define an AO mode combination as the combination of the acoustic and optical modes involved in the AO interactions of interest.) We have also proposed a novel antisymmetric-wavefront (ASW) interdigital transducer (IDT) design to selectively excite the A1 mode into the AO waveguide, without introducing notable loss or reflections to the optical modes. After propagating through the AO waveguide, the wavevector- and frequency-matched input TE0 (TM0) mode is converted into the Doppler-shifted TM0 (TE0) mode within the narrow filter band, while the input modes outside the filter band remain unaltered. For our representative AO waveguide design, to achieve an ultrawide wavelength tuning range between 1.25–1.65 µm, which covers from telecom O-band to L-band, it only requires the acoustic frequency to be varied within a small range between 380–520 MHz, which can be readily achieved with chirped IDT designs. With coupled-mode theory, we have quantitatively modeled the co-propagation of the AO modes and the conversion between the optical modes, taking into account the propagation loss of the acoustic modes. Complete mode conversion in the telecom C-band (1550 nm) requires an acoustic power and an AO interaction length of only 0.1 mW and ∼0.5 mm, respectively. With the acoustic group velocity of ∼2.5 km/s, the tuning speed of the integrated AOTF is only ∼0.2 µs, which is the time it takes for the acoustic wave to propagate through the AO waveguide. The sub-mW power consumption and sub-µs tuning speed of the integrated AOTF are superior to those of the integrated TOTFs. Furthermore, for the first time, we have systematically and quantitatively explored the possibilities of exciting modulated acoustic waves, which contain multiple frequency components, along the AO waveguide to achieve independently reconfigurable multi-band operations, with tunable time-variant spectral shapes.
Finally, we propose and theoretically investigate several representative monolithic AOTF configurations, featuring different arrangements of single or cascaded identical AO waveguides connected with a complete set of ultrawide-band polarization-handling components. In addition to narrowed filter linewidths and suppressed sidelobes, such cascaded arrangements possess an important new feature that every other AO waveguide exactly recovers the mode conversion and Doppler shift of the previous one, resulting in a scalable cascade where all the AO waveguides are identical, and all the IDTs can be driven by the same one radio-frequency (RF) source. Also, the capability to recover the Doppler shift may be crucial for certain applications. In addition, more sophisticated functionalities such as reconfigurable multi-band add-drop filters (ADFs) can be realized with judiciously arranged polarization splitters and combiners. For a representative AOTF configuration with only one pair of cascaded AO waveguides, a linewidth of ∼16 nm (∼8 nm), a sidelobe suppression ratio of ∼20 dB (∼20 dB), and theoretically no excess loss at the center wavelength of 1550 nm (1310 nm) is achieved. For four pairs of cascaded AO waveguides, the linewidth and the sidelobe suppression ratio become ∼8 nm (∼4 nm) and ∼75 dB (∼75 dB) for the center wavelength of 1550 nm (1310 nm), respectively. The AOTF configurations with cascaded AO waveguides feature sub-mW or mW power consumption, which scales linearly with the number of the AO waveguides. Meanwhile, they also feature the sub-µs tuning speed and the hundred-nm tuning ranges of the center wavelength, inherited from those of the single AO waveguides. Combined with the capabilities of independently reconfigurable multi-band operations, with tunable time-variant spectral shapes, the present integrated AOTFs are promising for a diverse spectrum of applications.
2. Suspended 1D AO waveguides on LNOI
The schematic configuration and the operation principles of a single suspended 1D AO waveguide on LNOI is shown in Fig. 1(a). The AO waveguide performs as a tunable wavelength-selective narrow-band polarization rotator, where highly efficient conversion between co-propagating TE0 and TM0 modes is enabled by the torsional acoustic A1 mode. The A1 mode is excited into the waveguide, with its power decaying exponentially along the waveguide due to acoustic loss. Meanwhile, the wavevector- and frequency-matched input TE0 (TM0) mode is converted into the Doppler-shifted TM0 (TE0) mode within the narrow filter band, while the input modes outside the filter band remain unaltered.
Fig. 1. Suspended 1D AO waveguides on LNOI. (a) Schematic configuration and operation principles of a single suspended 1D AO waveguide on LNOI; Acoustic mode A1 (b) and its dispersion curve (c); (d) optical TE0 and TM0 mode dispersion curves with the phase-matched A1 mode wavevector; (e) the frequency of the A1 mode phase-matched with the TE0 and TM0 modes; (f) calculated interaction length for complete mode conversion as a function of the acoustic loss; (g) calculated spectra at the center wavelength of 1310 and 1550 nm for the acoustic loss of 0, 10, 20 dB/mm.
In the torsional acoustic A1 mode, the waveguide cross-sections rotate periodically with respect to the center axis along the waveguide, leading to nonvanishing overlap integral with the TE0 and TM0 modes. It is termed A1 mode because it is the 1st-order antisymmetric Lamb wave mode [28]. Alternatively, it can be regarded as the SV1 mode, that is the 1st-order shear-wave mode with dominantly vertical displacement. Its displacement field is antisymmetric with respect to the center of the waveguide cross-section. To achieve highly efficient and selective excitation of the A1 mode, here we propose a novel antisymmetric-wavefront (ASW) IDT with a taper structure between the suspended ridge waveguide and strip waveguide, as shown in Fig. 1(a). The IDT pair consists of two sub-IDTs, arranged on both sides of the slab at the entrance of the suspended waveguide. The individual fingers of the two sub-IDTs are aligned, but connected with opposite electrical polarities, resulting in antisymmetric wavefronts of the excited acoustic waves. The taper structure then guides the acoustic wave into the suspended waveguide, where the A1 mode is selectively excited. Meanwhile, the optical modes can propagate through the ASW IDT without notable loss or reflection.
In this work, to facilitate the demonstrations and discussions of the feasibility, performance metrics and diverse capabilities of the proposed integrated AOTF family, we adopt a specific representative AO waveguide design based on commercial x-cut LNOI wafers, with a 400-nm-thick lithium niobate (LN) top-layer, a 2-µm-thick silica buried layer and a silicon substrate. The suspended waveguide structure on LNOI is fabricated by removing the silica buried layer under the LN core [17]. The AO waveguide is along the z-axis of the LN crystal orientation, with the top width of 800 nm and the sidewall angle of 30°. The slab under the ASW IDT is etched to be 50-nm-thick to ensure sufficient confinement for both TE0 and TM0 modes, and the simulated A1 mode excitation is shown in Fig. 1(a), with calculated efficiency of over 26%, which can be further improved by optimizing the ASW IDT and taper structure design. The AO waveguide cross-section is shown in Fig. 1(a) with the simulated TE0 and TM0 mode profiles at 1550 nm. The simulated A1 mode profile (∼500 MHz) and its dispersion curve are shown in Figs. 1(b) and 1(c), respectively, while the TE0 and TM0 mode dispersion curves are shown in Fig. 1(d), together with the phase-matched A1 mode wavevector at 1550 nm. Therefore, at each optical wavelength within the range of 1.2–2.0 µm, the frequency of the A1 mode phase-matched with the TE0 and TM0 modes is calculated and shown in Fig. 1(e), where monotonic dependence is observed between 1.25–1.65 µm and 380–520 MHz. Consequently, the AOTF center wavelength can be continuously tuned across an ultrawide band between 1.25–1.65 µm, which covers from telecom O-band to L-band, by tuning the acoustic frequency between 380–520 MHz, which can be readily achieved with an RF signal source and chirped IDTs. In Fig. 1(e), monotonic dependence is also observed below 1.25 µm and above 1.75 µm, which can also be used for AOTF operations. Note that monotonic dependence of the acoustic frequency on the optical wavelength is required because, otherwise, for certain acoustic frequencies, there will be multiple phase-matched optical wavelengths, leading to multiple filter bands for a single acoustic frequency, which is undesired in most cases.
To quantify the AO interactions, we first consider the scenario without acoustic loss, such that the acoustic wave propagates through an infinitely long AO waveguide without decay, forming a uniform waveguide grating. Therefore, the optical power will be converting sinusoidally between the co-propagating TE0 and TM0 modes along the AO waveguide, assuming perfect phase matching. The coupling length, ${L_\textrm{c}}$, defined as the distance for complete conversion, is inversely proportional to the square root of the acoustic power ${P_\textrm{b}}$. Therefore, the normalized coupling length ${l_\textrm{c}}$, that is the coupling length for unit square root of the inversed acoustic power, can be defined as
Note that ${l_\textrm{c}}$ is a constant determined by the AO waveguide design and mode combination, hence a sound figure of merit to quantify the AO interactions. The smaller ${l_\textrm{c}}$ is, the stronger the AO interactions are. From the perturbation theory [26], the formed grating leads to the coupling of the originally orthogonal TE0 and TM0 modes, resulting in the sinusoidal power conversion between them, and ${l_{\textrm c}}$ can be calculated from the overlap integral of the AO mode combination. Alternatively, the grating is a 1D photonic crystal whose Bloch modes approximate the two superpositions of the original TE0 and TM0 modes [28], that is the two Bloch supermodes. The slight difference between the wavevectors of the two supermodes leads to the beating between them, hence the sinusoidal power conversion, and ${l_\textrm{c}}$ can be calculated from the dispersion curves of the two Bloch supermodes, that is the band structure of the 1D photonic crystal. For either approach, all the physical effects involved in the AO interactions [13] in thin-film LN should be accounted for, including the primary photoelastic effect, the secondary photoelastic effect, the roto-optic effect [29], and the dielectric tensor redistribution (especially at the material boundaries) [26,28].
Here we have adopted the Bloch-mode approach to calculate ${l_\textrm{c}}$ at 1550 nm and obtained a theoretical result of 123 µm·mW1/2, which features about two orders of magnitude enhancement of the AO interactions compared to the experimental result of 8.3 mm·mW1/2 from the diffusion waveguides on bulk LN [11], due to the drastically reduced waveguide cross-section, from tens of µm down to sub-µm. Note that the only experimental result for ${l_\textrm{c}}$ from the earlier work on suspended thin-film LN waveguides [26] is 133 µm·mW1/2, but it is inconclusive to compare our theoretical result with that experimental result obtained for a different AO waveguide design and mode combination.
To obtain complete mode conversion at the wavelength of 1550 nm, the frequency, wavelength, phase and group velocities of the phase-matched A1 mode are 507 MHz, 4.55 µm, 2.3 km/s and 2.8 km/s, respectively. Assuming the power of the A1 mode to be 0.1 mW, which should be low enough to avoid damage to the waveguide, the coupling length is 0.39 mm, which is a feasible length for the suspended waveguide. Therefore, the AOTF tuning speed is only ∼0.14 µs, which is the time it takes for the A1 mode to propagate through the AO waveguide.
To calculate the AOTF spectra with lossy and/or modulated acoustic waves, the coupled-mode equations for a single section of the AO waveguide are [28,30]
To account for the acoustic loss, the acoustic envelope can be expressed as
where $\alpha $ is the exponential amplitude decay constant, assuming that the acoustic wave is excited at one end of the AO waveguide ($z = 0$) and propagates in the positive direction to the other end ($z = L > 0$). To implement AOTF functionalities, the waveguide length L and initial acoustic power ${P_\textrm{b}}(0 )$ should be chosen to achieve complete optical mode conversion at the phase-matched center wavelength. Due to the exponential decay of the acoustic power along the waveguide, the complete optical mode conversion takes a longer distance, compared to the lossless case with the same ${P_\textrm{b}}(0 )$, such that $L > {l_\textrm{c}}\sqrt {1/{P_\textrm{b}}\left( 0 \right)}$, as shown in Fig. 1(f), which has been calculated by numerically solving Eqs. (2) for the case of ${P_\textrm{b}}(0 )$ = 0.1 mW and $\alpha $ \lt 22 dB/mm. For $\alpha $ ≥ ∼20 dB/mm, $L$ quickly becomes impractically long for suspended waveguides, due to vanishing acoustic power towards the end ($z = L$) of the waveguide, and higher ${P_\textrm{b}}(0 )$ should be required for complete optical mode conversion. For typical acoustic loss of ∼10 dB/mm [26], L increases from 0.39 mm for the lossless case to ∼0.52 mm, feasible for suspended waveguides. Even for acoustic loss as large as ∼20 dB/mm, L becomes ∼0.97 mm, still feasible for suspended waveguides.To further calculate the optical mode conversion spectra of the AO waveguide, defined as the ratio of the converted mode power, $\eta = {P_2}(L )/{P_1}(0 )$, Eqs. (2) are solved for the wavevector mismatch $\kappa $ as a function of the optical wavelength. The spectra are calculated for ${P_\textrm{b}}(0 )$ = 0.1 mW and $\alpha $ = 0, 10, and 20 dB/mm, respectively corresponding to $L$ = 0.390, 0.515, and 0.968 mm, such that complete mode conversion is always achieved at the center wavelength of 1550 nm, as shown in Fig. 1(g). Evidently, the spectra resemble the square of sinc functions, exhibiting center-lobe linewidths approximately inversely proportional to $L$, and more pronounced sidelobe apodization for larger $\alpha $. For $\alpha $ of 0 and 10 dB/mm, the 3-dB linewidths are 30 and 25 nm, respectively, and the sidelobe suppression ratios are both ∼10 dB, which can be significantly improved by cascading multiple identical AO waveguides. To change the center wavelength of the mode conversion spectra, only the acoustic frequency needs to be changed. For example, the center wavelength is moved to 1310 nm when the acoustic frequency is changed to 430 MHz, as shown in Fig. 1(g), which is calculated for the same ${P_\textrm{b}}(0 )$, $\alpha $, and L. Combined with polarization-handling components, such optical mode conversion (polarization rotation) performance of suspended 1D AO waveguides on LNOI is sufficient to implement basic AOTF functionalities.
3. Multi-band operations with tunable spectral shapes
Beyond the single-band AOTF operations elaborated above, here we further explore the possibilities of exciting modulated acoustic waves, which contain multiple frequency components, along the AO waveguide to achieve independently reconfigurable multi-band operations, with tunable time-variant spectral shapes. With an arbitrary waveform generator (AWG), an acoustic wave at a carrier frequency with simultaneous amplitude and phase modulation can be excited along the waveguide through a properly designed IDT. The modulated acoustic wave at $z = 0$ will propagate to $z = L$ according to its dispersion curve. Suppose that the group velocity dispersion is negligible within the acoustic frequency range of interest, as is the case in Fig. 1(c), where the dispersion curve is approximately linear, then the complex acoustic envelope should propagate along the waveguide unaltered, at the group velocity ${v_g}$, such that at any time instant t,
which forms a time-variant synthetic waveguide grating, leading to tunable time-variant spectral shapes. To focus on the effect of the acoustic modulation on the optical mode conversion performance, we neglect the acoustic loss, which is a valid approximation for moderate waveguide lengths $L < $ ∼0.5 mm and typical acoustic loss $\alpha < $ ∼10 dB/mm. We further assume that the modulated acoustic wave contains a finite number of discrete frequency components, such that,To demonstrate the diverse capabilities of the multi-band AOTF operations, we calculate three specific cases for our AO waveguide design and mode combination described in Section 2 with $L = $ 0.39 mm, ${v_g} = $ 2.8 km/s, ${\mathrm{\Omega }_\textrm{c}}/2\pi = $ 507 MHz. In Case 1, the carrier (${b_0} = \sqrt {0.1\; \textrm{mW}} $, $\mathrm{\Delta }{\mathrm{\Omega }_0}/2\pi = $ 0) and another frequency component (${b_1} = \sqrt {0.1\; \textrm{mW}} $, $\mathrm{\Delta }{\mathrm{\Omega }_1}/2\pi = $ 76.5 MHz) are excited, resulting in the beating of the two along the waveguide, hence the instantaneous sinusoidal power distribution $P_b{(z,0)}$ shown in Fig. 2(a). The time-variant acoustic power ${P_\textrm{b}}({z,t} )$ and envelope phase ${\phi _\textrm{b}}({z,t} )$ distributions within one temporal beating period (T = 13.1 ns) are shown in Figs. 2(b) and 2(c), respectively, illustrating the unaltered complex acoustic envelope during propagation. The corresponding instantaneous and time-variant optical mode conversion spectra are calculated and shown in Figs. 2(d), 2(e), and 2(f), including the efficiency and the phase, defined respectively as
Fig. 2. Multi-band operations with tunable spectral shapes. Case 1: Two-band operation. Instantaneous acoustic power distribution (a); time-variant acoustic power (b) and envelope phase (c) distributions within one temporal beating period (T = 13.1 ns); instantaneous optical mode conversion spectrum (d); time-variant optical mode conversion spectra, with efficiency (e) and phase (f).
Fig. 3. Multi-band operations with tunable spectral shapes. Case 2: Three-band operation. Instantaneous acoustic power distribution (a); time-variant acoustic power (b) and envelope phase (c) distributions within 100 ns; instantaneous optical mode conversion spectrum (d); time-variant optical mode conversion spectra, with efficiency (e) and phase (f).
In Case 3, five acoustic frequency components (including the carrier) with 7-MHz intervals (${b_n} = \sqrt {0.1\; \textrm{mW}} $, $\mathrm{\Delta }{\mathrm{\Omega }_n}/2\pi = $ 7n MHz, n = 1, 2, … 5) are used to synthesize an instantaneous flat-top spectral shape, as shown in Fig. 4. The beating of the five frequency components results in periodic acoustic pulses that propagate along the AO waveguide. When the pulse propagates to the center of the waveguide, the instantaneous acoustic power distribution in Fig. 4(a) resembles the square of a sinc function, leading to the desired flat-top spectra shape in Fig. 4(d), with a sidelobe suppression ratio of 7 dB, which can be significantly improved by cascading multiple identical AO waveguides. However, as the pulse propagates to the other locations along the waveguide, for example, at t = 0 and T = 143 ns, as shown in Figs. 4(b) and 4(c), the instantaneous spectra change significantly, exhibiting five distinct peaks, as shown in Figs. 4(e) and 4(f). Nevertheless, the synthesized flat-top spectrum can still be used in a stroboscopic fashion at selective time instants. The capability demonstrated here to achieve tunable time-variant spectral shapes is the most unique for AOTF operations.
Fig. 4. Multi-band operations with tunable spectral shapes. Case 3: Tunable spectral shapes. Instantaneous acoustic power distribution (a); time-variant acoustic power (b) and envelope phase (c) distributions within one temporal beating period (T = 143 ns); instantaneous optical mode conversion spectrum (d); time-variant optical mode conversion spectra, with efficiency (e) and phase (f).
4. Representative AOTF configurations
The suspended 1D AO waveguides on LNOI elaborated above constitute the key components of the proposed family of integrated AOTFs. Meanwhile, to implement complete and versatile AOTF functionalities, we propose and theoretically investigate several representative monolithic AOTF configurations, featuring different arrangements of single or cascaded identical AO waveguides connected with a complete set of ultrawide-band polarization-handling components. Drawing on our previous works [31,32], we have proposed and optimized the designs for ultrawide-band polarizers, polarization splitters/combiners and/or rotators based on monolithically integrated waveguide tapers and asymmetric directional couplers on LNOI. According to eigenmode expansion (EME) propagation simulation results, the set of polarization-handling components feature low excess loss of <0.1 dB and high extinction ratio of >30 dB across an unprecedented ultrawide bandwidth of 1.25–1.65 µm, consistent with the tuning range of the AO waveguides. However, the detailed designs of these components are out of the scope of this paper. In the following, we will theoretically demonstrate several representative AOTF configurations assuming perfect polarization-handling components.
The most compact AOTF configuration consists of a single AO waveguide connected with a polarization splitter rotator (PSR), as shown in Fig. 5(a). The output TE0 and TM0 modes from the AO waveguide are routed to the upper and lower output ports of the PSR, respectively, with the TM0 mode rotated into the TE0 mode, so that single-polarization operation can be maintained in the subsequent optical circuits, if any. Therefore, the filter spectra of the upper and lower output ports of the PSR are band-stop and band-pass, respectively, complementary to each other. Note that the TE0 mode from the PSR lower output port is Doppler-red-shifted by the acoustic frequency.
Fig. 5. Representative AOTF configurations. (a) A single AO waveguide connected with a PSR; (b) AO waveguide connected with a PS and further cascaded by a second AO waveguide and a TE0 polarizer, used as a drop filter; (c) AO waveguide connected with a PC and further cascaded by a second AO waveguide and a TE0 polarizer, used as an add filter.
To recover the Doppler shift, the PSR can be replaced with a polarization splitter (PS, a.k.a. PBS), which is further cascaded by a second AO waveguide and a TE0 polarizer, as shown in Fig. 5(b). Both AO waveguides are identical, and both IDTs are driven by the same one radio-frequency (RF) source, resulting in the mode conversion from TM0 back to TE0 with exact recovery of the Doppler shift. The TE0 polarizer is then used to remove the residue TM0 mode due to incomplete mode recovery detuned from the AOTF center wavelength. Now the AOTF configuration can be used as a drop filter, with the polarizer output port as the drop port. An add filter can be similarly configured, by replacing the PS with a polarization combiner (PC), which is simply the same PS used in the reverse way, as shown in Fig. 5(c), and the input port of the first AO waveguide becomes the add port.
Furthermore, more sophisticated functionalities can be realized with judiciously arranged drop and add filters described above. A reconfigurable multi-band add-drop filter (ADF) can be constructed by connecting the output port of a drop filter to the input port of an add filter, as shown in Fig. 6(a). In such an elegant configuration, an arbitrary subset of the input optical bands can be dropped and added without wavelength-(de)multiplexing components and/or switch arrays. In addition, if the TE0 mode from the output port of the drop filter is discarded, as shown in Fig. 6(b), then the configuration becomes a “unit” band-pass AOTF that can be directly cascaded multiple times to obtain narrowed filter linewidths and suppressed sidelobes. Again, all the AO waveguides are identical, and all the IDTs can be driven by the same one RF source in such a scalable cascade. Based on the Case 1 of the multi-band operation detailed in Fig. 2, the two-band-pass filter spectra of a single unit filter and a cascade of four unit filters are shown in Fig. 6(c), with center wavelengths of 1310 nm and 1550 nm. For a single unit filter with only one pair of cascaded AO waveguides, a linewidth of ∼16 nm (∼8 nm), a sidelobe suppression ratio of ∼17 dB (∼17 dB), and theoretically no excess loss at the center wavelength of 1550 nm (1310 nm) have been achieved. For the cascade of four unit filters, the linewidth and the sidelobe suppression ratio become ∼8 nm (∼4 nm) and ∼75 dB (∼75 dB) for the center wavelength of 1550 nm (1310 nm), respectively. Note that the linewidth is inversely proportional to the square root of the cascade size. Furthermore, based on the calculations in Fig. 1(g), we demonstrate the ultrawide tuning range of the band-pass filter spectra of a cascade of four unit filters in Fig. 6(d). For acoustic frequencies of 417, 437, 457, 477, 497, and 517 MHz, the corresponding center wavelengths are 1281, 1325, 1375, 1432, 1503, and 1625 nm, respectively. For both Figs. 6(c) and 6(d), typical acoustic loss of ∼10 dB/mm is assumed.
Fig. 6. Representative AOTF functionalities. (a) A reconfigurable multi-band ADF, constructed by connecting the output port of a drop filter to the input port of an add filter; (b) drop filter cascaded multiple times to obtain narrowed filter linewidths and suppressed sidelobes; (c) two-band-pass filter spectra of a single unit filter and a cascade of four unit filters with center wavelengths of 1310 and 1550 nm; (d) ultrawide tuning range of the band-pass filter spectra of a cascade of four unit filters.
The AOTF configurations with cascaded AO waveguides feature sub-mW or mW power consumption, which scales linearly with the number of the AO waveguides. Meanwhile, they also feature the sub-µs tuning speed and the hundred-nm tuning ranges of the center wavelength, inherited from those of the single AO waveguides. Combined with the capabilities of independently reconfigurable multi-band operations, with tunable time-variant spectral shapes, the present integrated AOTFs are promising for a diverse spectrum of applications.
5. Discussion and conclusion
The theoretical investigations above demonstrate the unique characteristics and versatile capabilities of the proposed family of integrated AOTFs based on thin-film LN waveguides. The generic AOTF designs and performance investigated above can be further tailored for diverse applications. To meet the requirements of WDM optical communications and interconnects, the dispersion curves of the acoustic and optical modes can be finetuned by engineering the AO waveguide design and mode combination. More specifically, the AO waveguide cross-sectional geometry and its propagation direction with respect to the LN crystal orientation can be varied, and the different acoustic and optical modes can be employed. Within the desired wavelength tuning range, the dependence of the phase-matched acoustic frequency on the optical wavelength, such as the curve in Fig. 1(e), should be preferably linear to ensure constant filter linewidths for all the wavelength channels. In addition, to achieve narrower linewidths, the slope of this curve should be as steep as possible, which translates to a large group velocity mismatch between the two optical modes. In addition to dispersion engineering, more cascaded unit filters may be required to achieve the sub-nm linewidths for dense WDM (DWDM).
For spectral analysis applications, the dispersion engineering should aim at shifting the wavelength tuning range to the visible or mid-infrared spectrum. Furthermore, multi-band operations with tunable spectral shapes are especially interesting for mid-infrared spectral analysis, to achieve customizable filter spectra that match certain molecular fingerprints. As demonstrated in Fig. 4, stroboscopic operation may be required for such a spectral analysis scheme, as the desired filter spectra may appear only at selective time instants. Alternatively, the deterministically tunable and time-variant spectral shapes are naturally suitable for sparse spectrum reconstruction based on random filters [33].
Finally, we discuss the experimental feasibility of the proposed suspended AO waveguides and the family of integrated AOTFs. First, the fabrication of long and thin suspended AO waveguides has been demonstrated with XeF2 vapor under-cut processes [26,28]. Specifically, in [26] an LNOI suspended waveguide that is 250 µm long, 1.25 µm wide and 250 nm thick has been released from the silicon substrate, while in [28], an AlN suspended waveguide that is 500 µm long, 800 nm wide and 330 nm thick has been released. Unfortunately, HF vapor under-cut processes cannot be used for LNOI because it appears that HF vapor can damage the LN surface, resulting in nonvolatile byproducts that are densely scattered on the surface. For suspended structures on LNOI, nevertheless, hydrofluoric (HF) buffered oxide etch (BOE) solution can be used for the under-cut process [17], followed by a critical-point drying (CPD) process to avoid the stiction problem. Once suspended, the AO waveguides will be subjected to much more significant thermomechanical excitations, which roughly fall into the following two categories. The thermomechanical displacement noise of the doubly-clamped-beam modes of the waveguides, generally in the kHz and lower MHz frequency ranges, are strongly damped in air. Meanwhile, the thermally excited acoustic waveguide modes, generally in the higher MHz and GHz frequency ranges, are negligible compared with the electromechanically excited acoustic waveguide modes. Therefore, optomechanical effects due to thermomechanical excitations are negligible for the AO waveguides and AOTF operations, which is also evident from the pioneering experimental results [26,28]. Furthermore, the ASW IDT and the taper structure design should be further optimized, so as to provide sufficient transduction efficiency and RF power-handling capabilities for the superior performance of the proposed suspended AO waveguides. Otherwise, mechanical nonlinearity or even structural failure may occur before sufficient acoustic power can be excited into the suspended AO waveguide for complete optical mode conversion [26].
In conclusion, we have proposed and theoretically investigated an innovative family of integrated AOTFs with suspended 1D AO waveguides in the collinear configuration on LNOI. The AO waveguides perform as tunable wavelength-selective narrow-band polarization rotators, where highly efficient conversion between co-propagating TE0 and TM0 modes is enabled by the torsional acoustic A1 (SV1) mode. The AOTF center wavelength can be continuously tuned across an ultrawide band between 1.25–1.65 µm, by tuning the acoustic frequency between 380–520 MHz. We have further explored the possibilities of exciting modulated acoustic waves, which contain multiple frequency components, along the AO waveguide to achieve independently reconfigurable multi-band operations, with tunable time-variant spectral shapes. To implement complete and versatile AOTF functionalities, we have proposed and theoretically investigated several representative monolithic AOTF configurations, featuring different arrangements of single or cascaded identical AO waveguides connected with a complete set of ultrawide-band polarization-handling components. For the present AOTF, a linewidth of ∼16 nm (∼8 nm), a sidelobe suppression ratio of ∼20 dB (∼20 dB), and theoretically no excess loss at the center wavelength of 1550 nm (1310 nm) have been achieved. For four pairs of cascaded AO waveguides, the linewidth and the sidelobe suppression ratio become ∼8 nm (∼4 nm) and ∼75 dB (∼75 dB) for the center wavelength of 1550 nm (1310 nm), respectively. The AOTF configurations with cascaded AO waveguides feature sub-mW or mW power consumption, sub-µs tuning speed, and hundred-nm tuning ranges of the center wavelength. Combined with the capabilities of independently reconfigurable multi-band operations, with tunable time-variant spectral shapes, the present integrated AOTFs are promising for a diverse spectrum of applications.
Funding
National Key Research and Development Program of China (2018YFB2200200, 2018YFB2200201); National Science Fund for Distinguished Young Scholars (61725503); National Natural Science Foundation of China (61961146003, 91950205); Primary Research and Development Plan of Zhejiang Province (2021C01199); Leading Innovative and Entrepreneur Team Introduction Program of Zhejiang (2021R01001); Natural Science Foundation of Zhejiang Province (LD19F050001, LZ18F050001, LZ22F050006); Fundamental Research Funds for the Central Universities (2021QNA5002); Startup Foundation for Hundred-Talent Program of Zhejiang University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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