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Abstract
Silicon photonics leverages mature semiconductor technology to produce cost-effective and high-performance components for various applications in data centers, artificial intelligence, and quantum computing. While the geometry of photonic integrated circuits can be characterized by existing means, their optimal and accurate performance requires detailed characterization of the light propagating within them. Here we demonstrate the first, to our knowledge, direct visualization of the light as it travels inside photonic integrated circuits. We employ the natural nonlinear optical properties of silicon to directly map the electric field of the waves guided inside the integrated circuits, characterizing waveguides and multimode splitters while extracting various parameters of the device—all in real-time and in a noninvasive manner. Our approach for visualizing light inside photonic circuits is the only solution directly providing such information without any overhead or penalty, potentially making it a crucial component for the characterization of photonic circuitry, toward their improved design, fabrication, and optimization.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Silicon-based integrated photonics has evolved into a mature technology with a myriad of applications [1], including telecommunications [2,3], high-performance computing [4,5], machine learning [6,7], ranging [8,9], biomedical imaging [10], sensing [11], and quantum computing [12,13]. As this technology advances, device designs become increasingly intricate, with an ever-increasing number of functions integrated onto a single chip. Silicon photonics takes advantage of the same manufacturing techniques used for decades in integrated circuit foundries to produce photonic devices with high precision and at a low cost. However, despite high-resolution lithographic techniques that enable the accurate fabrication of designed photonic structures, adequate characterization tools are still lacking to assess the functionality of the fabricated devices [14]. Defects and inaccuracies are challenging to model and inspect due to their small scale and irregularity [15] hence necessitating new means and approaches for characterizing the flow of light inside integrated photonic circuits.
Accessing and visualizing light propagation in waveguide-based devices is a challenging task. Current state-of-the-art characterization tools include far-field methods, such as far-field scattering microscopy, which rely on intrinsic scattering from the device, either due to periodicity (e.g., via coupling gratings [16], photonic crystals [17], etc.) or by defects [18]. Both approaches include inevitable perturbation of the guided modes that degrade the device performance and are not scalable, i.e., can only visualize light at the location of the defect. A transparent photodetector [19] provides a readout system integrated onto the Si photonic chip to monitor the power of light propagating in waveguide structures. While minimally perturbing the light field, it also relies on adding an electrical circuit to specific points on the chip, limiting again the scalability and the ability to integrate the device with existing photonic systems.
Conversely, near-field microscopy methods offer subwavelength imaging capabilities by detecting the evanescent field of the guided waves, using a scanning tip [20–22] or an electron beam [23–25]. However, these approaches require long scanning or integration times, and are unsuitable for most photonic circuits, which are typically covered by a thick protective layer that prevents the near-field probe from reaching the measured structure. Ultrafast photomodulation spectroscopy was suggested as a potential alternative to near-field microscopy [26], introducing optical pumping that locally alters the refractive index of silicon. While enabling the retrieval of a time- and space-dependent photomodulation map by monitoring the device’s output, it still necessitates scanning, is limited in resolution by the pump focal strength and—most importantly—cannot provide such a map when the device is faulty.
Fig. 1. (a) Schematics of the experimental setup for imaging propagating waves within photonic devices. 1550 nm signal pulses (orange) are grating-coupled into a silicon-on-insulator (SOI) waveguide, while 780 nm pump pulses (red) are focused onto the device using a long-working distance objective. When the two pulses overlap in time and space, a nonlinear wave is generated (green), separated from the pump by a dichroic mirror (DM) and collected by a standard CMOS camera. P, F, and $\lambda /{2}$ represent linear polarizer, spectral filter, and $\lambda /{2}$ wave plate, respectively. (b) Axes definitions and the propagation directions of the pump beam (normal incidence), signal beam (guided along the waveguide), and the nonlinearly generated beam (reflected at an angle according to the wave vector of the signal wave). (c) Cross section of the single waveguide.
Here, we introduce and experimentally demonstrate a real-time noninvasive approach for visualizing light inside silicon photonic devices. Our approach harnesses the high intrinsic optical nonlinearity of silicon [27–30] and the tight confinement of light in the Si waveguide for direct vector-field mapping of the guided modes. This is facilitated by the nonlinear wave mixing between the telecom-wavelength signal traveling in the device and a free-space pump beam illuminating the waveguide. We monitor the wave propagation inside waveguides and multimode beam splitters, while extracting their effective index and modal content. This simple-to-use approach can be readily applied to cavities and active components such as modulators and for further analysis such as power splitting ratio, polarimetry, group index and power monitoring of the loss mechanisms. All these without inducing defects and fabrication overhead.
2. RESULTS
The principle of operation is shown in Fig. 1. We employ the nonlinear process of partially degenerate four-wave mixing to convey the subwavelength information at telecom wavelengths into propagating waves in visible wavelengths, readily detectable by conventional means [31]. In this process, a photon is produced via the interaction between two pump photons, impinging the sample at normal incidence, and one photon of the guided wave within the photonic device. The emitted nonlinear field sustains energy conservation as well as momentum conservation along the transverse (in-plane) direction:
where the subscripts “pump,” “signal,” and “nl” represent the free-space pump, propagating wave within the device, and the nonlinearly generated free-space waves, respectively. Equation (1b) shows that a normally incident pump, corresponding to $| {{K_{{\rm pump},\|}}} | = 0$, generates a nonlinear transverse wave vector equal to that of the signal, but at the opposite direction in the ${k_x} - {k_z}$ plane. As a result, the nonlinear wave vector distribution reproduces the signal, but at a frequency ${\omega _{\rm{nl}}}$. When the magnitude of the in-plane wave vector of the nonlinearly generated field ${K_{{\rm nl},\|}}$ is smaller than its free-space wavenumber ${K_{{\rm nl},0}}$, it radiates to the far field [see Fig. 1(b)]. The results below are obtained using 140 fs pulses with a mean pump wavelength of ${\lambda _{\rm{pump}}} = 780\;{\rm nm} $ and a mean telecom signal wavelength of ${\lambda _{\rm{signal}}} = 1550\;{\rm nm} $, resulting in a mean nonlinear wave of ${\lambda _{\rm{nl}}} = 521\;{\rm nm} $ which is collected by a 0.9 NA objective and can easily be detected by a standard CMOS camera. The short pulse duration reduces significantly the likelihood of thermal effects that may affect the signal in the Si waveguides.We leverage this approach for direct mapping of the light inside silicon photonic devices fabricated in a standard silicon-on-insulator process. Namely, the device we characterize was not designed in any way for this demonstration but for unrelated purpose (specifically for biomedical imaging [10]). We first map the guided mode as it travels along a standard integrated linear waveguide, 450 nm wide and 220 nm high. The electric field of the guided mode is obtained by illuminating the pump pulse at a specific location on the waveguide while synchronizing it to overlap in space and time with the signal pulse. The field mapping is acquired by imaging the device’s plane, while collecting only the nonlinearly generated radiation. Additional white-light illumination further allows to visualize the waveguide structure simultaneously with the guided wave within. The electric field of normally incident pump beam can be assumed mostly in-plane, i.e., ${E_y}^{\rm{pump}} \ll {E_x}^{\rm{pump}},{E_z}^{\rm{pump}}$, where $x {\text -} z$ is the plane of the integrated circuit and $y$ is normal to the plane [see Fig. 1(b)]. Solving the nonlinear interaction equations for a linearly polarized pump yields a nonlinear field that replicates the same linear component of the signal electric field [31]. Therefore, by toggling the pump polarization, we obtain a selective imaging of the mapped electric field component of the signal. Figures 2(a) and 2(b) show the transverse (“x”) component of the guided mode, acquired by polarizing the pump beam along the same direction. Likewise, a pump polarized along the “$z$” direction extracts the longitudinal component [Figs. 2(c) and 2(d)]. Evidently, the opposite symmetry of guided waves—symmetric transverse component and antisymmetric longitudinal component—is clearly conveyed with excellent agreement with the simulation results, obtained by calculating the signal field distribution inside the waveguide using FDTD multiplied twice by the Gaussian profile of the pump beam (see Section 4) [Figs. 2(b) and 2(d)].
Fig. 2. Polarization-selective imaging of the guided mode. (a), (b) Transverse (“$x$”) component—experiment and simulation, respectively. A zoomed-in area of the experimental result is shown below (b). (c), (d) Longitudinal (“$z$”) component—experiment and simulation, respectively. A zoomed-in area of the experimental result is shown below (d).
Note that all images shown in Fig. 2 are acquired without scanning and the imaged mode area is dictated by the size of the pump beam, which was 8 µm full width at half-maximum (FWHM). This limitation stems from three physical parameters: the field of view (FOV) of the objective lens, the laser power, and the pulse duration. In the current setup, the FOV was ${\sim}{30}\;{\unicode{x00B5}{\rm m}}$ and the pulse duration multiplied by the speed of light in the sample was ${\sim}{25}\;{\unicode{x00B5}{\rm m}}$. The 8 µm limitation was, therefore, a result of the pump beam size which was chosen according to the laser power. Using higher power in the pump laser with longer pulse durations will allow an ultimate imaging area of tens of micrometers while keeping the current resolution but might incur added heating. Alternatively, a larger FOV, up to a wafer size, is possible using a lower numerical aperture (NA) lens, while compromising on the resolution.
The simplicity of the imaging system requires only minor adjustments of the imaging system for acquisition of the reciprocal (Fourier) plane, i.e., its spatial frequencies distribution across the ${k_x} - {k_z}$ plane. In particular, the ${k_z}$ component corresponds to the propagation constant of the mode, $\beta$, which determines the phase velocity and phase accumulation along the propagation direction. This constant is best represented by the effective index—a dimensionless quantity representing the ratio between $\beta$ and the free-space wavenumber ${k_{0.}}$ White-light illumination allows us to visualize the NA of the optical system and the maximal wave vector of ${k_{{\max}}} = \frac{{2\pi}}{{{\lambda _{{NL}}}}} \cdot {\rm NA} = \frac{{2\pi}}{{521\;{\rm nm}}} \cdot 0.9$ for the nonlinearly emitted wavelength of 521 nm.
Leveraging this information, we can extract the effective index of the mode, as portrayed in Fig. 3. The effective index is the ratio between the propagation constant and the free-space wavenumber at the same wavelength. The effective index of the guided mode is, therefore,
Fig. 3. Fourier-space imaging and extraction of the wave vector components. (a)–(c) Normally incident pump. The phase-matching condition results in a nonlinearly generated wave vector with a similar in-plane component as that of the propagation constant of the guided mode. (a) Schematic description. (b) Fourier-space image of the nonlinearly generated signal (bright line) on the background of the system’s NA. The red dashed circle marks the maximal wave vector white-light illumination, spectrally filtered about 521 nm wavelength. The ratio between the distance of the bright line from the center to the radius of the circle is used to extract the effective index. (c) The esulting real-space image, representing the field distribution of the guided mode. (d)–(f) Angled-incident pump. The phase-matching condition results in a nonlinearly generated wave vector with smaller in-plane “$z$” component compared to that of the guided mode. (d) Schematic description (e) Consequently, the entire distribution along the “$x$” direction can be captured by the system’s NA. The shift between the red circle and the full circle represents the difference in the in-plane “$z$” component of the nonlinearly generated beam and the propagation constant of the guided mode. (f) The field distribution now looks much cleaner as the larger wave vector component along “$x$” is not cut off.
For normally incident pump [see the sketch in Fig. 3(a)] the ratio $\frac{{{k_z}}}{{{k_{{\max}}}}}$ can be experimentally extracted from the Fourier-space measurement, through the location of the nonlinear signal in K-space. Figure 3(b) depicts the imaged Fourier plane, representing the wave vector distribution. Notably, the ratio between the normalized ${k_z}$ as depicted from the nonlinear signal, marked as “r,” and the radius of the circle, representing the normalized ${k_{{\max}}}$ marked as “R” is $\frac{r}{R} = \frac{{156}}{{177}}$. Substituting ${k_{{\max}}} = 0.9\frac{{2\pi}}{{521\;{\rm nm}}}$ and $k_{{\rm sig}}^0 = \frac{{2\pi}}{{1550\;{\rm nm}}}$ we obtain
While the numerical aperture of the system herein is sufficiently large to contain $\beta$, it fails to capture the entire span of the wave vectors along the “$x$” direction, resulting in partial loss of the information about the field distribution [Fig. 3(c)], manifested as additional lobes due to this cut-off. This deficiency can be resolved by tilting the pump beam at an angle [Fig. 3(d)], resulting in a shift of the wave vector distribution in the “$z$” direction, such that it can be fully captured by the NA [Fig. 3(e)]. This allows us to determine ${k_x}$ by measuring the ratio between ${k_x}$ and ${k_z}$. Substituting this ratio, we obtain ${k_x} = \frac{{110}}{{156}} \cdot {k_z} = 6.74 \cdot {{\unicode{x00B5}{\rm m}}^{- 1}}$. This also provides the value of ${k_y}$ by the dispersion relations $k_x^2 + k_y^2 + k_z^2 = {\varepsilon _{{\rm silicon}}}k_0^2$ resulting in ${k_y} = \sqrt {{\varepsilon _{{\rm silicon}}}k_0^2 - k_x^2 - k_z^2} \approx 8 \cdot {{\unicode{x00B5}{\rm m}}^{- 1}}$.
A. Imaging the Function of a Multimode Interference Splitter
Our approach is further capable of characterizing highly complex photonic devices. We provide here a study of a multimode interferometric (MMI) [32,33] splitter which is used for swift splitting a guided mode into several channels by propagation through a wide, multimode waveguide whose boundary conditions are engineered so as to create constructive interference at the outputs. Figure 4 presents a characterization of the light propagation inside the MMI at various locations, providing the ability to analyze its performance. We visualize the evolution of the light within the device by directing the pump to various regions, monitoring how its interference pattern evolves until forming two nearly equal fields at its output. Using this approach, we can assess the operational design of the MMI, for example, how equal is the splitting, whether it suffers losses, where and why. A Visualization 1 shows smooth tracking over the light evolution inside the device, achieved by continuously moving the device with respect to the pump beam. The pulse extension over 25 µm allowed for smooth scanning without the need to further synchronize the signal and pump pulses. Note that this movie is taken in real time and does not provide a temporal resolution as shown in free-electron-based near-field imaging [20–23]. This approach, however, can be readily adapted for such measurement, necessitating only integration with shorter laser pulses.
Fig. 4. Imaging light within the MMI splitter. (a) Optical imaging of the MMI device. (b) Direct mapping of the light evolution inside an MMI device. The figure comprises exposures of seven different locations along the device, stitched together to track the evolution in the MMI. The rightmost exposure is at the single-waveguide input while the leftmost is of the two waveguides. (c) Zoom-in of (b). (d) Simulation results on a similar scale to (c). (b)–(d) show the intensity of the transverse electric field. Evidently, the experimental results are in excellent agreement with the simulation of light evolution in such a system.
3. DISCUSSION
In conclusion, we developed a characterization tool for integrated photonic circuits, which occupy an ever-increasing volume in the semiconductor industry. Our scheme is based on the intrinsic nonlinearity of silicon or other semiconductors, e.g., ${{\rm Si}_2}{{\rm N}_3}$, GaAs, InP, ${{\rm LiNbO}_3}$, etc., and hence, does not require any changes to the devices that could impair their performance. Namely, neither additional coupling gratings or diffusers for verification, nor removal of oxide protective layers. As such, it has the potential to drastically decrease the cost and complexity of integrated photonic circuit characterization, while increasing their availability.
Our method is designed to be straightforward and easily accessible, providing comprehensive information essential for characterizing photonic circuit operation. It enables the mapping of light propagation within integrated circuits, capturing details such as its shape, phase, and group velocity. Additionally, it allows for the determination of the modal composition, including the ratio between various field components. With our characterization tool, it becomes possible to identify key features within the photonic circuit. Other than revealing the interference pattern within MMI, shown above, it can accurately detect enhancements occurring inside resonators, visualize the operation of active components such as modulators and lasers, and study in new ways nonlinear phenomena in integrated circuits such as frequency combs and solitons. These insights are invaluable for understanding the behavior and performance of integrated circuits, aiding in their design, optimization, and functionalities.
4. METHODS
A. Optical Setup
We used a beam splitter to split the output of a mode-locked Ti:sapphire laser (Chameleon Ultra II, 140 fs pulses, repetition rate of 80 MHz), to a photonic pump at a wavelength of 780 [nm] and a signal beam at 1550 [nm] (converted by an optical parametric oscillator; Chameleon). To enable temporal phase matching between the pump and signal pulses (i.e., both pulses hit at the same time in the device), we used a variable delay line that controls the pump pulse arrival time. The polarization states of the pump beam were determined by a polarizer (Thorlabs, LPVIS050-MP2) adjacent to the $\lambda/{2}$ (Thorlabs, WPH10M-808) wave plate. To enable a bigger spot size in the focal plane of the objective (active nonlinear area with of ${\sim}\;{8}\;{\unicode{x00B5}{\rm m}}$ FWHM), we used a telescopic system consisting of two lenses ($F = {400}\;{\rm mm}$ and $F = {50}\;{\rm mm}$). The average power of the pump beam was ${\sim}{50}\;{\rm mW}$ before the objective (100X Nikon CFI Plan Achromat Infinity Corrected, NA 0.9, working distance of 1 mm).
The free-space signal beam was injected into the fiber by a fiber collimator, and from there to a coupling grating, which inserted the signal into the waveguide. When the device is illuminated by the pump beam, and it temporarily and locally overlaps with the signal beam, a nonlinear wave is generated. This wave is separated from the pump beam using a dichroic mirror (Thorlabs, DMLP550R). The camera used to detect the images in all the experiments was a standard CMOS camera (DCC1545M, Thorlabs).
B. Simulations
Commercial full-wave finite-difference time-domain software, Ansys Lumerical FDTD Solutions, was employed to conduct the simulations, enabling analysis of the field distribution within the waveguide. Additionally, a Gaussian beam with a FWHM of 8 µm was multiplied with the results using MATLAB, to simulate the interaction between the signal and the pump [Figs. 2(b) and 2(d)]. For the effective index calculation and the MMI distribution, we employed Ansys Lumerical Mode finite difference.
C. Sample Fabrication
The photonic chip was fabricated using CMOS technology at IMEC (Si-Photonics Passives+). The silicon photonics layer is 220 nm thick with a width of 450 nm for a single-mode waveguide. The waveguides are buried in oxide cladding approximately 2 µm in each direction.
Acknowledgment
Author contributions: G. B. and S. T. conceived the research; M. I., K. C., and J. K. conducted the experiments; M. I., G. B., K. C., and S. T. analyzed the results; Y. H. and A. R. provided the silicon photonics chip. M. I. performed the numerical simulations. All authors contributed to writing the paper. S. T. acknowledges support by the Adams Fellowship Program of the Israel Academy of Science and Humanities.
Disclosures
The authors declare no conflicts of interest.
Data availability
All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.
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