
- Photonics Research
- Vol. 13, Issue 6, 1699 (2025)
Abstract
1. INTRODUCTION
Light is one of the key ingredients in the evolution of modern technology. An important contribution to this progress is made by the field of integrated photonics, which is currently undergoing rapid development [1]. Integrated photonics offers numerous substantial advantages, first and foremost its immense potential for miniaturization, cost-effectiveness at large scales, and the ability to integrate complex optical functionalities on a single chip [2,3]. These developments have led to the widespread adoption of integrated photonics in various applications, including light sensing. In this regard, one key aspect of interest is phase-sensitive detection, which is also the central focus of this manuscript. Phase-sensitive detection of light has many applications, including but not limited to methods of microscopy [4] such as optical coherence tomography [5], optical communication [6,7], and the characterization of optical elements [8] ranging from simple contact lenses to cutting-edge high-NA microscope objectives [9] and EUV-lithography optics [10,11].
With a few exceptions, such as Shack-Hartmann wavefront sensors [12], optical phase measurements predominantly rely on interferometry [13]. Methods are generally classified as either reference-free or reference-based, with the latter requiring an external reference signal that is coherent with the light being measured [14,15]. While reference-based methods offer benefits, they are not always applicable, and a detailed comparison is beyond the scope of this manuscript. We will focus exclusively on external-reference-free methods. In recent years, various integrated-photonics-based approaches have been developed for phase-resolved detection without the need for an external reference. One approach utilizes a tree-like mesh structure of Mach-Zehnder interferometers, operable by power minimization [16]—easy to implement but requiring precise design specifications. Alternatively, the photonic mesh throughput can be analyzed numerically [17], accommodating imperfect optical elements at the cost of computationally expensive data evaluation. While both are promising, their sequential measuring routine is limited to light fields with slow temporal variations. Other methods use a pairwise measurement scheme, which reduces complexity and enables fast readout times. For instance, Ref. [18] describes a narrow-band phase-only detection scheme. Notably, all methods described above were realized in the near-infrared spectral range. While integrated photonics for visible light has existed for a long time, it faces challenges, particularly with tunable phase shifters [19]. In addition, only recent advancements in reducing waveguide losses have made high-performance, large-scale photonic integrated circuits operating in the visible spectral range feasible [20,21].
In this manuscript, we propose and experimentally verify a passive silicon nitride (SiN) photonic integrated circuit for the phase-resolved detection of visible light. Fundamentally, these circuits utilize a fixed set of on-chip interferometers, whose output-intensity-only measurements allow retrieving the intensity and relative phase of the incident light. The photonic chips route the light in a fully passive manner, eliminating the need for complex control electronics and enabling true single-shot measurements, with speed being only limited by the detector measuring the output intensities of the chip. The data evaluation relies on a versatile calibration procedure that can even handle large deviations of chip elements from their design parameters, including the passive phase shifters. As a result, even though every element of the chip is subject to chromatic dispersion, it can be accounted for through calibration, making the approach suitable for application across different wavelengths within the visible spectrum. Furthermore, the method employs a pairwise external-reference-free measurement scheme, offering the potential for scaling to larger detection arrays.
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2. SENSOR DESIGN AND MEASUREMENT PRINCIPLE
We start by introducing the actual integrated photonic sensor layout and the underlying design and measurement principle. A photonic chip with two inputs is shown in Fig. 1 (inputs marked by red circles). This chip was designed such that it ultimately enables retrieval of intensity and relative phase of a light field illuminating the input interface, by measuring only the intensities at the outputs (highlighted in green in Fig. 1) of the photonic circuit. The input and output free-space-to-chip interface is realized via standard grating couplers [22]. At the input, these gratings couple the
Figure 1.Optical microscopy image of the chip. Free-space light is coupled into waveguides by means of two grating couplers. Subsequently, the signal is processed by passive on-chip interferometers. The on-chip interferometers consist of passive phase shifters and Y-branch combiners. In each interferometer, the phase shifters introduce a fixed phase difference between the waveguide modes. This is achieved by asymmetrically varying the waveguide widths in the two waveguides before the modes are combined in the Y-branch. Finally, the processed light is coupled out of the chip via grating couplers again. To simplify experiments, the chip layout was designed with some distances intentionally increased, resulting in a total footprint of
On the chip, each input signal propagating along a waveguide connected to the input grating coupler is evenly split and routed to four separate waveguides using Y-branch splitters [23]. One of the four waveguides per input is then routed directly to an output (labeled
As previously mentioned, the intensities can easily be determined directly from the outputs
We can now rearrange this equation to obtain an expression for the relative phase:
The final challenge we need to address in determining the phase of the free-space light from the output signals is the fact that Eq. (5) provides two possible solutions. To identify the correct sign of the inverse trigonometric function, additional measurements need to be performed with a known relative phase shift applied to the input signals of the interferometers. In our case, this is done through the use of multiple interferometers with fixed phase shifters. The correct solution can then be found as the one that is consistent across the different interferometers. This phase reconstruction technique is often used in signal processing and is known as I/Q—or in-phase and quadrature technique [25]. Theoretically, it would suffice to have two interferometers with a non-zero difference in their preceding phase shifts. We, however, opt for three interferometers, as this approach adds redundancy to the system and enhances measurement accuracy. Furthermore, the phase shifters are designed to introduce a relative phase difference of
3. SETUP
To investigate the proposed photonic structure, an experimental setup is required that allows for controlled illumination of the input section of the photonic circuit while simultaneously monitoring the intensity of the out-coupled light at the output section. A schematic of the key components of the experimental setup is shown in Fig. 2.
Figure 2.Illustration of the experimental setup. A Gaussian beam is weakly focused on the input section of the chip structure. The light is coupled to waveguide modes and subsequently processed by the on-chip architecture. The transmitted intensities of the outputs are monitored by means of an imaging system, which consists of a camera and an objective.
For the experiments, we analyze light emitted by a fiber coupled laser diode (center wavelength of
4. RESULTS AND DISCUSSION
After successfully calibrating the photonic chip using the procedure described in Appendix A, it can be used to measure the intensity and phase of unknown free-space light fields that impinge on the input grating couplers of the system. This solely requires a single intensity measurement at the outputs of the chip structure. The relative intensity at the two inputs is directly obtained using Eqs. (1) and (2). To determine the relative phase, Eq. (5) is used. As previously mentioned, each interferometer provides two solutions. Theoretically, one could now search for a common solution for all interferometers. In experiments, however, it is not realistic to obtain exactly the same solution at the different interferometers. Instead, one searches for the solutions of the interferometers that are closest to each other, e.g., by selecting the combination of retrieved phase values that produces the smallest standard deviation. The average of the selected phase values of the individual interferometers is finally used as the measured relative phase.
To demonstrate the intensity and phase measurement, we scan the chip through weakly focused Gaussian beams of different parameters. These scan measurements are very well suited to illustrate the function of the sensor, since both the relative phase and the intensity of the input signals change for different positions of the beam. The output intensities of the chip are recorded at each scan position individually. From the recorded output signals, the intensity and relative phases at the inputs are determined. Figure 3(a) shows a scan measurement of a Gaussian beam featuring a
Figure 3.Relative intensity and phase of a Gaussian beam as a function of the relative shift of the beam center with respect to the center of the input of the chip. (a) Measurements are performed with a beam at the design wavelength of the waveguides,
Figure 4.Relative phase of Gaussian beams of different wavefront curvatures
Note that for all the results presented, each amplitude and phase value are derived from individual measurements. The data is plotted with a common
To showcase the broadband capabilities of the presented chip design, scan measurements of non-collimated Gaussian beams were performed at a wavelength of
5. FIRST STEPS TOWARDS LARGER STRUCTURES
After having demonstrated experimentally the capabilities of the passive photonic circuit with respect to phase and intensity measurements, we now discuss a chip architecture featuring more input pixels and show corresponding measurement results. Multipixel architectures enable extended functionality, allowing the extraction of substantial information about the incident light field even with a very limited number of pixels. To showcase the extended capabilities of multipixel architectures, we designed and fabricated a photonic chip featuring a five-pixel input interface. A microscope image of the chip is shown in Fig. 5(a). Again, focusing grating couplers are used as free-space interfaces. The five couplers are arranged in a square, with four pixels at the corners and a fifth in the center. Each of the corner pixels is connected to the central pixel using a phase and intensity measuring unit, similar to the on-chip architecture discussed earlier. The pairwise phase and intensity measurements in the five-pixel chip follow the same principles as the previously discussed two-pixel architectures. This similarity allows the established calibration method to be applied again without any conceptual modifications. Moreover, this specific pixel arrangement not only facilitates the measurement of the relative phase and intensity between the corner pixels and the central pixel, but also enables the reconstruction of the parameters of a paraxial Gaussian beam through a single-shot measurement of the output intensities. A detailed description of the reconstruction of the beam parameters from measured intensity and phase data is provided in Appendix B.
Figure 5.(a) Optical microscope image of the chip featuring a five-pixel input interface for demonstration of scalability. The input interface consists of five grating couplers functioning as input pixels, arranged in a square configuration with four corner pixels and one central pixel. The on-chip architecture is designed such that each corner pixel is connected to the central pixel via a phase and intensity measurement unit. This design facilitates the complete characterization of a Gaussian beam and its parameters through a single-shot intensity measurement at the outputs. The chip layout was designed to simplify experiments, with some distances intentionally increased, resulting in a total footprint of
Figure 5(b) shows retrieved parameters of a Gaussian beam featuring a
6. CONCLUSION
A photonic integrated circuit capable of spatially resolving phase and intensity of visible free-space light has been proposed and experimentally demonstrated. The chip utilizes a fixed set of passive on-chip interferometers, whose output intensity measurements enable the retrieval of the intensity and relative phase information of the incident light field. The capabilities of the circuit have been demonstrated through scan measurements of uncollimated Gaussian beams of varying parameters. Additionally, the potential for broadband application of the structure has been showcased through measurements conducted at different wavelengths, specifically
Notably, recent advancements in integrated photonics could be incorporated into the presented chip design to enhance functionality and integration. Potential modifications include a more expansive and generic input interface, polarization splitting grating couplers [26,27] for resolving also light’s polarization, and on-chip photodiodes [28].
The presented approach and the actual integrated photonic system constitute a powerful, versatile, and small-footprint addition to the existing toolboxes of light field metrology.
Acknowledgment
Acknowledgment. The financial support by the Austrian Federal Ministry of Labor and Economy, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association is gratefully acknowledged.
APPENDIX A: CALIBRATION OF THE CHIP
Before conducting measurements, it is essential to determine all the unknown parameters of the chip elements through a precise calibration procedure. The calibration is based on illumination of the chip with known light fields; the output of the chip then provides information about the behavior of the chip components. From this information, we determine proportionality coefficients of the form
In the first step, we determine the amplitude of
In the second step, we aim to determine the phase information of the proportionality coefficients. This is done by illuminating the input section of the chip by means of a light field of known amplitude and phase distribution. All inputs are now exposed simultaneously, allowing light to enter both input arms of the on-chip interferometers. The relative phase of the waveguide signals determines the output intensity of the interferometers. The phase distribution of the input light is known, allowing the output signals from the interferometers to reveal the additional relative phase shifts introduced by the chip. However, measuring just a single set of amplitude and phase scenarios at the input pixels is not enough to determine the phase shifts accurately, as there is an ambiguity in the sign when extracting the phase from the interference signal. Theoretically, this issue can be resolved by conducting at least two measurements with different scenarios at the inputs. In practice, many more than two measurement points are collected, primarily to enhance the accuracy of the calibration and to account for the additional unknown parameters that need to be determined in this process. There are a variety of options for generating different scenarios at the inputs. The option of our choice is to scan a non-collimated Gaussian beam, as it features a curvature in its phase front, and therefore provides different input phases for different scan positions. This allows us to describe the entire system using Eqs. (
To ensure reproducibility and determine systematic errors, this calibration procedure was repeated a total of eight times with beams of four different parameters. This analysis revealed that the on-chip phase shifts exhibit completely random values, deviating significantly from the design parameters. However, the calibration procedure proved to be very robust, with the standard deviation of the determined phase values across different calibration scenarios being only
It should be noted that a standard least-squares fitting method from MATLAB was used. Furthermore, the calibration was carried out using modular code, which allows scalable logic and can therefore be easily extended to chip designs with arbitrary pixel arrangements and larger pixel counts.
APPENDIX B: CHARACTERIZING A PARAXIAL GAUSSIAN BEAM FROM PHASE AND INTENSITY INFORMATION OF FIVE PIXELS
Before we proceed with the calculation of the beam parameters from intensity and phase data obtained with the five-pixel architecture, it is important to first discuss the simplifications applied in the calculation.
First, it should be noted that, due to the design of the grating coupler, the chip is operated at an angle to the optical axis. This means that the chip is calibrated to a specific angle of incidence, so that if a plane wave strikes the chip at this angle, the phase measurement would yield zero relative phase between all inputs. However, it also means that different input pixels are situated in different planes along the direction of beam propagation. As the wavefront curvature and the Gouy phase of non-collimated Gaussian beams change during propagation, this results in different measured phase values depending on the position of the pixel. Nevertheless, since we only consider very weakly focused beams that are examined relatively far from their focus, and given the small angle of incidence and distance between the grating couplers, this phase contribution is assumed to be negligible and is therefore not treated in our model. Additionally, we only consider beams that hit the chip’s input at an angle that deviates only slightly from the calibration angle. Consequently, we can assume that the change in the distance of the pixels to the optical axis due to tilt is negligible. With all these assumptions, we can build a mathematical model as if the chip surface is placed perpendicular to the optical axis, simplifying calculations significantly. Note that all these assumptions introduce systematic errors in the reconstruction of beam parameters. Nevertheless, the model performs well enough to demonstrate the reconstruction of paraxial Gaussian beams.
The mathematical description begins with a very simple representation of the electric field of a paraxial Gaussian beam at the position of the chip at the optical axis. Here we neglect polarization and the time harmonic oscillation, leading to the following expression [
We can now separate this equation into two parts to analyze the amplitude and phase independently. Starting with the amplitude parts, we can express measured input intensity values at input
The measured intensities at the positions of the input pixels provide information about the relative position of the beam in the plane of the chip and its size
Figure 6.Illustration of the coordinate transformation.
By substituting the new coordinate system into Eq. (
Isolating
Repeating this procedure with the intensities at inputs 1, 2, and 4 reveals the displacement in the
Knowing
The same procedure can be applied to the equations for the intensities of inputs 1 and 4 to obtain an expression for the beam size, measured in the
Using the measured intensity values, we can determine both the in-plane displacement and the size of the beam at the position of the chip.
Next, we aim to determine the curvature of the wavefront and the tilt of the beam, which requires a closer examination of the measured relative phase values. The relative phase between two inputs
Similarly, we can perform the same process for the relative phases
Using an analogous procedure, we can ultimately derive the representation for the tilt terms associated with tilting around the
The tilt angles between the structure and the incident beam, associated with the measured phase values, can subsequently be determined using straightforward geometric considerations.
Above, we discussed the parameters of a paraxial Gaussian beam at the chip position. However, for a comprehensive characterization of the beam, it is also interesting to know its focal spot size
The preceding calculation illustrates how a paraxial Gaussian beam can be characterized through a single measurement of the input field’s intensities and relative phases at five pixel positions. We have derived an analytical description that allows us to determine the displacement of the beam relative to the chip, the beam’s inclination, the position of the focal point, and the size of the focal spot.
APPENDIX C: CHIP DESIGN AND BANDWIDTH CONSIDERATIONS
The design of the waveguide cross section is crucial to the performance of the presented chip, as it influences the number of supported modes and their propagation characteristics. Here, we discuss the design of the waveguide cross section and its effect on the bandwidth of the presented on-chip architecture.
The integrated circuit was designed and fabricated in a 100-nm-thick silicon nitride (SiN) platform with a silicon dioxide bottom cladding and a silica-like top cladding (see Appendix
The broadband design of most circuit components, combined with a calibration procedure that compensates for their inherent chromatic behavior, enables the sensor’s effective operation across different wavelengths. However, the constraint for the measurement principle to work is that the waveguides must strictly support only the fundamental modes; otherwise, the theoretical model of the chip becomes invalid. In Fig.
The passive phase shifters were implemented by introducing two waveguide branches with different widths. By varying the width of the waveguide, the effective refractive index experienced by the waveguide mode is tuned, which alters the optical path length. As a result, by using different widths for the two waveguide branches, different optical path lengths are created, leading to a relative phase difference between the two waveguide modes at the output of the phase shifter [
The widths of the two branches were chosen to be 1700 nm and 1900 nm, resulting in a 90-deg phase shift for a 93-μm-long section, and a 135-deg phase shift for a 140-μm-long section at a wavelength of 658 nm. The transition between the 500-nm-wide single-mode waveguide and the wider section was realized through 50-μm-long tapers to ensure adiabatic mode propagation.
However, the phase shifters exhibited random deviations from the target phase shift, producing repeatable results on a given device, but differing between different nominally identical devices. This behavior is most likely due to random width variability and surface roughness of the waveguide interfaces, which can introduce random phase shifts that build up to non-negligible values across the relatively long waveguides [
APPENDIX D: ALTERNATIVE CHIP ARCHITECTURE
Here, we present an alternative architecture for the passive on-chip interferometers. In this approach, the interferometers are designed using directional couplers instead of Y-branch combiners. Figure
Figure 7.(a) Effective index of fundamental and first order TE modes at three different wavelengths within the visible spectrum as a function of the waveguide width in our SiN platform. (b) Effective index of fundamental and first order TE and TM modes as a function of wavelength for a waveguide width of 500 nm.
Figure 8.Optical microscopy image of a chip featuring an alternative architecture. The on-chip interferometers consist of directional couplers.
APPENDIX E: FABRICATION
The photonic integrated chip was fabricated on a material platform purchased from LioniX International and consisting of a 100-nm-thick SiN film deposited through low-pressure chemical vapor deposition on an 8-μm-thick thermal silicon dioxide layer, mechanically supported by a 500-μm-thick silicon substrate. A 4-inch wafer was diced in
The integrated circuit was patterned onto the chip by spinning a 270-nm-thick layer of hydrogen silsesquioxane (HSQ), which was exposed at a dose of 1300 μC/cm2 and developed in 25% tetramethylammonium hydroxide (TMAH). The pattern was then transferred to the SiN film by inductively coupled plasma (ICP) and reactive ion etching (RIE) using a
Figure 9.(a) SEM image of etched SiN waveguide with residual HSQ mask. (b) SEM image of the fabricated Y-branch. (c) SEM image of the fabricated surface grating coupler.
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