Non-diffracting beam generated from a photonic integrated circuit based axicon-like lens

: We demonstrate an on-chip silicon-on-insulator (SOI) device to generate a non-diffracting beam of ≈ 850 µ m length from a diffractive axicon-like lens etched using a low resolution (200 nm feature size, 250 nm gap) deep-ultraviolet lithographic fabrication. The device consists of circular gratings with seven stages of 1x2 multimode interferometers. We present a technique to apodize the gratings azimuthally by breaking up the circles into arcs which successfully increased the penetration depth in the gratings from ≈ 5 µ m to ≈ 60 µ m. We characterize the device’s performance by coupling 1300 ± 50 nm swept source laser in to the chip from the axicon and measuring the out-coupled light from a grating coupler. Further, we also present the implementation of balanced homodyne detection method for the spectral characterization of the device and show that the position of the output lobe of the axicon does not change significantly with wavelength.


Introduction
Increasing utility of smaller and cheaper electro-optical devices has necessitated the development of various on-chip photonic devices in recent years. Integration of multiple devices into a single high index contrast photonic integrated circuit (PIC) could make such devices smaller, because high index contrast waveguides allow for smaller bends-which enables more compact integration. Integration of multiple devices in turn also reduces the optical and mechanical components needed for coupling and mode adaptation which also lowers the footprint and the overall cost of devices. This increases the accessibility of new and advanced technologies to a wider population, owing to the lower cost of fabrication. One such potentially useful device is an axicon. A traditional axicon, schematically depicted in Fig. 1, is a lens with a conical face on one side and a planar face on the other. An ideal axicon can convert a plane wave into a bessel beam, with a long non-diffracting central lobe which can be useful for technologies like optical traps [1]. Axicons have also been used in imaging techniques like optical coherence tomography to improve the depth of focus compared to more traditional focusing solutions [2,3]. However, traditional conical optical lens based axicons are not suitable for miniaturization in chip-based devices as they cannot be easily integrated onto the chip. A completely chip based device would benefit from all the integration based advantages discussed above.
Metasurface based lenses are also promising alternatives to traditional optical devices in terms of imaging capability and miniaturization. Various metasurface based axicon lenses from imaging to telecommunications wavelengths have been demonstrated recently [4][5][6][7][8][9]. However, these flat lenses require light incidence normal to the lens. Therefore, a source cannot be easily integrated, or light be manipulated, monolithically on the same chip. Moreover, metasurfaces currently require electron-beam lithography for fabrication, which is both more expensive as well as difficult to scale up for mass fabrication compared to traditional commercial complementary metal-oxide-semiconductor (CMOS) foundry based fabrication [10].
Other efforts to develop integrated photonic lenses have included a photonic crystal based device, where the holes in the system has been developed with genetic algorithms [11]. While this device has a beam waist of only 293 nm, the focus is only 5 µm from the device, and more importantly, the axicon behavior is two-dimensional (light does not focus in the third dimension), and therefore applicable only for applications involving light sheets. The short focal length, along with the fact that the focus is within the slab itself [11], makes it not particularly for applications such as imaging, optical traps, etc.
On-chip axicon itself has also been demonstrated previously, however that too is a two dimensional device designed for light sheet microscopy [12]. The silicon nitride based device focuses light out to free space ≈ 10 µm from the edge of the chip, and with a beam waist of ≈ 1 µm (the values are approximated from a figure in the paper by this author, as the paper did not quantify those parameters) [12].
Yet another on-chip axicon-like device was demonstrated, again in the silicon nitride platform, using optical phased arrays [13]. The device uses a one dimensional splitter-tree based architecture to generate a quasi-1D Bessel-beam with up to 14 mm Bessel length and a full-width at halfmaxima (FWHM) of 30 µm, perpendicular to the direction of light propagation [13].
In contrast to the above mentioned technologies, the device demonstrated in the present study focuses light from within the PIC perpendicular to the direction of light propagation using diffraction gratings. While the work presented by [13] does generate a beam perpendicular to the direction of light propagation, the beam is quasi-1D [13]. In the present work, the axicon focuses on all three dimensions, and the entire device is compatible with commercial CMOS foundry fabrication, which allows for easy scaling up for mass manufacturing.
In this study, we demonstrate an on-chip silicon-on-insulator (SOI) [14] axicon-like device etched using a low resolution deep-ultraviolet (DUV) lithographic fabrication [10,15]. The device produces an axicon-like long central non-diffracting lobe of 850 µm, which may be useful in several applications where traditional axicons could be used. The axicon here consists of circular gratings with seven stages of 1x2 multi-mode interferometers (MMI) [16][17][18]. Devices with circular structure have been demonstrated in context of focusing grating couplers, although spectral characterization of such structures has so far been incomplete [19]. Here we present a methodology to characterize the spectral performance of such devices as well. Moreover, we also present a technique to apodize the gratings azimuthally that is compatible with a low resolution fabrication technique, which allows deeper light penetration depth in the device -a necessity for an axicon.

Simulation
In a diffraction grating-based axicon, we design the device such that light would diffract from all sides towards the center, and a central lobe would form due to constructive interference at the center. In order to show how such an axicon would behave, we performed a 2D finite difference time domain (2D-FDTD) [20] simulation with two plane waves at a wavelength of 1310 nm. A full 3D simulation of the device would be computationally impractical, and a 2D simulation would not capture the apodization behavior employed here (discussed in Sec. 2.3). Therefore, in 2D-FDTD, we simulated propagation for the light diffracting at the average measured angle at our device sizes. We set the angle of the two sources, as well as the width of the individual source, based on the measurement results (discussed in detail in Sec. 4.1 and 4.2). Figure 2(b) shows the electric field intensity of the simulation results. Light from the two sources interfere constructively to form a central lobe that spans from ≈750 µm to 1000 µm above the chip, with a lobe diameter of ≈7 µm.

Device description
The axicon, shown in Fig. 2(a), is a 1.52 x 1.38 mm 2 device that consists of seven levels of 1x2 MMIs to combine or split light (depending on the coupling direction) which leads to 128 final ports around the central axicon structure. While a higher number of ports would have been ideal, we chose seven levels as optimum to keep MMI losses and the physical size of the device to a minimum. The central structure of gratings is ≈182 µm in diameter, and has a constant period of 600 nm and a constant duty cycle of 0.5. The constant period ensures a near-constant diffraction angle needed for axicon-like behavior.

Azimuthal apodization
In regular gratings, the intensity of light diffracted decreases exponentially with penetration depth. For a large gratings based device such as the axicon presented here, the majority of the light would diffract in the first few grating periods. The width of the central lobe depends on the penetration depth by their Fourier transform by virtue of the Fraunhauffer diffraction relationship [21]. Therefore, an axicon by design requires light to penetrate much deeper into the device, with a uniform intensity, as depicted in Fig. 2(b). In order to increase that penetration depth so that a longer and narrower depth of focus can be achieved, we broke up the circular gratings into small arcs, i.e. we azimuthally apodized the gratings, as shown in Fig. 3 and also described in a previous work [22]. Non-uniform widths of the gratings have also been demonstrated previously in conjunction with varying duty cycle in straight gratings in Si 3 N 4 platform [23].  Figure 3 illustrates the nature of azimuthal apodization employed here. The arc-length of the gratings are shortest at the circumference and increases exponentially with penetration depth, as shown in the schematic in Fig. 3(b), and the mask layout (defined using Graphic Design System (GDS)-a format used to define structures in integrated circuits) in Fig. 3(c). We obtained the extinction coefficient for the apodization from 2D-FDTD simulations. The arcs continued until the gap between two arcs at a given radius reached the feature-size limit for fabrication, which was at a radius of 29 µm in our device. Of the total radius of 91 µm, the first 62 µm are thus apodized, as clarified in Fig. 3(c). This apodization is designed to change the diffraction intensity as a function of penetration depth from exponential decay to nearly a constant, which is discussed further in Sec. 4.1, and Fig. 7.

Fabrication
The chips were fabricated using DUV lithography in the 10th multi-wafer project call by the CORNERSTONE Project [15]. The device is a SOI chip that consists of a 220±20 nm Silicon layer atop a 2 µm SiO 2 buried oxide (BOX) layer, which is on a Silicon substrate [24,25]. The chip also consists of a 1 µm protective SiO 2 layer [25]. All waveguides are rib waveguides etched 120±10 nm, and the gratings are etched 70±10 nm from the surface [25]. The fabricators reported waveguide propagation losses for a straight single mode rib waveguide based on test structures to be ≈4 dB/cm [25]. The feature sizes were limited by the fabrication parameters, with a minimum feature size of 200 nm and gap of 250 nm in the relevant gratings layer [25]. This coarse limit, compared to ≈25 nm resolutions available in the present day DUV lithography techniques and electron-beam lithography, prevents us from designing higher performance grating structures with the apodization in the radial direction, where the thickness of silicon (or the duty cycle of the grating) varies with radius. However, we were still able to design an axicon-like device while staying within the fabrication limits. Figure 4 shows the experimental setup used to characterize the power output of the device. For the source, we use a swept source laser (Santec HSL-20) that sweeps the wavelength λ from 1250 nm to 1350 nm, with an average optical power of 13 dBm. The laser sweeps through the wavelengths at 100 kHz, with a duty cycle of 42.7%. For power characterization, we used an InGaAs detector (Thorlabs S154C) with a USB powermeter (Thorlabs PM100D) where each data point was acquired after averaging over 50 ms. With this configuration for power characterization, the spectral peaks are averaged over time and thus the laser acts simply as a broadband source, as the detector cannot measure fast enough to differentiate between the different wavelengths. As such, the power characterization essentially is performed with a broadband source of wavelength λ = 1300 nm with a bandwidth of 100 nm. We use a much faster detector for spectral characterization, discussed later in Sec. 3.2. Instead of coupling light in from a grating coupler and measuring the output light at the axicon, as is typical in these kinds of devices, we did the reverse. We coupled light in from the axicon structure, and measured out from the grating coupler. Grating couplers are optimized for a specific wavelength of light at a given coupling angle. If we were to couple light into the chip from a grating coupler with a single mode fiber (SMF), as is traditional, we would be limited to a narrow bandwidth of light. Using the grating coupler to couple light out with a multi-mode fiber (MMF) allows us to take advantage of the wider acceptance cone of the MMF, and thus accept a wider bandwidth of light at a fixed angle. A typical SMF has a core diameter of 10 µm, and a numerical aperture (NA) of 0.14, which results in an acceptance cone of 16 degrees (n sin θ = NA, where n = refractive index, and 2θ = acceptance cone angle [14]). We used an OM2 MMF to collect the light from the grating coupler, which has a core diameter of 50 µm and a NA of 0.20, resulting in an acceptance cone of 23 degrees. The MMF has a 43% larger acceptance angle, which allows us to collect a wider spectral bandwidth of light from the device. Light was coupled in with a GRIN lens (NA 0.46, Thorlabs GRIN2913) mounted on a ferruled fiber and held vertically over the chip. The NA of 0.46 for a gaussian beam results in a beam waist w 0 of 0.87 µm and depth of focus 2z 0 of 3.63 µm (acceptance cone angle 2θ = 54.7 • , w 0 = λ/(πθ), and 2z 0 = (2πw 2 0 )/λ, where λ is the wavelength of light [14]). The spot size of 2w 0 = 1.7 µm and depth of focus 2z 0 = 3.63 µm of the GRIN lens enables a high resolution measurement for the characterization of the axicon-lens. We note that since this is a two-lens system, which is linear and reciprocal, coupling in from the GRIN lens or measuring the output from GRIN lens would result in identical measurement.

Power characterization setup
We first optimized the polarization of the light with the manual paddle polarizers (27 mm diameter paddles, with 4-3-4 loops) and the power meter readings. We then moved the GRIN lens point-by-point using a motorized xyz translation stage (Thorlabs NanoMax313D) to acquire planar data from the chip. We note that we did not adjust the phase of different paths in the device.

Spectral characterization setup
The power meter measurements do not need very high speed data acquisition rate, but faster systems were needed in order to resolve the wavelength. We used AlazarTech ATS9350 data acquisition (DAQ) card and a balanced detector (Thorlabs PDB430C) to acquire data at 500MHz for the spectral measurements. However, the spectral power density out from the chip was in the order of the noise floor of the detector due to losses in the system, so we implemented a balanced homodyne detection method to acquire the signal. Since this setup requires us to mix two signals, all the fibers used in this measurement are single mode fibers. Figure 5 shows the setup for our implementation of balanced homodyne detection based measurements. The source laser is first split using a commercial 1:99 splitter. The 99% line goes through the polarization rotator, and out of the assembled GRIN coupler to couple light onto the chip. Light out of the chip is coupled onto a cleaved fiber held at a fixed angle. The cleaved fiber is mounted on a manual xyz-stage and the GRIN lens is mounted on a motorized xyz-stage. The 1% line is the local oscillator, which has a pair of GRIN collimators (Thorlabs 50-1310A-APC) to adjust the path length. While the local oscillator is only 1%, the 99% portion of the chip ultimately becomes smaller than the local oscillator component because of the losses it undergoes through the PIC. One of the GRIN lens is mounted on a motorized linear translation stage, which allows us to increase or decrease the path length as needed. This is specially important when we acquire data of a plane perpendicular to the chip. As the input GRIN moves away from the chip, the path length increases. Having a synced motor to change the path length by the corresponding distance on the local oscillator line would maintain that equality in path length. The light out of the chip is then mixed with the light from the local oscillator line in a 2x2 mixer, which feeds into the balanced detector. The voltage data from the balanced detector is then acquired using the DAQ card. If we assume two signals A s sin (θ + ϕ) and B LO sin θ entering the 2x2 mixer (where θ is an arbitrary phase, and ϕ is the phase difference between the two signals), then the output of the 2) cos θ. The photo-diodes in the balanced detector measure the intensities, and the balanced detection is the difference of the two intensities. Thus, we obtain the difference of the intensities  Figure 6 shows an example implementation of this algorithm to extract the chip signal from the homodyne setup. Prior to beginning the experiment, we record a signal (average of 50 measurements) without the chip connected (no chip signal). When the chip is connected, the local oscillator and the chip signal is mixed in the 2x2 mixer. If the two path lengths of the chip signal and the local oscillator signal are nearly equal, then we can observe an interference pattern in the balanced detection signal (difference of the two signals, raw signal). The envelope of the interference pattern is the component representing the signal from the chip. The fluctuations in the envelope are the fluctuations we see when directly measuring a reference waveguide. To extract the desired chip signal, we first smooth the raw signal and no chip signal over 60 ns, and normalize it with their individual maxima. We take the difference of the two signals to extract only the interference component, which we pass through a high pass filter, filtering out any signal lower than 5MHz. We assume that any signal less than 1% of the sampling frequency (500 MHz) to be related to the first two slowly varying terms in Eq. (1), compared to the third term, which corresponds to the interference component. This leaves us with high pass filtered signal. We then implement the Hilbert function to extract the envelope of the oscillation, which is the component from the chip, shown as extracted signal. Since we use a swept source laser, we can extract different sections at the required wavelengths to study the spectral dependence. Figure 7 shows the measured power for the apodized and the non-apodized gratings for the device as a function of radius. For non-apodized gratings, we see that the intensity of the diffracted light drops from a peak of 2.6 nW at the radius of 91 µm, to the background level of 0.17 ± 0.11 nW (drop of ≈93%) within the first 8 gratings near the outer radius of the device, and the penetration depth is ≈5 µm. In contrast, for the apodized-gratings based device, we observe that light makes it through two-thirds of the device. The diffracted light intensity is nearly constant at an average of 1.48 ± 0.27 nW for the first ≈60 µm (from ≈ 90 to ≈ 30 µm in Fig. 7). It is at this radius that the gaps between the grating arcs reach the minimum gap limit set by the fabricators and the full, non-apodized gratings begin. This measured radial value of ≈ 30 µm, where the transition happens is consistent with the designed parameter radius shown in Fig. 3(c) within 1 µm. At this radius, due to the gratings being completely circular (i.e. they are not apodized), we observe the intensity of light increase rapidly, reaching a peak of 3.5 nW at the radius of 25 µm and all of the light diffracts away to the background level within the next few grating periods, at the radius of 21 µm. With a high-resolution fabrication technique, we would likely be able to flatten that spike in intensity and increase the penetration depth past the current ≈60 µm. Fig. 7. Power measured at central location of the device for apodized and non-apodized gratings. Azimuthally apodized gratings allow for deeper penetration of light, to ≈60 µm, while the non-apodized gratings fall off exponentially within ≈5 µm due to rescattering.

Power characterization
In Fig. 8(b), we present the power measured at the xy-plane at the surface of the chip at 10 µm step size. The 2D view of the surface also shows the effect of apodization, consistent with the 1D measurement of Fig. 7. We note that the shape is not quite circular due to mechanical effects in the translation stage. We used a dial test indicator to measure true linear movement corresponding to the input rotation of the micrometer head of the translation stage, and found that the true linear movement was larger than the micrometer dials graduation based step size by up to 80% near x max and y min positions, and that the true linear movement was smaller than the micrometer dial graduation based step size by up to 60% near x min and y min . The difference is non-linear, and present in the fine-adjust range of the device. The non-linearity of the deviation within the fine adjust range makes the position correction in post-process an ambiguous affair, as we often do not know where exactly we fall within the full range of the fine-adjust. Figure 8(a) shows a similar xy-plane measurement at a height of 400 µm above the chip surface, acquired with 1 µm step size. We fitted a gaussian function to this data to find that lobe width at full-width half-maxima (FWHM) was 7.6 µm. The noise we see in Figs. 8(a) and 8(b) is likely a result of random scattering of light, possibly due to the side-wall roughness around the waveguides. Figure 8(c) shows the xz-plane with 5 µm step size in x and 15 µm in z. We note that the the z zero position has an uncertainty of 25 µm. From Fig. 8(c), we can see that the central lobe extends from ≈350 µm to ≈1200 µm.

Spectral characterization
While Fig. 8 shows the absolute power measurements, we also analyzed the spectral performance of the axicon, within the range that our source laser could provide, and at a fixed grating angle at the output. We employed a balanced homodyne detection technique, described in Sec. 3.2, to investigate the spectral performance of the axicon.  Figure 9 shows the spectral behavior of the axicon at wavelengths of 1300, 1310, 1320, and 1330 nm. In Fig. 9(a), we show the normalized intensity of light above the chip in xz-plane for 1310 ± 5 nm, acquired at a resolution of 2 µm in x and 15 µm in z. We averaged the intensity around the central position x = 0 over a distance of 5.7 µm and plotted the normalized intensity as a function of height above the chip in Fig. 9(b). We find that the central lobe of the axicon is relatively stable spanning from ≈600 µm to ≈1000 µm at the different wavelengths discussed in Fig. 9.

Discussion and conclusions
We demonstrate a chip-based axicon-like lens that produces a non-diffracting beam, developed with a low-resolution fabrication technique that limits the design to 200 nm feature sizes, and gaps of 250 nm. We employed azimuthal apodization by breaking up the circular gratings to increase the penetration depth of the light, from ≈5 µm to ≈60 µm, and also changed the diffraction intensity profile from exponential to nearly constant. We characterized this device by coupling light in through the axicon itself with a GRIN lens and measuring the combined light via a grating coupler with a MMF using a power meter. The multimode fiber has a larger acceptance angle and therefore, a larger spectral bandwidth can be measured. Using this setup, we measured the axicon to have a central lobe that is 7.6 µm in diameter, and of length ≈850 µm. To the best of our knowledge, this is the first axicon focusing the light perpendicular to the PIC in full 3D using diffractive gratings. Compared to the quasi-1D Bessel beam that has a beam length of 1400 µm and beam waist 30 µm generated using optical phase arrays [13], the present work has a shorter beam length at ≈850 µm and a narrower beam waist of 7.6 µm. The other work demonstrating chip-based axicon device did not report the quantitative values for the beam [12]. However, based on a figure in the paper, the two-dimensional system reported a ≈ 10 µm long central lobe, of ≈ 1 µm diameter, with a focus ≈ 10 µm from the edge of the chip. The estimated loss in the present system is 32.2 dB (7.5 dB each from input and output, 12 dB from 7 stages of MMI, and 5.2 dB from the waveguides at 4 dB/cm loss). The use of reflecting structure on the bottom of the silicon such as distributed Bragg reflector, higher fabrication tolerances, and waveguide fabrication process optimized for minimal sidewall roughness may lead to lower overall losses.
Further, we implemented homodyne detection in order to perform a spectral analysis and determined that the vertical position of the central lobe does not significantly change its axial position at different wavelengths tested, from 1300 nm to 1330 nm. A device like this, with the longer depth of focus and wavelength independence, could be beneficial in various applications such as optical coherence tomography.