[2022D] J. Huang, C. Coverstone, and J. Chisum, "Low-dispersion Metasurfaces for Wideband Gradient-index (GRIN) Media up to Ka-band," 2022 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI), 2022, pp. 1-2, doi: 10.23919/USNC-URSI52669.2022.9887514, https://ieeexplore.ieee.org/abstract/document/9887514

W. Wang and J. Chisum, "3D Wide-Angle Beam-Scanning Compound Lens Using A Fast Hybrid Optimization Workflow," 2024 IEEE International Symposium on Antennas and Propagation and INC/USNC‐URSI Radio Science Meeting (AP-S/INC-USNC-URSI), Firenze, Italy, 2024, pp. 1499-1500, doi: 10.1109/AP-S/INC-USNC-URSI52054.2024.10686465.

[2022C] W. Wang and J. Chisum, "Hybrid Geometrical Optics and Uniform Asymptotic Physical Optics for Rapid and Accurate Practical GRIN Lens Design," 2022 IEEE/MTT-S International Microwave Symposium - IMS 2022, 2022, pp. 20-23, doi: 10.1109/IMS37962.2022.9865499, https://ieeexplore.ieee.org/abstract/document/9865499

[2019A] A. Papathanasopoulos, Y. Rahmat-Samii, N. Garcia, and J. D. Chisum, “A Novel Collapsible Flat-Layered Metamaterial Gradient-Refractive-Index (GRIN) Lens Antenna,” IEEE Trans. Antennas Propag., vol. 68, no. 3, pp. 1312 - 1321, Oct 4, 2019, https://ieeexplore.ieee.org/abstract/document/8859611

For lower frequencies and larger lenses (e.g., 4” to 18”) we use a drilled PCB process (upper images at left) wherein a standard drill set is used to produce circular voids in a low-loss microwave substrate[2020A]. Substrates are stacked to produce a 3D GRIN profile. Unit-cell sizes are limited by drill bit diameters and the minimum permittivity is limited by packing density limits (circles on hexagonal lattice). By using concentric rings of a range of substrates we can achieve an effective permittivity range from 1.57 to 9.20 (see colored traces in figure below).

Aimsof microscopepractical

One of the key challenges in GRIN lens design is managing the complexity. A GRIN lens provides too-many degrees of freedom for traditional closed-form design methods (e.g., based on simple ray tracing) and simulation methods (e.g., full-wave EM with optimization). Therefore, we have explored a variety of design tools such as intrinsically matched unit-cells from which to apply ray tracing or optimization methods. Our current design tools allow us to create a candidate lens design, solve it with 2D FDTD full-wave EM solvers, and compute a wide variety of figures of merit and cost functions for e.g. scan loss optimization, bandwidth, and more in just a few minutes [2021A]. This allows us to perform lens design optimization with all of our lenses. We have two basic solvers: i) Geometrical Optics Ray Tracing with Field Amplitude Curvature, and ii) 2D FDTD. The ray tracing with field curvature is able to solve for the full vector EM field through an arbitrary GRIN profile with very high accuracy relative to rigorous full-wave analysis but in a small fraction of the time. Accuracy is dramatically improved, especially for scanned beams, by incorporating diffraction effects. We have incorporated diffraction through uniform asymptotic physical optics (UAPO) theory [2022C]. The 2D FDTD is a full-wave solver that takes advantage of rotational symmetry present in most GRIN lenses. It is not capable of solving the full vector field but can be used to optimize higher level system metrics such as impedance match, scan loss, etc. By combining the two codes we can arrive at highly optimized lens designs which take advantage of the righ parameter space available in a GRIN profile. This would not be possible if we relied solely on full-wave simulation or simplified ray trace anslysis.

GRIN media based on gyroid unit-cells using both Rogers Radix 2.8 and alumina are printed in UV DLP printers (Fortify FluxOne). Depending upon unit-cell size, various values or permittivity can be achieved up to 40 GHz (X-band shown below). These materials can be combined to create a large range of effective Dk from 1.5 to about 5.5. Both materials exhibit very low loss (bulk loss tangent is 0.004 and 0.0002 for Radix and alumina, respectively). Measured radiation efficiency of an electricallly large (30dB gain) lens is above 80%, confirming that 3D-printed GRIN lenses are viable for high-performance antennas.

Funding: NSF BWAC I/UCRC award #CNS-1439682-011, Parry Labs (Satcom-on-the-move) award #PL2018-SB-001, ONR (high-power, wideband radar systems) award #N00014-20-C-1067.

W. Wang, N. Estes, N. C. Garcia, M. Roddy, A. K. Bolstad and J. D. Chisum, "Beamforming Phased-Array-Fed Lenses With >0.5λ-Spaced Elements," in IEEE Transactions on Antennas and Propagation, vol. 71, no. 3, pp. 2208-2223, March 2023, doi: 10.1109/TAP.2023.3240085

In order to characterize our GRIN lens antennas we conduct both far-field and near-field measurements. Our far-field range takes advantage of time-domain gated S-parameters in order to perform preliminary characterizations with line cuts. In order to produce a full characterization we perform near-field antenna measurements including our soon-to-be-completed in-house planar near-field antenna range as well as spherical near-field ranges with collaborators.

Learn the correct magnification for your experiment and how to tell if your objective can be used with air, oil, or other immersion media.

[2021A] N. Garcia and J. Chisum, "Reduced dimensionality optimizer for efficient design of wideband millimeter-wave 3D metamaterial GRIN lenses," Microwave and Optical Technology Letters,  2021, v.63, pp. 1372– 1376. https://onlinelibrary.wiley.com/doi/10.1002/mop.32755.

[P1] (Granted) “High Contrast Gradient Index Lens Antennas,” #US 20200018874A1, Granted: Nov 2021. https://patents.google.com/patent/US20200018874A1

The Immersion medium is what's between the objective and the coverslip (or the bottom of the dish or flask that holds your sample).

Numerical aperture is a property of the objective that indicates how good the resolution can be in the image you collect (basically how much fine detail you can see).

Compared with alternative methods such as perforated dielectrics, advancements in 3D-printing offer a stream-lined fabrication process at a significantly reduced cost. The primary advantage of perforated dielectrics is the use of multiple materials to realize a wide range of dielectric constants (Dk) for improved matching and increased compression ratios. Prior use of single 3D-printed materials in GRIN lens design was limited by either a low maxDk (leading to bulky lenses) or high-loss materials (lowering the realized gain). This work use a hybrid GRIN media in which discretely latticed, low-loss 3D -printed materials are combined to maximize the available Dk range while taking advantage of low-cost fabrication through additive manufacturing.

In addition to circular apertures with typical gain of 30dB we have designed a variety of high-performance fan-beam antennas that provide up to 80% aperture efficiency across similarly wide operating bandwidths. And, using compound lens systems we can achieve high-performance wide-angle beam-scanning with scan loss exponents close to the theoretical limit of 1.0 out to 45-degrees and broadside aperture efficiency of 60%. An example of a compound lens system is the aperture lens and feed-correction lenslet (FCL) concept shown below [2022A]. The FCL squints the feed pattern toward the center of the lens recovering almost all of the power lost to spillover at the edge of the lens (resulting in up to ~3dB increase in gain). In addition, the FCL shifts the phase center of the feed closer to the Petzval surface and results in more linear phase collimation, reducing coma lobe and improving aperture efficiency. This concept can be taken to the extreme in which a single monolithic GRIN feed lens is incorporated into the compound lens system [2022B]. The feed lens can be designed with a variety of objective functions to improve overall beamscan. For example, the one shown below is used to flatten the Petzval surface and reduce spillover loss as in the FCL concept but has the added benefit of being monolithic such that feeds can exist at any continuous offset. Full-wave simulations indicates a scan loss exponent of 1.1 and a measured scan loss exponent of 1.5, which is not ordinarily possible in lens antenna systems. This underscores the benefit of a compound lens system.

The objective is an essential part of the microscope and can greatly influence image quality. Objectives come with lots of information written on them, and most of it is written in code. But don’t worry; it’s easy to decipher.

Figure 4. The pencil appears bent or broken because the refractive indexes of water and glass are different than that of air.

Compoundmicroscope

Light will travel through different types of materials at different rates. When light travels through one material (such as air) and into another (such as water), the light is refracted. It appears bent. For instance, when you put a pencil in a glass of water and view the glass from the side, the pencil will look bent. This is because air has a different refractive index than water.

A microscope objective is composed of a complex set of lenses and optics, and different objectives are designed for different imaging tasks. Capturing good images relies on choosing the correct objective.

Figure 3. Use of immersion media matched to the objective can minimize the refractive index differences between the objective and the sample.

MicroscopeObjectives magnification

We have developed two approaches to high-contrast GRIN media. One uses industry-standard drilling of low-loss microwave substrates (e.g., Rogers AD-series) and is preferred for GRIN lens designs operating from 8 to 100 GHz [2020A]. The other uses an advanced deep-reactive ion etching [P1,2017B] process (Bosch) and our in-house annular masking method to achieve a wide range of effective permittivity by etching hexagonal voids on a hexagonal lattice in high-resistivity silicon wafers. This method targets lens designs from 100-500 GHz.

[P2] (Provision patent) “Compound lenses for improving beam-scan performance of reflector and lens antennas,” File: Apr 16, 2020. Application # 63/011,197.

[2022E] W. Wang, J. Huang, H. Ouassal and J. Chisum, "Inverse GRIN Lens Design Using Artificial Neural Network and Geometrical Optics," 2022 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI), 2022, pp. 1-2, doi: 10.1109/AP-S/USNC-URSI47032.2022.9887332, https://ieeexplore.ieee.org/abstract/document/9887332

[2022A] N. Garcia, W. Wang, and J. Chisum, "Feed corrective lenslets for enhanced beamscan in flat lens antenna systems," Opt. Express 30, 13047-13058 (2022), https://opg.optica.org/oe/fulltext.cfm?uri=oe-30-8-13047&id=471156

[2017B] N. Garcia, W. Bai, T. Twahirwa, D. Connell, J. Chisum, “Silicon Micromachined High-contrast Artificial Dielectrics for Millimeter-wave Transformation Optics Antennas” APS/URSI 2017, https://ieeexplore.ieee.org/abstract/document/8073028

Stagemicroscopefunction

[PhD Thesis] N. Garcia, "High-efficiency, Wideband Beam-scanning GRIN Lenses For Millimeter Wave Communications," March 2022, https://curate.nd.edu/show/wm117m0509s (Current POC: nico@cheshirgrin.com)

Magnification tells you the optical magnification the objective provides. The magnification you choose depends on what you want to see. The usefulness of magnification will be limited by your resolution. Making a big fuzzy blob of light even bigger won’t give you a better picture. Provided you have similar resolution at different magnifications, using higher magnification will allow you to see smaller things (such as organelles inside a cell) better. On the other hand, using a lower magnification will give you a better image of the big picture—such as a field of cells or interactions between cells.

[2020A] N. Garcia and J. Chisum, “ High-efficiency, Wideband GRIN Lenses with Intrinsically Matched Unit-cells,” IEEE Trans. Antennas Propag., vol. 68, no. 8, pp. 5965 - 5977, Apr 30, 2020, https://ieeexplore.ieee.org/abstract/document/9082819

Phased-arrays can be used to feed lenses (phased-array-fed lens (PAFL)) with the advantage that the combined system can realize dynamic pattern synthesis like a phased array but with a fraction of the power dissipation of a phased-array. Whereas a phased array realizes programmable pattern sythesis by producing a critically sampled (half-wavelength) aperture field distribution using a very large number of inefficient, programmable phase-shifters, a phased-array-fed lens performs beamforming in the far-field. That is, a phased-array-fed lens uses the superposition of far-field directional beams to produce a desired far-field pattern. And, since most desirable far-field patterns are highly directive, possibly with nulls, these can be efficiencly constructed with a small number of directional beams. In other words, PAFL can produce desireable, high-gain, and complex patterns by using only 5-10 active feeds. This translates to usually <1% of the power consumption of a phased array to achieve the same pattern.  An added benefit of PAFL is that, since the lens creates a continuous aperture field, the feed array below the lens does not need to be critically-spaced. Using feed spacing of 0.7-0.8 of a wavelength can provide high-performance. This means that half the number of phase-shifting channels are needed (saving on cost).

Microscopeparts

What isobjectivelens inmicroscope

Lots of times, you will hear people talk about the “NA” of an objective. “NA” stands for numerical aperture and its value partly depends on the refractive index of the material that is between the objective and the glass coverslip that your sample is on. In general, objectives with higher NA give you better resolution. Higher NA objectives often have higher magnification and use some sort of immersion medium. Immersion medium is used to alter the refractive index of the space between the objective and glass coverslip so that it is closer to the refractive index of the glass coverslip itself. This minimizes refraction and loss of light, ultimately giving you a better image.

[2017A] W. Bai and J. Chisum, “A Compact, Wide Field-of-View Gradient-index Lens Antenna for Millimeter-wave MIMO on Mobile Devices,” VTC2017-Fall, https://ieeexplore.ieee.org/abstract/document/8288369

Improved beam shape can be achieved by taking advantage of the PSO algorithm’s greater degrees of freedom, especially as the target beam angle increases. Two examples are shown to demonstrate beams optimized specifically for SLL and BW.

[2022B] N. C. Garcia and J. D. Chisum, "Compound GRIN Fanbeam Lens Antenna With Wideband Wide-Angle Beam-Scanning," in IEEE Transactions on Antennas and Propagation, vol. 70, no. 9, pp. 7501-7512, Sept. 2022, doi: 10.1109/TAP.2022.3182420, https://ieeexplore.ieee.org/abstract/document/9799774

The working distance is the distance between the objective and the cover glass, or between the objective and the top (or bottom) of whatever vessel you are imaging through, when your sample is in focus. When you are imaging through something thin, like a cover glass, you can use objectives with shorter working distances. But when you are imaging samples that are in a thicker vessel, such as a plastic plate or dish, you will probably need an objective that has a longer working distance. The working distance of an objective is often written on the objective. The working distance of the objective in this example is 7.4 mm. It is considered to have an ‘extra-long working distance’ and is abbreviated as ELWD on the objective.

Typesof microscopeobjectives

Using the GRIN media discussed above we have developed several lens design architectures that promote high aperture efficiency over wide bandwidths [2021A,2020A] and with high-performance beam scan [2022A,2022B]. Using intrinsically matched unit-cells we have demonstrated an 8” lens antenna with 30-80% aperture efficiency from 8-40 GHz with simulated operation up to 50 GHz [2020A]. With a switch-feed architecture, this lens can provide low-power, high-efficiency beam-scan for all current X-band, Ku- and Ka-band satcom systems as well as all proposed 5G millimeter-wave bands including 28 GHz, and 39 GHz. More recent work has focused on establishing unit-cell size limits for high-frequency GRIN lenses. Using this approach along with more advanced lens matching methods we have designed lenses with greater than 60% aperture efficiency from 8-80 GHz.

Figure 2. Same field of cells captured at different magnifications. Each magnification can offer different information, and the best choice for your experiment will vary depending on what you want to know.

Our codes also include rapid generation of 3D models for 3D EM simulation as well as Gerber files for fabrication. Using our wide array of design tools as leveraging our relationships with third party manufacturers we can go from lens specifications, through automated design and multi-objective optimization, to fabrication and first measurement in one to two months. This allows us to rapidly iterate on new concepts and push the limits of lens performance.

In contrast to traditional homogeneous lens antennas, GRIN lens antennas continuously manipulate the electromagnetic wave as it passes through the lens volume. These many degrees of freedom allow for high performance including efficiency with wide scan angle, thinner lenses, and aggressive F/D ratios [2019A]. A 3D GRIN profile can be achieved in a variety of ways including 3D printing, or stacked layers of perforated dielectrics (shown at right). Due to a variety of material and practical limitations, most artificial dielectrics used in GRIN lenses have a low maximum dielectric constant (around 6—8) and a high minimum dielectric constant (around 2—4) resulting in thick lenses which are poorly matched. Our GRIN media was developed from the beginning to provide high-contrast with low minimum permittivities [2017A]. The high maximum permittivity allows us to design thin lenses which can still produce a true time delay and thus wideband performance. The low minimum permittivity allows us to achieve unprecedented impedance matching performance over polarization and achieves record aperture efficiency over wide bandwidths.

Objective microscopefunction

Beam-scanning MMW antennas have become the backbone of next-generation wireless communications systems, are necessary for satellite-tracking base-stations, satellite-communications (Satcom) on the move, are heavily used in radio astronomy and earth/planetary science missions, and even now in 5G millimeter-wave base-stations. We have developed a number of key technologies to enable high aperture efficiency, ultra-wideband, and wide-angle beam-scanning gradient-index (GRIN) lens antennas which provide a low-power and low-cost alternative to the conventional phased array. Our lenses are intrinsically matched over extremely wide bandwidths, covering from 8-80 GHz with aperture efficiency above 30% but typically from 50-80%.

Each objective is designed for a specific immersion medium, which is marked on the objective. The main types of immersion media are air, oil, and water. It is important that you never put air objectives in oil or other liquids. Doing this will make the person in charge of the microscope really angry! The main purpose of using different types of immersion media is to minimize the refractive index differences that are present in the space between the objective and the sample. This includes the substrate (i.e., glass coverslip) that the sample is on and the imaging medium (i.e., buffer) that the sample is in. Minimizing this difference will result in better image resolution.

Another application of interest is in very low energy spectrum sensing and direction of arrival detection. Here we combine a GRIN lens with passive angular filtering with a compact filter bank (such as a cochlear filter) with a zero-bias diode energy detector. The result is a completely passive, zero-energy direction of arrival (DoA) spectrum sensor (except for the final readout which is effectively DC).  This configuration is useful to deployment of SWaP constrained platforms such as micro-UAVs.

For higher frequency applications where unit-cells must be an order of magnitude smaller, we have developed a custom deep-reactive ion etching (DRIE) process based on the well-known Bosch process to achieve hexagonal perforations on a hexagonal lattice. Since the voids are lattice-matched we can achieve a lower fill factor and thus the entire permittivity range can be realized in a single wafer of silicon. The effective dielectric constant of our silicon DRIE GRIN media is 1.25 to 9.8. In order to achieve this in-plane gradient we have developed an annular-ring masking process. The DRIE GRIN media was developed for millimeter-wave and submillimeter-wave lens antennas in the 100-500 GHz range and targeting applications in space and planetary science spectroscopy as well as ultra-high data rate point-to-point communication links.