The first is injection molding which, as the name implies, uses a fixed mold with a predetermined shape that dictates the final configuration of the lens. Most often a polymer-based optical material then fills the mold and sets in place as it cools. While this method does not achieve the level of precision offered by individually polished lenses, it does allow for mass production at extremely low cost following relatively high up-front tooling charges.  Polymer-based optics also have a limited range of refractive index values when compared to optical glasses.  A perfect example of an asphere made using this technique most likely sits in front of your smart phone’s camera right now.

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Another optical benefit is the ability to correct for off-axis aberration such as field curvature. Often times, optical designers must “stop-down” their optical systems to physically exclude the outermost region of a lens that produces warping of an image near its edge. As an aspheric design allows for better correction of the incident light onto the focal point, this increases the usable aperture of the lens, which in turn allows for greater light throughput.

Wildes, A. R. et al. Magnetic structure of the quasi-two-dimensional antiferromagnet NiPS3. Phys. Rev. B 92, 224408 (2015).

Esco Optics, Inc. 95 Chamberlain Road, Oak Ridge, New Jersey 07438 Tel: 1-800-922-3726 | Fax: 1-973-697-3011Sales@EscoOptics.com

Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).

Linear polarizationof light

Jungwirth, N. R. & Fuchs, G. D. Optical absorption and emission mechanisms of single defects in hexagonal boron nitride. Phys. Rev. Lett. 119, 057401 (2017).

We pride ourselves on nimble manufacturing. Interested in a quote for your custom asphere just use our simple online tool.

As the leader for military and defense optics in the United States, Esco Optics adheres to the International Traffic in Arms Regulations.

Source data are provided with this paper. All other data that support results in this article are available from the corresponding authors on reasonable request.

Kimel, A. V. et al. Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses. Nature 435, 655–657 (2005).

Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).

The second Sub-Aperture method uses an inflatable bladder attached to a generating or polishing pad. Unlike the durometer balls which have a predetermined, fixed value of hardness, the inflatable bladder can adjust its hardness, in effect replacing the need for different durometer balls. Again, using CNC controls to apply pressure to a small point along the lens as it rotates around a fixed axis, this produces an aspheric contour generated and polished to the required surface precision.

The second concept to understand is that the equation governs a rotationally symmetric aspheric lens. This means that, once again using the vertex of the lens as the starting point, the Sag values generated by the equation are exactly the same at a specific distance from the center regardless of what direction along the X or Y axis is followed (or combination thereof). For example, if you drew a circle around the vertex of the lens that was 0.5” from the central point, the Sag value will always be the same at any point along that circle. Now because we are describing an aspheric surface, the Sag Equation will generate a value that is different at another fixed distance from the center, perhaps at 1.0” or 2.0”. What is important to remember is that at any given distance, although the values may be different from one another, following a circle at the same distance from the center, those values are the same – and that is why it’s called rotationally symmetric.

Tesařová, N. et al. Systematic study of magnetic linear dichroism and birefringence in (Ga,Mn)As. Phys. Rev. B 89, 085203 (2014).

Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).

Saidl, V. et al. Optical determination of the Néel vector in a CuMnAs thin-film antiferromagnet. Nat. Photon. 11, 91–96 (2017).

Bramwell, S. T., Day, P., Hutchings, M. T., Thorne, J. R. G. & Visser, D. Neutron scattering and optical study of the magnetic properties of the two-dimensional ionic rubidium chromium bromide chloride ferromagnets Rb2CrCl3Br and Rb2CrCl2Br2. Inorg. Chem. 25, 417–421 (1986).

Optical SpecificationsOnce the Sag equation is used to define the aspheric shape of the lens surface and the physical parameters such as diameter and center and/or edge thickness are chosen, designers then rely on the same optical concepts used for standard lenses to define their level of precision, i.e. power, irregularity, surface roughness, aperture, etc. For a refresher in these characteristics, here’s a link to our last article – Concepts in Light and Optics - Lenses Part 3.

Aspheric surface form can be tested and verified in several ways. The most precise relies on the tried and true method of interferometry. For a refresher on the concept of interferometric measurements and instrumentation, please see our previous article Concepts in Light and Optics – Interferometry.

Olejník, K. et al. Antiferromagnetic CuMnAs multi-level memory cell with microelectronic compatibility. Nat. Commun. 8, 15434 (2017).

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While aspheres offer a number of advantages over standard lenses, their unique configuration makes them more difficult to manufacture and optical designers must therefore weigh the performance benefits against their higher cost.

X.W. and X.L. conceived the experiment. X.W. carried out PL and absorption measurements. X.W., J.C. and Z.L. conducted the magneto-PL measurements with assistance from D.S. at the National High Magnetic Field Laboratory. J.C. and X.W. prepared samples. J.C., H.K., T.L. and Q.T. carried out the sample characterization. A.C. and S.S. performed theoretical calculations. M.W. performed the time-resolved PL measurement under the supervision of C.H.L.; X.W. and X.L. performed the analysis and interpretation of the data. All authors assisted in the interpretation of data and contributed to the writing of the manuscript.

Piacentini, M., Khumalo, F. S., Olson, C. G., Anderegg, J. W. & Lynch, D. W. Optical transitions, XPS, electronic states in NiPS3. Chem. Phys. 65, 289–304 (1982).

Steiner, S. et al. Calculation of the Magnetic Anisotropy with Projected-AugmentedWave Methodology and the Case Study of Disordered Fe1−xCox Alloys. Phys. Rev. B 93, 224425, (2016).

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Kriegner, D. et al. Multiple-stable anisotropic magnetoresistance memory in antiferromagnetic MnTe. Nat. Commun. 7, 11623 (2016).

Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

Antiferromagnets are promising components for spintronics due to their terahertz resonance, multilevel states and absence of stray fields. However, the zero net magnetic moment of antiferromagnets makes the detection of the antiferromagnetic order and the investigation of fundamental spin properties notoriously difficult. Here, we report an optical detection of Néel vector orientation through an ultra-sharp photoluminescence in the van der Waals antiferromagnet NiPS3 from bulk to atomically thin flakes. The strong correlation between spin flipping and electric dipole oscillator results in a linear polarization of the sharp emission, which aligns perpendicular to the spin orientation in the crystal. By applying an in-plane magnetic field, we achieve manipulation of the photoluminescence polarization. This correlation between emitted photons and spins in layered magnets provides routes for investigating magneto-optics in two-dimensional materials, and hence opens a path for developing opto-spintronic devices and antiferromagnet-based quantum information technologies.

Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. Antiferromagnetic spintronics. Nat. Nanotechnol. 11, 231–241 (2016).

Finally, one of the greatest benefits of using aspheric designs is the reduction in the number of overall lenses needed to achieve a given result. Since an asphere allows for greater control of light through the system, in many cases, a single asphere may provide the same level of precision that previously required several standard lenses used in series. This reduces the overall weight, size and possibly even the cost of the final design.

What each of these optics have in common, regardless of being convex or concave, is that no single radius of curvature can be used to define their overall shape. So how exactly do optical designers characterize the surface shape of an aspheric lens? Well, we promised at the very beginning of these articles we’d avoid mathematics wherever possible and concentrate on the governing concepts – however, in this case, we will need to present the Sag Equation, commonly written as follows:

Linear polarizationantenna

The ability to design, fabricate and precisely quantify the complex surface shape of aspheric lenses has transformed the field of optics. Modern optical systems can now incorporate a single lens in place of multiple lens designs while still maintaining, and often times exceeding, the performance of earlier models. While more expensive than traditional lenses, the reduction in overall weight, need for fewer elements, and ability to produce more compact systems, makes aspheres an attractive choice and powerful option in the optical toolkit.

Chu, H. et al. Linear magnetoelectric phase in ultrathin MnPS3 probed by optical second harmonic generation. Phys. Rev. Lett. 124, 027601 (2020).

Linear polarizationin physics

The first advantage is the reduction in spherical aberration. Spherical aberration occurs when a lens is not capable of focusing all the incident light on the exact same point. Even when fabricated to its theoretical limit, a standard spherical lens can never achieve the level of precision-focus that an asphere offers. It is the very nature of an asphere’s irregular surface shape that allows it to simultaneously manipulate the many wavelengths of light more precisely, resulting in sharper images.

Another mass-production method is glass molding. This process differs from injection molding in that the optical material is glass instead of a polymer and each lens is individually pressed with a fixed mold once the material is heated and softened. At higher temperatures, the glass material readily takes the shape of the mold but then requires an annealing step to alleviate any residual stress once the material has set in place. This process also does not produce aspheric surfaces with the level of precision offered by polishing but does offer cost benefits for volume production.

Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).

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The final important concept in the Sag equation is the conic constant. This variable, “k” defines the overall shape of the aspheric surface in terms of it being parabolic, hyperbolic, ellipsoid or spherical.

Sun, Z. et al. Giant nonreciprocal second-harmonic generation from antiferromagnetic bilayer CrI3. Nature 572, 497–501 (2019).

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

Esco uses both Optotech and OptiPro aspheric generators and polishers to fabricate very complex and high performing aspheric lenses.

The final method, and the one employed by Esco Optics, is a process called Sub-Aperture Generating and Polishing. During this process, a lens is set in place on a rotating fixture. One of two options are then employed to apply pressure to a small point on the lens while it rotates around the fixed axis. The first uses a durometer ball in contact with a rotating belt. Each durometer ball has a defined hardness that helps control the amount of pressure applied to the optical surface as a generating or polishing belt moves between it and the optic. A good analogy of this concept is to consider the different amount of “give” you can feel with your fingers if you squeezed a racquet ball, tennis ball and baseball. It's the choice of hardness in the durometer ball and type of generating/polishing belt that the CNC operated machine uses to apply the appropriate amount of pressure needed to achieve the specific aspheric contour and surface figure. The below graphic demonstrates this process:

Bramwell, S. T. & Holdsworth, P. C. W. Magnetization and universal sub-critical behaviour in two-dimensional XY magnets. J. Phys. Condens. Matter 5, L53–L59 (1993).

At Esco, we have years of aspheric manufacturing experience. We work with a wide range of optical materials, employ several fabrication techniques and have on site, the metrology equipment necessary to characterize our finished product. We welcome the opportunity to assist in providing your aspheric lenses and commit to working closely with our customers to seek the most cost-effective solution to their optical needs. We have the ability to make 1 or 100,000 pieces.

Kuo, C.-T. et al. Exfoliation and Raman spectroscopic fingerprint of few-layer NiPS3 van der Waals crystals. Sci. Rep. 6, 20904 (2016).

Peer review information Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

We welcome you back to our technical series on the Concepts in Light and Optics. In our previous 3 articles we discussed different types of lens configurations, the manner in which they manipulate light, as well as, the terminology and specifications used by optical fabricators to define the quality and precision of their lenses. Building on this knowledge, we’ll now explore one specific lens design that provides significant benefits over those with standard spherical radii. These unique optics are called aspheres. As you will see throughout this article, while complicated in design and often difficult to manufacture, aspheric lenses solve many of the inherent issues found in standard spherical optics that are polished to the very limit of their theoretical performance.

Esco Optics is a leading manufacturer of custom and catalog optics, precision optical components, and ITAR optics in the United States.

Aspheres Defined So what exactly is an asphere? The simplest definition is to compare the difference between a surface contour that is “typical” verses one that is “atypical”. Consider the two following examples:

Concepts in Light and Optics – Lenses – Part 3 Concepts in Light and Optics – Lenses – Part 2Concepts in Light and Optics – Lenses – Part 1

This material is based upon work supported by the National Science Foundation under grant no. 1945364. X.W. and X.L. acknowledge the financial support from Boston University and the Photonics Center at Boston University. The transmission electron microscopy imaging was performed at the Center for Nanoscale Systems, a member of the National Nanotechnology Coordinated Infrastructure Network, which is supported by the National Science Foundation under award no. 1541959. The Center for Nanoscale Systems is part of Harvard University. A.C. and S.S. acknowledge financial support from the US Department of Energy, Office of Science, Basic Energy Sciences Early Career Program under award no. DE-SC0018080. We acknowledge the computational resources through the Extreme Science and Engineering Discovery Environment, which is supported by National Science Foundation grant no. ACI-1548562; and the National Energy Research Scientific Computing Center, a US Department of Energy Office of Science User Facility supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231. Z.L. and D.S. acknowledge support from the US Department of Energy (no. DE-FG02-07ER46451) for high-field magnetospectroscopy measurements performed at National High Magnetic Field Laboratory, which is supported by the National Science Foundation through NSF/DMR-1644779 and the state of Florida. C.H.L. acknowledges support from the American Chemical Society Petroleum Research Fund (ACS PRF No. 61640-ND6).

Null interferometry uses a null lens as a reference surface to compare against the aspheric surface being tested. This reference induces a known amount of spherical aberration that is equal to the difference between the aspheric surface and a standard lens. Comparing the null lens to the interferometric pattern produced by the aspheric lens quantifies how precise the aspheric contour has been generated and polished. Another method of null interferometry uses a computer generated hologram (CGH) as the reference to produce a known wavefront pattern. Again, the interferometric comparison between the CGM and aspheric pattern determines the level of surface accuracy. While null interferometry is highly precise, its complicated set-up, and in the case of CGM’s, expense, both add to the complexity and cost of aspheric lens production.

Gao, W. B., Fallahi, P., Togan, E., Miguel-Sanchez, J. & Imamoglu, A. Observation of entanglement between a quantum dot spin and a single photon. Nature 491, 426–430 (2012).

Kim, K. et al. Suppression of magnetic ordering in XXZ-type antiferromagnetic monolayer NiPS3. Nat. Commun. 10, 345 (2019).

The good news is that you only need to understand a few simple concepts included in the Sag Equation in order to know how the aspheric contour is generated. The first concept deals with what information the Sag Equation provides. Basically, using the vertex (center) of the lens as a starting point, the equation tells us how much the lens surface deviates or "sags" along the Z axis (up or down) at any given distance “r” from the center when plotted perpendicularly to the optical axis (or horizontally along the X or Y axis from the center if conceptually easier to picture). Consider the following example of the X, Y, Z coordinates for a visual reference.

Du, K. et al. Weak van der Waals stacking, wide-range band gap, and Raman study on ultrathin layers of metal phosphorus trichalcogenides. ACS Nano 10, 1738–1743 (2016).

Kirilyuk, A., Kimel, A. V. & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010).

Chittari, B. L. et al. Electronic and magnetic properties of single-layer MPX3 metal phosphorous trichalcogenides. Phys. Rev. B 94, 184428 (2016).

Linear polarizationexample

Linear polarizationvs circularpolarization

A second method, while not as precise as interferometry, is to use a surface profilometer. This involves applying a probe which through actual contact with the aspheric contour, offers a physical measurement of its shape.

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While we will focus primarily on the manufacturing techniques employed by Esco to fabricate aspheres, there are several other processes worth mentioning.

Schmidt, T., Lischka, K. & Zulehner, W. Excitation-power dependence of the near-band-edge photoluminescence of semiconductors. Phys. Rev. B 45, 8989–8994 (1992).

In figure 1, we see a standard “typical” lens with a predefined radius of curvature. As discussed in our previous article, the radius of curvature is the distance between a central, fixed point and the surface of the lens.   Since the radius of curvature remains constant, the surface contour of the lens follows a regular arc where the lens surface is always the same distance from the central point. Now consider the surface shape of the aspheric surface in figure 2. You will notice it has a very distinct shape that deviates from the regular spherical curve of a standard lens. It is this “atypical” surface contour that characterizes both the shape and performance of an aspheric lens.

Wang, X. et al. Raman spectroscopy of atomically thin two-dimensional magnetic iron phosphorus trisulfide (FePS3) crystals. 2D Mater. 3, 031009 (2016).

Setyawan, W. & Curtarolo, S. High-Throughput Electronic Band StructureCalculations: Challenges and Tools. Comput. Mater. Sci. 49, 299–312, (2010).

An aspheric lens can be convex, concave and even free-form depending on the desired optical performance. Consider the following 3 examples.

Kresse, G. & Hafner, J. Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements. J. Phys. Condens. Matter 6, 8245–8257 (1994).

Diamond Turning is a third method that does offer a high level of precision in the quality of the optical surfaces but is somewhat limited in choice of materials. Standard optical glasses cannot be diamond turned while crystals and polymers can. This method employs a diamond-tipped tool that moves across the lens surface generating its shape and surface form. Only one lens can be generated at a time.

ITAR registered and compliant, Esco manufactures ITAR optics for all of its customers with the strictest confidentiality.

Wang, X., Cao, J., Lu, Z. et al. Spin-induced linear polarization of photoluminescence in antiferromagnetic van der Waals crystals. Nat. Mater. 20, 964–970 (2021). https://doi.org/10.1038/s41563-021-00968-7