All-nanoparticle concave diffraction grating fabricated by self-assembly onto magnetically-recorded templates

Using the enormous magnetic field gradients present near the surface of magnetic recording media, we assemble diffraction gratings with lines consisting entirely of self-assembled magnetic nanoparticles that are transferred to flexible polymer thin films. These nanomanufactured gratings have line spacings programmed with commercial magnetic recording and are inherently concave with radii of curvature controlled by varying the polymer film thickness. This manufacturing approach offers a low-cost alternative for realizing concave gratings and more complex optical materials assembled with single-nanometer precision. © 2013 Optical Society of America OCIS codes: (050.1950) Diffraction Grating; (050.2770) Gratings; (220.4241) Nanostructure fabrication; (160.4236) Nanomaterials. References and links 1. F. Kneubühl, “Diffraction grating spectroscopy,” Appl. Opt. 8, 505–519 (1969). 2. T. M. Hard, “Laser wavelength selection and output coupling by a grating,” Appl. Opt. 9, 1825–1830 (1970). 3. 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Introduction
Diffraction gratings consisting of a large number of equally spaced parallel slits or grooves play an important role in many technologies, including spectroscopy [1], laser systems [2], and information communication [3], where, for example, gratings increase the capacity of fiber-optic networks using wavelength division multiplexing/demultiplexing [4].High-resolution commercial diffraction gratings were originally fabricated with ruling engines, and the ruling process is slow and requires precise control of mechanical motion and external vibration [5].Other fabrication methods include photographic recording of a stationary interference fringe field in photoresist to create a holographic grating [6], electron beam lithography [7], and focused ion beam etching [8].Recently, gratings have been fabricated using laser pulses to ablate metal nanoparticles or thin films, with interference to create the grating pattern [9][10][11].Given the evolving need for control over optical element fabrication, lower cost and sustainable manufacturing technologies with nanometer precision are needed to create novel optical materials, and maintain the pace of technological innovation in optical technologies.
Nanoparticle self-assembly has promise as a sustainable manufacturing technology for construction of complex patterns including linear chains, and close packed arrays [12].For optical applications, self-assembly has been used to create dynamic diffraction gratings in liquid from colloidal nanoparticles using electrophoresis [13].Similarly, self-assembly via DNA and other surface anchoring techniques has been employed to pattern diffraction gratings on surfaces [14].In this paper, we describe the nanomanufacture of diffraction gratings from cobalt #177719 -$15.00USD Received 10 Oct 2012; revised 27 Nov 2012; accepted 28 Nov 2012; published 10 Jan 2013 (C) 2013 OSA ferrite (CoFe 2 O 4 ) nanoparticles that are first self-assembled onto magnetic disk drive substrates and are then transferred as assembled to standalone, polymer thin films.

Grating nanomanufacturing
Previously, our group has demonstrated a novel nanomanufacturing technology that employs magnetic recording to direct self-assembly of magnetic nanoparticles [15].Here we employ magnetic recording to generate patterns that yield diffraction gratings.Using magnetic recording to create nanoscale templates, we can direct self-assembly of magnetic nanoparticles onto disk drive magnetic media (i.e. the disks used in magnetic recording).Equally-spaced, oppositely-magnetized regions are recorded onto a 95 mm diameter longitudinal disk drive medium (disk) via magnetic recording with a conventional write/read head.The length of these regions are precisely controlled during the recording process to yield equal spacing lines patterned on the disk surface.Enormous magnetic field gradients (> 4 x 10 6 T m −1 at 25 nm to ∼5000 T m −1 at 1 µm above the disk drive surface) exist at the junction (called a transition) between the oppositely recorded regions [16].These field gradients exert a force on colloidally suspended superparamagnetic nanoparticles, i.e., a ferrofluid [17,18] deposited on the media.This spatially-localized magnetic force attracts the nanoparticles to these transitions, and by creating arrays of transitions over the disk surface, we precisely assemble nanoparticles into large-area patterned materials.Pattern sizes and shapes are controlled by magnetic recording, with the magnetic medium acting as a template for nanoparticle assembly that can be both reused and reprogrammed with different patterns.For the diffraction gratings we manufacture using the template, the lines lie parallel to the disk radius with the grating spacing along the disk circumference.Our gratings are written at a 28 mm radius, and over a 0.65 x 0.65 mm 2 illuminated area [e.g.0.65 mm Gaussian full width at half maximum (FWHM) of our HeNe laser beam], the saggita for a 0.65 mm long chord is 2 µm.Therefore, relative to a 0.65 mm wide band, the deviation of our grating from square along the circumferential direction is ∼0.3% and can be neglected.Moreover, we can also perform xy rectilinear recording using a contact write read tester [19].Figures 1(a)-1(d) show the entire process schematically.
As shown in Fig. 1(a), magnetic recording media are diced into ∼12 mm diameter circular coupons.After cleaning a coupon, ∼0.5 mL of diluted ferrofluid (∼10 -20 nm diameter cobalt ferrite nanoparticles with ∼10 µg/mL nanoparticle concentration) is pipetted onto the coupon.The nanoparticles suspended in the ferrofluid just above the coupon surface are magnetized by the transitions' fields, and are then attracted to the transition region ["T" in Figs.1(a)-1(c)], by the field gradient.The ferrofluid solution remains on the coupon for 60 minutes, and is then removed.Nanoparticles coat the transitions on the coupon [Fig.1(b)].Here we employ CoFe 2 O 4 as opposed to Fe 3 O 4 nanoparticles discussed in Ref. [15] because the pattern formation process takes longer (60 minutes as opposed to 1 minute for Fe 3 O 4 nanoparticles), making the process easier to control.A representative dark-field microscope image of the nanoparticle patterns assembled on the coupon is shown in Fig. 1(e).After imaging the assembled nanoparticles we spin-coat a liquid polymer solution onto the coupon surface [Fig.1(c)].The polymer (Diskcoat 4220 from General Chemical Corp., Brighton, MI) is diluted with DI water (Diskcoat:DI water = 4:1) and spun at 2000 rpm for 20s, and the resulting film is ∼ 1.1 µm thick as determined using both stylus and optical profilometry.Varying the ratio of Diskcoat to DI water enables different polymer film thicknesses.After curing the polymer thin film for 15 minutes in air at room temperature, the polymer-nanoparticle assembly is peeled from the coupon surface with adhesive tape [Fig.1(d)].This peeling transfers the nanoparticle patterns to the polymer film.The adhesive tape has a 5 mm diameter central hole, yielding a window of suspended film containing patterned nanoparticles [Fig.1(f)].Figure 1(g) shows a dark-field image of the patterned nanoparticles as embedded in the suspended film after peeling.We optically measure  grating spacing (d) using a 100X objective lens, and, assuming equal spacing for these features, multiple measurements of 50 µm patterned regions (L = 50 µm) yield 742 ± ∼12 nm.Similar measurements on the peeled patterns yield 750 ± ∼12 nm.The 12 nm error bars (σ ) are obtained via where N is the average groove number within the 50 µm patterned regions and δ N is the standard deviation in N measurements.For peeled patterns, N = 66.4 and δ N = 1.03.As no nanoparticles are observed on the coupon after peeling, and with the same pattern spacing after transfer within experimental error, this approach yields near-perfect transfer of the assembled grating from the coupon to the film.parallel to the z-axis.Diffraction spectra are obtained using the experimental geometry shown in Fig. 2(a), with light incident onto the grating surface at normal incidence.Four optical sources [HeNe gas laser (632 nm), green (532 nm) and blue (405 nm) diode lasers and a tungstenhalogen bulb] are aligned with the x-axis for illuminating the grating identically at the origin (O).A photodetector is used to monitor the intensity of laser transmission.A charge-coupled device (CCD) line camera (LC) is mounted on a xy-translation stage.The LC incorporates a 3045 pixel CCD array (7 µm horizontal pixel size and ∼21.3 mm long in total) with 350 -1100 nm spectral range.For all spectral measurements the pixel line array is parallel to the x-axis and vertically aligned to be in the same plane as the incident light.Figure 2(b) shows representative first-order diffraction spectra for a 1.1 µm thick polymer grating for 405, 532, and 632 nm laser lines, which we employ for calibrating the spectrograph.The calibration is performed by finding the angle of diffraction for the three reference laser lines as follows.We translate the LC by a known ∆y and record the corresponding peak position shift ∆x.We perform this calculation for the three lines to determine absolute x and y positions of LC pixels.Both absolute and relative x and y LC positions are related to the angle of diffraction β , via

Spectral measurement and calibration
The diffraction angle is related to grating spacing and wavelength by the diffraction grating equation [20] d(sin α where α is the incident angle, = 0 in our geometry, λ is the wavelength and m is the order number, = 1.We fit λ as a function of β and obtain d = 770 ± 10 nm.This result agrees within error bars with the 50 µm scale bar measurements discussed above.Using y = 13.7 mm and d = 770 nm, Eq. ( 2) and Eq. ( 3) allow us to convert an arbitrary x-position on the LC into units of wavelength to generate the lower axis in Figs.2(b)-2(c).The error in this spectral calibration is ∼13 nm, which is calculated using the pixel positions that correspond to the 550 nm center wavelength of our detection window.This 13 nm error arises from combining the 10 nm uncertainty in our measurement of d with 7 µm and 12 µm uncertainties in LC pixel position and y-stage translation respectively.The solid line in Fig. 2(c) shows the diffraction spectrum for a tungsten-halogen bulb recorded with our spectrograph.We observe 5 peaks at ∼425 nm, 455 nm, 495 nm, 535 nm, and 595 nm.The inset to Fig. 2(c) shows a photograph of the tungsten-halogen spectrum displayed on a white card for reference.The diffraction spectrum for the tungsten-halogen bulb recorded with a commercial spectrometer (Ocean Optics, Red Tide USB650 with ∼2.0 nm optical resolution) is also shown [the dotted line in Fig. 2(c)] for comparison.The two spectra match closely, however the solid line peaks for the nanomanufactured grating are more prominent (∼2x).
The absolute efficiency of these nanomanufactured gratings measured with the HeNe laser (10 mW) is 0.00071 ± 0.00002.Assuming a 750 nm period lamellar grating with ∼100 nm FWHM assembled nanoparticle feature size and 30 nm groove depth [15], and given the small ratio of feature height to wavelength ∼ 0.05, asymptotic theory predicts 0.0045 absolute efficiency at 633 nm for the Littrow geometry [21].While the measured efficiency is ∼ 6 times lower, our gratings are measured at normal incidence and are not true lamellar structures.By sputtering 20 nm of Au on a grating, we achieve an order of magnitude efficiency improvement, suggesting that further optimization of the fabrication process could yield better diffraction efficiency.Moreover, absolute efficiency can be enhanced by increasing the groove width relative to the grating period [21].

Concave grating
While calibrating the spectra discussed above, we noticed that a y-translation also causes a change in spectral peak intensity and width.Figure 3(a) shows a representative set of diffraction peaks on the LC during a series of y translations using the 532 nm laser.Starting at x = 6 mm, the peak intensity first increases until x = 12.7 mm and then decreases until x = 18.5 mm.Similarly the spectral width decreases and then increases as x increases with the minimum peak width corresponding to the maximum intensity.Figure 3(a) labels the corresponding y-position in millimeters above each peak.Changing peak intensity and width as a function of x and y lead to the hypothesis that the grating is focusing the spectrum, and that our gratings are not planar but concave.As the LC records a projection parallel to the incident beam and β remains the same regardless of LC position, the peak center position is accurately detected by the LC.Therefore, we can precisely obtain the spectral focus as a function of x and y by recording spectral profiles while translating the y stage.This measurement configuration is known as the Wadsworth geometry [22,23].
Figure 3(b) shows a concave grating geometry, where the origin O of the Cartesian system is at the center of the grating, the x-axis is the grating normal and the z-axis is parallel to the grating grooves.As for the plane grating, the light path difference for neighboring grooves must be an integral multiple of λ so that the diffracted waves are in phase.The light path difference for any two grooves of the concave grating separated by w is (w/d)mλ .Thus for light from point A(x 0 , y 0 , z 0 ) with incident angle α on any point P(u, w, l) of the concave grating, where w/d is an integral number, forms a spectral image at point B(x, y, z) with diffraction angle β , light has to satisfy the light path function (F) [24,25] where < AP > (< PB >) is the distance between points A and P (P and B).According to Fermat's principle of least time, point B is located such that F is an extreme for any point, P, and all extremes for focusing light from A at B must be equal [24,25].Thus the condition for focusing light that diffracts from grating points along w [i.e., y direction in Fig. 3(b)] is Since the LC pixel array records spectra only along the x-axis, we expand Eq. ( 4) in a series with respect to w [24].We insert Eq. ( 4) into Eq.( 5) using α = 0 and < AP > = ∞ (Wadsworth geometry).Ignoring orders above first in w [24],) we find y as a function of x and for convenience this function is expressed in terms of y and β using Eq. ( 2) where R is the radius of curvature of the grating.We nanomanufactured 11 gratings, 3 are 0.45 µm thick, 5 are 1.1 µm thick, and 3 are 6.25 µm thick.Their focal positions measured with 632 nm, 532 nm, and 405 nm lasers are shown in Fig. 3(c) as triangles, dots, and crosses for each thickness respectively.We then fit these data with Eq. ( 6) and find R = 43.1 ± 0.7 mm, 57.1 ± 1 mm, and 71.6 ± 0.8 mm for 0.45 µm, 1.1 µm, and 6.25 µm thick gratings respectively [solid lines in Fig. 3(c)].We observe thicker films have larger radii of curvature, meaning the films are flatter, while thinner films have smaller radii of curvature, meaning the films are more curved [inset to Fig. 3(c)].The focal positions of the images diffracted by these three different curvatures as indicated in Fig. 3(c x(mm)  (C) 2013 OSA that our gratings have nearly identical spacings for differing polymer film curvatures [dotted lines drawn along a constant angle in Fig. 3(c)].Further, the zeroth-order term of an expansion of F with respect to w leads to the diffraction grating equation [i.e.Eq. ( 3)], demonstrating that grating curvature does not affect the diffraction angle, only the focused spectrum position.The nearly identical spacings and < 2% variations in R measurements show these nanomanufactured gratings are highly reproducible.These measurements demonstrate that not only does our nanomanufacturing process create repeatable concave gratings, but also allows control of the radius of curvature.This inherent curvature eliminates a second curved mirror that is found in the Czerny-Turner [26], Ebert-Fastie [27], and Littrow monochromators [28].The spectral bandpass (B S ) of our concave grating spectroscopic system in the Wadsworth geometry is imaging limited, since there is no entrance slit and the line camera pixel size is 7µm, where P F and W S are the plate factor for concave gratings and the entrance slit width respectively [29].Using 0.65 mm for our entrance slit, i.e.W S = 0.65 mm, and with ∼2 x 2 mm 2 grating size, i.e. much smaller than R, we employ the Rowland circle concave grating P F [30] with an extra factor of sin β to account for the orientation of the LC pixels parallel to the x-axis.Thus we have For 57.1 mm radius gratings, Eq. ( 8) predicts B S = 4.1 nm for the HeNe laser, and the measured FWHM of the HeNe diffraction peak is 4.2 nm, i.e. suggesting our measured resolution agrees closely with that predicted for our particular imaging geometry.The measured and predicted resolutions agree closely for all three radii of curvature.

Repeatability of tungsten-halogen spectra
Figure 4(a) shows tungsten-halogen spectra for 5 nominally identical  are not linearly scaled with respect to y.For the 532 nm laser the diffraction foci for these 5 gratings are slightly different, and therefore we record tungsten-halogen spectra with the LC located at the average position, y = 11.33 mm.Each spectrum has 5 peaks, and we fit each peak's position using the Lorentzian function [31], as displayed in Figs.4(b)-4(f).Figure 4(b) shows that the first peak of 5 identical gratings occurs at nearly the same spectral position with <10 nm variation.Figures 4(c)-4(f) show almost same behavior as Fig. 4(b) with ∼ 3 nm average standard deviation.Thus multiple grating studies both for differing radii of curvature and of tungsten-halogen spectra together demonstrate that our nanomanufacturing process is highly repeatable.

Conclusion
We have nanomanufactured an all-nanoparticle diffraction grating embedded in a flexible, curved, polymer thin film and demonstrated its performance in a calibrated optical spectrograph.Appropriate entrance slits could be incorporated to improve spectral resolution, larger gratings could be illuminated, and Rowland circle mounts could be used to reduce aberrations in the diffracted spectrum [24].This approach to programmable self-assembly is not limited in terms of how large the line-spacing can be, since larger magnetic patterns can easily be recorded.The minimum line spacing depends on the smallest magnetic pattern that the recording system can support, which is 10 -30 nm for areal densities from 100 Gbit/in 2 -1 Tbit/in 2 , and will continue to be reduced as magnetic recording technology advances.In principle, grating size is limited by mechanical positioning and the availability of sufficiently large magnetic media materials, however the size and quality of the grating transferred will depend on the polymer properties, and limits to the peeling process.Here different polymers with suitable properties could be employed to potentially create large-scale gratings.Different magnetic media could be used to increase grating thickness, and importantly, different species of nanoparticles with more uniformity and narrow polydispersity could allow better control of groove microstructure, and potentially allow one to create blazed gratings.Future work will include determining how grating efficiency, resolving power, and repeatability depend on parameters of the coating process (e.g.coating time) and nanoparticle magnetic properties.Quantitative measurements of grating scatter and stray light emission will help elucidate the factors that impact absolute efficiency.By combining the unique attributes of nanomaterials with large area reprogrammable patterning, this approach could yield more cost-effective and sustainable materials for optical applications.

Fig. 1 .
Fig. 1.Diffraction grating nanomanufacturing using programmable magnetic recording and pattern transfer.(a)-(d) Schematic diagrams showing entire nanomanufacturing process.Gray ellipses: projections of coupons.Parallelograms: projections of magnetized regions on coupons and arrows enclosed denote magnetization directions.T: magnetic transition.Black dots: superparamagnetic nanoparticles.Yellow ellipses: projections of polymer thin films.(e) Dark-field optical image of nanoparticle arrays assembled on a coupon.(f) Polymer film containing patterned nanoparticles after peeling.(g) Dark-field optical image of the black square in (f) showing the assembled nanoparticle grating lines embedded in the polymer film.

Figure 2 Fig. 2 .
Figure 2 demonstrates operation of our nanomanufactured gratings in an optical spectrograph.A grating is mounted on a rotation stage with the lines of nanoparticles in the y-z plane [front view in Fig.2(a)].The rotation stage can orient the grating such that the nanoparticle lines are

Fig. 3 .
Fig. 3. Curvature inherent in our nanomanufactured concave gratings.(a) 532 nm diffraction spectra recorded while translating the LC in the y direction demonstrate changes in both peak intensity x-position (bottom axis) and width (corresponding y positions in millimeters are shown above each peak).(b) Schematic diagram of an optical system showing image formation with a concave grating.(c) Red, green and blue dots (crosses and triangles) show focal positions for 632 nm, 532 nm and 405 nm lasers respectively.Polymer film thicknesses are indicated in the legend.Three solid lines show fitted trajectories of focal positions for the three grating thicknesses with fitted radii of curvature, R, as indicated.Red (green and blue) dashed lines display linear fits of diffraction angles for the 632, 532, and 405 nm lasers.Inset: R vs grating thickness.