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Abstract
Dammann grating (DG) is a binary beam splitter. Traditional DG is pure solid and cannot be modulated for different working wavelength. We report a tunable multi-wavelength DG based on a liquid-solid hybrid structure. Two glass plates are bonded by UV adhesive strips, one has a periodic grooves structure made by photoresist, the other has two drilled holes as inlet and outlet, respectively. A microfluidic mixer connected the inlet mixes of two miscible liquids with different flow rates to adjust the refractive index of the mixed liquid entering DG from 1.351 to 1.473. In the experiment, the real-time tunability has shown the DG achieves well beam splitting effect when parameter N is integer, 7 × 7 light spots are arranged in order with good uniformity. For λ = 632.8 nm, spot size uniformity is about 78.38% and power uniformity is ∼71.01%. For λ = 532 nm, the spot size and power uniformity are about 77.17% and 64.32%, respectively. The experiment also demonstrates this DG’s suitability for near-infrared light. This work is the first study of tunable DG based on liquid-solid hybrid structure and possesses special merits as compared to its solid counterpart, such as simple fabrication, tunability and multi-wavelength applicability, which make it have an extensive prospect in optofluidic networks and optical devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Dammann grating (DG) is a kind of binary phase grating with special aperture function [1]. The Fraunhofer diffraction pattern generated by DG is an array of light spots with uniform intensity [2]. Its phase structure is periodic distribution, in each period, there is a group of phase mutation points [3]. The grating structure and its diffraction pattern are determined by the positions of those phase abrupt points [3,4]. In recent years, DG has been widely used in optical interconnection, parallel information reading or as the light source of logic array devices. However, for conventional DGs, all kind of them are made of solid materials, they are just for only one working wavelength, once they are manufactured, they are settled. This feature makes traditional DG cannot be modulated in real time for different working wavelength, which will restrict its application.
Liquid media possesses strong fluidity and good reconfigurability, allowing much flexible tunability. Optofluidics [5–7] is a combination of optics and microfluidics. It aims to manipulate light and fluids at the chip level and to realize and enrich optical functions in a compact, reconfigurable, and high-sensitive platform. Lots of tunable optical components, including laser [8], switch [9], optical filter [10], lens [11–13], waveguide [14], have been developed into an optofluidic system for various applications. Besides, some optofluidic devices with periodic grating structure have been used as cavity [15], filter and Fresnel zone plate [16]. However, tunable multi-wavelength optofluidic DG, which has great potential in integrated optics, has not been realized in optofluidic systems so far.
In this paper, we firstly proposed a tunable multi-wavelength optofluidic DG. Unlike its solid counterpart, the hybrid solid-liquid DG consists of alternate and variable half-wave zones. A microfluidic mixer connects the DG and mixes two miscible liquids with different flow rates to modulate the refractive index (RI) of the mixed liquid entering the DG chip. With the gradually changing of RI of the liquid, the DG chip will regularly be phase-reversal at some specific RI and modulate beam splitting properties simultaneously. Meanwhile, because the RI is controllable, our hybrid DG is also adaptive to other operating wavelengths.
2. Design and theoretical analysis
2.1 Device design
The schematic design of the hybrid DG is shown in Fig. 1(a). Two glass plates firmly bonded by UV adhesive strips form the main structure of DG, in which the lower glass plate has a periodic grooves structure made by photoresist. The distance between the upper and lower glass plates is 125 µm. Figure 1(b) is an enlarged view of the smallest repeating cell of the periodic structure, which is designed according to the rules of DG. The blue part is photoresist, its thickness is 9 µm, and the depth of each groove is 9 µm. The period length of each cell is 60 µm. Two holes are drilled in the upper glass plate as the inlet and outlet respectively.
Fig. 1. (a) 3D view of optofluidic DG chip. (b) Enlarged view of the smallest repeating unit of the periodic structure.
2.2 Theoretical analysis
DG’s phase structure is periodic distribution. The phase in each period is binary, that is zero or π. In each period, there is a group of phase mutation points. It is necessary to find a set of phase mutation coordinates {XK} (see Fig. 1(b)), so that the intensity of the obtained (2M + 1) beams evenly distributed [2,3,17–19].
Let the phases on both sides of the phase mutation point be (θ + π/2) and (θ - π/2) respectively, the phase difference between them is π. θ represents an arbitrary phase for reference. The transmittance of the complex amplitude tp(x) is obtained as
Applied Fourier transform to Eq. (2), the spectrum function of phase grating is
where m means the diffraction order and can be an integer between -M and M. Insert tp(x), when m is not 0, we can get here Ta(m) is the the Fourier transform of ta(x). When m is 0, we can getAnd the power spectrum function
According to Eqs. (4), (5) and (6), the ideal numerical structure of binary diffractive optical elements can be obtained by changing reasonable coordinate values. The optimization objective function we adopted is
The optical path difference between two adjacent half-wave zones $\Delta \varepsilon$ is equal to the odd times of half-wavelength, we can express it as
where nP and nL are the RIs of photoresist and the mixed liquid, respectively. h is the depth of the grooves. N needs to be an integer and equals to 0, ±1, ±2, ±3… λ is the working wavelength. Here, nL could be described as nL = (Q1n1 + Q2n2)/(Q1 + Q2), Q1, Q2 and n1, n2 are defined as the flow rates and RIs of the two miscible liquids. The relationship between Q1/Q2, N and λ can be described as3. Experimental section and results
3.1 Device fabrication
Figure 2 indicates the detailed procedures for fabricating the optofluidic DG. Photolithography technique was used to prepare the diffraction structure of DG. As shown in Fig. 2(a), a 9 µm photoresist (Futurrex, PR1-4000A1) was spin-coated onto the surface of the glass substrate, which was then exposed to UV light through a photomask with DG structure pattern. Then a developer was used to remove the photoresist in the exposed regions, and a periodic grooves structure was formed on the substrate, as shown in Fig. 1(b). Finally, a top glass plate drilled with two holes was bond with the substrate with the lithographic structure with UV adhesive strips to complete the sealing (see Fig. 2(c)).
Fig. 2. Fabrication processes of optofluidic DG: (a) spin-coating photoresist and exposure to UV light through a photomask; (b) obtaining DG pattern via development; (c) bond with the top glass to complete the sealing.
Figure 3 shows an image of the DG diffraction structure observed using an optical microscope (OM). All repeating cells have uniform size and consistent morphology. The effective area of the glass substrate is 1 cm × 1 cm. The period length of each cell is 60 µm, and the depth of every groove is ∼9 µm. The photoresist is extremely transparent, and its RI is about 1.628.
3.2 Beam splitting experiment
The two miscible liquids are deionized water (n1 = 1.332) and glycerol (n2 = 1.473). They are kept in two 10-ml syringes, which are driven by a syringe pump (Suzhou Wenhao Microfluidic Technology Co. Ltd, WH-SSP-08) for controlling the flow rates of the two liquids entering the microfluidic mixer separately. After flow through the mixer, the mixed homogeneous medium pours into the DG structure and immerses into the grooves. During the experiment, the mixed liquid fills up the chip and completely immerses into the grating structure, and the liquid sloshing caused by gravity will not affect the device performance. Figure 4(a) records the relationship between the mixed liquid’s RI (nL) and flow rate ratio of two miscible liquids (Q1/Q2). With the change of Q1/Q2, the refractive index range (1.351-1.473) of the mixed liquids could be used to achieve different beam splitting results.
Fig. 4. (a) The relationship between the mixed liquid’s RI (nL) and flow rate ratio of two miscible liquids (Q1/Q2). (b) Relationships between parameters N and Q1/Q2: 532 nm (green solid line) and 632.8 nm (red solid line).
To test the light beam splitting property of the optofluidic DG chip, an optical test setup was built as shown in Fig. 5. Light emitted from the laser is collimated by lens L1 and L2, and then irradiated the DG chip. L3 is a Fourier transform lens. After passing through L3, the light beam is focused on the image surface of CCD camera and detected by it.
A 632.8-nm He-Ne laser is selected as the light source, and the relationship between its parameter N and flow rate ratio of two miscible liquids (Q1/Q2) is described in Fig. 5(b) (red solid line). In this experiment, with the change of the flow rate ratio of deionized water and glycerol, the value of N will be integer twice, that is, N = 2 and N = 3.
Figure 6 shows the beam splitting properties of our DG chip under the real time tuning of Q1/Q2. The total flow rate (Q1 + Q2) is constant. Distance between the adjacent spots is about 760 µm. When N is integer, Q1/Q2 = 0.04 (here, N = 2) and Q1/Q2 = 1.76 (N = 3) (Fig. 6(a) and 6(e)), DG achieves the well beam splitting effect, 7 × 7 light spots are arranged in order with good uniformity. Among them, the light intensity of some spots decreases when N = 3 compared with the situation of N = 2. This is because with the increase of N, the optical path difference between the two adjacent half-wave zones will increase, which will reduce the diffraction efficiency. Figures 6(b) and 6(d) show that when Q1/Q2 = 0.24 (N = 2.25) and Q1/Q2 = 0.98 (N = 2.75) respectively, the diffraction effect of DG becomes worse and some light spots are lost. When N is equal to integer + 0.5 (or integer - 0.5), DG has the worst splitting effect (see Fig. 6(c), here, N = 2.5, Q1/Q2 = 0.53), and many diffraction spots are missing. At this time, the diffraction is insufficient, which is the reason for the losing of several light spots.
Fig. 6. Beam splitting properties of our DG chip: (a) Q1/Q2 = 0.04, N = 2; (b) Q1/Q2 = 0.24, N = 2.25; (c) Q1/Q2 = 0.53, N = 2.5; (d) Q1/Q2 = 0.98, N = 2.75; (e) Q1/Q2 = 1.76, N = 3.
In order to quantify the light splitting properties of our DG chip, we analyse the uniformities of the size and optical power of the spots obtained by the beam splitting experiment. We binarize the photo obtained by CCD camera at N = 2, and calculate the area of the spots. The 49 light spots are numbered successively as shown in Fig. 7(a). Figure 7(b) records the area distribution of 48 light spots except the 25th light spot. The area of the 25th light spot is 0.412 mm2, and the area of the remaining 48 spots is in the range of 0.018 mm2 ∼ 0.063 mm2, with an average value of 0.032 mm2, and the standard deviation value is ∼0.0091 mm2. Here, we defined the spot size uniformity as
Fig. 7. (a) Binary boundary image of the beam splitting picture at N = 2. (b) The area distribution of 48 light spots except the 25th light spot. They distribute in the range of 0.018 mm2 ∼ 0.063 mm2, with an average value of 0.032 mm2. (c) The power distribution of 48 light spots except the 25th light spot. They distribute in the range of 1.87 pW ∼ 13.85 pW, with an average value of 6.22 pW. (d) 3D optical power distribution diagram. λ = 632.8 nm.
Then we replaced the CCD camera in Fig. 5 with a spot analyzer (BC106N-VIS(/M), Thorlabs) to obtain the light power of every spot and intensity distribution. A neutral-density filter was used to control the light intensity. The optical power of the 25th light spot is 77.30 pW, which is the 20.58% of the total optical power of 49 points. Figure 7(c) records the power distribution of 48 light spots except the 25th light spot and Fig. 7(d) shows its corresponding three-dimensional (3D) optical power distribution map. The power of these 48 spots is in the range of 1.87 pW ∼ 13.85 pW, with an average value about 6.22 pW, and the standard deviation value is ∼2.6402 pW. Here, we defined the optical power uniformity as
Fig. 8. (a) Intensity distribution at N = 2 of 632.8 nm. Light intensity of spots array in the (b) x coordinate and (c) y coordinate.
3.3 Multi-wavelength experiment
Theoretically, once the optical path difference between the adjacent half-wave zones equals to the odd times of the half-wavelength of the working source, DG splitter will have a good beam splitting effect. Therefore, we also use a laser diode (LD) with 532 nm wavelength as the light source to carry out the above experiment, and the relationship between its corresponding parameter N and Q1/Q2 is represented by the green solid line in Fig. 4(b). Figure 9(a) shows the diffraction pattern at N = 3 of 532 nm. A group of 7 × 7 spots are arranged uniformly, and the distance between adjacent spots is about 686 µm. The corresponding light intensity distribution is given in Fig. 9(b), and the average intensity of these spots is ∼51 arbitrary units. Figure 9(c) depicts the area distribution of 48 light spots except the 25th light spot. The area of the 25th light spot is 0.177 mm2, and the area of the remaining 48 spots is in the range of 0.007 mm2 ∼ 0.022 mm2, with an average value of 0.011 mm2, and the standard deviation value is ∼0.0035 mm2. The spot size uniformity here is about 77.17%. Figure 9(d) records the power distribution of 48 light spots except the 25th light spot. The power of these 48 spots ranges from 1.17 pW to 10.74 pW, with an average value about 4.87 pW and the standard deviation value is about 2.2681 pW. The power of the 25th light spot is 27.34 pW, which is the 10.48% of the total optical power of 49 points. The power uniformity here is about 64.32%. Figures 9(d) and 9(e) show the normalized average intensity of lights in the x coordinate and y coordinate, respectively. For this two diagrams, the light intensity of the 25th spot is also involved. This indicates that, unlike its solid counterpart, our DG chip is available for more than one working wavelength.
Fig. 9. (a) Diffraction pattern at N = 3 of 532 nm. (b) Intensity distribution map. (c) Area distribution of 48 light spots except the 25th light spot. They distribute in the range of 0.007 mm2 ∼ 0.022 mm2, with an average value of 0.011 mm2. (d) The power distribution of 48 light spots except the 25th light spot. They distribute in the range of 1.17 pW ∼ 10.74 pW, with an average value of 4.87 pW. Light intensity of spots array in the (e) x coordinate and (f) y coordinate. λ = 532 nm.
Compared with the wavelength of 632.8 nm, the uniformity of the spot with a wavelength of 532 nm, both in size and optical power, has decreased. This is because in the same test system, for 532 nm, the first integer N encountered within the nL range (1.351-1.473) is 3, while for 632.8 nm, it is 2. Theoretically, the smaller the absolute value of integer N, the greater the diffraction efficiency will be obtained. When N is zero, there will be the maximum diffraction efficiency, which can be achieved by switching to a long wavelength light source or by reducing the depth of the grooves (i.e., the thickness of the photoresist).
A 405-nm LD and a 1310-nm super laser diode (SLD) are employed as the light source as well, and the diffraction patterns are shown in Figs. 10(a) and 10(b), respectively. For 405 nm, the size uniformity is ∼69.13%. And for 1310 nm, a fiber collimator replaces L1, aperture and L2 in Fig. 5, the size uniformity here we detected is about 72.21%. This means that our hybrid DG is not only suitable for visible light, but also for near-infrared light. Compared with λ = 632.8 nm, the uniformity of λ = 1310 nm decreases slightly. This is due to the change of the experimental test system, light emitted by the fiber collimator is not strictly parallel light.
4. Discussion
Our novel tunable optofluidic DG regulated by Q1/Q2 manipulation exhibits many advantages. First, easy fabrication. Our approach provides a simple method for fabricating tunable DG, it does not require any complicated etching process or manufacturing technology, and its main functional structure is directly processed by photolithography. Second, tunability. The DG chip we designed can adjust the optical path difference of the adjacent half-wave zones, and different optical path differences will correspond to different light splitting effects, which makes up for the non-tunable shortcoming of traditional DG. Third, multi-wavelength applicability. Unlike the solid counterpart of our DG chip, the hybrid solid-liquid DG consists of alternate and variable half-wave zones. As long as the optical path difference between two neighbouring half-wave zones meets the odd times of the half-wavelength of the working source, it will produce a good beam splitting effect.
There are still deficiencies in our DG. Due to the high depth of the grooves (9 µm, which is several times of the working wavelengths), the splitting uniformity of our DG still needs to be improved. We will improve the processing technology to reduce h and make N closer to 0 so as to improve the uniformity in the future. We can also explore other miscible liquids to expand the RI range of the mixed liquid (nL), so that nP falls within the variation range of nL, and (nP - nL) will reduce to make N closer to 0. Meanwhile, we can also obtain DG beam splitter with different splitting ratios by changing {XK}. In the future, we would like to explore wavelength-independent tunable DG that can meet the requirements of different splitting ratios.
5. Conclusion
In summary, we have demonstrated a novel tunable hybrid DG based on an optofluidic chip. It consists of alternating solid-liquid half-wave zones. Photolithography processes the main functional structure. The light splitting tunability could be realized by changing the flow rate ratios. The experimental results have successfully shown the real-time tuning of splitting properties and multi-wavelength adaptivity. With the merits of simple fabrication, tunability and suitable for multiple wavelengths, our hybrid DG may find wider applications in optofluidic systems.
Funding
National Natural Science Foundation of China (61675153, U2006216).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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