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Abstract
In this paper, a switchable micro-focusing Fresnel device based on phase-change materials (PCMs) is proposed, which can selectively display the functions of transmission and reflection without the use of mechanical adjustment on micro scale. The switchable function is realized by combining Fresnel structure with PCM. A four-level switchable Fresnel device consisting of a typical PCM Ge3Sb2Te6 (GST-326) is designed to focus light into a focal length of 30 µm at wavelength of 3.1 µm. The optical performance of the switchable device has been analyzed by using finite-difference time-domain (FDTD) method, showing bright convergence point near pre-designed focal length with focusing efficiencies larger than 18%, depth of focus (DOF) less than 4.65 µm and the full width at half-maximum (FWHM) not larger than 1.30 µm. Furthermore, by precisely manipulating the variation of PCM thickness, we also obtain a device that possesses the characteristics of a transmission-reflection focusing beam splitter. The devices show good potential for the combination of traditional binary optical devices and PCM to produce new functions, and provides a promising innovative approach for miniature focal length switching device.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Among multi-functional optical devices, the focal length switchable device is very important for improving system performance and achieving specific applications. It can be used in many applications such as target tracking [1–3], imaging [4–6], and microscopy [7,8]. The traditional ways to switch focal lengths include mechanical modulation [9–11], changing path length [12–14], using the liquid crystal lenses [15,16], and using the liquid lens [17–20]. With the development of instruments in multifunction and integration, the focal length switchable device has to become more and more miniaturized. However, most of the traditional methods are not able to meet the requirement well. Therefore, more and more researchers are looking for methods to design and fabricate the focal length switchable device on micro scale.
Fresnel lenses or reflectors with flat surfaces and small volumes are transformed from traditional optical elements with curved shapes and bulky volumes, and have attracted much attention in various fields because of simple design principle, high diffraction efficiency [21–23]. Unlike the traditional curved elements, Fresnel lenses or reflectors use diffraction instead of refraction or reflection [22–25]. Due to the subwavelength units, Fresnel lenses can meet the requirements of modern optical instruments for integration and miniaturization well. However, Fresnel lenses usually do not have the ability to adjust the focal length, or switch between transmission and reflection functions. If Fresnel lenses are used for focal length switching, they need to be carefully designed in a new way.
Phase-change materials (PCMs) can switch between two solid states—amorphous and crystalline, causing changes in the related physical properties such as optical absorption, electrical conductance, and refractive index [26–28]. Because of the extraordinary properties such as extreme scalability, fast switching speeds, and high switching endurance [26,27], PCMs have been the key materials in rewritable optical disks and memory devices [28,29]. Meanwhile, they show great potential for applications in tunable photonic devices, which have attracted much attention from the optics community [30–36]. Recently, a typical PCM Germanium antimony telluride Ge3Sb2Te6 (GST-326) has widely employed for constructing tunable nanophotonic devices [37–41], because its amorphous and crystalline states are both metastable at room temperature, and its lower mid-infrared losses compared to other common materials [29,37]. So the combination of Fresnel devices and PCMs may have the potential to integrate the advantages of both.
In this paper, we introduce and demonstrate a novel design concept for micro switchable focusing device that employs a combination of Fresnel structure and the PCM GST-326. By precisely adjusting the height of each level, switchable devices with different focusing functions can be designed. A device is modeled and the results are in good agreement with the theoretical prediction, which prove the feasibility of the novel design principle. We also model a device that can simultaneously function as a beam splitter and a focusing element. Compared with traditional binary optical elements, the switchable device designed with our novel concept can have many focusing modes, such as single reflection focusing, single transmission focusing, reflection-transmission dual focusing, and can realize focal length switching without relying on mechanical motion. Compared with other devices with GST-326, the switchable device adopts the Fresnel structure, whose related theoretical analysis is already mature [29,40,42].
2. Theoretical background
The proposed device is on micro scale and comprised of PCMs (e.g., GST-326) whose refractive index varies greatly in different solid states. The device is completely surrounded by low index materials (e.g., air). Figure 1 shows the schematic geometry of the switchable device. A four-level micro-Fresnel device is located in the X-Y plane, where point o is the geometrical center of device and the optical axis is Y-axis. The grooves are toward the incident light. There are three physical parameters that define the device: PCM radius (denoted as R), PCM thickness (denoted as HT), and air thickness (denoted as HR, which is defined by subtracting the HT value from the maximum PCM thickness). Specific wavefront control can be performed by precisely manipulating the structural parameters.
Fig. 1. Schematic geometry of a switchable Fresnel device based on PCMs. The device is surrounded by low index materials, typically air. Incident light enters the device from the grooved side. When the device functions as a focusing lens, the transmitted light will focus at point FT; and the reflected light will focus at point FR, when the device functions as a focusing reflector.
According to geometric optics, to realize a plane wave ideally converging to a point, the spatial phase retardation in the X-Y plane is [41]:
where f is the designed focal length, λ is the wavelength of the incident plane wave, and n0 is the refractive index of the surrounding medium. φ(x) is the phase retardation of the plane wave located at x. φF(x) (satisfying 0≤φF(x) ≤ 2π) is the phase retardation of a standard Fresnel focusing device, and given by dividing φ(x) with a modulus 2π [41]. Here, m is the ordinal number of the zone. When x<<f, using rm the radius of mth zone, f can be approximated as [41]:For a L-level Fresnel device, we can use Rp the radius of pth level to calculate f. Then Eq. (3) can be transformed into:
Equation (4) shows that f the focal length of a L-level Fresnel device is only related to the radius of each level, and has no relationship with the phase retardation of each level.
The transmission and reflection mechanism of a micro-focusing device is described as the following: The incident light (marked by the red arrow in Fig. 1) will be transmitted and reflected on the grooved surface of the device. The transmissivity and reflectivity are related to the ratio in refractive index between the device and surrounding medium. If the ratio is larger, the reflectivity will be larger, too. The phase modulation of the transmitted light depends on HT. Due to different values of HT, the reflected light at different levels pass through different spatial lengths (2HR). When the values of HT are properly selected, the reflected or transmitted light can effectively converge to one point when the PCM is in a solid state. The values of HT affect the diffraction efficiency, and the focal length of Fresnel device is only related to the radius of each level. So the focal length for reflected light fR and the focal length for transmitted light fT have the relationship of fR=fT (In this paper, focal lengths are all defined as positive values).
3. Lens design
In this paper, we design and simulate the device model with GST-326 to verify the feasibility of our proposed method. The wavelength of incident light is chosen at 3.1 µm, where the optical dielectric constants between the amorphous (na≈3.5 + 0.001i) and crystalline (nc≈6.5 + 0.06i) states are large [29,38]. The device contains fourteen zones, and the focal length f is chosen to be 30 µm. Considering the relatively large number of zones, Eqs. (1) and (2) are used to calculate the radius of each level. So the outer radius of the outermost zone is 72.89 µm. In order to have more parameters to adjust diffraction efficiencies, there are four levels in each zone. The phase retardation of the transmitted and reflected light can be obtained by
where φT(x) and φR(x) is the phase retardation of transmitted and reflected light in x, ns is the refractive index of GST-326 (3.5 in amorphous state, 6.5 in crystalline state), HT(x) is the PCM thickness in x, HTmax is the max PCM thickness value. And n0 is the refractive index of the surrounding medium, here is chosen to be 1 (air). When GST-326 is in amorphous state with relatively high transmissivity, the device functions as a focusing lens. Correspondingly, the device works as a focusing reflector when GST-326 is in crystalline state. Because the solid states of GST-326 are converted by heating or other means, the thinner the thickness of GST-326 in the device, the shorter the heating and cooling time and the faster the switching speed of the device. In addition, considering the absorption of light energy by material, reducing the thickness of GST-326 is beneficial to improve the energy efficiency of the device. Figure 2 presents φT(x) and φR(x) as a function of HT, when HTmax is 1.03 µm.To balance the focusing effects in both states, the thickness values of GST-326 are taken as 1.03, 0.73, 0.43, 0.03 µm, and corresponding phase retardations are 1.66π, 1.18π, 0.69π, 0.05π for transmitted light, and 0, 0.39π, 0.77π, 1.29π for reflected light. The ranges of these two phase modulation exceed π in both states, so the transmitted or reflected light can be modulated effectively.
4. Simulation results
In order to verify the results of the theoretical analysis, numerical simulations are performed using finite-difference time-domain (FDTD) solutions by Lumerical Solutions, in the x-y plane. A plane wave with TE polarization is used as an incident source and is positioned at 7 µm above the device. When GST-326 is in amorphous state or in crystalline state, the E-field intensity distributions on both the reflection side and the transmission side are shown in Figs. 3(a) and 3(b), respectively. The diffraction efficiencies at these foci are 20.92% and 18.14%, respectively. The y coordinates are 29.68 µm (fR=28.65 µm) for reflected focus and -29.14 µm (fT=29.14 µm) for transmitted focus, respectively. The small focal shift is because of the effect of finite size of the device. The values of depth of focus (DOF) for both foci are very close. For comparing the focal pattern across the actual foci in the y direction, the E-field intensity distributions for both amorphous state and crystalline state are shown in Fig. 3(c). And intensity profiles at the actual foci in the x direction are shown in Fig. 3(d). For the purpose of comparison, the curves in Figs. 3(c) and 3(d) are normalized with the maximum value. According to Fig. 3(c), estimated DOFs are 4.62 µm for the transmitted focus and 4.51 µm for the reflected focus. From Fig. 3(d), it can be seen that the full width at half-maximum (FWHM) at the transmitted focus is larger (1.30 µm close to diffraction limit) and the E-field intensity at the transmitted focus is stronger than that at the reflection focus, which is determined by the transmissivity and diffraction efficiency of the device. From Fig. 3, we can see the device has a good switching function between transmission and reflection as well as a significant focusing function, which are consistent with the features we designed.
Fig. 3. The focusing performance of the device when GST-326 is in different states. Intensity distribution when GST-326 is in (a) crystalline state; (b) amorphous state. The designed focal length is 30 µm (indicated by the white line). (c) E-field intensity distributions across the y direction at x = 0. (d) Intensity profiles on the actual focal planes.
It is worth noting that when GST-326 is in amorphous state, the focusing lens function also works if the incident light enters from the flat side. However, when in crystalline state, the incident light should not enter from the flat side. Because the incident light will be largely reflected by the first surface, and the Fresnel structure composed of air does not exist on the flat side.
As can be seen from Figs. 3(b) and 3(c), the reflected light also partially converges when GST-326 is in amorphous state. This is because the reflection Fresnel structure composed of air still exists. The intensity at the reflected focus can be reduced by choosing materials with lower refractive index or manipulating the thickness variation of GST-326. On the contrary, choosing higher refractive index or manipulating the thickness variation of GST-326, we may also achieve a bifocal device, which can be used in laser technology, detection technology, and other fields.
To construct the device, the GST-326 is still used. The designed focus length and diameter of the device are kept constant. We only adjust the four values of HT to balance the diffraction efficiencies for reflected light and transmitted light. The adjusted values are 1.13, 0.73, 0.381, and 0.23 µm. For transmitted light, the phase retardations are 1.8226π, 1.1774π, 0.6145π, and 0.3710π; for reflected light, the phase retardations are 0, 0.4960π, 0.9288π, and 1.1160π. The simulation results are shown in Fig. 4.
Fig. 4. Intensity distributions when GST-326 is in (a) crystalline state; (b) amorphous state. The designed focal length is 30 µm (indicated by the white lines). (c) E-field intensity distribution across the y direction at x = 0. (d) Intensity profiles on the three actual focal planes.
The E-field intensity distribution on both the reflection side and the transmission side is plotted in Figs. 4(a) and 4(b). In Fig. 4(a), it can be found that the device shows a good focusing and reflection function with fR=28.96 µm. And in Fig. 4(b), the bifocal phenomenon is clearly, both the reflected light and transmitted light converge to points near the designed focus points, where the E-field intensities are nearly the same. The y coordinates are 29.68 µm (fR=28.68 µm) for reflected focus and -29.14 µm (fT=29.14 µm) for transmitted focus, respectively. These features can also be clearly seen in Figs. 4(c) and 4(d), which show the intensity distribution across the actual foci in the x direction and y direction, respectively. The DOF is 4.01 µm for transmitted focus, and 4.03 µm for reflected focus. The largest FWHM among these three foci is 1.24 µm (for transmitted focus in amorphous state). The diffraction efficiencies are 21.05% for reflected focus in crystalline state, 18.49% for reflected focus in amorphous state, and 18.40% for transmitted focus in amorphous state, respectively. Obviously, the simulation results show the devices can simultaneously perform the functions of a focusing element and a beam splitter, which are consistent with the design goals. It is indicated that our design method can flexibly modulate the transmitted and reflected light for achieving multifunctional devices, such as various types of focal length or adjustable devices.
5. Discussions
Based on the simulation results above, the proposed switchable device based on PCMs is able to dynamically switch between the focusing lens and the focusing reflector, or between the focusing reflector and the beam focusing splitter. But the diffraction efficiency is not high enough. This is due to two main reasons. Firstly, it is mainly because of the refractive indexes of the PCM in different states. The refractive indexes of GST-326 are na=3.5 and nc=6.5. For on-axis light, the corresponding transmittances are 0.69 and 0.46, according to Fresnel principle. So only part of the energy is used for convergence. If the PCM have a lager optical dielectric constants between different solid states, and the lower refractive index value is near that of the surrounding medium, the energy utilization will be higher. Secondly, in order to balance the focusing effects in two states, the PCM thickness in each level are adjusted. But it will bring a loss in diffraction efficiency. Increasing the number of levels per zone can improve the diffraction efficiency.
To verify the adaptability of the switchable function to different NA values, the focusing effects under different states are analyzed. Switchable devices with the same parameters in Section 3 are designed and checked by simulation. Figure 5(a) shows the diffraction efficiency as a function of diameter (D), where the maximum value of D is 184 µm corresponding to an NA of 0.95. It can be found that the efficiency gap between amorphous state and crystalline state is stable, and the diffraction efficiencies are more than 16% when D is less than 187 µm. This means that the switchable function of the device does not fail as NA increases. The slightly decrease in diffraction efficiency when D is around 70 µm may be due to the interference of multiple modes within the structure, which cause more transmitted light absorbed by the device.
Fig. 5. (a) is diffraction efficiency on the focal plane as a function of D. The red curve and blue curve are obtained when GST-326 is in crystalline state and amorphous state, respectably. (b) is FWHM as a function of D. FWHM generally decreases with D. This is because NA increases with D increases, improving the focusing power.
Figure 5(b) shows the FWHM as a function of D. All the FWHM values are near diffraction limit, and the red and blue curves almost overlap. This means that as the NA increases, the device maintains a good focusing effect in both states.
From the analysis above, our design method can be applied to structures with different NA values, and the device adopts Fresnel structure with a small ratio of depth to width. Therefore, the electron beam lithography and the ion beam etching can be used for manufacturing the device. In addition, the thinner part of the device can be DC-magnetron sputter-deposited with a background pressure of 2×10−6 mbar [38].
By the simulation and analysis of the device with only PCM in free space, the working principle and the expected effect of the design concept can be studied directly and in detail. In practical case, the device needs protection like a 15 nm Si3N4, ZnS or SiO2 capping layer [29,38]. With covering layers on both sides of the device, the external medium changes from air to capping layer with a higher refractive index value. So the reflection coefficient will decrease and the transmission coefficient will increase, which will result in a lower reflection efficiency and a higher transmission efficiency of the device. Because of the small refractive index (less than 2) and the small thickness of the capping layer, its effect on the device is relatively small. We add a 50 nm SiO2 capping layer on both sides of the device shown in Fig. 3, and simulate it. The simulation results show that the variation of diffraction efficiency is less than 1%. We can manipulate the four level heights of GST-326 to reduce this effect.
The substrate will produce problems similar to those of capping layer. So compared with Si (nSi=3.44 [43]), SiO2 (nSiO2=1.42 [43]) and CaF2 (nCaF2=1.47 [38]) are more suitable as the substrate.
Usually, the main purpose of experiments is to verify the concept. GST-326 in amorphous state can be induced crystallization by being heated above 160°C and kept in the heat state for enough time [38,42]. So we can use a hot plate to realize crystallization, which is the method that many researchers do to verify the optical properties in both the amorphous and crystalline phases as well as the mechanical and chemical stability of the proposed design [38,40,42]. To be switched back to crystalline state, GST-326 needs to be heated above its melting temperature (640°C) and then melt quenched rapidly [38,42]. It needs electric or optical pulses to achieve this conversion [38,40]. Therefore, we can not cycle the different phases using the hot plate induced heating approach. Femtosecond laser pulses help to achieve fast conversion of optical performance [42].
To analyze the impact of manufacturing errors on device performance, new simulations have been done by adding random coefficients to the ideal device structure parameters. Figure 6 depicts the impact of radius error and thickness error on the diffraction efficiency of the device shown in Fig. 3.
Fig. 6. (a) diffraction efficiency of the device as a function of the radius error. (b) diffraction efficiency of the device as a function of the thickness error. The diffraction efficiencies for the reflected and transmitted focus of the ideal device are 18.14% and 20.92%, respectively.
When the tolerance coefficient is less than ± 5%, the diffraction efficiency of the device is kept relatively stable. Compared with the tolerance in PCM radius of the device, tolerance in PCM thickness is more critical on the diffraction efficiency. It can be seen that the variation trends of the diffraction efficiency of the transmitted focus and the reflected focus are opposite, which is mainly because when the thickness of PCM increases, the thickness of Fresnel device composed of air decreases, and vice versa. In addition, we observe that when the manufacturing errors in both PCM radius and PCM thickness is less than ± 7%, the FWHM and the focal length of the device are kept constant.
6. Conclusion
A novel design concept for switchable micro-focusing Fresnel device has been presented. The design concept utilizes the characteristics that the focal length of Fresnel device is only related to the radius of each level and that the transmissivity and reflectivity of GST-326 are different between two solid states. Subsequently, we model two novel models designed with this novel design principle, and numerical simulation results show promising optical performance, which shows the design concept proposed in this paper can be used for focal length switching and does not require mechanical motion on micro scale. These two models in this paper also embody that this design concept can achieve a variety of focusing functions, such as reflection focusing, transmission focusing and reflection-transmission dual focusing.
Using Fresnel device with more level number, such as six-level or eight-level, can increase the energy utilization of the device. Inspired by Fresnel zone plate, the device in this paper can also be composed of separated GST-326 particles, which will make it easy to use standard electrical switching devices for accurate solid state switching. In a word, this novel design concept provides a new design approach to fabricate highly integrated switchable devices in infrared spectral region, which is very important for thermal imaging, detection and measurement, etc.
Funding
National Natural Science Foundation of China (61420106014, 61975014, 61575024); Newton Fund.
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