2.1 Theory

SLM software is embedded with CGHs of common patterns, such as vortex phase, concentric ring segments, axicon, binary beam-splitter gratings, and sinusoidal grating. Axicon CGH can generate an annular Bessel beam. The intensity distribution of the Bessel beam can be described by the first kind of Bessel function:

(1)

where r and φ are polar coordinates in the observation plane, z is the distance of the observation plane in the direction of beam propagation, and are axial and radial wave vectors, respectively, and is the first-class Bessel function of order n. Since intensity is the square of the electric field, the intensity of the Bessel beam is . The Bessel beam energy distribution at the cross-section is a series of concentric rings with decreasing intensities from the inside out. The intensity distribution of Bessel light remains constant in the direction of propagation, which can be used for a deep hole or microchannel machining.

After being focused by the objective lens, the energy distribution of the Bessel beam is no longer multiple concentric rings, but a focused ring. The transmission function is as follows:

(2)

where r and are polar coordinates in the computational holographic plane and is controllable constant. n represents the nth order Bessel beam. The corresponding phase expression is

(3)

Equation (2) has two components. The first component is related to the azimuth phase and represents the singularity of the phase. The second component produces a zero-order Bessel beam. To obtain Eq. (3) on the SLM, r is rewritten as , where Δ is the pixel period. The p and q are integers, representing the position of each pixel on the liquid crystal surface. The electric field distribution of a beam focused on a plane with distance z from the liquid crystal surface can be described as:

(4)

where and are polar coordinates in the plane of observation, and Jn represents the first class of n-order Bessel functions.

Therefore, after being focused by the objective lens, the Bessel beam is shaped into a focusing ring, which can be used to machine circular zones on the surface of the material.

2.2 Experimental methods

Figure 1 shows the SLM femtosecond laser parallel processing system. The SLM is a silicon-based liquid crystal modulator (model Pluto-II IR-011) produced by HOLOEYE, Germany, with 1920 pixel×1080 pixel, 256 gray levels, a pixel period of 8 μm, and an effective area of 0.7 inches diagonally. The Gaussian laser irradiation source is a Yb: KGW femtosecond laser amplifier (Pharos, Light Conversion Co. Ltd.) with a center wavelength of 1030 nm, a pulse repetition rate of 10 kHz, and a pulse width of 216 fs. After exiting from the laser amplifier, the energy of the femtosecond laser is adjusted by the attenuator, and the polarization direction is adjusted to horizontal polarization by the half-wave plate. The laser beam has a beam diameter of 15 mm, which is slightly larger than the short-axis size of the SLM. The phase of the femtosecond laser beam is modulated after it is cast on the SLM, loaded with CGH. Then, the femtosecond laser passes through a 4F system composed of two lenses and performs pulse shaping in the time and frequency domains. The focal lengths of the two lenses are 300 mm and 150 mm, respectively. So the laser beam is reduced and the modulated beam enters the objective lens (10×, numerical apprture=0.3, Nikon) completely. The objective lens focuses the femtosecond laser on sample, while the 3D platform is driven by high-precision linear motor (displacement accuracy is 0.5 μm). The laser is filtered through the dichroscope and enters the monitoring system charge coupled device (CCD). CCD can observe the processing situation in real-time, which provides a guarantee for high efficiency and high precision processing.

Figure 1全屏查看

(a) Schematic diagram of SLM femtosecond laser machining system; (b) The transmittance wavelength range of GaAs; (c) GaAs wafer

The experimental sample used for processing is gallium arsenide (GaAs). GaAs is an important semiconductor material, and GaAs FZPs can be used in infrared detector, integrated circuit substrate, γ photon detector and so on. Figure 1(b) shows that GaAs is transparent in infrared light, the wavelength range of light transmission is 0.9 to 20 μm. Figure 1(c) shows the GaAs wafer used in the experiment.

Fresnel circular diffraction is the physical mechanism of the FZP. As shown in Figure 2(a), the incident light irradiated into the FZP diffracts, and the diffracted light interferes behind the FZP and forms energy convergence on the optical axis. The optical path difference between adjacent zones to P is an integral multiple of the wavelength, so the light intensity of the P point is greatly enhanced, forming the focus of the FZP. The diffraction efficiency is the ratio of the energy of the main focus of the FZP to the total incident energy. It is an important parameter of the diffraction characteristics of FZP.

Figure 2全屏查看

(a) Diagram of converging light beams after passing through the Fresnel zone plat; (b) Schematic diagram of the diffraction characteristic detection system

The diffraction characteristic detection system is shown in Figure 2(b). The incident laser beam passes through the FZP, objective lens, iris and attenuation plate placed coaxial successively, and finally enters the beam quality analyzer. The diffraction characteristic detection system can measure the diffraction efficiency, observe the beam convergence process, measure the focal length, and display the imaging effect. Since the diameter of the main focus spot is less than 50 μm, it needs to be amplified by the objective lens for observation and analysis. The attenuator can adjust the power of the incident light to avoid the detector being oversaturated and unable to measure accurately. The experimental laser is near-infrared light with a wavelength of 1.03 μm, so a beam quality analyzer is used to detect the practical effect. When the diffraction efficiency is measured, the energy E₁ of the main focus of the FZP is measured first. To avoid other energy entering the detector, an aperture is used to limit the beam so that only the energy of the first order diffraction is received by the detector. Then, the FZP is removed, GaAs of the same thickness is placed in the optical path, and the diaphragm is adjusted to the size of the FZP, so that the reflection loss of the GaAs can be taken into account, and the total incident energy value E₂ is obtained. According to the measured data, the diffraction efficiency of the first order of the FZP can be obtained as [8].

3.1 Annular optical field modulation

The first method is annular optical field modulation. The CGH of the annular optical field is obtained and the annular beam is produced. When designing the shape of the optical field, all the zones of the FZP are drawn, so that the entire FZP can be processed with only one irradiation. Although the processing efficiency is high, this method has some defects. First, the energy of the laser focus is spread over multiple zones, significantly reducing the pulse energy per unit area. Consequently, increase in incident laser energy is required to attain the ablation threshold, while the liquid crystal panel of SLM cannot bear the high-power incident laser. Then, the larger the focal spot area, the more uneven the energy distribution, which will lead to variation in energy intensity across the focal area and inconsistent machined morphology with the designed optical field pattern. Therefore, the FZP is decomposed into multiple zones to improve the processing precision, and only one zone is drawn for each light field. The complete FZP can be processed by switching multiple optical fields.

Figure 3 shows the light field and processing of a single zone. Figure 3(a) is the shape of the designed optical field with 400 pixel×400 pixel. The white ring represents a light spot, while the black zone represents a no light region. Laser beams of different widths can be modulated by drawing different widths rings. As shown is Figure 3(b), the pattern is converted into a CGH by the algorithm of SLM after iterative calculation, producing an 8-bit gray level map. The intensity of the gray level of each pixel represents the magnitude of the phase, that is, the modulation amount of the phase. Figure 3(c) shows a zone processed by the modulated annular beam, with an inner diameter of 200 μm and a width of 82 μm, consistent with the theoretical design values.

Figure 3全屏查看

Annular optical field modulation method: (a) Designed annular optical field; (b) CGH of the annular optical field; (c) Zone processed by femtosecond laser

However, there is an obvious ablation hole in the center of the annular zone, and the central hole is not in the designed optical field. This is caused by the presence of zero-order light of SLM. There are gaps between the pixels of the liquid crystal board of SLM, which means that the light incident on the gaps cannot be modulated. In addition, a small amount of light on the upper glass surface of the liquid crystal board is reflected directly without being modulated. These unmodulated lights converge on the posterior focal point of the lens to form zero-order light, which ablate into holes in the center of the zone.

According to whether the central zone is transparent, the FZPs can be divided into two types: open-FZP and closed-FZP. The inner zone should be ablated when the closed-FZP is processed, and the radius of the inner zone is much larger than the radius of the central ablation hole. Therefore, if SLM is used to process the closed-FZP, the influence of the central ablation hole on the diffraction performance can be reduced. At present, there are few researches on the difference in diffraction properties between open-FZP and closed-FZP. To further clarify the influence of whether the center is transparent or not on the diffraction performance of the FZP, the diffraction performance of the open-FZP and closed-FZP with an inner radius of 120 μm is simulated and measured experimentally. Figures 4(a) and (b) show the simulation results of the diffraction performance by ZEMAX software. The focal radius of the closed-FZP is smaller than that of the open-FZP, and the focal depth of the closed-FZP is larger than that of the open-FZP. Figure 4(c) shows the experimental measurement results. The focal length of both closed-FZP and open-FZP is 18 mm, and there is no difference. The diffraction efficiency of closed-FZP is 6.96%, and that of open-FZP is 8.42%. This is because the laser energy passing through the center of the open-FZP is higher, and the energy of interference laser at the focus is higher. The diffraction efficiency of the FZP determines the energy transfer efficiency and image quality, which is one of the most essential diffraction properties. So the closed-FZP is inappropriate to reduce the influence of the SLM central ablation hole, and open-FZP should be selected for research.

Figure 4全屏查看

Comparison of diffraction properties of open-FZP and closed-FZP: (a) Comparison of simulation results of main focus energy; (b) Comparison of simulation results of Z-axis energy; (c) Comparison of experimental results of diffraction processes

The influence of the central ablation hole on the diffraction performance can be calculated by simulation when SLM is machining an open-FZP. Four models of FZP are established with the simulation software to analyze the influence of the ablation hole, located at the center of the FZP, on the diffraction performance of the FZP. The radii of the ablation holes are 0, 50, 60 and 70 μm, respectively. As shown in Figure 5(a), the inner radius of the model FZP is 120 μm, the number of zones is 8, and the focal length is 11.08 μm. As shown in Figure 5(b), with the absence of an ablation hole at the center, the peak value of focus is 100 W/mm². The energy peak decreased with the presence of an ablation hole at the center of the plate. When the radius of the ablation hole is increased, the energy peak becomes lower, and the focus peak value of the ablation hole with a radius of 70 μm is reduced to 86.5 W/mm². Therefore, the zero-order light should be eliminated to avoid the influence of the central ablation hole on the diffraction performance of the FZP.

Figure 5全屏查看

(a) FZP model established in ZEMAX; (b) Comparison of focus energy distribution of FZPs with different radii of ablation holes in the center

As shown in Figure 6(a), there is not only an annular light on the focal plane but also a zero-order light in the center after SLM modulation. The effect of zero-order light can be eliminated by superimposed background CGH in three ways: axial removal, center cancellation, and radial removal. The axial removal is shown in Figure 6(b), a superimposed Fresnel lens CGH separates the diffraction image from the zero-order light in the Z-axis direction. The zone without a central spot can be obtained by machining on the plane where the ring focus is located. Axial removal is relatively simple but cannot eliminate zero-order light entitely. Moreover, the superimposed when processing the FZP which disrupts the experimental operation. As shown in Figure 6(c), the center cancellation method is to design a CGH with the opposite phase to the zero-order light in the center, to make it eliminate interference with the zero-order light. This method has a simple optical path, however, the time taken to identify the optimal intensity and phase is challenging. The radial removal is shown in Figure 6(d), a superimposed grating CGH separates the central spot of the original beam in the radial plane without changing the position of the focal plane. An aperture is placed in the optical path so that the +1 order-diffracted ring beam enters the focal plane and completely blocks the zero-order light. Radial removal method has outstanding advantages, so this method is adopted to eliminate zero-order light. To concentrate more energy at the +1 ring, the blazed grating is chosen for superposition. In addition, the position of the optical element should be determined according to the transmission direction of the +1 diffracted light when adjusting the optical path of radial removal.

Figure 6全屏查看

Schematic diagram of removing central light spot: (a) Original beam; (b) Axial removal; (c) Central cancellation; (d) Radial removal

Figure 7(a) shows the zones processed by radial division processing, and Figure 7(b) shows the corresponding CGH of the zones. It can be clearly seen that there is no ablation hole in the center of the zones. Moreover, the zones have small roundness and high concentricity, and the radius is consistent with the theoretical value, which shows that radial removal is an effective method for processing circular zones. The radius and width of Figures 7(a₁)-(a₅) zones meet the requirement of FZP for radius ratio, so the FZP can be obtained by successively processing Figure 7(a) on GaAs.

Figure 7全屏查看

Zones processed by radial division processing: (a) Ultra-depth-of-field microscope images; (b) CGHs

Figure 8 shows open-FZP formed by switching multiple optical fields. The preparation time of a single FZP is 1 min, and the processing efficiency is highly improved. However, the effect could be better due to the discontinuous and dotted distribution in each zone. That’s because when SLM modulates multiple focal points, the energy distribution of each point is not uniform. There are many reasons for the inconsistent focal spot energy, including the approximation of the CGH algorithm, the bias caused by SLM and the bias caused by the high numerical aperture objective lens. Among them, deviations caused by SLM, such as crosstalk error between pixels, non-uniform spatial phase error, pixel unit time-domain fluctuation error and multi-beam pointing error, lead to reduced diffraction efficiency and discontinuous points in processing [37, 38]. In addition, as shown in Figure 8(b), the design pattern is composed of 400 pixel×400 pixel. When drawing a pattern with radians, square pixels with small dimensions are drawn in approximated arcs. Due to the small radius and narrow width of the designed zone, the corresponding light spot in some radians is only 1 pixel, which also easily causes breakpoints. The number of modulated focal points is large, and the energy of a single focal point is low. Therefore, the energy of some focal points tends to be lower than the ablation threshold of GaAs, and the processed GaAs FZPs show intermittent spots.

Figure 8全屏查看

FZPs processed by annular optical field modulation method: (a) Open-FZP; (b) Designed zone optical field pattern

The efficient machining of FZP is achieved by using the annular optical field modulation method. However, the surface topography of the FZP is poor, so it is difficult to achieve high-quality diffraction characteristics. Therefore, further research and optimization are needed.

3.2 Bessel beam modulation

The second modulation method is using the Axicon CGH of SLM to modulate the Bessel beam. A blazed grating is superimposed on the CGH of an axial conical lens to eliminate the effect of zero-order light, and the generated beam is directed in the radial direction . The phase expression of the grating required to create the migration is

(5)

The total phase expression of the resulting Bessel beam and radial offset is

(6)

The synthesis process of computational holography is shown in Figure 9.

Figure 9全屏查看

Superposition of CGHs of blazed grating and axicon

After the Bessel beam focuses on the objective lens, it forms a Bessel annular beam with a diameter of D, which can be calculated as:

(7)

where , and are the focal lengths of the 4f system lens, respectively, is the wavelength of the incident light, is the parameter required to the Bessel beam. It can be found that , that is, the diameter of the annular optical field is only related to , however, it is independent of the order of the Bessel beam. Therefore, it is not necessary to make any changes to the optical path when processing FZPs with different diameters. The diameter of the annular optical field can be controlled quantitatively by adjusting the CGH. Figures 10(a) and (d) show the CGHs of axicon and 40, and Figure 10(b) and Figure 10(e) show the annular light modulated by axicon CGHs superimposed by blazed grating, with uniform energy distribution, low roundness, and smooth radian. Figures 10(c) and (f) show the annular pattern processed by annular light on GaAs material with good connectivity with no intermittent points appearing.

Figure 10全屏查看

Axicon CGH, Bessel beam and the processed zones: (a-c) Parameter r₀=20; (d-f) Parameter r₀=40

The Bessel beam modulation method can easily achieve annular beams with different diameters but cannot easily adjust the width of annular beams. So the width of each zone needs to be adjusted through other processes during processing, such as adjusting the exposure time and laser power. It is worth noting that at constant laser power, the widths of smaller radius zones are thicker than those of larger radius zones due to the fact that increase in radius results in reduced focal spot energy per unit area.

Figure 11(a) shows the open-FZP processed by the Bessel beam modulation method. The inner radius of the FZP is 15 μm, and the number of zones is 6. The exposure time of the inner zone is 100 ms, and the exposure time of the outer zone is systematically reduced to 50 ms. The laser energy is 50-60 mW, and the processing time of a single FZP is 1.5 min. The figure shows that each FZP has a higher concentricity with no intermittent points, which is greatly improved, compared to the FZP processed by the annular optical field modulation method. Moreover, the outer diameter of the FZP processed by the Bessel beam is only 60 μm. This is much less than the outer diameter of the FZP processed by the annular optical field modulation method of 381 μm. Therefore, Bessel beam modulation can be applied to the optical system with higher precision requirements. The application for array structure is on the high side in practice, therefore the design and fabrication of FZP array are required. The translation and copy function are used to array the FZP in the X direction and the Y direction, and the interval length is the outer diameter of the FZP. Figure 11(b) shows the FZP array fabricated with SLM and photographed by the ultra-depth of field microscope. The actual machining size is consistent with the theoretical design. Figure 11(c) shows the FZP processed by femtosecond laser point-by-point scanning without SLM. The processing time is 30 min, which is much longer than that of SLM. Since Figure 11(c) is point-by-point processing, the starting point and end point of processing are in the same position. This makes the width of the joint point larger than the width of other positions and decreases the surface quality of the machined morphology. Therefore, the FZP machined by the SLM modulating Bessel beam has good morphology and high precision and significantly improves processing efficiency.

Figure 11全屏查看

(a) FZP processed by Bessel beam; (b) FZP array processed by Bessel beam; (c) FZP processed without Bessel beam

3.3 Diffraction characteristic detection

The FZPs processed above are placed in the diffraction characteristic detection system, and the diffraction characteristics are compared. As shown in Figure 12(a), the beam is focused at 218 μm behind the FZP, indicating that the FZP processed by the SLM with the Bessel beam can achieve the focusing effect of incident light. Figure 12(b) shows the focus formed by the point-by-point processed FZP, and the focal spot is visible. However, Figure 12(c) shows that bright rings also exist on the focal plane in addition to energy convergence, which is caused by the point-by-point machining not realizing the precise regulation of the zones, and the existence of bright rings will affect the beam convergence and the focus application. Figures 12(d) and (e) show the energy distribution image and energy value obtained by the diffraction characteristic detection system. Figure 12(d) shows the total energy E₂ entering the FZP, and Figure 12(e) shows the main focus energy E₁ on the focal plane. The ratio of E₁ and E₂ can obtain the diffraction efficiency of the FZP.

Figure 12全屏查看

(a) Focus of the FZP processed by Bessel annular beam; (b) Focus of the FZP by point-by-point machining; (c) Energy distribution of (a) and (b); (d) Measurement of total energy E₂; (e) Measurement of focus energy E₁

The diffraction efficiency of the amplitude-type FZP is related to the order, and the diffraction efficiency of the main focus is the largest, with a theoretical value of 10.13%. As shown in Table 1, the diffraction efficiency of SLM machining and point-by-point machining FZPs is 8.02% and 7.95%, respectively. Therefore, the diffraction efficiency of SLM-machined FZP is slightly higher than that of point-by-point machined FZP, which is close to the theoretical maximum.

When the femtosecond laser is modulated as a Bessel beam for multi-focus parallel processing, only a few optical fields need to be switched to process the zones, and the processing steps of the FZP are very simple. When single-focus serial processing is adopted, the single-focus fits the circular arc line along the circumference of the zone in a short straight line, and the processing is hundreds of steps. When the process steps are very complex, the stability of the processing will be reduced. Therefore, the SLM Bessel beam can improve the processing efficiency of the femtosecond laser, the optical element morphology and diffraction performance.