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Abstract
We report on a new type of a random phase plate (RPP) that can be applied for effective homogenization of coherent laser beams. The RPP is fabricated on a uniaxial birefringent crystal, ensuring the absence of speckles within the processing plane due to two orthogonally polarized beamlets with π phase difference. High fabrication speed ∼ 2 mm2/s of RPP takes at least 10 minutes to fabricate it. RPPs test showed the transformation of Gauss intensity distribution to the flat-top one characterized by low-intensity modulation ∼1% of the coherent laser beam. Then, RPP was applied in a picosecond laser setup for ZnO film microprocessing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The rapid development of laser technologies and their active integration into various industries have increased the requirements for a laser beam as an universal tool for micro- and nanoscale materials processing [1–3]. The realization of flat-top intensity distribution in a laser beam by applying spatial smoothing devices is always accompanied by speckles in the lens focal plane (processing plane) [4]. In some cases that leads to the distortion of temperature distribution during the fabrication of micro- and nanoscale structures [2,3]. There are well-known schemes aimed to change the intensity distribution: multilevel diffractive optical elements [5]; individual case random phase plates (RPP) [4], multilevel RPP [6] or RPP with continuous profile [7]; and refractive micro-optical elements in schemes of imaging integrator and non-imaging integrator [8]; diffusers of various types [9]. Among these elements, the RPP possesses high efficiency and relatively low energy losses, as well as the simplicity of calculation and fabrication. Generally, the RPP pattern consists of elementary cells etched on the surface of optically transparent material at a specific depth h = λ/2(n – 1), where n is the refractive index of the optical material and λ is the wavelength used [10]. The half of the cells located in a random order across the RPP. The random location of the cells leads to the chaotic distribution of speckles in the processing plane [11].
This issue is especially important for laser micromachining systems, where the requirements for the degree of homogenization are particularly strict. The use of polarization phenomenon is one of the promising solutions to speckle suppression, or at least a significant reduction in their contrast. The coherence reduction can be achieved by the reflection of laser radiation from a photonic crystal [12]. Continuous change of the photonic crystal relief (in the range of 0 – λ/4) leads to the phase shift in the range of 0 –π, that causes different states of polarization. Thus, linear polarization with different orientations of the polarization vector, circular polarization, as well as various types of elliptical polarization could exist in the reflected beam.
Here, we report on the fabrication of RPP operating in a transmission mode and produced by laser-induced plasma action on optically transparent birefringent material. We have successfully tested fabricated RPPs with a high coherent laser source and achieved speckle modulation on the level of 1%. The result was compared with the similar one achieved for an RPP fabricated on fused silica.
2. Background
2.1 The choice of base material
In our case, the operating principle of RPP fabricated on the birefringent material is based on conditions under which speckle appearance is impossible. Such conditions are possible when two groups of linearly polarized beamlets with orthogonal polarization overlap in the lens focal plane [13]. It is realizable, if the RPP is fabricated on the surface of an uniaxial birefringent crystal with a crystal axis oriented parallel to the surface of the plate (so-called Y-cut). Herewith, a half of cells (as in the case of the classic RPP) is located in the random order across the RPP and etched to the depth hc, providing the phase shift π for passed radiation. This is done by orienting the main axes of the crystal plate at an angle 45° with respect to the direction of the linear polarization vector of the incident wave. In this case, each fabricated cell rotates the polarization vector of beamlets by the angle of 90°. This occurs when the path difference of ordinary and extraordinary waves in the unit cell with depth h determined by Eq. (1) [13]:
This path difference corresponds to the phase shift φ (defined by Eq. (2)), which becomes equal to π (subject to Eq. (3)). Equations (2) and (3) allow to determine minimal depth hc (realized at m = 0): Thus, we choose Iceland spar with maximum birefringence value of known and available materials that significantly reduces the required cells depth and possesses high optical transparency.2.2 The choice of microprocessing technology
Today, the lithography and laser technologies are often used for the fabrication of phase optical elements [14,15]. We employed method of laser-induced micro-plasma (LIMP) processing [16] of Iceland spar to obtain a RPP. The distinctive features of the LIMP method: (i) the processing zone is restricted in the size by plasma volume, which is limited by the laser beam; (ii) plasma extension is limited by close contact of Iceland spar and the target; and (iii) high efficiency of laser energy conversion into micro-plasma is close to 100%, which is achieved by utilization of the ‘blackbody’ target containing carbon compounds. Note, the LIMP processing method has never been applied to birefringent or crystal materials, as it is a complicated task since the material is prone to destruction, and it is difficult to avoid stresses during mechanical or direct laser processing.
3. Experimental procedure
3.1 RPP fabrication procedure
In this work, the LIMP method is adapted for a laser marking system (Fig. 1(a)). The formation of RPPs on Iceland spar is accomplished by the scanning of a focused laser beam in the contact of Iceland spar and the graphite target (Fig. 1(b)) according to the pre-calculated template, which is schematically shown in Fig. 1(c). The elements of the laser setup are shown in Fig. 1.
Fig. 1. The procedure of RPP fabrication on Iceland spar: (a) experimental setup of LIMP method includes: 1 – fiber Yb-laser (wavelength λ = 1.06 µm, varied pulse duration τ = 4–200 ns, pulse repetition rate ν = 1–100 kHz); 2 – a two-coordinate galvanometric scanning system; 3 – f-theta scan lens (focal length f = 210 mm); 4 – Iceland spar plate; 5 – graphite target; (b) LIMP processing of Iceland spar; (с) template of RPP.
The depth and roughness of the relief achieved on Iceland spar were measured by profilometer (Hommel Tester T8000) with the resolution of ∼ 0.01 µm. Optical polarized microscopy (Carl Zeiss Axio Imager A1) was applied to prove the absence of cracks and stresses in RPP.
3.2 RPP test
Experimental setups for RPP testing with laser sources (λ1 = 405 nm (M2 ∼ 1.9) and λ2 = 780 nm (M2 ∼ 1.4)) is presented in Fig. 2(a). The ability to provide the intensity distribution with the flat-top shape within the focal spot of the lens (5) positioned behind RPP was proved during the test. Initially, the registration of the laser beam intensity distribution occurred in the lens focal plane. Then, RPP was located on the optical path in front of the lens (5) and the intensity distribution in the focal plane was registered again. The test results allowed to evaluate the efficiency of RPP and to reveal the reduction of the speckle contrast.
Fig. 2. Experimental setup to test fabricated RPP: (a) with laser modules: 1 – laser modules (operated at 405 nm or 780 nm); 2 – polarizer; 3 – telescope (3х); 4 – RPP; 5 – lens (focal distance f = 150 mm); 6 – CCD camera (Gentec beamage 3.0); (b) with picosecond laser: 1 – laser source; 2, 3 – mirrors; 4 – CCD camera; 5 – RPP; 6 – lens (10x, NA = 0.3, focal length f = 6 mm); 7 – ZnO film; 8 – coordinate table.
Another RPP was designed for Nd:YAG laser (Ekspla PL 2143) with picosecond pulse duration (τ = 30 ps, ν = 10 Hz, operated at third harmonic λ = 355 nm, beam quality M2 < 2.0) (Fig. 2(b)). The test was performed in the following way: the intensity profile of the initial beam was registered on the film (7) by the pulse train (100 pulses per region), then RPP was set in front of the micro-objective (6), and the beam profile registration occurred on the untreated site of the film (7) repeatedly.
4. Results and discussion
4.1 RPP fabrication
It was necessary to determine the correlation between the depth of a possible relief and laser parameters before RPP fabrication. The Iceland spar is rather fragile, its firmness on Moss scale is 3. It was experimentally determined that with the increase in the number of laser scans the probability of material destruction is reduced. Figure 3 shows the fragment of a square cell with size 250 × 250 µm. Images of the cells formed were also taken by using linearly polarized light with a crossed polarizer/analyzer pair (Fig. 3(b)), indicating the absence of residual mechanical stresses around or inside the cell. The increase in power led to cracks and stresses (Figs. 3(c) and 3(d)).
Fig. 3. Microphotograph of squares: (a, b) without cracks (5 scans, at 3 W and 4 W, consequently and V = 800 mm/s, ν = 80 kHz, τ = 50 ns); (c, d) with cracks (1 scan, at 2 W and 3 W, consequently V = 700 mm/s, ν = 60 kHz, τ = 50 ns).
The required hc is equal to 0.8–2.4 µm (according to Eq. (4)) to produce RPPs designed for three different wavelengths. However, for small etching depths, satisfactory quality of the cell was achieved with a single scan. Laser processing values are listed in the Table 1. Laser cleaning step is an integral part of RPP fabrication procedure. This step was chosen as the most optimal one compared to chemical and thermal cleaning, these methods being described in detail elsewhere [17].
Table 1. Regime of laser processing parameters for RPPs fabrication.
The template of RPP contains a set of squared cells located randomly (Fig. 4(a)). Applied LIMP setup allowed fabricating the squared elements with the minimum side of 100 µm. Therefore, the size of the RPP cell was set as 250 µm to provide more defined shape of the cell. The fragment of the RPP designed for λ = 355 nm is shown in Fig. 4(b). The profilometry shows the real depth and the roughness Rz of the cell (Fig. 4(c)). The deviation of the experimentally fabricated cell depth is about 4%. Achieved roughness does not exceed 0.05 µm. Thus, we fabricated the 3 different RPPs designed for 3 wavelengths by LIMP technique. The time required for fabrication of RPP with area of 8 mm2 does not exceed 10 minutes. The recording speed per area by LIMP technique depends on the required depth of the relief and equals 2.0 mm2/s in the case of RPP designed for 355 nm.
Fig. 4. RPP designed for λ = 355 nm: (a) template of RPP; (b) RPP’s fragment microphotograph in transmitted light; (c) profilometry of the fabricated cells.
4.2 RPP testing
The profile of the intensity distribution (for lasers with λ1 = 405 nm and λ2 = 780 nm) in the focal plane of the lens is presented in Fig. 5(a). The resulted distributions in Figs. 5(b) and 5(c) are made with the RPP. Figure 5(d) illustrates the testing results of RPP fabricated on fused silica applied according to the same scheme. The reduction of the intensity modulation is clearly seen. The experiments conducted confirmed the reliability of RPP principle work, which is based on polarization phenomenon, showing the absence of speckles.
Fig. 5. RPP test results for two wavelengths 405 nm and 780 nm: (a) initial intensity distribution; (b) intensity distribution after post the RPP into the setup without the telescope; (c) intensity distribution after insertion of RPP into the setup with the telescope; (d) intensity distribution after posting the RPP fabricated on fused silica into the setup with the telescope.
The diameter of the initial laser beam waist is evaluated by Eq. (5) [18]:
where M2 – beam quality, D0 – the size of initial laser beam, f – focal length of the lens. The diameter of the homogenized beam by using the RPP in the optical scheme can be evaluated by Eq. (6) [11]: where del – the size of the square in RPP.It is obvious that smaller del is, the bigger d2. When f = 150 mm and del = 250 µm for wavelengths λ1 = 405 nm and λ2 = 780 nm, the diameter of the homogenized beam is equal to d2 = 486 µm and d2 = 936 µm, respectively. The results of the calculation correlate with the experimental results obtained successfully.
The degree of homogenization of the laser radiation for all the cases indicated was evaluated according to the results achieved by Eq. (7) [9]:
where σ is a standard deviation of intensity, <I> is an average value of intensity, both are evaluated according to Eq. (8):The values estimated and experimental results are listed in Table 2. Thus, the intensity modulation does not exceed 1.3%.
Table 2. Homogenization quality.
It is important to note that fabricated RPPs are very sensitive to the depth of every cell and its roughness. The achieved roughness value equal to 50 nm can be considered as the deviation cell depth, leading to the phase deviation Δφ and consequently to an increase in the contrast of the interference pattern. The deflection of Δφ in the part of π (in the case of the laser module) is equal to 0.044, which corresponds to 4.4% deviation. It is evident that Δφ can be decreased with increasing a radiation wavelength.
4.3 RPP for film processing
The RPP designed for the laser with λ = 355 nm was tested with the picosecond laser (Fig. 2(b)) having the beam quality M2 < 2.0. The test results are presented in Fig. 6. The result of 2 µm thickness ZnO film processing using the fabricated RPP demonstrates higher quality compared with processing quality without the RPP. The microphotograph of the processing plane using the RPP shows that the speckles are reduced significantly. The pulse energy was slightly increased from 50 µJ to 60 µJ in order to cover the diffraction losses on the optical element (∼ 16%).
Fig. 6. Microphotographs of ZnO film laser processing regions by the action of picosecond laser pulses: (a) without RPP; (b) with RPP.
5. Conclusion
In conclusion, we have proposed the principle of RPP fabricated on the birefringent material (Iceland spar) with a crystal axis oriented parallel to the surface of the plate. The RPPs show effective homogenization of laser beam. The polarization effect explains this phenomenon. The rotation of the linear polarization vector by 90° after passing through RPP cells is realized under the following conditions: (i) at the minimum depth hc (see Eq. (4)) creating between ordinary and extraordinary waves a phase shift equal to π; (ii) when the main axis of the crystal plate is oriented with respect to the vector of linear polarization in the initial wave at an angle of 45°.
The possibility of surface precision processing (± 50 nm) of Iceland spar was shown experimentally by LIMP. The RPPs designed for three different wavelengths (λ = 355, 405, 780 nm) were successfully fabricated on Iceland spar. During the RPP test, the laser modules demonstrated a significant reduction in speckle contrast in the lens focal plane (intensity modulation < 1%).
One fabricated RPP was utilized for the intensity distribution correction of the picosecond Nd:YAG laser. Results on ZnO film processing with RPP application demonstrate high homogeneity of the processed region compared to the processing without RPP.
Funding
Ministry of Education and Science of the Russian Federation (Minobrnauka) (14.587.21.0037).
Acknowledgments
The reported study was financially supported by the Ministry of Education and Science of the Russian Federation, research agreement No. 14.587.21.0037 (RFMEFI58717X0037). The authors would like to thank N. M. Verzhbinskaya for assistance in relief analysis by profilometry.
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