This research was supported by Generalitat Valenciana (PROMETEO 2016-079), Universitat Jaume I (UJI) (UJIB2016-19); and Ministerio de Econom&#237;a y Competitividad (MINECO) (FIS2016-75618-R). The authors are very grateful to the SCIC of the Universitat Jaume I for the use of the femtosecond laser.

1. Encoding the Complex Field into a Single Phase Element
<ol>
	<li>From the technical specifications of the SLM, find its spatial resolution (for instance 1920 pixels x 1800 pixels).</li>
	<li>Define and generate the desired amplitude A(x,y) and phase &#966;(x,y) patterns as digital images.
	<ol>
		<li>Set the spatial resolution of abovementioned digital images equal to that of the SLM display.</li>
		<li>Set abovementioned digital images in gray level format.</li>
		<li>Set the minimum and maximum values of the amplitude and phase images from 0 to 255, and from -&#960;/2 to &#960;/2, respectively.</li>
		<li>Set Amax = 2 in equations 2 and 3, and computer-generate the phase patterns &#977;(x,y) and &#952;(x,y) from them.</li>
	</ol>
	</li>
	<li>Computer generate the checkerboard patterns M1(x,y) and M2(x,y).
	<ol>
		<li>Set the spatial resolution of these checkerboard patterns equal to that of the SLM display.</li>
		<li>To reduce the effect of pixel crosstalk, generate other pairs of checkerboard patterns M1(x,y) and M2(x,y) constructed with different pixel cells having an increased number of pixels (for instance: 2x2, 3x3, and 4x4 pixel cells, etc.). 
		CAUTION: When increasing the pixel cell, the total number of pixels of checkerboard patterns must be kept unchanged and equal to the spatial resolution of the SLM. Ensure that final number of pixels of all checkerboard patterns remains the same after modifying their pixel cells.</li>
	</ol>
	</li>
	<li>Computer generate the single phase element &#945;(x,y) from equation 5. 
	NOTE: See supplemental material named &#8220;MATLAB_code_1.m&#8221; for related tasks on step 1 of this protocol.</li>
</ol>
2. Reconstruction of the Complex Field
<ol>
	<li>Use a collimated, linear polarized, and spatially coherent laser beam as a light source.</li>
	<li>Use a phase-only SLM with at least 2&#960; phase range.</li>
	<li>When necessary, use a proper beam expander to adjust the size of the beam to the size of the SLM display.</li>
	<li>When necessary, use an optical polarizer to set laser beam polarization to the horizontal direction. This is usually important for the proper operation of phase-only SLMs, which are typically designed to modulate the spatial phase of the electromagnetic field that oscillate in the horizontal direction, keeping unchanged its vertical components.</li>
	<li>In order to send a phase pattern to the SLM, follow standard communication protocols given by the SLM&#8217;s manufacturer to connect and control the SLM with the computer. 
	NOTE: Common protocol for this purpose includes the use of a calibration curve to transform the values in radians (due to mathematical operations with angles) into gray level ones, which the electronic control unit of the SLM will finally convert into voltage levels. Additionally, as the SLM is connected to computer as an external device with its own screen, an extension of the computer screen is usually necessary, as well as a proper program to send the corresponding gray level images to this extra screen. An example of these codes is also included as supplemental material (please, see MATLAB_code_2.m).</li>
	<li>Implement an image optical system and put the display of the SLM in the input plane of this system.
	<ol>
		<li>Use a refractive lens of a focal length f to construct a 2f x 2f optical image system (a 4f optical system is also valid for this task). In accordance with the expected output size of the complex field, beam width, wavelength of light, and the available physical space, employ lens/lenses with suited technical specifications (e.g., coating, size, focal length, etc.).</li>
		<li>To find the position of the output plane of the imaging system, send the phase pattern &#945;(x,y) to the SLM and visually look for the recorded image (depending on the position of the camera) with the best spatial resolution. 
		CAUTION: In the case of low-size pixel cells (for instance, 1x1 pixel cells) and SLM displays with pixel widths of a few microns (for instance, 8 &#181;m), only beam propagation can produce interference between encoded uniform waves, getting a reconstructed images without including the circular iris in the imaging system. Use low-size pixel cells to locate the position of the output plane.</li>
		<li>Place a circular iris of variable diameter at the Fourier plane of the optical system and align its center with that of the laser beam focus.</li>
		<li>To adjust the size of the circular iris at the Fourier plane, send the phase pattern &#945;(x,y) and visually look for the recorded image (depending on the diameter of the circular iris) with best spatial resolution. 
		CAUTION: In the case of long-size pixel cells (for instance, 4x4 pixel cells), the interference between encoded uniform waves is basically carried out with the spatial filter. Use long-size pixel cell to adjust the size of the circular iris. In this protocol, the terms low-size and long-size are referred to the number of pixels contained within a pixel cell. However, the abovementioned interference depends also on the pixel width. Employ SLMs with pixel widths equal or less than 8 &#181;m.</li>
	</ol>
	</li>
	<li>Send the gray level image corresponding to the phase element &#945;(x,y) to the SLM.
	<ol>
		<li>To minimize the crosstalk effect, look for the best pixel cell size which allow achieving the recorded image with the higher spatial resolution.</li>
	</ol>
	</li>
</ol>
3. Measure the Reconstructed Complex Field
<ol>
	<li>Implement the polarization-based phase shifting technique8.
	<ol>
		<li>Place and align the rotation angle of the first optical polarizer, located just before the SLM (see Figure 2). To set the rotation angle of the first polarizer, visually look for the maximum and minimal light transmittance in the CCD camera (placed at the output plane of the imaging system), depending on the rotation of the polarizer. Write down the two corresponding angles of the polarizer. Fix the final angle of the polarizer to that between the two previous-recorded angles.</li>
		<li>Place and align the rotation angle of the second optical polarizer, located after the Fourier plane of the imaging system (see Figure 2). To set the rotation angle of the second polarizer, visually look for the sharpest and most blurred images in the CCD camera (placed at the output plane of the imaging system) after sending the phase pattern &#945;(x,y) to the SLM. Write down the two corresponding angles of the polarizer. Fix the final angle of the second polarizer to that between the previous-recorded angles.</li>
	</ol>
	</li>
	<li>Record the interferograms.
	<ol>
		<li>Keep the CCD camera at the output plane of the imaging system.</li>
		<li>To record the first interferogram, add a matrix of 0 radians to the phase element &#945;(x,y) and send it to the SLM. Record corresponding image I1(x,y) with the CCD.</li>
		<li>To record the second interferogram, add a matrix of &#960;/2 radians to the phase element &#945;(x,y) and send it to the SLM. Record corresponding image I2(x,y) with the CCD camera.</li>
		<li>To record the third interferogram, add a matrix of &#960; radians to the phase element &#945;(x,y) and send it to the SLM. Record corresponding image I3(x,y) with the CCD camera.</li>
		<li>To record the fourth and last interferogram, add a matrix of 3&#960;/2 radians to the phase element &#945;(x,y) and send it to the SLM. Record corresponding image I4(x,y) with the CCD camera.</li>
	</ol>
	</li>
	<li>Reconstruct the complex field. 
	NOTE: See supplemental material named &#8220;MATLAB_code_3.m&#8221; for related tasks on this point of the protocol.
	<ol>
		<li>Retrieve the amplitude of the complex field Aretrieved(x,y) by using the expression 
		<img alt="Equation 8" src="/files/ftp_upload/59158/59158eq8.jpg" />&#160;(8)</li>
		<li>Retrieve the phase of the complex field &#966;retrieved(x,y) by using the expression 
		<img alt="Equation 9" src="/files/ftp_upload/59158/59158eq9.jpg" />&#160;(9)</li>
	</ol>
	</li>
</ol>

<ol>
	<li>Hsueh, C. K., Sawchuk, A. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Computer-generated+double-phase+holograms.">Computer-generated double-phase holograms.</a> Applied Optics. 17 (24), 3874-3883 (1978).</li><li>Arriz&#243;n, V. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Complex+modulation+with+a+twisted-nematic+liquid-crystal+spatial+light+modulator:+double-pixel+approach.">Complex modulation with a twisted-nematic liquid-crystal spatial light modulator: double-pixel approach.</a> Optics Letters. 28 (15), 1359-1361 (2003).</li><li>Arriz&#243;n, V., Ruiz, U., Carrada, R., Gonz&#225;lez, L. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Pixelated+phase+computer+holograms+for+the+accurate+encoding+of+scalar+complex+fields.">Pixelated phase computer holograms for the accurate encoding of scalar complex fields.</a> Journal of the Optical Society of America A. 24 (11), (2007).</li><li>Shibukawa, A., Okamoto, A., Takabayashi, M., Tomita, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Spatial+cross+modulation+method+using+a+random+diffuser+and+phase-only+spatial+light+modulator+for+constructing+arbitrary+complex+fields.">Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields.</a> Optics Express. 22 (4), 3968-3982 (2014).</li><li>Mart&#237;nez-Fuentes, J. L., Moreno, I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Random+technique+to+encode+complex+valued+holograms+with+on+axis+reconstruction+onto+phase-only+displays.">Random technique to encode complex valued holograms with on axis reconstruction onto phase-only displays.</a> Optics Express. 26 (5), 5875-5893 (2018).</li><li>Clark, T. W., Offer, R. F., Franke-Arnold, S., Arnold, A. S., Radwell, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Comparison+of+beam+generation+techniques+using+a+phase+only+spatial+light+modulator.">Comparison of beam generation techniques using a phase only spatial light modulator.</a> Optics Express. 24 (6), 6249-6264 (2016).</li><li>Mendoza-Yero, O., M&#237;nguez-Vega, G., Lancis, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Encoding+complex+fields+by+using+a+phase-only+optical+element.">Encoding complex fields by using a phase-only optical element.</a> Optics Letters. 39 (7), 1740-1743 (2014).</li><li>Yamaguchi, I., Zhang, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Phase-shifting+digital+holography.">Phase-shifting digital holography.</a> Optics Letters. 22 (16), 1268-1270 (1997).</li><li>Shao, Y., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Addressable+multiregional+and+multifocal+multiphoton+microscopy+based+on+a+spatial+light+modulator.">Addressable multiregional and multifocal multiphoton microscopy based on a spatial light modulator.</a> Journal of Biomedical Optics. 17 (3), 030505 (2012).</li><li>Mendoza-Yero, O., Carbonell-Leal, M., M&#237;nguez-Vega, G., Lancis, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Generation+of+multifocal+irradiance+patterns+by+using+complex+Fresnel+holograms.">Generation of multifocal irradiance patterns by using complex Fresnel holograms.</a> Optics Letters. 43 (5), 1167-1170 (2018).</li><li>Kuang, Z., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Diffractive+Multi-beam+Ultra-fast+Laser+Micro-processing+Using+a+Spatial+Light+Modulator+(Invited+Paper).">Diffractive Multi-beam Ultra-fast Laser Micro-processing Using a Spatial Light Modulator (Invited Paper).</a> Chinese Journal of Lasers. 36 (12), 3093-3115 (2009).</li><li>Kuang, Z., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=High+throughput+diffractive+multi-beam+femtosecond+laser+processing+using+a+spatial+light+modulator.">High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator.</a> Applied Surface Science. 255, 2284-2289 (2008).</li></ol>

The authors have nothing to disclose.

In this protocol, practical parameters as the pixel width of the phase-only SLM or the number of pixels contained within pixel cells of a computer-generated pattern are key points to successfully implement the encoding method. In steps 1.2, 1.3, and 1.4 of the protocol, the shorter the pixel width, the better the spatial resolution of the retrieved amplitude and phase patterns. In addition, as the codification into the SLM of abrupt pixel-to-pixel phase modulations can originate unexpected phase responses (pixel crosstal...

Almost all laser applications are in close relation with the management of the optical wavefront of light. In the paraxial approximation, the complex field associated with the laser radiation can be described by two terms, the amplitude and the phase. Having control over these two terms is necessary to modify both the temporal and the spatial structure of laser beams at will. In general, the amplitude and the phase of a laser beam can be properly changed by several methods including the use of optical components that range from single bulk lenses, beam splitters and mirrors to most complex devices like deformable mirrors or spatial light modulators. Here, we show a method for encoding and reconstructing the complex field of coherent laser beams, which is based on dual-phase hologram theory1, and the utilization of a common-path interferometer.
Nowadays, there exists a wide variety of methods to encode the complex fields of laser beams2,3,4,5. In this context, some well-established methods to produce phase and amplitude modulation rely on the use of digital holograms6. A common point in all these methods is the necessity of generating a spatial offset to separate the desired output beam from the zeroth-order coming from the reflection of light at the SLM display. These methods are basically off-axis (usually applying for the first diffraction order of the grating), employing phase grating not only to encode the phase, but also to introduce necessary amplitude modulation. In particular, amplitude modulation is performed by spatially lowering the grating height, which clearly degrades the diffraction efficiency. The hologram reconstruction process mostly gets an approximate, but not exact, reconstruction of the amplitude and phase of the desired complex field. Discrepancies between theory and experiment seem to appear from an inaccurate encoding of the amplitude information as well as other experimental issues happening during the spatial filtering of the first diffraction order or due to SLM pixilation effects. In addition, the intensity profile of the input beam can introduce restrictions on the output power.
In contrast, with the introduced method7, all light management is carried out on-axis, which is very convenient from an experimental point of view. Additionally, it takes advantage of considering, in the paraxial approximation, the complex field associated with laser beams as a sum of two uniform waves. The amplitude information is synthetized by the interference of these uniform waves. In practice, such interference is carried out by spatial filtering of light frequencies at the Fourier plane of a given imaging system. Previously, the phase patterns associated with the uniform waves are spatially multiplexed and encoded into a phase-only SLM (placed at the entrance plane of this imaging system). Hence, the whole optical setup can be regarded as a common-path interferometer (very robust against mechanical vibrations, temperature changes, or optical misalignments). Please, note that the abovementioned interference process can be alternatively accomplished by using other optical layouts: with a couple of phase-only SLMs properly placed within a typical two-arm interferometer, or by time sequentially encoding the two phase patterns into the SLM (previous introduction of a reference mirror in the optical setup). In both cases, there is no necessity of spatial filtering, and consequently no loss of spatial resolution, at the expense of increasing the complexity of the optical system, as well as the alignment process. Here, it should be also emphasized that by using this encoding method, the full spectrum of the desired complex field can be exactly retrieved at the Fourier plane, after filtering all diffraction orders but the zeroth one.
On the other hand, the efficiency of the method depends on several factors: the manufacturer&#39;s specifications of the SLM (e.g., fill factor, reflectivity, or diffraction efficiency), the size of the encoded pattern, and the way at which the light impinges onto the SLM (reflection with a small hitting angle, or normal incidence by using a beam splitter). At this point, under proper experimental conditions, the measured total light efficiency can be more than 30%. However, note that that the total light efficiency just due to the use of the SLM can be less than 50%. The lack of random or diffuser elements within the optical setup allows the retrieving of amplitude and phase patterns without coherent noise (speckle). Other significant aspects to point out are the utilization of a direct codification algorithm rather than iterative procedures and its ability to perform arbitrary and independent amplitude and phase modulation at the frequency refresh time of the SLM (up to hundreds of hertz according to the current technology).
In principle, the method7 is intended to be used with input plane waves, but it is not limited to that. For instance, if a Gaussian beam is hitting the SLM, it is possible to modify its irradiance shape at the output of the system by encoding a suited amplitude pattern into the SLM. However, as the intensity of the output beam cannot exceed that of the input beam at any transversal position (x,y), the shaping of the amplitude is performed by intensity losses originated by a partially destructive interference process.
The theory underlining the encoding method7 is as follows. Any complex field represented in the form U(x,y)= A(x,y)ei&#966;(x,y) can be also rewritten as:
<img alt="Equation 1" src="/files/ftp_upload/59158/59158eq1.jpg" />&#160;(1)
where
<img alt="Equation 2" src="/files/ftp_upload/59158/59158eq2.jpg" />&#160;(2)
<img alt="Equation 3" src="/files/ftp_upload/59158/59158eq3.jpg" />&#160;(3)
In equations 1-3, the amplitude and phase of the two-dimensional complex field U(x,y)is given by A(x,y) and &#966;(x,y), respectively. Note that, terms Amax (maximum of A(x,y)) and B = Amax/2 do not depend on the transversal coordinates (x,y). From the theory, if we set Amax=2, then B =1. Hence, the complex field U(x,y) can be obtained, in a simple manner, from the coherent sum of uniform waves Bei&#977;(x,y) and Bei&#952;(x,y). In practice, this is accomplished with a common-path interferometer made up of a single phase element &#945;(x,y), placed at the input plane of an imaging system. The single phase element is constructed by spatial multiplexing of the phase terms &#977;(x,y)
and &#952;(x,y) with the help of two-dimensional binary gratings (checkerboard patterns) M1(x,y) and M2(x,y) as follows
<img alt="Equation 4" src="/files/ftp_upload/59158/59158eq4.jpg" />&#160;(4)
hence,
<img alt="Equation 5" src="/files/ftp_upload/59158/59158eq5.jpg" />&#160;(5)
These binary patterns fulfill the condition M1(x,y) + M2(x,y) = 1. Note that, the interference of uniform waves cannot happen if we do not mix the information contained in the phase element&#945;(x,y). In the present method, this is carried out by using a spatial filter able to block all diffraction orders but the zeroth one. In this way, after the filtering process at the Fourier plane, the spectrum H(u,v)= F{ei&#945;(x,y)} of the encoded phase function is related to the spectrum of the complex field F{U(x,y)} by the expression
<img alt="Equation 6" src="/files/ftp_upload/59158/59158eq6.jpg" />&#160;(6)
In Eq. (6), (u,v) denote coordinates in the frequency domain, P(u,v) holds for the spatial filter, whereas the Fourier transform of a given function &#920;(x,y) is represented in the form F{&#920;(x,y)}. From Eq. (6), it follows that, at the output plane of the imaging system, the retrieved complex field URET(x,y), (without considering constant factors), is given by the convolution of the magnified and spatially reversed complex field U(x,y) with the Fourier transform of the filter mask. That is:
<img alt="Equation 7" src="/files/ftp_upload/59158/59158eq7.jpg" />&#160;(7)
In Eq. (7), the convolution operation is denoted by the symbol <img alt="Equation 10" src="/files/ftp_upload/59052/59052eq10.jpg" />, and the term Mag represents the magnification of the imaging system. Hence, the amplitude and phase of U(x,y) is fully retrieved at the output plane, except for some loss of spatial resolution due to the convolution operation.

<table border="0" cellpadding="0" cellspacing="0" style="width:1083px;" width="1083">
	<tbody>
		<tr height="21">
			<td height="21" style="height:21px;width:251px;">Achromatic Doublet</td>
			<td style="width:191px;">THORLABS</td>
			<td style="width:211px;">AC254-100-B-ML</td>
			<td style="width:431px;">Lens Diameter 25.4 mm, focal length 100 mm</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:251px;">Achromatic Galilean Beam Expander</td>
			<td style="width:191px;">THORLABS</td>
			<td style="width:211px;">GBE05-A</td>
			<td>AR Coated: 400 - 650 nm</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">Basler camera</td>
			<td>BASLER</td>
			<td>avA1600-50gm GigE camera</td>
			<td>sensor size 8.8 mm x 6.6 mm, pizel size 5.5 microns</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:251px;">Mounted Zero-Aperture Iris</td>
			<td style="width:191px;">THORLABS</td>
			<td style="width:211px;">ID12Z/M</td>
			<td>Max Aperture 12 mm</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:251px;">Pellicle Beamsplitter</td>
			<td style="width:191px;">THORLABS</td>
			<td style="width:211px;">CM1-BP145B2</td>
			<td>45:55 (R:T), Coating: 700 - 900 nm</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">PLUTO Spatial Light Modulator</td>
			<td>HOLOEYE Photonics AG</td>
			<td>NIR-II</td>
			<td>Phase Only Spatial Light Modulator (Optimized for 700 -1000 nm)</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">Two thin film laser polarizers</td>
			<td>EKSMA OPTICS</td>
			<td>420-0526M</td>
			<td>material BK7, diameter 50 mm, wavelength 780-820 nm</td>
		</tr>
	</tbody>
</table>

shaping the amplitude and phase of laser beams by using a phase-only spatial light modulator

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser radiation. The method is based on the coherent sum of two uniform waves, previously encoded into a phase-only spatial light modulator (SLM) by spatial multiplexing of their phases. Here, the interference process is carried out by spatial filtering of light frequencies at the Fourier plane of certain imaging system. The correct implementation of this method allows arbitrary phase and amplitude information to be retrieved at the output of the optical system.
It is an on-axis, rather than off-axis encoding technique, with a direct processing algorithm (not an iterative loop), and free from coherent noise (speckle). The complex field can be exactly retrieved at the output of the optical system, except for some loss of resolution due to the frequency filtering process. The main limitation of the method might come from the inability to operate at frequency rates higher than the refresh rate of the SLM. Applications include, but are not limited to, linear and non-linear microscopy, beam shaping, or laser micro-processing of material surfaces.

The spatial resolution of the employed phase-only SLM is 1920 pixels x 1080 pixels, with a pixel pitch of 8 &#181;m. The selected amplitude A(x,y) and phase &#966;(x,y) of the complex field are defined by two different gray level images corresponding to the well-known Lenna&#8217;s picture (amplitude pattern) and a young girl sticking out her tongue (phase pattern), respectively. In general, for both, the generation of necessary patter...

Watch this Scientific Journal Video about Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator at JoVE.com

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

We show how to encode the complex field of laser beams by using a single phase element. A common-path interferometer is employed to mix the phase information displayed into a phase-only spatial light modulator to finally retrieve the desired complex field pattern at the output of an optical imaging system.

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser ...

shaping-amplitude-phase-laser-beams-using-phase-only-spatial-light

Universidad San Sebastian

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9.6K Views.  Universitat Jaume I. We show how to encode the complex field of laser beams by using a single phase element. A common-path interferometer is employed to mix the phase information displayed into a phase-only spatial light modulator to finally retrieve the desired complex field pattern at the output of an optical imaging system.

Video: Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Characterization of Surface Modifications by White Light Interferometry: Applications in Ion Sputtering, Laser Ablation, and Tribology Experiments

In materials science and engineering it is often necessary to obtain quantitative measurements of surface topography with micrometer lateral resolution. From the measured surface, 3D topographic maps can be subsequently analyzed using a variety of software packages to extract the information that is needed.
In this article we describe how white light interferometry, and optical profilometry (OP) in general, combined with generic surface analysis software, can be used for materials science and engineering tasks. In this article, a number of applications of white light interferometry for investigation of surface modifications in mass spectrometry, and wear phenomena in tribology and lubrication are demonstrated. We characterize the products of the interaction of semiconductors and metals with energetic ions (sputtering), and laser irradiation (ablation), as well as ex situ measurements of wear of tribological test specimens.
Specifically, we will discuss:
<ol class="lroman">
	<li>Aspects of traditional ion sputtering-based mass spectrometry such as sputtering rates/yields measurements on Si and Cu and subsequent time-to-depth conversion.</li>
	<li>Results of quantitative characterization of the interaction of femtosecond laser irradiation with a semiconductor surface. These results are important for applications such as ablation mass spectrometry, where the quantities of evaporated material can be studied and controlled via pulse duration and energy per pulse. Thus, by determining the crater geometry one can define depth and lateral resolution versus experimental setup conditions.</li>
	<li>Measurements of surface roughness parameters in two dimensions, and quantitative measurements of the surface wear that occur as a result of friction and wear tests.</li>
</ol>
Some inherent drawbacks, possible artifacts, and uncertainty assessments of the white light interferometry approach will be discussed and explained.

White light microscope interferometry is an optical, noncontact and quick method for measuring the topography of surfaces. It is shown how the method can be applied toward mechanical wear analysis, where wear scars on tribological test samples are analyzed; and in materials science to determine ion beam sputtering or laser ablation volumes and depths.

In materials science and engineering it is often necessary to obtain quantitative measurements of surface topography with micrometer lateral resolution. ...

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light.
We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry.

Large laser-interferometers are being constructed to create a new type of astronomy based on gravitational waves. Their sensitivities, as for many other high-precision experiments, are approaching fundamental noise limits such as the atomic vibration of their components. We are pioneering technologies to overcome these limits using novel laser beam shapes.

Thermal noise in high-reflectivity mirrors is a major impediment for several  types of high-precision interferometric experiments that aim to reach the  ...

Spatial Separation of Molecular Conformers and Clusters

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold molecular beams. However, these beams often contain multiple conformers and clusters, even at low rotational temperatures. We present an experimental methodology that allows the spatial separation of these constituent parts of a molecular beam expansion. Using an electric deflector the beam is separated by its mass-to-dipole moment ratio, analogous to a bender or an electric sector mass spectrometer spatially dispersing charged molecules on the basis of their mass-to-charge ratio. This deflector exploits the Stark effect in an inhomogeneous electric field and allows the separation of individual species of polar neutral molecules and clusters. It furthermore allows the selection of the coldest part of a molecular beam, as low-energy rotational quantum states generally experience the largest deflection. Different structural isomers (conformers) of a species can be separated due to the different arrangement of functional groups, which leads to distinct dipole moments. These are exploited by the electrostatic deflector for the production of a conformationally pure sample from a molecular beam. Similarly, specific cluster stoichiometries can be selected, as the mass and dipole moment of a given cluster depends on the degree of solvation around the parent molecule. This allows experiments on specific cluster sizes and structures, enabling the systematic study of solvation of neutral molecules.

We present a technique that allows the spatial separation of different conformers or clusters present in a molecular beam. An electrostatic deflector is used to separate species by their mass-to-dipole moment ratio, leading to the production of gas-phase ensembles of a single conformer or cluster stoichiometry.

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold ...

Flame Experiments at the Advanced Light Source: New Insights into Soot Formation Processes

The following experimental protocols and the accompanying video are concerned with the flame experiments that are performed at the Chemical Dynamics Beamline of the Advanced Light Source (ALS) of the Lawrence Berkeley National Laboratory1-4. This video demonstrates how the complex chemical structures of laboratory-based model flames are analyzed using flame-sampling mass spectrometry with tunable synchrotron-generated vacuum-ultraviolet (VUV) radiation. This experimental approach combines isomer-resolving capabilities with high sensitivity and a large dynamic range5,6. The first part of the video describes experiments involving burner-stabilized, reduced-pressure (20-80 mbar) laminar premixed flames. A small hydrocarbon fuel was used for the selected flame to demonstrate the general experimental approach. It is shown how species&#8217; profiles are acquired as a function of distance from the burner surface and how the tunability of the VUV photon energy is used advantageously to identify many combustion intermediates based on their ionization energies. For example, this technique has been used to study gas-phase aspects of the soot-formation processes, and the video shows how the resonance-stabilized radicals, such as C3H3, C3H5, and i-C4H5, are identified as important intermediates7. The work has been focused on soot formation processes, and, from the chemical point of view, this process is very intriguing because chemical structures containing millions of carbon atoms are assembled from a fuel molecule possessing only a few carbon atoms in just milliseconds. The second part of the video highlights a new experiment, in which an opposed-flow diffusion flame and synchrotron-based aerosol mass spectrometry are used to study the chemical composition of the combustion-generated soot particles4. The experimental results indicate that the widely accepted H-abstraction-C2H2-addition (HACA) mechanism is not the sole molecular growth process responsible for the formation of the observed large polycyclic aromatic hydrocarbons (PAHs).

Gas sampling from laboratory-scale flames with online analysis of all species by mass spectrometry is a powerful method to investigate the complex mixture of chemical compounds occurring during combustion processes. Coupled with tunable soft ionization via synchrotron-generated vacuum-ultraviolet radiation, this technique provides isomer-resolved information and potentially fragment-free mass spectra.

The following experimental protocols and the accompanying video are concerned with the flame experiments that are performed at the Chemical Dynamics ...

Atomic Force Microscopy of Red-Light Photoreceptors Using PeakForce Quantitative Nanomechanical Property Mapping

Atomic force microscopy (AFM) uses a pyramidal tip attached to a cantilever to probe the force response of a surface. The deflections of the tip can be measured to ~10 pN by a laser and sectored detector, which can be converted to image topography. Amplitude modulation or &#8220;tapping mode&#8221; AFM involves the probe making intermittent contact with the surface while oscillating at its resonant frequency to produce an image. Used in conjunction with a fluid cell, tapping-mode AFM enables the imaging of biological macromolecules such as proteins in physiologically relevant conditions. Tapping-mode AFM requires manual tuning of the probe and frequent adjustments of a multitude of scanning parameters which can be challenging for inexperienced users. To obtain high-quality images, these adjustments are the most time consuming.
PeakForce Quantitative Nanomechanical Property Mapping (PF-QNM) produces an image by measuring a force response curve for every point of contact with the sample. With ScanAsyst software, PF-QNM can be automated. This software adjusts the set-point, drive frequency, scan rate, gains, and other important scanning parameters automatically for a given sample. Not only does this process protect both fragile probes and samples, it significantly reduces the time required to obtain high resolution images. PF-QNM is compatible for AFM imaging in fluid; therefore, it has extensive application for imaging biologically relevant materials.
The method presented in this paper describes the application of PF-QNM to obtain images of a bacterial red-light photoreceptor, RpBphP3 (P3), from photosynthetic R. palustris in its light-adapted state. Using this method, individual protein dimers of P3 and aggregates of dimers have been observed on a mica surface in the presence of an imaging buffer. With appropriate adjustments to surface and/or solution concentration, this method may be generally applied to other biologically relevant macromolecules and soft materials.

A method for investigating the structure of a protein photoreceptor using atomic force microscopy (AFM) is described in this paper. PeakForce Quantitative Nanomechanical Property Mapping (PF-QNM) reveals intact protein dimers on a mica surface.

Atomic force microscopy (AFM) uses a pyramidal tip attached to a cantilever to probe the force response of a surface. The deflections of the tip can be ...

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

A procedure for a technique to measure the transverse coherence of synchrotron radiation X-ray sources using a single phase grating interferometer is reported. The measurements were demonstrated at the 1-BM bending magnet beamline of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). By using a 2-D checkerboard &#960;/2 phase-shift grating, transverse coherence lengths were obtained along the vertical and horizontal directions as well as along the 45&#176; and 135&#176; directions to the horizontal direction. Following the technical details specified in this paper, interferograms were measured at different positions downstream of the phase grating along the beam propagation direction. Visibility values of each interferogram were extracted from analyzing harmonic peaks in its Fourier Transformed image. Consequently, the coherence length along each direction can be extracted from the evolution of visibility as a function of the grating-to-detector distance. The simultaneous measurement of coherence lengths in four directions helped identify the elliptical shape of the coherence area of the Gaussian-shaped X-ray source. The reported technique for multiple-direction coherence characterization is important for selecting the appropriate sample size and orientation as well as for correcting the partial coherence effects in coherence scattering experiments. This technique can also be applied for assessing coherence preserving capabilities of X-ray optics.

The measurement protocol and data analysis procedure are given for obtaining transverse coherence of a synchrotron radiation X-ray source along four directions simultaneously using a single 2-D checkerboard phase grating. This simple technique can be applied for complete transverse coherence characterization of X-ray sources and X-ray optics.

A procedure for a technique to measure the transverse coherence of synchrotron radiation X-ray sources using a single phase grating interferometer is ...

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.

A protocol to detect and automate mode locking in a pre-adjusted nonlinear polarization rotation fiber laser is presented. The detection of a sudden change in the output polarization state when mode locking occurs is used to command the alignment of an intra-cavity polarization controller in order to find mode-locking conditions.

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a ...

Using Synchrotron Radiation Microtomography to Investigate Multi-scale Three-dimensional Microelectronic Packages

Synchrotron radiation micro-tomography (SR&#181;T) is a non-destructive three-dimensional (3D) imaging technique that offers high flux for fast data acquisition times with high spatial resolution. In the electronics industry there is serious interest in performing failure analysis on 3D microelectronic packages, many which contain multiple levels of high-density interconnections. Often in tomography there is a trade-off between image resolution and the volume of a sample that can be imaged. This inverse relationship limits the usefulness of conventional computed tomography (CT) systems since a microelectronic package is often large in cross sectional area 100-3,600 mm2, but has important features on the micron scale. The micro-tomography beamline at the Advanced Light Source (ALS), in Berkeley, CA USA, has a setup which is adaptable and can be tailored to a sample&#39;s properties, i.e., density, thickness, etc., with a maximum allowable cross-section of 36 x 36 mm. This setup also has the option of being either monochromatic in the energy range ~7-43 keV or operating with maximum flux in white light mode using a polychromatic beam. Presented here are details of the experimental steps taken to image an entire 16 x 16 mm system within a package, in order to obtain 3D images of the system with a spatial resolution of 8.7 &#181;m all within a scan time of less than 3 min. Also shown are results from packages scanned in different orientations and a sectioned package for higher resolution imaging. In contrast a conventional CT system would take hours to record data with potentially poorer resolution. Indeed, the ratio of field-of-view to throughput time is much higher when using the synchrotron radiation tomography setup. The description below of the experimental setup can be implemented and adapted for use with many other multi-materials.

For this study synchrotron radiation micro-tomography, a non-destructive three-dimensional imaging technique, is employed to investigate an entire microelectronic package with a cross-sectional area of 16 x 16 mm. Due to the synchrotron&#39;s high flux and brightness the sample was imaged in just 3 min&#160;with an 8.7 &#181;m spatial resolution.

Synchrotron radiation micro-tomography (SR&#181;T) is a non-destructive three-dimensional (3D) imaging technique that offers high flux for fast data ...

Subsurface Defect Localization by Structured Heating Using Laser Projected Photothermal Thermography

The presented method is used to locate subsurface defects oriented perpendicularly to the surface. To achieve this, we create destructively interfering thermal wave fields that are disturbed by the defect. This effect is measured and used to locate the defect. We form the destructively interfering wave fields by using a modified projector. The original light engine of the projector is replaced with a fiber-coupled high-power diode laser. Its beam is shaped and aligned to the projector&#39;s spatial light modulator and optimized for optimal optical throughput and homogeneous projection by first characterizing the beam profile, and, second, correcting it mechanically and numerically. A high-performance infrared (IR) camera is set up according to the tight geometrical situation (including corrections of the geometrical image distortions) and the requirement to detect weak temperature oscillations at the sample surface. Data acquisition can be performed once a synchronization between the individual thermal wave field sources, the scanning stage, and the IR camera is established by using a dedicated experimental setup which needs to be tuned to the specific material being investigated. During data post-processing, the relevant information on the presence of a defect below the surface of the sample is extracted. It is retrieved from the oscillating part of the acquired thermal radiation coming from the so-called depletion line of the sample surface. The exact location of the defect is deduced from the analysis of the spatial-temporal shape of these oscillations in a final step. The method is reference-free and very sensitive to changes within the thermal wave field. So far, the method has been tested with steel samples but is applicable to different materials as well, in particular to temperature sensitive materials.

This method aims at locating vertical subsurface defects. Here, we couple a laser with a spatial light modulator and trigger its video input to heat a sample surface deterministically with two anti-phased modulated lines while acquiring highly resolved thermal images. The defect position is retrieved from evaluating thermal wave interference minima.

The presented method is used to locate subsurface defects oriented perpendicularly to the surface. To achieve this, we create destructively interfering ...

Electric-field Control of Electronic States in WS2 Nanodevices by Electrolyte Gating

A method of carrier number control by electrolyte gating is demonstrated. We have obtained WS2 thin flakes with atomically flat surface via scotch tape method or individual WS2 nanotubes by dispersing the suspension of WS2 nanotubes. The selected samples have been fabricated into devices by the use of the electron beam lithography and electrolyte is put on the devices. We have characterized the electronic properties of the devices under applying the gate voltage. In the small gate voltage region, ions in the electrolyte are accumulated on the surface of the samples which leads to the large electric potential drop and resultant electrostatic carrier doping at the interface. Ambipolar transfer curve has been observed in this electrostatic doping region. When the gate voltage is further increased, we met another drastic increase of source-drain current which implies that ions are intercalated into layers of WS2 and electrochemical carrier doping is realized. In such electrochemical doping region, superconductivity has been observed. The focused technique provides a powerful strategy for achieving the electric-filed-induced quantum phase transition.

Electric-field Control of Electronic States in WS2 Nanodevices by Electrolyte Gating

Here, we present a protocol to control the carrier number in solids by using the electrolyte.

A method of carrier number control by electrolyte gating is demonstrated. We have obtained WS2 thin flakes with atomically flat surface via scotch tape ...