This work was funded by the Science and Technology Facilities Council (STFC).

<ol>
	<li>Cohadon, P. F., Heidmann, A., Pinard, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Cooling+of+a+Mirror+by+Radiation+Pressure.">Cooling of a Mirror by Radiation Pressure.</a> Physical Review Letters. 83, 3174-3177 (1999).</li><li>Corbitt, T., 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=An+All-Optical+Trap+for+a+Gram-Scale+Mirror.">An All-Optical Trap for a Gram-Scale Mirror.</a> Physical Review Letters. 98, 150802 (2007).</li><li>M&#252;ller-Ebhardt, H., Rehbein, H., Schnabel, R., Danzmann, K., Chen, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Entanglement+of+Macroscopic+Test+Masses+and+the+Standard+Quantum+Limit+in+Laser+Interferometry.">Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry.</a> Physical Review Letters. 100, 013601 (2008).</li><li>Kimble, H. J., Levin, Y., Matsko, A. B., Thorne, K. S., Vyatchanin, S. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Conversion+of+conventional+gravitational-wave+interferometers+into+quantum+nondemolition+interferometers+by+modifying+their+input+and+output+optics.">Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and output optics.</a> Physical Review D. 65, 022002 (2001).</li><li>Numata, K., Kemery, A., Camp, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Thermal-Noise+Limit+in+the+Frequency+Stabilization+of+Lasers+with+Rigid+Cavities.">Thermal-Noise Limit in the Frequency Stabilization of Lasers with Rigid Cavities.</a> Physical Review Letters. 93, 250602 (2004).</li><li>Aufmuth, K., Danzmann, <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Gravitational+wave+detectors.">Gravitational wave detectors.</a> New Journal of Physics. 7, 202 (2005).</li><li>Harry, G. M., 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=Thermal+noise+in+interferometric+gravitational+wave+detectors+due+to+dielectric+optical+coatings.">Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings.</a> Classical and Quantum Gravity. 19, 897-917 (2002).</li><li>Crooks, D. R. M., 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=Excess+mechanical+loss+associated+with+dielectric+mirror+coatings+on+test+masses+in+interferometric+gravitational+wave+detectors.">Excess mechanical loss associated with dielectric mirror coatings on test masses in interferometric gravitational wave detectors.</a> Classical and Quantum Gravity. 19, 883-896 (2002).</li><li>Yu, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Internal+thermal+noise+in+the+LIGO+test+masses:+A+direct+approach.">Internal thermal noise in the LIGO test masses: A direct approach.</a> Physical Review D. 57, 659-663 (1998).</li><li>Harry, G. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=the+LIGO+Collaboration.+Advanced+LIGO:+the+next+generation+of+gravitational+wave+detectors.">the LIGO Collaboration. Advanced LIGO: the next generation of gravitational wave detectors.</a> Classical and Quantum Gravity. 27, 084006 (2010).</li><li>Accadia, T., Acernese, F., Antonucci, F., Astone, P., Ballardin, G., Barone, F., 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=Status+of+the+VIRGO+project.">Status of the VIRGO project.</a> Classical and Quantum Gravity. 28, 114002 (2011).</li><li>Sathyaprakash, B., Abernathy, M., Acernese, F., Ajith, P., Allen, B., Amaro-Seoane, P., 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=Scientific+objectives+of+Einstein+Telescope.">Scientific objectives of Einstein Telescope.</a> Classical and Quantum Gravity. 29 (12), 124013 (2012).</li><li>Bondarescu, M., Thorne, K. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=New+family+of+light+beams+and+mirror+shapes+for+future+LIGO+interferometers.">New family of light beams and mirror shapes for future LIGO interferometers.</a> Physical Review D. 74, 082003 (2006).</li><li>Bondarescu, M., Kogan, O., Chen, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optimal+light+beams+and+mirror+shapes+for+future+LIGO+interferometers.">Optimal light beams and mirror shapes for future LIGO interferometers.</a> Physical Review D. 78, 082002 (2008).</li><li>Tournefier Mours, E., Vinet, J. Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Thermal+noise+reduction+in+interferometric+gravitational+wave+antennas:+using+high+order+TEM+modes.">Thermal noise reduction in interferometric gravitational wave antennas: using high order TEM modes.</a> Classical and Quantum Gravity. 23, 5777 (2006).</li><li>Chelkowski, S., Hild, S., Freise, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Prospects+of+higher-order+Laguerre-Gauss+modes+in+future+gravitational+wave+detectors.">Prospects of higher-order Laguerre-Gauss modes in future gravitational wave detectors.</a> Physical Review D. 79, 122002 (2009).</li><li>Vinet, J. Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Reducing+thermal+effects+in+mirrors+of+advanced+gravitational+wave+interferometric+detectors.">Reducing thermal effects in mirrors of advanced gravitational wave interferometric detectors.</a> Classical and Quantum Gravity. 24, 3897 (2007).</li><li>Fulda, P., Kokeyama, K., Chelkowski, S., Freise, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Experimental+demonstration+of+higher-order+Laguerre-Gauss+mode+interferometry.">Experimental demonstration of higher-order Laguerre-Gauss mode interferometry.</a> Physical Review D. 82, 012002 (2010).</li><li>Bond, C., Fulda, P., Carbone, L., Kokeyama, K., Freise, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Higher+order+Laguerre-Gauss+mode+degeneracy+in+realistic,+high+finesse+cavities.">Higher order Laguerre-Gauss mode degeneracy in realistic, high finesse cavities.</a> Physical Review D. 84, 102002 (2011).</li><li>Sorazu, B., 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=Experimental+test+of+higher-order+Laguerre-Gauss+modes+in+the+10+m+Glasgow+prototype+interferometer.">Experimental test of higher-order Laguerre-Gauss modes in the 10 m Glasgow prototype interferometer.</a> Class. Quantum Grav. 30, 035004 (2013).</li><li>Carbone, L., Bogan, C., Fulda, P., Freise, A., Willke, W. <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+High-Purity+Higher-Order+Laguerre-Gauss+Beams+at+High+Laser+Power.">Generation of High-Purity Higher-Order Laguerre-Gauss Beams at High Laser Power.</a> Physical Review Letters. 110, 251101 (2013).</li><li>Fulda, P., 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=Phaseplate+design+for+Laguerre-Gauss+mode+conversion.">Phaseplate design for Laguerre-Gauss mode conversion.</a> , (2013).</li><li>Willke, B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Stabilized+lasers+for+advanced+gravitational+wave+detectors.">Stabilized lasers for advanced gravitational wave detectors.</a> Laser &amp; Photonics Rev. , 1-15 (2010).</li><li>Granata, M., Buy, C., Ward, R., Barsuglia, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Higher-Order+Laguerre-Gauss+Mode+Generation+and+Interferometry+for+Gravitational+Wave+Detectors.">Higher-Order Laguerre-Gauss Mode Generation and Interferometry for Gravitational Wave Detectors.</a> Physical Review Letters. 105, 231102 (2010).</li><li>Matsumoto, N., Ando, T., Inoue, T., Ohtake, Y., Fukuchi, N., Hara, T. <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+high-quality+higher-order+Laguerre+Gaussian+beams+using+liquid-crystal-on-silicon+spatial+light+modulators.">Generation of high-quality higher-order Laguerre Gaussian beams using liquid-crystal-on-silicon spatial light modulators.</a> J. Opt. Soc. Am. 25, 1642-1651 (2008).</li><li>Kennedy, S. A., Szabo, M. J., Teslow, H., Porterfield, J. Z., Abraham, E. R. I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Creation+of+Laguerre-Gaussian+laser+modes+using+diffractive+optics.">Creation of Laguerre-Gaussian laser modes using diffractive optics.</a> Physical Review A. 66, 043801 (2002).</li><li>Black, E. D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=An+introduction+to+Pound-Drever-Hall+laser+frequency+stabilization.">An introduction to Pound-Drever-Hall laser frequency stabilization.</a> American Journal of Physics. 69, 79-87 (2001).</li><li>Freise, A., Heinzel, G., Lueck, H., Schilling, R., Willke, B., Danzmann, K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Frequency-domain+interferometer+simulation+with+higher-order+spatial.">Frequency-domain interferometer simulation with higher-order spatial.</a> Class.Quant.Grav. 21, (2004).</li><li>Uehara, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mode+cleaner+for+the+Initial+LIGO+10+Watt+Laser.">Mode cleaner for the Initial LIGO 10 Watt Laser.</a> LIGO internal report. 12, (1997).</li></ol>

Authors have nothing to disclose.

The output beams of most lasers used in high-precision measurements are designed to have a shape well described as a fundamental Gaussian mode. This particular beam geometry combines low diffraction with a spherical wave front. While the low diffraction is one of the key advantages of laser light, the spherical wave front is equally important, as it allows the low-loss transformation of the laser beam by standard optical components with spherical surfaces. Different beam shapes can be created as well, and recently Laguerre-Gauss beams have become of interest for their potential application in high-precision interferometry.
In this paper we demonstrated the experimental procedure to create higher-order Laguerre-Gauss modes with 95% purity for high-power, ultra stable laser beams. To achieve this, we have combined standard techniques from different aspects of optical research, namely diffractive phase plates and laser pre-stabilization to mode cleaner cavities. Our experiment provides a simple, modular and very reliable method to create high power beams in user defined higher-order modes. A commercial ultra-stable laser is used as the light source. Its output is injected to a diffractive phase plate, which can convert up to 75% of the light into the desired Laguerre-Gauss mode. This light is then injected to a small optical cavity and an electronic feedback loop is used to stabilize the laser frequency of the laser to the cavity length. The beam transmitted by the cavity is to 95% in the desired mode and, like the fundamental mode beam at the origin of the setup, has very good frequency stability at audio frequencies. All the parts represent standard components in modern optical experiments. We have successfully demonstrated this technique for laser powers up to 80 W pure Laguerre-Gauss 33 mode.
It could be possible to achieve similar results by replacing the phase plate with another mode-converting element (for example, other diffractive elements or astigmatic mode converters). Alternatively a laser could be setup with an optical resonator tuned for the desired Laguerre-Gauss modes, using for example, an amplitude mask. Finally the laser frequency stabilization to the reference optical cavity could be exchanged with a similar scheme that uses an atomic reference. The need for an electronic feedback system is probably the main disadvantage, but this is inevitable for any light source used for precision interferometer.
However, we believe that the method demonstrated in this paper provides a simple and modular scheme which can be scaled to all ranges of required laser frequency, power, or shape and thus presents a powerful and versatile method. Each part, the laser source, the diffractive element, as well as the optical cavity can be changed or optimized individually, which means that also existing laser injection systems can be upgraded to use Laguerre-Gauss modes.

During the past decades high-precision interferometric experiments were pushed towards an ultimate sensitivity regime where quantum effects are starting to play a decisive role. In these ongoing and future experiments, such as laser cooling of mechanical oscillators 1, optical traps for mirrors 2, generation of entangled test masses 3, quantum non-demolition interferometry 4, frequency stabilization of lasers with rigid cavities 5, and gravitational wave detection 6, 7, 8, researchers are facing a multitude of limiting fundamental and technical noise sources. One of the most severe problems is the thermal noise of the cavity mirrors of the interferometric setups, which is caused by the thermal excitation of the atoms that make up the mirror substrates and the mirror reflective coatings 7, 8, 9. This effect, also called Brownian motion, will cause an uncertainty in the phase of the light reflected from any test masses and will therefore manifest as a fundamental noise limitation in the interferometer output. For instance, the projected design sensitivity of advanced gravitational wave antennae, such as Advanced LIGO, Advanced VIRGO, and the Einstein Telescope, is limited by this type of noise in the most sensitive region of the observation frequency band 10, 11, 12.
Experimental physicists in the community work hard in a continuous effort to minimize these noise contributions and to improve the sensitivity of their instruments. In the particular case of mirror Brownian noise, one method for mitigation is to employ a larger beam spot size of the currently used standard fundamental HG00 beam on the test mass surfaces, since a larger beam averages more effectively over the random motions of the surface 13, 14. The power spectral density of the mirror thermal noise has been shown to scale with the inverse of the Gaussian beam size for the mirror substrate and with the inverse square for the mirror surface 9. However, as the beam spots are made larger, a larger fraction of the light power is lost over the edge of the reflective surface. If one uses a beam with a more homogeneous radial intensity distribution than the commonly used HG00 beam (see for example Figure 1), the Brownian thermal noise level can be reduced without increasing this type of loss. Amongst all the more homogeneous beam types that have been suggested for new versions of high-precision interferometry, for example Mesa beams or conical modes 13, 14, the most promising are higher-order LG beams due to their potential compatibility with the currently used spherical mirror surfaces 15. For instance, the detection rate of binary neutron star in spiral systems - which are considered the most promising astrophysical sources for a first GW detection - could be enhanced by about a factor of 2 or more 16 at the cost of a minimal amount of modifications in the design of second-generation interferometers currently under construction 10, 11. In addition to the thermal noise benefits, the wider intensity distributions of higher-order LG beams (see as an example Figure 2) have been shown to mitigate the magnitude of thermal aberrations of optics within the interferometers. This would reduce the extent to which thermal compensation systems are relied upon in future experiments to reach design sensitivities 19.
We have investigated and successfully demonstrated the feasibility of generating LG beams at the levels of purity and stability required to successfully operate GW interferometers at the best of their sensitivity 16, 18, 19, 20, 21, 22. The proposed method combines techniques and expertise developed in diverse areas of physics and optics such as the generation of high stability, low noise single mode laser beams 23, the use of spatial light modulators and diffractive optical elements for the manipulation of the spatial profiles of light beams 18, 22, 24, 25, 26, and the use of advanced techniques for the sensing, control and stabilization of resonant optical cavities 27 aiming at a further purification and stabilization of the laser light. This method has been successfully demonstrated in the laboratory experiments, exported for tests in large-scale prototype interferometers 20, and for generating LG modes at high laser powers up to 80 W 21. In this article we present the details of the method of generating higher order LG beams and discuss a methodology for the characterization and validation of the resulting beam. Further, in Step 4 a method for numerical investigations of cavities with non-perfect mirrors 19 is outlined.

<table border="1">
	<tbody>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td>The experimental apparatus discussed in this paper requires the following types of instruments:</td>
		</tr>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td>Instrument</td>
		</tr>
		<tr>
			<td>Solid state Laser source, Nd:YAG 1064 nm CW laser</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>Faraday Isolator</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>Electro-Optic Modulator (EOM)</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>CCDcamera beam profiler</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>Lenses</td>
			<td></td>
			<td></td>
			<td>Quantity: depending on apparatus design</td>
		</tr>
		<tr>
			<td>Steering Mirrors</td>
			<td></td>
			<td></td>
			<td>Quantity: depending on apparatus design</td>
		</tr>
		<tr>
			<td>Aperture</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>High reflectivity mirrors (for normal incidence)</td>
			<td></td>
			<td></td>
			<td>Quantity: 2</td>
		</tr>
		<tr>
			<td>Piezoelectric ring</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>Cavity spacer</td>
			<td></td>
			<td></td>
			<td>Quantity: 1</td>
		</tr>
		<tr>
			<td>Photodiodes and related control electronics</td>
			<td></td>
			<td></td>
			<td>Quantity: 1 or more, depending on apparatus design</td>
		</tr>
		<tr>
			<td>Spatial light modulator</td>
			<td></td>
			<td></td>
			<td>Quantity: 1 
			Holoeye LCR-2500</td>
		</tr>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td>All the above instruments are commercially available and no particular specification is required. We leave the choice of the most suitable instruments to the experimenter's discretion.</td>
		</tr>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td>For the interest of the experimenter interested in reproducing the protocol, we recommend the following tools used in our experiment:</td>
		</tr>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td>Tools</td>
		</tr>
		<tr>
			<td>Innolight OEM 300NE, 1064 nm, 300 mW</td>
			<td></td>
			<td></td>
			<td>Laser Source:</td>
		</tr>
		<tr>
			<td>SIMTOOLs</td>
			<td></td>
			<td></td>
			<td>Software for data analysis, available at <a href="http://www.gwoptics.org/simtools/" target="_blank">www.gwoptics.org/simtools/</a></td>
		</tr>
		<tr>
			<td>FINESSE</td>
			<td></td>
			<td></td>
			<td>Software for optical simulations, <a href="http://www.gwoptics.org/finesse/" target="_blank"> www.gwoptics.org/finesse/</a></td>
		</tr>
		<tr>
			<td></td>
			<td></td>
			<td></td>
			<td>Finally, the phase plate employed in the present experiment was manufactured by Jenoptik GmbH, based on a custom design provided by the Authors.</td>
		</tr>
	</tbody>
</table>

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.

All the experimental results so far described in the text and shown in the figures constitute a representative example of a successful execution of the beam conversion protocol. The most representative result is the purity of the generated beam: a successful beam conversion should lead to a beam purity on the order of 95% or above. A good example of successful beam conversion is the measurement of the intensity profile of an 82.8 Watts, 96% pure LG33 beam obtained in 21 and here shown in Figure 12.
Similarly, as discussed in protocol sections, the mode conversion efficiencies of the phase plate and of the overall experimental setup are a good indicator of the successful design of the experimental apparatus, including the phase plate and the mode cleaner cavity. Values of order 50% to 60% and above are generally considered a good value for the mode conversion efficiency. The highest conversion efficiency reported so far with this type of setup is about 70% 21.
The simulation investigation described in Protocol Sec 4 should result in numbers for beam purity with realistic mirrors, suggested mirror specifications and the resulting beam purity when these specifications are adopted. An example of the results you can expect with realistic mirror maps are shown in 19 where an original LG33 purity of 89% is obtained, compared to a purity of &gt;99% for HG00. A purity of &gt;99% for the LG33 mode is achieved using specific mirror requirements with a major reduction of astigmatism in the mirror surface.
<img alt="Figure 1" src="/files/ftp_upload/50564/50564fig1.jpg" /> 
Figure 1. Intensity patterns for Hermite-Gauss (HG) modes up to order 6. The intensity patterns are normalized to have the same peak intensity, for visibility.
<img alt="Figure 2" src="/files/ftp_upload/50564/50564fig2.jpg" /> 
Figure 2. Intensity patterns for helical LG modes up to order 9. The intensity patterns are normalized to have the same peak intensity, for visibility.
<img alt="Figure 3" fo:conten-width="5in" fo:src="/files/ftp_upload/50564/50564fig3highres.jpg" src="/files/ftp_upload/50564/50564fig3.jpg" /> 
Figure 3. Sketch of a conventional setup for production and stabilization of HG00 beams.
<img alt="Figure 4" fo:conten-width="5in" fo:src="/files/ftp_upload/50564/50564fig4highres.jpg" src="/files/ftp_upload/50564/50564fig4.jpg" /> 
Figure 4. A sketch of the experimental setup discussed in this paper. The HG00 beam is first mode-matched to a desired waist size via a telescope then injected on the phase plate. The main diffracted beam is separated from the higher diffraction orders with an aperture and then sent to the Mode Cleaner cavity. A photodiode is used to extract the error signal for controlling the cavity length. The beam intensity is analyzed by a CCD camera.
<img alt="Figure 5" src="/files/ftp_upload/50564/50564fig5.jpg" /> 
Figure 5. Phase modulation profile to convert a HG00 mode to LG33 mode.
<img alt="Figure 6" src="/files/ftp_upload/50564/50564fig6.jpg" /> 
Figure 6. Example of blazed phase modulation profiles for generating LG33 modes.
<img alt="Figure 7" src="/files/ftp_upload/50564/50564fig7.jpg" /> 
Figure 7. Comparison between the intensity distribution of the composite beam generated by the phase plate (left) and the theoretical intensity distribution for a pure LG33 beam with same parameters.
<img alt="Figure 8" src="/files/ftp_upload/50564/50564fig8.jpg" /> 
Figure 8. Example of beam intensity profile fitting applied to a real LG33 beam transmitted from a phase plate (left) compared to fit results (center) and residuals of fit (right). <a href="https://www.jove.com/files/ftp_upload/50564/50564fig8large.jpg" target="_blank"> Click here to view larger figure</a>.
<img alt="Figure 9" fo:conten-width="4.5in" fo:src="/files/ftp_upload/50564/50564fig9highres.jpg" src="/files/ftp_upload/50564/50564fig9.jpg" /> 
Figure 9. Profile of an LG33 beam with Gaussian fit shown for comparison.
<img alt="Figure 10" fo:conten-width="4.5in" fo:src="/files/ftp_upload/50564/50564fig10highres.jpg" src="/files/ftp_upload/50564/50564fig10.jpg" /> 
Figure 10. Light power transmitted by a linear cavity as a function of the cavity length, when injecting a beam generated by the phase plate. The resonant peaks at 0 and 1 FSR correspond to the desired LG33 mode. A fit to this dominant mode is shown for comparison (blue line). The red curve shows the result of the numerical model, based on the modal content described in Table 2. Pictures of the unwanted beams to be filtered by the cavity are shown in the insets.
<img alt="Figure 11" fo:conten-width="5in" fo:src="/files/ftp_upload/50564/50564fig11highres.jpg" src="/files/ftp_upload/50564/50564fig11.jpg" /> 
Figure 11. An example of a mirror surface map for one of the Advanced LIGO optical mirrors 19.
<img alt="Figure 12" src="/files/ftp_upload/50564/50564fig12.jpg" /> 
Figure 12. Intensity profile of a 82.8 W LG33 beam transmitted by a linear cavity (left) compared with fit residuals (right).
<table border="1">
	<tbody>
		<tr>
			<td>p</td>
			<td>l</td>
			<td>0</td>
			<td>1</td>
			<td>2</td>
			<td>3</td>
			<td>4</td>
			<td>5</td>
			<td>6</td>
			<td>7</td>
			<td>8</td>
			<td>9</td>
		</tr>
		<tr>
			<td colspan="2">0</td>
			<td>1.0</td>
			<td>2.8</td>
			<td>1.7</td>
			<td>2.0</td>
			<td>2.2</td>
			<td>2.5</td>
			<td>2.6</td>
			<td>3.1</td>
			<td>3.0</td>
			<td>3.2</td>
		</tr>
		<tr>
			<td colspan="2">1</td>
			<td>1.7</td>
			<td>2.7</td>
			<td>2.2</td>
			<td>2.4</td>
			<td>2.6</td>
			<td>2.8</td>
			<td>2.9</td>
			<td>2.8</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td colspan="2">2</td>
			<td>2.2</td>
			<td>2.4</td>
			<td>2.5</td>
			<td>2.7</td>
			<td>2.9</td>
			<td>3.0</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td colspan="2">3</td>
			<td>2.5</td>
			<td>2.7</td>
			<td>2.8</td>
			<td>3.0</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td colspan="2">4</td>
			<td>2.9</td>
			<td>3.0</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
	</tbody>
</table>
Table 1. Optimum ratio between input HG00 beam size and LGpl phase image beam size for LG modes up to the order 9.
<table border="1">
	<tbody>
		<tr>
			<td>Mode</td>
			<td>LG33</td>
			<td>LG63</td>
			<td>LG43</td>
			<td>LG53</td>
			<td>LG32</td>
			<td>LG62</td>
		</tr>
		<tr>
			<td>Power</td>
			<td>75%</td>
			<td>8%</td>
			<td>4%</td>
			<td>4%</td>
			<td>4%</td>
			<td>1%</td>
		</tr>
	</tbody>
</table>
Table 2. Mode content analysis described by the cavity scan shown in Figure 10.

Watch this Scientific Journal Video about The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry at JoVE.com

The Generation of Higher-order Laguerre-Gauss Optical Beams for 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  ...

the-generation-higher-order-laguerre-gauss-optical-beams-for-high

Research

Education

JoVE Journal

JoVE Core

Physics

Engineering

Unit 1

Gravitation

SCIENTISTS IN ACTION

21.4K ビュー.  University of Birmingham. 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.

ビデオ: The Generation of Higher-order Laguerre-Gauss Optical Beams for 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...

covalent labeling with diethylpyrocarbonate for studying protein higher-order structure by mass spectrometry

Covalent Labeling with Diethylpyrocarbonate for Studying Protein Higher-Order Structure by Mass Spectrometry

The experimental procedures for performing diethylpyrocarbonate-based covalent labeling with mass spectrometric detection are described. Diethylpyrocarbonate is simply mixed with the protein or protein complex of interest, leading to the modification of solvent accessible amino acid residues. The modified residues can be identified after proteolytic digestion and liquid chromatography/mass spectrometry...

novel object exploration as a potential assay for higher order repetitive behaviors in mice

Novel Object Exploration as a Potential Assay for Higher Order Repetitive Behaviors in Mice

Higher order restricted, repetitive behaviors (RRBs) disrupt the lives of affected individuals.  These behaviors are challenging to model in rodents, making basic biomedical research into potential treatments or interventions for RRBs difficult.  Here we describe novel object exploration as a potential assay for higher order RRBs in...

laser-free hydroxyl radical protein footprinting to perform higher order structural analysis of proteins

Laser-free Hydroxyl Radical Protein Footprinting to Perform Higher Order Structural Analysis of Proteins

This protocol presents a method to use inline radical dosimetry and a plasma light source to perform flash oxidation protein footprinting. This method replaces the hazardous UV laser to simplify and improve the reproducibility of fast photochemical oxidation of protein...

wideband optical detector of ultrasound for medical imaging applications

Wideband Optical Detector of Ultrasound for Medical Imaging Applications

Optical detection of ultrasound is impractical in many imaging scenarios because it often requires stable environmental conditions. We demonstrate an optical technique for ultrasound sensing in volatile environments with miniaturization and sensitivity levels appropriate for optoacoustic imaging in restrictive scenarios, e.g. intravascular...

high precision fret at single-molecule level for biomolecule structure determination

High Precision FRET at Single-molecule Level for Biomolecule Structure Determination

A protocol for high-precision FRET experiments at the single molecule level is presented here. Additionally, this methodology can be used to identify three conformational states in the ligand-binding domain of the N-methyl-D-aspartate (NMDA) receptor. Determining precise distances is the first step towards building structural models based on FRET...

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

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...

high-resolution optical mapping of the mouse sino-atrial node

High-resolution Optical Mapping of the Mouse Sino-atrial Node

Here, we present a protocol for optical mapping of electrical activity from the mouse right atrium and especially the sino-atrial node, at a high spatial and temporal...

detecting the water-soluble chloride distribution of cement paste in a high-precision way

Detecting the Water-soluble Chloride Distribution of Cement Paste in a High-precision Way

A protocol for obtaining a water-soluble chloride profile by using a high precision milling method is...

high-speed optical diagnostics of a supersonic ping-pong cannon

High-Speed Optical Diagnostics of a Supersonic Ping-Pong Cannon

We describe a method for the construction of a supersonic ping-pong cannon (SSPPC) along with optical diagnostic techniques for the measurement of ball velocities and the characterization of propagating shock waves during the firing of the...

construction of a high resolution microscope with conventional and holographic optical trapping capabilities

Construction of a High Resolution Microscope with Conventional and Holographic Optical Trapping Capabilities

The system described herein employs a traditional optical trap as well as an independent holographic optical trapping line, capable of creating and manipulating multiple traps. This allows for the creation of complex geometric arrangements of refractive particles while also permitting simultaneous high-speed, high-resolution measurements of the activity of biological...

rapid optical clearing for semi-high-throughput analysis of tumor spheroids

Rapid Optical Clearing for Semi-High-Throughput Analysis of Tumor Spheroids

Tumor spheroids are becoming increasingly utilized to assess tumor cell-microenvironment interactions and therapy response. The present protocol describes a robust but simple method for semi-high-throughput imaging of 3D tumor spheroids using rapid optical...

acquisition of a high-precision skilled forelimb reaching task in rats

Acquisition of a High-precision Skilled Forelimb Reaching Task in Rats

A paradigm is presented to analyze the acquisition of a high-precision skilled forelimb reaching task in...

high precision zinc isotopic measurements applied to mouse organs

High Precision Zinc Isotopic Measurements Applied to Mouse Organs

We present the technique to measure with high precision zinc isotope ratios in mouse...

application of biolayer interferometry (bli) for studying protein-protein interactions in transcription

Application of Biolayer Interferometry BLI for Studying Protein-Protein Interactions in Transcription

Interactions of transcription factors (TFs) with the RNA polymerase are usually studied using pulldown assays. We apply a Biolayer Interferometry (BLI) technology to characterize the interaction of GrgA with the chlamydial RNA polymerase. Compared to pulldown assays, BLI detects real-time association and dissociation, offers higher sensitivity, and is highly...

Application of Biolayer Interferometry (BLI) for Studying Protein-Protein Interactions in Transcription

characterization of surface modifications by white light interferometry: applications in ion sputtering, laser ablation, and tribology experiments

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

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...

generation of high quality chromatin immunoprecipitation dna template for high-throughput sequencing (chip-seq)

Generation of High Quality Chromatin Immunoprecipitation DNA Template for High-throughput Sequencing ChIP-seq

The combination of chromatin immunoprecipitation and ultra-high-throughput sequencing (ChIP-seq) can identify and map protein-DNA interactions in a given tissue or cell line. Outlined is how to generate a high quality ChIP template for subsequent sequencing, using experience with the transcription factor TCF7L2 as an...

Generation of High Quality Chromatin Immunoprecipitation DNA Template for High-throughput Sequencing (ChIP-seq)

high-pressure, high-temperature deformation experiment using the new generation griggs-type apparatus

High-pressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus

Rock deformation needs to be quantified at high pressure. A description of the procedure to perform deformation experiments in a newly designed solid-medium Griggs-type apparatus is here given. This provides technological basis for future rheological studies at pressures up to 5...

high-throughput analysis of optical mapping data using electromap

High-Throughput Analysis of Optical Mapping Data Using ElectroMap

This protocol describes the setup and use of ElectroMap, a MATLAB-based open-source software platform for analysis of cardiac optical mapping data. ElectroMap provides a versatile high-throughput tool for analysis of optical mapping voltage and calcium datasets across a wide range of cardiac experimental...

generation of high-throughput three-dimensional tumor spheroids for drug screening

Generation of High-Throughput Three-Dimensional Tumor Spheroids for Drug Screening

Across a wide variety of disease indications, more physiologically relevant models are being developed and implemented into drug discovery programs. The new model system described here demonstrates how three-dimensional tumor spheroids can be cultured and screened in a high-throughput 1536-well plate-based system to search for new oncology...

Construction and Testing of Coin Cells of Lithium Ion Batteries

Rechargeable lithium ion batteries have wide applications in electronics, where customers always demand more capacity and longer lifetime. Lithium ion batteries have also been considered to be used in electric and hybrid vehicles1 or even electrical grid stabilization systems2. All these applications simulate a dramatic increase in the research and development of battery materials3-7, including new materials3,8, doping9, nanostructuring10-13, coatings or surface modifications14-17 and novel binders18. Consequently, an increasing number of physicists, chemists and materials scientists have recently ventured into this area. Coin cells are widely used in research laboratories to test new battery materials; even for the research and development that target large-scale and high-power applications, small coin cells are often used to test the capacities and rate capabilities of new materials in the initial stage. 
 In 2010, we started a National Science Foundation (NSF) sponsored research project to investigate the surface adsorption and disordering in battery materials (grant no. DMR-1006515). In the initial stage of this project, we have struggled to learn the techniques of assembling and testing coin cells, which cannot be achieved without numerous help of other researchers in other universities (through frequent calls, email exchanges and two site visits). Thus, we feel that it is beneficial to document, by both text and video, a protocol of assembling and testing a coin cell, which will help other new researchers in this field. This effort represents the "Broader Impact" activities of our NSF project, and it will also help to educate and inspire students.
In this video article, we document a protocol to assemble a CR2032 coin cell with a LiCoO2 working electrode, a Li counter electrode, and (the mostly commonly used) polyvinylidene fluoride (PVDF) binder. To ensure new learners to readily repeat the protocol, we keep the protocol as specific and explicit as we can. However, it is important to note that in specific research and development work, many parameters adopted here can be varied. First, one can make coin cells of different sizes and test the working electrode against a counter electrode other than Li. Second, the amounts of C black and binder added into the working electrodes are often varied to suit the particular purpose of research; for example, large amounts of C black or even inert powder were added to the working electrode to test the "intrinsic" performance of cathode materials14. Third, better binders (other than PVDF) have also developed and used18. Finally, other types of electrolytes (instead of LiPF6) can also be used; in fact, certain high-voltage electrode materials will require the uses of special electrolytes7.

A protocol to construct and test coin cells of lithium ion batteries is described. The specific procedures of making a working electrode, preparing a counter electrode, assembling a cell inside a glovebox and testing the cell are presented.

Rechargeable lithium ion batteries have wide applications in electronics, where customers always demand more capacity and longer lifetime.  Lithium ion ...

Fabricating Metamaterials Using the Fiber Drawing Method

Metamaterials are man-made composite materials, fabricated by assembling components much smaller than the wavelength at which they operate 1. They owe their electromagnetic properties to the structure of their constituents, instead of the atoms that compose them. For example, sub-wavelength metal wires can be arranged to possess an effective electric permittivity that is either positive or negative at a given frequency, in contrast to the metals themselves 2. This unprecedented control over the behaviour of light can potentially lead to a number of novel devices, such as invisibility cloaks 3, negative refractive index materials 4, and lenses that resolve objects below the diffraction limit 5. However, metamaterials operating at optical, mid-infrared and terahertz frequencies are conventionally made using nano- and micro-fabrication techniques that are expensive and produce samples that are at most a few centimetres in size 6-7. Here we present a fabrication method to produce hundreds of meters of metal wire metamaterials in fiber form, which exhibit a terahertz plasmonic response 8. We combine the stack-and-draw technique used to produce microstructured polymer optical fiber 9 with the Taylor-wire process 10, using indium wires inside polymethylmethacrylate (PMMA) tubes. PMMA is chosen because it is an easy to handle, drawable dielectric with suitable optical properties in the terahertz region; indium because it has a melting temperature of 156.6 &deg;C which is appropriate for codrawing with PMMA. We include an indium wire of 1 mm diameter and 99.99% purity in a PMMA tube with 1 mm inner diameter (ID) and 12 mm outside diameter (OD) which is sealed at one end. The tube is evacuated and drawn down to an outer diameter of 1.2 mm. The resulting fiber is then cut into smaller pieces, and stacked into a larger PMMA tube. This stack is sealed at one end and fed into a furnace while being rapidly drawn, reducing the diameter of the structure by a factor of 10, and increasing the length by a factor of 100. Such fibers possess features on the micro- and nano- scale, are inherently flexible, mass-producible, and can be woven to exhibit electromagnetic properties that are not found in nature. They represent a promising platform for a number of novel devices from terahertz to optical frequencies, such as invisible fibers, woven negative refractive index cloths, and super-resolving lenses.

Metamaterials at terahertz frequencies offer unique opportunities, but are challenging to fabricate in bulk. We adapt the fabrication procedure for microstructured polymer optical fibers to inexpensively fabricate metamaterials potentially on an industrial scale. We produce polymethylmethacrylate fibers containing ~10 &mu;m diameter indium wires separated by ~100 &mu;m, which exhibit a terahertz plasmonic response.

Metamaterials are man-made composite materials, fabricated by assembling components much smaller than the wavelength at which they operate 1. They owe ...

Optical Trapping of Nanoparticles

Optical trapping is a technique for immobilizing and manipulating small objects in a gentle way using light, and it has been widely applied in trapping and manipulating small biological particles. Ashkin and co-workers first demonstrated optical tweezers using a single focused beam1. The single beam trap can be described accurately using the perturbative gradient force formulation in the case of small Rayleigh regime particles1. In the perturbative regime, the optical power required for trapping a particle scales as the inverse fourth power of the particle size. High optical powers can damage dielectric particles and cause heating. For instance, trapped latex spheres of 109 nm in diameter were destroyed by a 15 mW beam in 25 sec1, which has serious implications for biological matter2,3.
A self-induced back-action (SIBA) optical trapping was proposed to trap 50 nm polystyrene spheres in the non-perturbative regime4. In a non-perturbative regime, even a small particle with little permittivity contrast to the background can influence significantly the ambient electromagnetic field and induce a large optical force. As a particle enters an illuminated aperture, light transmission increases dramatically because of dielectric loading. If the particle attempts to leave the aperture, decreased transmission causes a change in momentum outwards from the hole and, by Newton's Third Law, results in a force on the particle inwards into the hole, trapping the particle. The light transmission can be monitored; hence, the trap can become a sensor. The SIBA trapping technique can be further improved by using a double-nanohole structure.
The double-nanohole structure has been shown to give a strong local field enhancement5,6. Between the two sharp tips of the double-nanohole, a small particle can cause a large change in optical transmission, thereby inducing a large optical force. As a result, smaller nanoparticles can be trapped, such as 12 nm silicate spheres7 and 3.4 nm hydrodynamic radius bovine serum albumin proteins8. In this work, the experimental configuration used for nanoparticle trapping is outlined. First, we detail the assembly of the trapping setup which is based on a Thorlabs Optical Tweezer Kit. Next, we explain the nanofabrication procedure of the double-nanohole in a metal film, the fabrication of the microfluidic chamber and the sample preparation. Finally, we detail the data acquisition procedure and provide typical results for trapping 20 nm polystyrene nanospheres.

The following setup approach details low power optical trapping of dielectric nanoparticles using a double-nanohole in metal film.

Optical trapping is a technique for immobilizing and manipulating small objects in a gentle way using light, and it has been widely applied in trapping ...

Bringing the Visible Universe into Focus with Robo-AO

The angular resolution of ground-based optical telescopes is limited by the degrading effects of the turbulent atmosphere. In the absence of an atmosphere, the angular resolution of a typical telescope is limited only by diffraction, i.e., the wavelength of interest, &lambda;, divided by the size of its primary mirror's aperture, D. For example, the Hubble Space Telescope (HST), with a 2.4-m primary mirror, has an angular resolution at visible wavelengths of ~0.04 arc seconds. The atmosphere is composed of air at slightly different temperatures, and therefore different indices of refraction, constantly mixing. Light waves are bent as they pass through the inhomogeneous atmosphere. When a telescope on the ground focuses these light waves, instantaneous images appear fragmented, changing as a function of time. As a result, long-exposure images acquired using ground-based telescopes - even telescopes with four times the diameter of HST - appear blurry and have an angular resolution of roughly 0.5 to 1.5 arc seconds at best.
Astronomical adaptive-optics systems compensate for the effects of atmospheric turbulence. First, the shape of the incoming non-planar wave is determined using measurements of a nearby bright star by a wavefront sensor. Next, an element in the optical system, such as a deformable mirror, is commanded to correct the shape of the incoming light wave. Additional corrections are made at a rate sufficient to keep up with the dynamically changing atmosphere through which the telescope looks, ultimately producing diffraction-limited images.
The fidelity of the wavefront sensor measurement is based upon how well the incoming light is spatially and temporally sampled1. Finer sampling requires brighter reference objects. While the brightest stars can serve as reference objects for imaging targets from several to tens of arc seconds away in the best conditions, most interesting astronomical targets do not have sufficiently bright stars nearby. One solution is to focus a high-power laser beam in the direction of the astronomical target to create an artificial reference of known shape, also known as a 'laser guide star'. The Robo-AO laser adaptive optics system2,3 employs a 10-W ultraviolet laser focused at a distance of 10 km to generate a laser guide star. Wavefront sensor measurements of the laser guide star drive the adaptive optics correction resulting in diffraction-limited images that have an angular resolution of ~0.1 arc seconds on a 1.5-m telescope.

Light from astronomical objects must travel through the earth's turbulent atmosphere before it can be imaged by ground-based telescopes. To enable direct imaging at maximum theoretical angular resolution, advanced techniques such as those employed by the Robo-AO adaptive-optics system must be used.

The angular  resolution of ground-based optical telescopes is limited by the degrading  effects of the turbulent atmosphere. In the absence of an ...

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats &amp; Spheres

Convergent Polishing is a novel polishing system and method for finishing flat and spherical glass optics in which a workpiece, independent of its initial shape (i.e., surface figure), will converge to final surface figure with excellent surface quality under a fixed, unchanging set of polishing parameters in a single polishing iteration. In contrast, conventional full aperture polishing methods require multiple, often long, iterative cycles involving polishing, metrology and process changes to achieve the desired surface figure. The Convergent Polishing process is based on the concept of workpiece-lap height mismatch resulting in pressure differential that decreases with removal and results in the workpiece converging to the shape of the lap. The successful implementation of the Convergent Polishing process is a result of the combination of a number of technologies to remove all sources of non-uniform spatial material removal (except for workpiece-lap mismatch) for surface figure convergence and to reduce the number of rogue particles in the system for low scratch densities and low roughness. The Convergent Polishing process has been demonstrated for the fabrication of both flats and spheres of various shapes, sizes, and aspect ratios on various glass materials. The practical impact is that high quality optical components can be fabricated more rapidly, more repeatedly, with less metrology, and with less labor, resulting in lower unit costs. In this study, the Convergent Polishing protocol is specifically described for fabricating 26.5 cm square fused silica flats from a fine ground surface to a polished ~&#955;/2 surface figure after polishing 4 hr per surface on a 81 cm diameter polisher.

A novel optical polishing process, called &#8220;Convergent Polishing&#8221;, which enables faster, lower cost polishing, is described. Unlike conventional polishing processes, Convergent Polishing allows a glass workpiece to be polished in a single iteration and with high surface quality to its final surface figure without requiring changes to polishing parameters.

Convergent Polishing is a novel polishing system and method for finishing flat and spherical glass optics in which a workpiece, independent of its initial ...

Patterning via Optical Saturable Transitions - Fabrication and Characterization

This protocol describes the fabrication and characterization of nanostructures using a novel nanolithographic technique called Patterning via Optical Saturable Transitions (POST). In this technique the chemical properties of organic photochromic molecules that undergo single-photon reactions are exploited, enabling rapid top-down nanopatterning over large areas at low light intensities, thereby, allowing for the circumvention of the far-field diffraction barrier.4 Simple, cost-effective, high throughput and resolution alternatives to nanopatterning are being explored, such as, two-photon polymerization5,6, beam pen lithography (BPL)7, scanning electron beam lithography (SEBL), and focused ion beam (FIB) patterning. However, multi-photon approaches require high light intensities, which limit their potential for high throughput and offer low image contrast. Although, electron and ion beam lithographic processes offer increased resolution, the serial nature of the process is limited to slow writing speeds, which also prevents patterning of features over large areas. Beam-pen lithography is an approach towards parallel near-field optical lithography. However, the gap between the source of the beam and the surface of the photoresist needs to be controlled extremely precisely for good pattern uniformity and this is very challenging to accomplish for large arrays of beams. Patterning via Optical Saturable Transitions (POST) is an alternative optical nanopatterning technique for patterning sub-wavelength features1-3. Since this technique uses single photons instead of electrons, it is extremely fast and does not require high light intensities1-3, opening the door to massive parallelization.

We report that the diffraction limit of conventional optical lithography can be overcome by exploiting the transitions of organic photochromic derivatives induced by their photoisomerization at low light intensities.1-3 This paper outlines our fabrication technique and two locking mechanisms, namely: dissolution of one photoisomer and electrochemical oxidation.

This protocol describes the fabrication and characterization of nanostructures using a novel nanolithographic technique called Patterning via Optical ...

Writing Bragg Gratings in Multicore Fibers

Fiber Bragg gratings in multicore fibers can be used as compact and robust filters in astronomical and other research and commercial applications. Strong suppression at a single wavelength requires that all cores have matching transmission profiles. These gratings cannot be inscribed using the same method as for single-core fibers because the curved surface of the cladding acts as a lens, focusing the incoming UV laser beam and causing variations in exposure between cores. Therefore we use an additional optical element to ensure that the beam shape does not change while passing through the cross-section of the multicore fiber. This consists of a glass capillary tube which has been polished flat on one side, which is then placed over the section of the fiber to be inscribed. The laser beam enters the fiber through the flat surface of the capillary tube and hence maintains its original dimensions. This paper demonstrates the improvements in core-to-core uniformity for a 7-core fiber using this method. The technique can be generalized to larger multicore fibers.

We describe a technique for inscribing identical fiber Bragg gratings into each core of a multicore fiber. This is achieved by introducing an additional surface into the optical path to mitigate lensing by the curved surface of the fiber cladding.

Fiber Bragg gratings in multicore fibers can be used as compact and robust filters in astronomical and other research and commercial applications. Strong ...

Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

A micro-electro-mechanical-system (MEMS) is a widely used component in many industries, including energy, biotechnology, medical, communications, and automotive. However, effective inspection and characterization metrology systems are needed to ensure the functional reliability of MEMS. This study presents a system based on digital holography as a tool for MEMS metrology. Digital holography has gained increasing attention in the past 20 years. With the fast development and decreasing cost of sensor arrays, resolution of such systems has increased broadening potential applications. Thus, it has attracted attention from both research and industry sides as a potential reliable tool for industrial metrology. Indeed, by recording the interference pattern between an object beam (which contains sample height information) and a reference beam on a CCD camera, one can retrieve the quantitative phase information of an object. However, most of digital holographic systems are bulky and thus not easy to implement on industry production lines. The novelty of the system presented is that it is lens-less and thus very compact. In this study, it is shown that the Compact Digital Holographic Microscope (CDHM) can be used to evaluate several characteristics typically consider as criteria in MEMS inspections. The surface profiles of MEMS in both static and dynamic conditions are presented. Comparison with AFM is investigated to validate the accuracy of the CDHM.

We present a compact reflection digital holographic system (CDHM) for inspection and characterization of MEMS devices. A lens-less design using a diverging input wave providing natural geometrical magnification is demonstrated. Both static and dynamic studies are presented.

A micro-electro-mechanical-system (MEMS) is a widely used component in many industries, including energy, biotechnology, medical, communications, and ...

Scanning Light Scattering Profiler (SLPS) Based Methodology to Quantitatively Evaluate Forward and Backward Light Scattering from Intraocular Lenses

The scanning light scattering profiler (SLSP) methodology has been developed for the full-angle quantitative evaluation of forward and backward light scattering from intraocular lenses (IOLs) using goniophotometer principles. This protocol describes the SLSP platform and how it employs a 360&#176; rotational photodetector sensor that is scanned around an IOL sample while recording the intensity and location of scattered light as it passes through the IOL medium. The SLSP platform can be used to predict, non-clinically, the propensity for current and novel IOL designs and materials to induce light scatter. Non-clinical evaluation of light scattering properties of IOLs can significantly reduce the number of patient complaints related to unwanted glare, glistening, optical defects, poor image quality, and other phenomena associated with the unintended light scattering. Future studies should be conducted to correlate SLSP data with clinical results to help identify which measured light scatter is most problematic for patients that have undergone cataract surgery subsequent to IOL implantation.

Scanning Light Scattering Profiler SLPS Based Methodology to Quantitatively Evaluate Forward and Backward Light Scattering from Intraocular Lenses

This protocol describes the scanning light scattering profiler (SLSP) that enables the full-angle quantitative evaluation of forward and backward scattering of light from intraocular lenses (IOLs) using goniophotometer principles.

The scanning light scattering profiler (SLSP) methodology has been developed for the full-angle quantitative evaluation of forward and backward light ...

Fabrication of Polymer Microspheres for Optical Resonator and Laser Applications

This paper describes three methods of preparing fluorescent microspheres comprising &#960;-conjugated or non-conjugated polymers: vapor diffusion, interface precipitation, and mini-emulsion. In all methods, well-defined, micrometer-sized spheres are obtained from a self-assembling process in solution. The vapor diffusion method can result in spheres with the highest sphericity and surface smoothness, yet the types of the polymers able to form these spheres are limited. On the other hand, in the mini-emulsion method, microspheres can be made from various types of polymers, even from highly crystalline polymers with coplanar, &#960;-conjugated backbones. The photoluminescent (PL) properties from single isolated microspheres are unusual: the PL is confined inside the spheres, propagates at the circumference of the spheres via the total internal reflection at the polymer/air interface, and self-interferes to show sharp and periodic resonant PL lines. These resonating modes are so-called "whispering gallery modes" (WGMs). This work demonstrates how to measure WGM PL from single isolated spheres using the micro-photoluminescence (&#181;-PL) technique. In this technique, a focused laser beam irradiates a single microsphere, and the luminescence is detected by a spectrometer. A micromanipulation technique is then used to connect the microspheres one by one and to demonstrate the intersphere PL propagation and color conversion from coupled microspheres upon excitation at the perimeter of one sphere and detection of PL from the other microsphere. These techniques, &#181;-PL and micromanipulation, are useful for experiments on micro-optic application using polymer materials.

Protocols for the synthesis of microspheres from polymers, the manipulation of microspheres, and micro-photoluminescence measurements are presented.