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

<ol>
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J., Levin, Y., Matsko, A. B., Thorne, K. S., Vyatchanin, S. 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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. 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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. 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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.

In den vergangenen Jahrzehnten hochpräzisen interferometrischen Experimente wurden auf eine ultimative Empfindlichkeit Regime, wo Quanteneffekte beginnen, eine entscheidende Rolle spielen geschoben werden. In dieser laufenden und zukünftigen Experimenten, wie Laserkühlung von mechanischen Oszillatoren 1, optische Fallen für Spiegel 2, Generation verstrickt Testmassen 3, quantum non-Abriss Interferometrie 4, Frequenz Stabilisierung von Lasern mit starren Hohlräumen 5 und Gravitationswellendetektion 6 , 7, 8, Forscher stehen vor einer Vielzahl von einschränkenden fundamentalen und technischen Lärmquellen. Eines der schwerwiegendsten Probleme ist das thermische Rauschen der Resonatorspiegel der interferometrischen Konfigurationen, die durch die thermische Anregung der Atome, aus denen die Spiegelträger und der Spiegel reflektierende Beschichtungen 7, 8, 9 verursacht wird. Dieser Effekt ist auch als Brownsche Bewegung, verursacht eine Unsicherheit in der Phasedas reflektierte Licht von allen Test-Massen und wird daher offenbar als eine grundlegende Lärmbegrenzung im Interferometer-Ausgang. Zum Beispiel wird das projizierte Design Empfindlichkeit von fortschrittlichen Gravitationswellen-Antennen, wie Advanced LIGO, Advanced JUNGFRAU, und dem Einstein-Teleskop, durch diese Art von Lärm in den empfindlichsten Bereich der Beobachtung Frequenzband 10, 11, 12 begrenzt. Experimentalphysiker in der Gemeinschaft hart zu arbeiten in einem kontinuierlichen Bemühungen um diese Geräusche Beiträge zu minimieren und die Empfindlichkeit ihrer Instrumente zu verbessern. In dem besonderen Fall der Spiegel Brownsche Rauschen ist ein Verfahren zur Abschwächung eine größere Punktgröße des aktuell verwendeten Standard grundlegende HG 00 Strahls auf die Probemasse Oberflächen eingesetzt, da ein größerer Strahl beträgt effektiver über die zufällige Bewegung der Oberfläche 13, 14. Die spektrale Leistungsdichte des Spiegels thermisches Rauschen hat sich gezeigt, mit Skaladie Umkehrung der Gaußschen Strahl Größe für den Spiegelträger und umgekehrt proportional zum Quadrat der Spiegelfläche 9. Da jedoch die Lichtflecken gebildet werden größer, wird ein größerer Teil der Lichtleistung über die Kante der reflektierenden Oberfläche hat. Wenn man einen Träger verwendet mit einer homogeneren radiale Intensitätsverteilung als die üblicherweise verwendeten HG 00 abgelesen werden (siehe z. B. Figur 1) kann die Brownsche thermischen Rauschpegel ohne Erhöhung dieser Art von Verlust reduziert werden. Unter allen homogener Strahl-Typen, die für neue Versionen von hochpräzisen Interferometrie vorgeschlagen worden, zum Beispiel Balken oder Mesa konischen Moden 13, 14, sind die vielversprechendsten höherer Ordnung LG Strahlen aufgrund ihrer potentiellen Kompatibilität mit dem derzeit verwendeten sphärischen Spiegelflächen 15. Zum Beispiel, die Erkennungsrate von binären Neutronenstern in Spiralsysteme - erkennen, welche die vielversprechendsten astrophysikalischen Quellen betrachtet werden für eine erste GWIonen - konnte um etwa einen Faktor von 2 oder mehr 16 auf Kosten einer minimalen Änderungen in der Gestaltung der zweiten Generation Interferometer im Bau 10, 11 verbessert werden. Neben den thermischen Rauschens Vorteile, die breiter Intensitätsverteilungen höherer Ordnung LG Balken (siehe als Beispiel 2) gezeigt wurde, dass die Größe der thermischen Aberration von Optiken innerhalb der Interferometer zu mildern. Dies würde den Umfang, in dem thermische Vergütungssysteme auf in zukünftigen Experimenten herangezogen werden, um zu erreichen Design Empfindlichkeiten 19. Wir haben untersucht und erfolgreich demonstriert die Machbarkeit der Erzeugung LG Balken auf der Ebene der Reinheit und Stabilität erforderlich, um erfolgreich zu betreiben GW Interferometer zum besten ihrer Empfindlichkeit 16, 18, ​​19, 20, 21, 22. Das vorgeschlagene Verfahren kombiniert Techniken und Know-how in den verschiedensten Bereichen der Physik und Optik erfolgreich entwickelth als die Erzeugung hoher Stabilität, strahlt rauscharmen Einmodenlaser 23, die Verwendung von räumlichen Lichtmodulatoren und diffraktiven optischen Elementen zur Beeinflussung der räumlichen Profile der Lichtstrahlen 18, 22, 24, 25, 26, und die Verwendung von fortgeschrittenen Techniken für die Erfassung, Überwachung und Stabilisierung der resonanten optischen Kavitäten 27, die auf eine weitere Reinigung und Stabilisierung des Laserlichts. Diese Methode wurde erfolgreich in den Laborexperimenten nachgewiesen, exportiert für Tests in großem Maßstab Prototyp-Interferometer 20 und zum Erzeugen LG Modi bei hohen Laserleistungen bis zu 80 W 21. In diesem Artikel präsentieren wir die Details des Verfahrens zum Erzeugen höherer Ordnung LG Balken und diskutieren eine Methodik für die Charakterisierung und Validierung der resultierende Strahl. Ferner wird in Schritt 4 ein Verfahren zur numerischen Untersuchungen von Hohlräumen mit nicht perfekter Spiegel 19 skizziert.

<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

Thermisches Rauschen in hohem Reflexionsvermögen Spiegel ist ein großes Hindernis für verschiedene Arten von hochpräzisen interferometrischen Experimenten, um den Standard Quantenlimit erreichen oder mechanische Systeme, um ihre Quanten Grundzustand zu kühlen wollen. Dies ist zum Beispiel der Fall der künftigen Gravitationswellenobservatorien, dessen Empfindlichkeit gegenüber Gravitationswellen-Signale wird voraussichtlich im empfindlichsten Frequenzbereich begrenzt werden, durch atomare Schwingung ihrer Spiegel Massen. Ein vielversprechender Ansatz verfolgt, um diese Beschränkung zu überwinden, ist höherer Ordnung Laguerre-Gauss (LG) optischen Strahlen anstelle des üblicherweise verwendeten Grundmode beschäftigen. Aufgrund ihrer homogenere Lichtverteilung diese Strahlen durchschnittlich mehr effektiv über den thermisch angetrieben Schwankungen der Spiegelfläche, was wiederum die Unsicherheit in den Spiegel Position erfaßt durch das Laserlicht. Wir zeigen eine vielversprechende Methode zur Erzeugunghöherer Ordnung LG Strahlen durch Formen eines grundlegenden Gaußschen Strahl mit Hilfe von diffraktiven optischen Elementen. Wir zeigen, dass mit herkömmlichen Mess-und Regeltechnik, die zur Stabilisierung fundamentalen Laserstrahlen bekannt sind, höherer Ordnung LG Modi gereinigt werden kann und genauso gut auf einem vergleichsweise hohen Niveau stabilisiert. Eine Reihe von Diagnose-Tools ermöglicht es uns, zu kontrollieren und Schneider die Eigenschaften der erzeugten LG Balken. Dies ermöglichte es uns, ein LG Strahl mit höchster Reinheit bis heute berichtet produzieren. Die nachgewiesene Verträglichkeit höherer Ordnung LG Modi mit Standard-Interferometrie Techniken und mit der Verwendung von Standard-sphärische Optik macht sie zu einem idealen Kandidaten für den Einsatz in einer künftigen Generation von hochpräzisen Interferometrie.

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.

Die Generation von höherer Ordnung Laguerre-Gauss optischen Strahlen für Präzisions-Interferometrie

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

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SCIENTISTS IN ACTION

21.6K Aufrufe.  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.

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

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.

Bau und Erprobung von Knopfzellen von Lithium Ionen Batterien

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

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Ingenieurwesen

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.

Herstellung Metamaterialien Mit dem Fiber Drawing Methode

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 von Nanopartikeln

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.

Bringing the Visible Universe in Focus mit 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 ...

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 Polieren: Eine einfache und schnelle, Schmalrandpolierprozess der Hochwertiges optisches Wohnungen &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 ...

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.

Strukturierung via Optical Saturable Transitions - Herstellung und Charakterisierung

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.

Schreiben-Bragg-Gitter 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 ...

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.

Compact-Objektiv lose digitale holografische Mikroskop für MEMS-Inspektion und Charakterisierung

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.

Scanning Light Scattering Profiler (SLPS) basierte Methodik zur quantitativen Bewertung von Vorwärts- und Rücklichtlichtstreuung aus Intraokularlinsen

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.