OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 17 — Aug. 25, 2003
  • pp: 2053–2059
« Show journal navigation

High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay

William J Hossack, Eirini Theofanidou, Jason Crain, Kevin Heggarty, and Martin Birch  »View Author Affiliations


Optics Express, Vol. 11, Issue 17, pp. 2053-2059 (2003)
http://dx.doi.org/10.1364/OE.11.002053


View Full Text Article

Acrobat PDF (213 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate the advantages of a ferroelectric liquid crystal spatial light modulator for optical tweezer array applications. The fast switching speeds of the ferroelectric device (compared to conventional nematic systems) is shown to enable very rapid reconfiguration of trap geometries, controlled, high speed particle movement, and tweezer array multiplexing.

© 2003 Optical Society of America

1. Introduction

Since the principle of optical trapping was demonstrated in the 1980’s [1

1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single beam gradient force optical tap for dielectric particles,” Opt. Lett. 11, 288 (1986). [CrossRef] [PubMed]

], laser tweezers have emerged as a powerful micromanipulation tool in both the physical and life sciences. Over this period, it has been recognised that the functionality of a single-gradient optical tweezer can be extended significantly by engineering multiple steerable traps [2

2. K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Physics World 15-10 (October 2002)

]. These optical tweezer arrays bring major potential advantages for aspects of colloidal science [3

3. P.T. Korda, G.C. Spalding, and D.G. Greir, “Evolution of a colloidal critical state in an optical pinning potential landscape”, Phys. Rev. B 66, 024504 (2002) [CrossRef]

], cell biology [4

4. R.L. Eriksen, V.R. Daria, P.J. Rodrigo, and J. Gluckstad, “Computer controlled orientation of multiple optically-trapped particles,” Microelectronic Engineering 67–68, 872, (2003) [CrossRef]

] and single molecule biophysics [5

5. S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989). [CrossRef] [PubMed]

, 6

6. M. D Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997) [CrossRef]

].

The most powerful and versatile approach for creating complex trapping landscapes involves the use of dynamic diffractive optical elements. Here, steering and manipulation is realised by encoding holographic patterns onto a reconfigurable device [2

2. K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Physics World 15-10 (October 2002)

, 7

7. W.M. Lee, X.C. Yuan, and D. Y. Tang, “Optical tweezers with multiple optical forces using double-hologram interference,” Opt. Express 11, 199 (2003). [CrossRef] [PubMed]

, 8

8. P.J. Rodrigo, R. L. Eriksen, V.R. Daria, and J. Glueckstad, “Shack-Hartmann multiple-beam optical tweezers,” Opt. Express 11, 208 (2003). [CrossRef] [PubMed]

]. The method relies on computer-generated phase-only holographic patterns for optical fan-out which date back to Dammann [9

9. H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3312 (1971) [CrossRef]

] and have been extended to two-dimensional formulations by Dames [10

10. M.P. Dames, R.J. Dowling, P. McKee, and D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 302685 (1991) [CrossRef] [PubMed]

]. Holographic elements for optical tweezers and beam shaping were first implemented by Heckenberg [11

11. N.R Heckenburg, R. McDuff, C.P. Smith, H. Rubinsztein-Dunlop, and M.J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951 (1992) [CrossRef]

, 12

12. C. D’Helon, E.W. Dearden, H. Rubinsztein-Dunlop, and N.R. Heckenburg, “Measurement of the Optical Force and Trapping Range of a Single-beam Gradient Optical Trap for Micron-sized Latex Spheres,” J. Mod. Opt. 41, 595 (1994). [CrossRef]

] to form Laguerre Gaussian beams, and by Grier et al, for multiple tweezers, initially with fixed holograms [13

13. E.R. Dufresne and D.G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optics,” Rev. Sci. Inst. 69, 1974 (1998). [CrossRef]

], and subsequently using dynamic holograms [14

14. E.R. Dufresne, G.C. Spalding, M.T. Dearing, S.A. Sheets, and D.G. Grier “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Inst. 72, 1810, (2002) [CrossRef]

].

To our knowledge, nearly all reported dynamic holographic laser tweezer applications have used spatial light modulators (SLMs) based on nematic liquid crystals; the most common being the Programmable Phase Modulator from Hamamatsu [15

15. Hamanatsu Photonics, http://www.hamamatsu.com

]. These have been used by several authors as described in the review by Dholokia [2

2. K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Physics World 15-10 (October 2002)

] and references therein. However, the reconfiguration speed of these devices is strictly limited by the relatively slow switching times (tens of milliseconds) characteristic of nematic liquid crystals. The resulting speed v of particle movement (imposed by device response time) is therefore restricted to regimes far slower than the “ultimate” speed limit which is not reached until the Stokes drag force (FD=6πηRν) becomes comparable to the trap strength (of order 10 piconewtons). Here η is the viscosity of the medium, R is the particle radius. As a result, the opportunities in optical tweezer technology that may be created by faster switching devices have been largely unexplored.

Unlike nematic materials, ferroelectric liquid crystal molecules form low-symmetry chiral phases which support a net spontaneous polarisation that couples linearly to applied electric fields. As a result, SLM’s based on ferroelectric materials show extremely fast (<100µs) switching. This is nearly two orders of magnitude faster than conventional nematic devices. The advantages of this ultrafast response time for optical trapping applications is explored in the present paper.

Specifically, we demonstrate the operation of a holographic trap array system based on a ferroelectric liquid crystal light modulator. We focus on those applications of optical trap arrays than may benefit most directly from the large increase in switching speed afforded by ferroelectric liquid crystal technology. In particular, we demonstrate rapid reconfiguration of the trap landscape, high speed particle movement up to 35µms-1, (approaching the practical limit imposed by viscous drag) and trap multiplexing which we demonstrate as an efficient method of populating traps of complex geometries.

2. Ferroelectric liquid crystal microdisplays for laser tweezer applications

For the diffractive element in the optical tweezer system we use the CRL Opto SXGA1-R2-H1 microdisplay [16

16. CRL Opto Ltd, http://www.crlopto.com

]. This is a 1280×1024 reflective pixel array on a 13.62µm pitch switching a ferroelectric liquid crystal modulator layer. The commercial display version of this device is designed for visible light display applications with a 33° switching angle for green light. For optimal use as a reconfigurable diffractive device, pure-binary phase modulation is preferable requiring a switching angle of 90°. Such devices are currently under development at CRL Opto with diffraction efficiencies of 25% being obtained in each useful order. The results presented here however, were obtained using the commercial display (33° switching angle) with a correspondingly reduced optical throughput. For use as a binary phase modulator the device is placed between crossed polarisers with the the incident polarisation aligned to half the cone switching angle giving an absolute phase shift of π between pixels in the two switched states [17

17. K.M Johnson, M.A. Handschy, and L.A. Pagano-Stauffer “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 16, 385 (1987)

]. By Babinet’s principal, for diffractive applications the positive and negative DC balanced frames are identical. Due to the binary phase operation of ferroelectric devices, the arrangement of tweezer traps must always form a centro-symmetric pattern.

As ferroelectric device displays only binary images, for display applications, colour images are built up by colour sequential temporal multiplexing synchronised with the light sources. The device is driven from a PC through a Digital Video Interface (DVI) with 24 bit colour images at 60 Hz. For our purposes this means 24 different bit-planes are available in each 60Hz time slot giving a binary image refresh rate of 1440 Hz. To use effectively such high refresh rates the diffraction patterns must be sent to the device at comparable rates.We have used two techniques to take advantage of the ferroelectric liquid crystal speed in optical tweezer applications.

  1. Non-Multiplexed Hologram. The same binary pattern is in all 24 bit planes:
    1. The patterns are a series of pre-calculated images stored in PC memory and flashed out to the SLM through the video link. The refresh rate is PC dependent but rates of >10 images/s are generally achieved on a standard PC.
    2. For some diffractive patterns which can be described as vector structures (gratings, diffractive lenses, Dammann gratings) the patterns can be drawn as vector patterns and manipulated (rotated, shifted, scaled causing the trap position to move accordingly) using the hardware accelerated video routines of the video card. With this technique rates of >30 images/s have been obtained making real time control of trap position possible
  2. Multiplexed Holograms: Different diffractive patterns can be loaded into the different bitplanes which are then displayed in order by the microdisplay interface. This allows 24 different holograms to be displayed sequentially within one 60Hz video frame. Due to the high update speed the optical laser power is shared equally between the 24 holograms. Again, the whole pattern can be updated as for the non-multiplexed hologram mode, allowing a highly flexible dynamically programmable diffractive device.

The system control software runs under Linux/KDE on a standard PC with a Matrox G550 dual-head video card enabling the diffracting pattern data to be sent to the SLM video port and controlled from a user interface on the monitor port. The software uses OpenGL routines to access the video hardware acceleration.

3. Optical system

A schematic of the optical system is shown in Fig. 1. Collimated output from a red Kr+-ion or He-Ne laser is expanded to illuminate a circular area of the microdisplay approximately 1000 pixels (11mm) in diameter. The polarising beam splitter acts as the analyser giving pure binary phase modulation. The 250 mm and 120 mm lens pair form a 4-f imaging system that project an image, into the back aperture of the microscope objective scaled in size by 0.48 via a second polarised beam splitter oriented to transmit 100% of the tweezer illumination. The microscope objective is a Nikon×100, 1.4 NA, oil objective with a back exit pupil of 6.5 mm with bright field imaging to a video camera giving a field of view of 40×60µm. The whole system is incorporated in an inverted microscope geometry as detailed in Fig. 1.

Fig. 1. Schematic layout of optical system

With this optical layout, a binary grating on the input microdisplay of 12 pixels pitch results in first order diffraction spots at ±20.8µm using He-Ne illumination; the full field of view of the objective.

4. Non-multiplexed hologram results

All trapping experiments take place with 1µm polystyrene spheres suspended in distilled water.

In Fig. 2 we show a 4-by-4 tweezer array on a 5µm pitch. The holographic pattern was calculated using the iterative techniques proposed by Dames[10

10. M.P. Dames, R.J. Dowling, P. McKee, and D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 302685 (1991) [CrossRef] [PubMed]

] in which a 128×128 pixel pattern is replicated across the microdisplay. Initial trapping of the spheres was achieved using a Kr+ laser power of 700mW. All traps were then be maintained at a reduced power of 300mW. This gives an estimated input requirement of approximately 43 mW per trap.

Based on these static experiments, and keeping within the 4W incident power damage limit of the device, we estimate that a maximum of approximately 90 usable traps could be created with the commercial display oriented device. This figure rises to several hundred with the binary-phase-optimised device under development. This is comparable with results obtained from nematic devices.

Movable traps were implemented by writing binary gratings described as OpenGL vector objects. This permitted real-time scaling and rotation of the pattern using the built-in graphics acceleration hardware. Strong traps were formed with approximately 50 mW input power per trap from the Krypton laser. Motion was obtained by scaling or rotating the gratings to move the trap. Results are shown in Fig. 3 and in associated linked movies.

Fig. 2. (0.6 MB) Movie of 4×4 array of traps on 5µm pitch with 700 mW total input power showing capture of final trap.
Fig. 3. (1.5 MB) Movie of two movable array of traps rotating two beads in a 10.5µm circle with maximum speed of 35µms-1.

The maximum speed obtained for stable traps with the current graphics hardware was 35µms-1 while rotating two traps in a 10.5µm diameter circle by rotation the grating in 12° steps using 700 mW of laser power which corresponds to approximately 32 scaled frame per with approximately 1.1µm between successive traps. Higher speeds, implemented by increasing the angle step and thus separation between successive traps, resulted in loss of beads. It is unclear from initial experiments if this loss results from the Stokes drag limit or excessive separation between the successive traps.

The video hardware is operating at half the operation speed of the the microdisplay which operates at 60 Hz, so giving the system a potential trap movement speed in excess of 66µms-1 with the current step size. Using a nematic device the maximum demonstrated trap movement speed is 2.5µms-1 [4

4. R.L. Eriksen, V.R. Daria, P.J. Rodrigo, and J. Gluckstad, “Computer controlled orientation of multiple optically-trapped particles,” Microelectronic Engineering 67–68, 872, (2003) [CrossRef]

] and the maximum proposed is 10µms-1 [18

18. J.E. Curtis, B.A. Kes, and D.G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002). [CrossRef]

].

5. Multiplexed holographic trap geometries

The most powerful feature of holographic optical traps based on ferroelectric devices is the possibility of multiplexing trap landscapes to enhance flexibility and functionality of the arrays. Here the fast-switching property of the ferroelectric device is deployed not only to move particles rapidly but to time-share between geometries. Here we illustrate the operation by partitioning the output of the 24 bitplane device to create a multiplexed configuration comprising independent static and dynamic arrays.

Specifically, a linear 5×1 static array of traps was formed by using 16 of the 24 bitplanes (denoted as the “red” and “green” channels) and two movable traps by the remaining 8 bitplanes (“blue” channel). This results in the composite hologram illustrated in Fig. 4 which shows a Specifically, a linear 5×1 static array of traps was formed by using 16 of the 24 bitplanes (denoted as the “red” and “green” channels) and two movable traps by the remaining 8 bitplanes (“blue” channel). This results in the composite hologram illustrated in Fig. 4 which shows a “yellow” vertical grating to generate the 5×1 array, overlaid with the “blue” grating at 45° which generates the two movable traps. The optical trapping results are shown in Fig. 5 and its associated linked movie.

Fig. 4. Composite hologram for 5×1 static hologram in “red” and “green” channels and two trap hologram in “blue” channel.

Fig. 5. (2.46 MB) Movie showing five fixed and two movable traps formed by two-to-one multiplex.

Due to the complex structure of the multiplexed hologram the full 24 bit images is currently calculated by using the control computer without the advantage of OpenGL acceleration. The required holograms were generated in real-time from a pre-calculated 5×1 fan-out hologram formed by the Dames [10

10. M.P. Dames, R.J. Dowling, P. McKee, and D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 302685 (1991) [CrossRef] [PubMed]

] technique overlaid by a dynamically calculated grating with pitch and orientation controlled from an X-windows control panel. This resulted in an update rate of 3 images per second with the current 1.4 GHz PC.We believe that with faster computer / graphics hardware and optimised coding image rates of 10 images per second will be obtainable. This will be faster if the bit-level image is formed using OpenGL acceleration. The ultimate limit is 60 images per second determined by the microdisplay frame display rate.

6. Conclusions

In conclusion we have demonstrated the potential advantages of a ferroelectric liquid crystal light modulator relative to a conventional nematic device for optical trap array applications. In addition to the direct increase in trap reconfiguration speed, we also demonstrate the first multiplexed holographic trap geometries consisting of combinations of static and dynamic arrays.

Acknowledgements

We are grateful to the Royal Society for support through the Paul Instrument Fund, the COS-MIC Research Centre at The University of Edinburgh and Nikon UK.We also acknowledge the Graphics and MultimediaWorkshop, The University of Edinburgh for assistance in preparation of video clips.

References and links

1.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single beam gradient force optical tap for dielectric particles,” Opt. Lett. 11, 288 (1986). [CrossRef] [PubMed]

2.

K. Dholakia, G. Spalding, and M. MacDonald, “Optical tweezers: the next generation,” Physics World 15-10 (October 2002)

3.

P.T. Korda, G.C. Spalding, and D.G. Greir, “Evolution of a colloidal critical state in an optical pinning potential landscape”, Phys. Rev. B 66, 024504 (2002) [CrossRef]

4.

R.L. Eriksen, V.R. Daria, P.J. Rodrigo, and J. Gluckstad, “Computer controlled orientation of multiple optically-trapped particles,” Microelectronic Engineering 67–68, 872, (2003) [CrossRef]

5.

S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature (London) 338, 514 (1989). [CrossRef] [PubMed]

6.

M. D Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997) [CrossRef]

7.

W.M. Lee, X.C. Yuan, and D. Y. Tang, “Optical tweezers with multiple optical forces using double-hologram interference,” Opt. Express 11, 199 (2003). [CrossRef] [PubMed]

8.

P.J. Rodrigo, R. L. Eriksen, V.R. Daria, and J. Glueckstad, “Shack-Hartmann multiple-beam optical tweezers,” Opt. Express 11, 208 (2003). [CrossRef] [PubMed]

9.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3312 (1971) [CrossRef]

10.

M.P. Dames, R.J. Dowling, P. McKee, and D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 302685 (1991) [CrossRef] [PubMed]

11.

N.R Heckenburg, R. McDuff, C.P. Smith, H. Rubinsztein-Dunlop, and M.J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951 (1992) [CrossRef]

12.

C. D’Helon, E.W. Dearden, H. Rubinsztein-Dunlop, and N.R. Heckenburg, “Measurement of the Optical Force and Trapping Range of a Single-beam Gradient Optical Trap for Micron-sized Latex Spheres,” J. Mod. Opt. 41, 595 (1994). [CrossRef]

13.

E.R. Dufresne and D.G. Grier, “Optical tweezer arrays and optical substrates created with diffractive optics,” Rev. Sci. Inst. 69, 1974 (1998). [CrossRef]

14.

E.R. Dufresne, G.C. Spalding, M.T. Dearing, S.A. Sheets, and D.G. Grier “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Inst. 72, 1810, (2002) [CrossRef]

15.

Hamanatsu Photonics, http://www.hamamatsu.com

16.

CRL Opto Ltd, http://www.crlopto.com

17.

K.M Johnson, M.A. Handschy, and L.A. Pagano-Stauffer “Optical computing and image processing with ferroelectric liquid crystals,” Opt. Eng. 16, 385 (1987)

18.

J.E. Curtis, B.A. Kes, and D.G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169 (2002). [CrossRef]

OCIS Codes
(090.0090) Holography : Holography
(090.1970) Holography : Diffractive optics
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.7010) Lasers and laser optics : Laser trapping
(180.0180) Microscopy : Microscopy
(230.0230) Optical devices : Optical devices
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Research Papers

History
Original Manuscript: July 17, 2003
Revised Manuscript: August 15, 2003
Published: August 25, 2003

Citation
William Hossack, Eirini Theofanidou, Jason Crain, Kevin Heggarty, and Martin Birch, "High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay," Opt. Express 11, 2053-2059 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-17-2053


Sort:  Journal  |  Reset  

References

  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm and S. Chu, �??Observation of a single beam gradient force optical tap for dielectric particles,�?? Opt. Lett. 11, 288, (1986) [CrossRef] [PubMed]
  2. K. Dholakia, G. Spalding and M. MacDonald, �??Optical tweezers: the next generation,�?? Physics World 15-10 (October 2002)
  3. P.T. Korda, G.C. Spalding and D.G. Greir, �??Evolution of a colloidal critical state in an optical pinning potential landscape�??, Phys. Rev. B 66, 024504 (2002) [CrossRef]
  4. R.L. Eriksen, V.R. Daria, P.J. Rodrigo, J. Gluckstad, �??Computer controlled orientation of multiple optically trapped particles,�?? Microelectronic Engineering 67-68, 872, (2003) [CrossRef]
  5. S. M. Block, H. C. Blair and H. C. Berg, �??Compliance of bacterial flagella measured with optical tweezers,�?? Nature (London) 338, 514, (1989) [CrossRef] [PubMed]
  6. M. D.Wang, H. Yin, R. Landick, J. Gelles and S. M. Block, �??Stretching DNA with optical tweezers,�?? Biophysics J.72, 1335 (1997) [CrossRef]
  7. W.M. Lee, X.C. Yuan and D. Y. Tang, �??Optical tweezers with multiple optical forces using double-hologram interference,�?? Opt. Express 11, 199, (2003) [CrossRef] [PubMed]
  8. P.J. Rodrigo, R. L. Eriksen, V.R. Daria and J. Glueckstad, �??Shack-Hartmann multiple-beam optical tweezers,�?? Opt. Express 11, 208, (2003) [CrossRef] [PubMed]
  9. H. Dammann and K. Gortler, �??High-efficiency in-line multiple imaging by means of multiple phase holograms,�?? Opt. Commun. 3 312 (1971) [CrossRef]
  10. M.P. Dames, R.J. Dowling, P. McKee and D. Wood, �??Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,�?? Appl. Opt. 30 2685 (1991) [CrossRef] [PubMed]
  11. N.R Heckenburg, R. McDuff, C.P. Smith, H. Rubinsztein-Dunlop, and M.J. Wegener, �??Laser beams with phase singularities,�?? Opt. Quantum Electron. 24, S951 (1992) [CrossRef]
  12. C. D�??Helon, E.W. Dearden, H. Rubinsztein-Dunlop and N.R. Heckenburg, �??Measurement of the Optical Force and Trapping Range of a Single-beam Gradient Optical Trap for Micron-sized Latex Spheres,�?? J. Mod. Opt. 41, 595, (1994) [CrossRef]
  13. E.R. Dufresne and D.G. Grier, �??Optical tweezer arrays and optical substrates created with diffractive optics,�?? Rev. Sci. Inst. 69, 1974, (1998) [CrossRef]
  14. E.R. Dufresne, G.C. Spalding, M.T. Dearing, S.A. Sheets and D.G. Grier �??Computer-generated holographic optical tweezer arrays,�?? Rev. Sci. Inst. 72, 1810, (2002) [CrossRef]
  15. Hamanatsu Photonics, <a href="http://www.hamamatsu.com"</a>http://www.hamamatsu.com
  16. CRL Opto Ltd, <a href="http://www.crlopto.com">http://www.crlopto.com</a>
  17. K.M Johnson, M.A. Handschy and L.A. Pagano-Stauffer �??Optical computing and image processing with ferroelectric liquid crystals,�?? Opt. Eng. 16, 385 (1987)
  18. J.E. Curtis, B.A. Kes and D.G. Grier, �??Dynamic holographic optical tweezers,�?? Opt. Commun. 207, 169, (2002) [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: MOV (603 KB)     
» Media 2: MOV (1547 KB)     
» Media 3: MOV (2516 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited