## Beam shaping and high-speed, cylinder-lens-free beam guiding using acousto-optical deflectors without additional compensation optics |

Optics Express, Vol. 21, Issue 12, pp. 14627-14635 (2013)

http://dx.doi.org/10.1364/OE.21.014627

Acrobat PDF (2764 KB)

### Abstract

Using acousto-optical deflectors at high deflection speeds via acoustical frequency chirping induces astigmatism, deforming the laser beam in an unfavorable way. Within the paper, we present a method to prevent this effect for an ultrashort pulsed laser beam via acoustical frequency jumps synchronized to the pulse-to-pulse pause. We also demonstrate and give a method to calculate beam shaping capability of acousto-optical deflectors via arbitrary spatial frequency developments during ultrashort laser pulse transit through the deflector. Cylinder-lens-free deflection at >2000 rad/s and beam shaping capability is demonstrated experimentally. In our experiments the switching time between two beam shapes is 1 µs.

© 2013 OSA

## 1. Introduction

4. G. Duemani Reddy, K. Kelleher, R. Fink, and P. Saggau, “Three-dimensional random access multiphoton microscopy for functional imaging of neuronal activity,” Nat. Neurosci. **11**(6), 713–720 (2008). [CrossRef] [PubMed]

5. S. Bruening, G. Hennig, S. Eifel, and A. Gillner, “Ultrafast scan techniques for 3D-μm structuring of metal surfaces with high repetitive ps-laser pulses,” Phys. Procedia **12**, 105–115 (2011). [CrossRef]

6. I. Chang, “I. Acoustooptic devices and applications,” IEEE Trans. Sonics Ultrason. **23**(1), 2–21 (1976). [CrossRef]

2. V. Iyer, T. M. Hoogland, and P. Saggau, “Fast functional imaging of single neurons using random-access multiphoton (RAMP) microscopy,” J. Neurophysiol. **95**(1), 535–545 (2005). [CrossRef] [PubMed]

4. G. Duemani Reddy, K. Kelleher, R. Fink, and P. Saggau, “Three-dimensional random access multiphoton microscopy for functional imaging of neuronal activity,” Nat. Neurosci. **11**(6), 713–720 (2008). [CrossRef] [PubMed]

7. A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast focus scanning,” Opt. Lett. **26**(14), 1078–1080 (2001). [CrossRef] [PubMed]

8. N. Friedman, A. Kaplan, and N. Davidson, “Acousto-optic scanning system with very fast nonlinear scans,” Opt. Lett. **25**(24), 1762–1764 (2000). [CrossRef] [PubMed]

^{2}down to η

^{3}or η

^{4}with approximately η = 75% … 90%. In microscopy, such decrease of diffraction efficiency is easily compensated by increasing laser power. In microstructuring applications, ablation speed is limited by the available maximum laser power. A decrease of diffraction efficiency would therefore directly impact the ablation efficiency and thus prolong processing time.

9. K. Du, “Thin layer ablation with lasers of different beam profiles: energy efficiency and over filling factor,” Proc. SPIE **7202**, 72020Q (2009). [CrossRef]

14. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “Dynamic pulsed-beam shaping using a TAG lens in the near UV,” Appl. Phys., A Mater. Sci. Process. **93**(1), 231–234 (2008). [CrossRef]

## 2. Method and experimental setup for cylinder-lens-free acousto-optical beam deflection

_{y}/dt of the temporal acoustic frequency according to Eq. (1) [6

6. I. Chang, “I. Acoustooptic devices and applications,” IEEE Trans. Sonics Ultrason. **23**(1), 2–21 (1976). [CrossRef]

_{y}/dt = const. = Δf

_{y}/Δt, the AOD will act as a cylinder lens with refraction power D following Eq. (2) [6

6. I. Chang, “I. Acoustooptic devices and applications,” IEEE Trans. Sonics Ultrason. **23**(1), 2–21 (1976). [CrossRef]

_{AOD}(n is the index of refraction of the acousto-optical crystal material and c

_{0}the vacuum speed of light). For typical crystal thicknesses and crystal materials, t

_{T}lies in a range of approximately 20 ps to 200 ps. Thus, it is comparable to or longer than ultrashort laser pulse durations τ. The acoustic wave does propagate approximately d = 20 nm to 600 nm during t

_{T}. The typical acoustical grating spacing of > 5 µm is much wider than d. Accordingly, the acoustical grating remains practically static when an ultrashort laser pulse transmits an AOD. If dθ/dy = 0 is satisfied during t

_{T}, the laser pulse will be deflected, but no cylinder-lens effect occurs.

_{AOD}is the size of the AOD aperture in acoustic wave propagation direction (if raw beam diameter 2w

_{0}is smaller than l

_{AOD}, it is save to approximate l

_{AOD}by 2w

_{0}). If the prerequisites are met (practically static acoustical grating for a single pulse passing through the AOD and pulse-to-pulse pause longer than the acousto-optic fill time), beam deflection as shown in Fig. 1 is feasible.

_{y0}to f

_{y0}+ f

_{y}. As c

_{0}/n is much faster than V, the laser pulse is deflected depending on the acoustic frequency before the frequency jump (f

_{y0}) during time frame (2). Time frame (3) shows the end of the acoustic fill time t

_{F}, shortly before a second laser pulse triggers the second frequency jump at time frame (4) and is deflected depending on the acoustic frequency f

_{y0}+ f

_{y}(5). Time frame (6) is equivalent to (3). It is important to note, that one detected laser pulse triggers the frequency jump for deflection of the next laser pulse. A similar approach is already used in communication technology [15

15. Y. Naciri, A. Perennou, V. Quintard, and J. Le Bihan, “Acousto-optic deflector-based optical packet synchronization,” Microw. Opt. Technol. Lett. **26**(6), 394–396 (2000). [CrossRef]

_{x}and AOD

_{y}can be delayed in time independently from each other.

## 3. Experimental results of cylinder-lens-free acousto-optical beam deflection

^{13}1/s

^{2}. According to Eq. (1), a cylinder lensing effect with focal distance of 3.0 m would result, which is roughly twice the distance between the beam profile camera and the AODs. The beam profiles shown in Fig. 3(b) would then be strongly elliptic with circularities of approximately 50%.

## 4. Method and basic demonstration of beam shaping via acousto-optical deflection

_{x}and AOD

_{y}. For shapes (f) through (j), the applied frequencies differ between AOD

_{x}and AOD

_{y}.Note, that especially for shapes (d) and (h), the shown profiles represent single laser pulses, which are split up to different directions. Note also, that we obtained the shown profiles from a collimated beam, so that focussing will map these profiles into the corresponding Fraunhofer diffraction patterns.

_{F}= 2w

_{0}/V = 450 ns. Shorter switching times may be reached by reducing the raw beam diameter 2w

_{0}. To our knowledge, such short time spans for switching from one beam shape to another were not demonstrated with other technologies before (the TAG lens achieves 2.6 µs to 7 µs periodicity for resonant beam shaping [16,17

17. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. **33**(18), 2146–2148 (2008). [CrossRef] [PubMed]

## 5. Discussion of beam shaping via acousto-optical deflection

_{x}and AOD

_{y}. Change of divergence (i.e. focus shifting), astigmatism, beam splitting and self-interference are feasible. When not limiting the frequency change to a step function, but using arbitrary functions instead, Eq. (5) can be rewritten as Taylor-series, for instance, and then Eq. (6) can be established.Equation (6) is similar to the Cartesian notation of Zernike polynomials. Quantifying the differences between Zernike polynomials and Eq. (6) allows for estimating the ability to generate or compensate aberrations. In Table 2, a selection of Zernike polynomials (Noll’s indices) in Cartesian notation and the resulting error when using Eq. (6) to approximate the Zernike polynomials are given (the latter being all terms with x

^{n}y

^{m}and n,m ≥ 1; values for x

^{0}y

^{0}(piston) are ignored). Additionally, to roughly estimate the capability to create or compensate aberrations, the most right column displays the fraction

^{2}+ y

^{2})

^{1/2}. The result quantifies the maximum relative OPD error when applying a Zernike polynomial via AOD beam shaping.

^{2}beam diameter of a Gaussian laser beam, the range r = 0 … 1 covers 86.5% = 1 – exp(−2) of the total beam power. For the same aperture size, but a 1/e beam diameter instead, the range r = 0 … 2

^{-1/2}covers 63.2% = 1 – exp(−1). The difference between the two equals only 23.3%. In order to deflect a significant fraction of the beam power such that a desired aberration is met, it is thus more important to reach low values of the maximum relative OPD error for the smaller range than for the larger range when shaping a Gaussian laser beam.

_{2}, Z

_{3}, Z

_{4}, Z

_{6}and Z

_{12}) are represented fully via Eq. (6) including Defocus, the latter making the AOD beam shaper perfect for focus shifting. Some Zernike polynomials are not representable by Eq. (6) including Z

_{5}and Z

_{13}. For Zernike polynomials Z

_{7}, Z

_{8}and especially Z

_{11}(spherical aberration) some of the aberration can be represented and max. relative OPD error for the range r = 0…2

^{-1/2}is below 1. For Zernike polynomials Z

_{9}, Z

_{10}and Z

_{14}some of the aberration can also be represented, but the max. relative OPD error exceeds 1, which means that a large part of the laser beam wavefront will depart from the aimed aberration.

_{11}(spherical aberration), which is a most important aberration in microscopy and laser materials processing, the resulting error ΔZ

_{11AOD}equals -√2 ΔZ

_{14AOD}. Therefore, when using an AOD beam shaper (Eq. (6)), spherical aberration may be compensated better by accepting a resulting wavefront error Z

_{14}. In this case Z

_{11}is fully transformed to -√2 Z

_{14}, and the max. relative OPD error

## 6. Summary and outlook

## Acknowledgments

## References and links

1. | P. A. Kirkby, K. M. N. Srinivas Nadella, and R. A. Silver, “A compact acousto-optic lens for 2D and 3D femtosecond based 2-photon microscopy ,” Opt. Express |

2. | V. Iyer, T. M. Hoogland, and P. Saggau, “Fast functional imaging of single neurons using random-access multiphoton (RAMP) microscopy,” J. Neurophysiol. |

3. | D. Vučinić, T. J. Sejnowski, and B. Lu, “A compact multiphoton 3D imaging system for recording fast neuronal activity ,” PLoS ONE |

4. | G. Duemani Reddy, K. Kelleher, R. Fink, and P. Saggau, “Three-dimensional random access multiphoton microscopy for functional imaging of neuronal activity,” Nat. Neurosci. |

5. | S. Bruening, G. Hennig, S. Eifel, and A. Gillner, “Ultrafast scan techniques for 3D-μm structuring of metal surfaces with high repetitive ps-laser pulses,” Phys. Procedia |

6. | I. Chang, “I. Acoustooptic devices and applications,” IEEE Trans. Sonics Ultrason. |

7. | A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast focus scanning,” Opt. Lett. |

8. | N. Friedman, A. Kaplan, and N. Davidson, “Acousto-optic scanning system with very fast nonlinear scans,” Opt. Lett. |

9. | K. Du, “Thin layer ablation with lasers of different beam profiles: energy efficiency and over filling factor,” Proc. SPIE |

10. | A. Laskin and V. Laskin, “πShaper – Refractive beam shaping optics for advanced laser technologies,” J. Phys.: Conf. Ser. |

11. | K. Nemoto, T. Fujii, N. Goto, T. Nayuki, and Y. K. Kanai, “Transformation of a laser beam intensity profile by a deformable mirror,” Opt. Lett. |

12. | N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett. |

13. | F. M. Dickey and S. C. Holswade, |

14. | A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “Dynamic pulsed-beam shaping using a TAG lens in the near UV,” Appl. Phys., A Mater. Sci. Process. |

15. | Y. Naciri, A. Perennou, V. Quintard, and J. Le Bihan, “Acousto-optic deflector-based optical packet synchronization,” Microw. Opt. Technol. Lett. |

16. | M. Duocastella and C. B. Arnold, “Enhanced depth of field laser processing using an ultra-high-speed axial scanner ,” Appl. Phys. Lett. |

17. | A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. |

**OCIS Codes**

(120.5800) Instrumentation, measurement, and metrology : Scanners

(140.3390) Lasers and laser optics : Laser materials processing

(220.1000) Optical design and fabrication : Aberration compensation

(230.1040) Optical devices : Acousto-optical devices

(320.0320) Ultrafast optics : Ultrafast optics

(320.7080) Ultrafast optics : Ultrafast devices

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: April 30, 2013

Revised Manuscript: June 5, 2013

Manuscript Accepted: June 7, 2013

Published: June 12, 2013

**Citation**

Peter Bechtold, Ralph Hohenstein, and Michael Schmidt, "Beam shaping and high-speed, cylinder-lens-free beam guiding using acousto-optical deflectors without additional compensation optics," Opt. Express **21**, 14627-14635 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14627

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### References

- P. A. Kirkby, K. M. N. Srinivas Nadella, and R. A. Silver, “A compact acousto-optic lens for 2D and 3D femtosecond based 2-photon microscopy,” Opt. Express 18, 13720 (2010).
- V. Iyer, T. M. Hoogland, and P. Saggau, “Fast functional imaging of single neurons using random-access multiphoton (RAMP) microscopy,” J. Neurophysiol.95(1), 535–545 (2005). [CrossRef] [PubMed]
- D. Vučinić, T. J. Sejnowski, and B. Lu, “A compact multiphoton 3D imaging system for recording fast neuronal activity,” PLoS ONE 2, e699 (2007).
- G. Duemani Reddy, K. Kelleher, R. Fink, and P. Saggau, “Three-dimensional random access multiphoton microscopy for functional imaging of neuronal activity,” Nat. Neurosci.11(6), 713–720 (2008). [CrossRef] [PubMed]
- S. Bruening, G. Hennig, S. Eifel, and A. Gillner, “Ultrafast scan techniques for 3D-μm structuring of metal surfaces with high repetitive ps-laser pulses,” Phys. Procedia12, 105–115 (2011). [CrossRef]
- I. Chang, “I. Acoustooptic devices and applications,” IEEE Trans. Sonics Ultrason.23(1), 2–21 (1976). [CrossRef]
- A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast focus scanning,” Opt. Lett.26(14), 1078–1080 (2001). [CrossRef] [PubMed]
- N. Friedman, A. Kaplan, and N. Davidson, “Acousto-optic scanning system with very fast nonlinear scans,” Opt. Lett.25(24), 1762–1764 (2000). [CrossRef] [PubMed]
- K. Du, “Thin layer ablation with lasers of different beam profiles: energy efficiency and over filling factor,” Proc. SPIE7202, 72020Q (2009). [CrossRef]
- A. Laskin and V. Laskin, “πShaper – Refractive beam shaping optics for advanced laser technologies,” J. Phys.: Conf. Ser. 276, 12171 (2011).
- K. Nemoto, T. Fujii, N. Goto, T. Nayuki, and Y. K. Kanai, “Transformation of a laser beam intensity profile by a deformable mirror,” Opt. Lett.21(3), 168–170 (1996). [CrossRef] [PubMed]
- N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett.30(12), 1479–1481 (2005). [CrossRef] [PubMed]
- F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).
- A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “Dynamic pulsed-beam shaping using a TAG lens in the near UV,” Appl. Phys., A Mater. Sci. Process.93(1), 231–234 (2008). [CrossRef]
- Y. Naciri, A. Perennou, V. Quintard, and J. Le Bihan, “Acousto-optic deflector-based optical packet synchronization,” Microw. Opt. Technol. Lett.26(6), 394–396 (2000). [CrossRef]
- M. Duocastella and C. B. Arnold, “Enhanced depth of field laser processing using an ultra-high-speed axial scanner,” Appl. Phys. Lett. 102, 61113 (2013).
- A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett.33(18), 2146–2148 (2008). [CrossRef] [PubMed]

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