## Two-dimensional optical beam deflector operated by wavelength tuning

Optics Express, Vol. 14, Issue 9, pp. 4092-4100 (2006)

http://dx.doi.org/10.1364/OE.14.004092

Acrobat PDF (159 KB)

### Abstract

A new method based on an optical delay line structure is proposed for two-dimensional raster optical beam steering. For one-dimensional beam steering, the laser beam to be deflected is split into *N* co-directional sub-beams of equal intensity with the aid of a plane-parallel plate. These sub-beams experience a relative time delay, which translates into a phase difference, thus forming a phased array. When the laser wavelength is tuned, the relative phase varies and the far-field interference footprint can be steered across a receive plane. By employing two plane-parallel plates in series, the described scheme can be extended to produce a two-dimensional *N* × *N* array of sub-beams, allowing two-dimensional beam steering via wavelength tuning. In this case, wavelength tuning over a larger range leads to a linear deflection which repeats itself in a raster-like fashion. One direction of deflection repeats itself multiple times as wavelength is scanned over larger range, that is, a raster effect. In this paper, the principle is theoretically derived and formulated, and the preliminary experimental results with four sub-beams are presented.

© 2006 Optical Society of America

## 1. Introduction

5. H. S. Hinton, “Photonic switching fabrics,” IEEE Communications Magazine **28**, April 1990, 71–89. [CrossRef]

8. J.-P. Herriau, A. Delboulbe, J.-P. Huignard, G. Roosen, and G. Pauliat, ”Optical-beam steering for fiber array using dynamic holography,” J. Lightwave Technol. **4**, 905–907 (1986). [CrossRef]

11. K. Inagaki and Y. Karasawa, “Three-element fiber-type optical phased array antenna with high-speed two-dimensional optical beam steering,” Electron. Commun. Jpn. **82**, 42–51 (1999). [CrossRef]

*N*co-directional sub-beams of equal intensity with the aid of a plane-parallel plate. These sub-beams experience a relative time delay, which translates into a phase difference, thus forming a phased array. When the laser wavelength is tuned, the relative phases vary and, as a consequence, the far-field interference footprint is steered across the receive plane. Beam steering can be very fast, limited only by the rate of laser wavelength tuning. According to recent results, optical frequency modulation techniques [12

12. T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada, and M. Izutsu, “LiNbO_{3} highspeed optical FSK modulator,” Electron. Lett. **40**, 691–692 (2004). [CrossRef]

13. T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada, and M. Izutsu, “High-speed optical FSK modulator for optical packet labeling,” J. Lightwave Technol. **23**, 87–94 (2005). [CrossRef]

*N*×

*N*array of sub-beams, allowing two-dimensional beam steering via wavelength tuning. Section 3 describes the experimental setups for the two-dimensional beam scanning and presents the measurement results.

## 2. Principle of the beam deflection

### 2.1. Equal intensity multibeam generation

*R*

_{1}so that an output beam becomes available at point A. The light reflected by the beam splitter is then reflected by the mirror surface, and a second output beam is transmitted parallel to the first one at point

*C*. In a similar manner, the

*i*-th beam is reflected by a beam splitter with reflectance

*R*

_{i}. The reflectance

*R*

_{i}on the beam splitter surface at the

*i*-th beam is chosen as [14]

*N*is the total number of beams on one axis. For example, when the number of sub-beams equals

*N*=4, the reflectance on the first output window is

*R*

_{1}=3/4. The reflectances on the successive windows are

*R*

_{2}=2/3,

*R*

_{3}=1/2, and

*R*

_{4}=0.

### 2.2. Optical phase difference

*AB*¯ and

*ADC*¯, we obtain

*n*

_{1}sin

*θ*

_{1}=

*n*

_{2}sin

*θ*

_{2}. With

*θ*

_{1}and

*θ*

_{2}, we denote the incident and refractive angles of the beam, where

*n*

_{1}and

*n*

_{2}are the refractive indices of the media. The optical phases Φ

_{B}and Φ

_{C}at points

*B*and

*C*relative to that at point

*A*are given by

*k*

_{0}is the wave number (=2

*π*/

*λ*

_{0}),

*λ*

_{0}the vacuum wavelength, and

*d*the thickness of the MBG. When the wavelength is changed to

*λ*

_{1}, the phase at points

*B*and

*C*change by

*n*

_{1}and

*n*

_{2}. The OPD due to wavelength tuning between points

*B*and

*C*is

*n*

_{1}=1.

*R*=0.96 (compare Fig. 1) corresponding to an aluminum mirror at

*λ*= 1.5 μm, the transmission efficiency is calculated to be -0.26 dB. With higher reflectance, a higher efficiency can be realized: A reflectance of R=0.99 would reduce the transmission loss to -0.07 dB.

### 2.3. Beam deflection

*a*is the aperture spacing of the beams on the beam splitter surface and

*k*

_{1}= 2

*π*/

*λ*

_{1}is the wave number after wavelength tuning. The aperture spacing between two consecutive beams is given by

*a*= 2

*d*tan

*θ*

_{2}. Substituting

*θ*

_{2}= tan

^{-1}(

*a*/2

*d*) into Eq. (9) and using the relation

*n*

_{1}sin

*θ*

_{1}=

*n*

_{2}sin

*θ*

_{2}, the deflection angle follows as

*θ*

_{def}≪

*π*/2. Defining a sensitivity coefficient

### 2.4. Two-dimensional beam scanning

*N*output beams of identical intensity; the second one was arranged orthogonally and again produces

*N*times output beams. Thus, the output was a

*N*×

*N*beam array. Each MBG has a different optical delay in order to produce different deflection sensitivities in vertical and horizontal direction. The deflection angles for the

*x*and

*y*directions are given by

*λ*

_{0}and

*λ*

_{1}are the wavelengths before and after wavelength tuning, respectively. One can show that the deflection sensitivity coefficients for the

*x*and

*y*directions are given by

*γ*=(2

*d*/

*a*) and the scaling factor

*m*relates the thicknesses

*d*' and

*d*of the two MBG devices in the form

*d*’ =

*md*. When the deflection sensitivity for the

*y*axis becomes

*N*times larger than that for the

*x*axis,

*N*is the number of multiple beams for the

*x*and

*y*directions. Substituting Eqs. (15) and (16) into Eq. (17), we obtain the solution for the scaling factor

*m*as

*n*

_{2}=1, the scaling factor

*m*equals

*N*, that is

*d*’ =

*Nd*.

*y*axis achieved with the first MBG of 2-mm thickness shows a higher deflection sensitivity as a function of wavelength than that along the

*x*axis achieved with the second MBG of 1-mm thickness. One direction of beam deflection repeats itself multiple times as the wavelength is scanned over a larger range, resulting in a raster effect.

### 2.5. Maximum deflection angle

*D*is given by ~

*λ*/

*D*. For a high filling factor, the beam divergence of an

*N*-array beam becomes ~

*λ*/((

*N*-1)

*a*cos

*θ*

_{1}), where

*a*is the aperture spacing of the beams. The side lobe is separated by

*λ*/(

*a*cos

*θ*

_{1}) from the main lobe. Therefore, the maximum deflectable angle becomes

*θ*

_{max}= ±

*λ*/(2

*a*cos

*θ*

_{1}), which is the range within the main lobe can be steered. For example, the maximum deflection angles are calculated to be

*θ*

_{max,x}= ±1.1 mrad and

*θ*

_{max,y}= ±0.91 mrad when one uses the parameters given in Table 1. The resolution of beam scanning along one axis can be equal to the diffracted beam width of

*λ*/(

*Na*cos

*θ*

_{1}) when the condition in Eq. (18) is maintained, which is the same divergence angle of the beam. A more precise resolution of raster beam scanning can be realized if the thickness of the MBG for the

*y*-axis deflection is larger than

*Nd*.

## 3. Experimental setup and results

### 3.1 Two-dimensional beam scanning

*d*= 2 mm and 1 mm, respectively, and with reflective coatings according to Eq. (1). They were incorporated into the experimental setup shown in Fig. 4 for two-dimensional beam scanning. The first MBG generated two output beams of identical intensity; the second one was arranged orthogonally and again doubled the number of beams. Thus, the output was a 2 × 2 beam array. With the configuration shown in Fig. 4 the optical beam pattern was measured using a wavelength of 1550 nm (see Fig. 5). The beams differ in intensity because the incident angle was set to 45 deg in spite of the design value of 40.8 deg to arrive at an easier layout for the optical elements. For the following beam deflection measurement, only 2 × 2 laser beams were used; otherwise, the low resolution of the beam profiler available (i.e. 1 mrad) would not have been sufficient. (With a smaller total aperture, the deflection angle will be larger.)

*x*and

*y*axes as a function of wavelength, demonstrating that the peak intensity is steered. The two-dimensional deflection characteristics as a function of the optical wavelength are shown in Fig. 8. The direction of the peak intensity is plotted as a function of the wavelength. Because of the low resolution of the measurement setup of 1 mrad, the discrete 3-level result was to be expected. The deflection characteristic along the

*y*axis (MBG with 2-mm thickness) shows higher deflection sensitivity against the wavelength than that along the

*x*axis (MBG with the 1-mm thickness). As the sensitivity coefficients are different for orthogonal directions, a two-dimensional raster scan is achieved.

### 4. Conclusion

12. T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada, and M. Izutsu, “LiNbO_{3} highspeed optical FSK modulator,” Electron. Lett. **40**, 691–692 (2004). [CrossRef]

13. T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada, and M. Izutsu, “High-speed optical FSK modulator for optical packet labeling,” J. Lightwave Technol. **23**, 87–94 (2005). [CrossRef]

## References

1. | P. F. Mcmanamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proceeding of IEEE |

2. | K. H. Kudielka, A. Kalmar, and W. R. Leeb, “Design and breadboarding of a phased telescope array for free-space laser communications,” |

3. | D. Bushuev, D. Kedar, and S. Arnon, “Analyzing the performance of a nanosatellite cluster-detector array receiver for laser communication,” J. Lightwave Technol. |

4. | A. Polishuk and S. Arnon, “Communication performance analysis of microsatellites using an optical phased array antenna,” Opt. Eng. |

5. | H. S. Hinton, “Photonic switching fabrics,” IEEE Communications Magazine |

6. | M. Yamaguchi, T. Yamamoto, K. Hirabayashi, S. Matsuo, and K. Koyabu, “High-density digital free-space photonic-switching fabrics using exciton absorption reflection-switch (EARS) arrays and microbeam optical interconnections,” IEEE J. Sel. Top. Quantum Electron. |

7. | T. Yamamoto, M. Yamaguchi, K. Hirabayashi, S. Matsuo, C. Amano, H. Iwamura, Y. Kohama, T. Kurokawa, and K. Koyabu, “High-density digital free-space photonic switches using micro-beam optical interconnections,” IEEE Photon. Technol. Lett. |

8. | J.-P. Herriau, A. Delboulbe, J.-P. Huignard, G. Roosen, and G. Pauliat, ”Optical-beam steering for fiber array using dynamic holography,” J. Lightwave Technol. |

9. | B. Winker, M. Mahajan, and M. Hunwardsen, “Liquid crystal beam directors for airborne free-space optical communications,” IEEE Aerospace Conference Proceedings |

10. | Y. Murakami, K. Inagaki, and Y. Karasawa, “Beam forming characteristics of a waveguide-type optical phased array antenna,” IEICE Trans. Commun. |

11. | K. Inagaki and Y. Karasawa, “Three-element fiber-type optical phased array antenna with high-speed two-dimensional optical beam steering,” Electron. Commun. Jpn. |

12. | T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada, and M. Izutsu, “LiNbO |

13. | T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada, and M. Izutsu, “High-speed optical FSK modulator for optical packet labeling,” J. Lightwave Technol. |

14. | M. Toyoshima and K. Araki, Japan Patent Application for a “Beam splitting method,” No. 3069703, filed 24 Nov. 1999. |

**OCIS Codes**

(010.3310) Atmospheric and oceanic optics : Laser beam transmission

(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

(060.4510) Fiber optics and optical communications : Optical communications

(110.5100) Imaging systems : Phased-array imaging systems

**ToC Category:**

Optical Devices

**History**

Original Manuscript: February 27, 2006

Revised Manuscript: April 14, 2006

Manuscript Accepted: April 21, 2006

Published: May 1, 2006

**Citation**

Morio Toyoshima, Franz Fidler, Martin Pfennigbauer, and Walter R. Leeb, "Two-dimensional optical beam deflector operated by wavelength tuning," Opt. Express **14**, 4092-4100 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-4092

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### References

- P. F. Mcmanamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp and E. A. Watson, "Optical phased array technology," Proceeding of IEEE 84, 1996, 268-298.
- K. H. Kudielka, A. Kalmar and W. R. Leeb, "Design and breadboarding of a phased telescope array for free-space laser communications," Proceeding of IEEE International Symposium on Phased Array Systems and Technology, (1996), pp. 419-424. [CrossRef]
- D. Bushuev, D. Kedar and S. Arnon, "Analyzing the performance of a nanosatellite cluster-detector array receiver for laser communication," J. Lightwave Technol. 21, 447-455 (2003). [CrossRef]
- A. Polishuk and S. Arnon, "Communication performance analysis of microsatellites using an optical phased array antenna," Opt. Eng. 42, No.7, 2015-2024 (2003). [CrossRef]
- H. S. Hinton, "Photonic switching fabrics," IEEE Communications Magazine 28, April 1990, 71-89. [CrossRef]
- M. Yamaguchi, T. Yamamoto, K. Hirabayashi, S. Matsuo and K. Koyabu, "High-density digital free-space photonic-switching fabrics using exciton absorption reflection-switch (EARS) arrays and microbeam optical interconnections," IEEE J. Sel. Top. Quantum Electron. 2, 47-54 (1996). [CrossRef]
- T. Yamamoto, M. Yamaguchi, K. Hirabayashi, S. Matsuo, C. Amano, H. Iwamura, Y. Kohama, T. Kurokawa and K. Koyabu, "High-density digital free-space photonic switches using micro-beam optical interconnections," IEEE Photon. Technol. Lett. 8, 358-360 (1996). [CrossRef]
- J.-P. Herriau, A. Delboulbe, J.-P. Huignard, G. Roosen and G. Pauliat, "Optical-beam steering for fiber array using dynamic holography," J. Lightwave Technol. 4, 905-907 (1986). [CrossRef]
- B. Winker, M. Mahajan and M. Hunwardsen, "Liquid crystal beam directors for airborne free-space optical communications," IEEE Aerospace Conference Proceedings 3, March 2004, 6-13.
- Y. Murakami, K. Inagaki and Y. Karasawa, "Beam forming characteristics of a waveguide-type optical phased array antenna," IEICE Trans. Commun. E80-B, 1997.
- K. Inagaki and Y. Karasawa, "Three-element fiber-type optical phased array antenna with high-speed two-dimensional optical beam steering," Electron. Commun. Jpn. 82, 42-51 (1999). [CrossRef]
- T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada and M. Izutsu, "LiNbO3 high-speed optical FSK modulator," Electron. Lett. 40, 691-692 (2004). [CrossRef]
- T. Kawanishi, K. Higuma, T. Fujita, J. Ichikawa, T. Sakamoto, S. Shinada and M. Izutsu, "High-speed optical FSK modulator for optical packet labeling," J. Lightwave Technol. 23, 87-94 (2005). [CrossRef]
- M. Toyoshima and K. Araki, Japan Patent Application for a "Beam splitting method," No. 3069703, filed 24 Nov. 1999.

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