Abstract

Abstract

We present a broadband nondispersive optical phase shifter array based on microelectromechanical systems (MEMS) technology. The device consists of an array of micro-grating elements. Each grating element utilizes an in-plane translational motion to produce a phase shift to the diffracted light beam. The phase shift is dependent only on the ratio of the grating displacement to its period, and thus independent of incident wavelength. The proposed operation principle was demonstrated with a prototype device developed using a silicon-on-insulator (SOI) micromachining process. This MEMS nondispersive phase-shifter array may be useful in many multispectral applications including broadband optical phased arrays.

©2007 Optical Society of America

1. Introduction

Dispersion-free beam steering of a broadband optical energy over wide angles is essential for many optical sensor systems, including laser radars [1]. In recent years, beam steering using optical phased array technology has attracted much attention. Compared with conventional mechanical beam deflectors, optical phased arrays offer many significant advantages, including low cost, light weight, fast response time, low power consumption, and capability for random-access pointing and dynamic focusing/defocusing. In an optical phased array, a linear phase ramp is introduced across the aperture, which tilts the wave-front and thereby steers an optical beam. To achieve wide angles, a large phase shift by thousands of waves is typically required, which is not practical for nonmechanical or micromechanical phase shifters. Thus, the linear phase shift across the aperture is usually divided into smaller phase ramps having modulo-2π resets. This “folded” phase profile represents a blazed grating.

For broadband operation, two major issues, namely the dispersion of the diffraction grating structure and chromatic nature of the phase modulating mechanism, have restricted the optical phased array beam deflectors to microradian steering angles [2]. The first issue results from the grating, which emulates the linear phase ramp by using a periodic saw-tooth function. Since a grating is a dispersive device, light with different wavelengths is diffracted into different directions. The second issue results from the chromatic nature of the phase modulation mechanism. If the phase profile is an ideal linear ramp with modulo-2π resets, then most of the energy is diverted into the first diffraction order. However, if the phase shifting elements in the phased array are dispersive (i.e. the phase shifts produced are wavelength-dependent and the desired phase shifts are obtained only at the design wavelength), then the unfolded phase profile at a wavelength other than design wavelength deviates from a straight line. As a result, more energy is scattered into undesired diffraction orders, resulting in increased sidelobe amplitudes and degraded system performances due to the interference from multiple diffraction orders. To overcome these problems, nondispersive phase shifters that produce phase shifts independent of wavelength are needed. They decouple the dispersion of the diffractive pattern from the phase modulation, thus allowing the grating dispersion to be corrected separately by using an achromatic Fourier transform lens [3]. Hence, one promising solution to broadband optical phased array is to combine an achromatic Fourier transform lens with an array of nondispersive phase shifters [4]. Recently, nondispersive phase shifters utilizing chiral smectic liquid crystals to achieve topological phase shifts have been reported [5]. These devices manipulate circular polarization to produce a change in optical phase, which is independent of wavelength.

In this paper, we report a novel nondispersive phase modulation mechanism based on microelectromechanical systems (MEMS) technology. Compared with devices based on liquid crystals, the proposed device has many advantages one of which is that it is a reflective device. It can thus be used over a wide spectral range without regard to the optical transmission properties of the materials. In addition, the MEMS grating phase modulation mechanism is not based on the manipulation of circular polarization, and hence the device can potentially be made polarization insensitive. Furthermore, since the MEMS device can have resonant frequencies of 100 kHz or higher [6], faster response times can be achieved. Last not least, the proposed device is fabricated using silicon micromachining technology with no “exotic” materials like liquid crystals, and hence can be easily integrated with electronic circuitry for addressing and control purposes.

2. Optical phase shifting using MEMS gratings

Optical phase modulators based on MEMS micromirrors which have been previously reported typically consist of a set of flat micromirrors wherein each can be individually controlled to move up and down along a direction perpendicular to the mirror surface [711] (see Fig. 1 (a)). Since the phase of light reflected off the micromirror is dependent on the incident wavelength, this modulation mechanism is dispersive in nature and suitable only for narrow-band applications.

In this paper, we propose a broadband nondispersive optical phase shifter array using MEMS micro-grating elements that move in-plane as shown schematically in Fig. 1(b). The grating lines of different elements are initially aligned collinearly such that the whole array represents a single grating. When a diffraction grating element executes an in-plane translational motion along a direction perpendicular to the grating lines with a velocity of v, according to the Doppler Effect, a frequency shift of the first-order diffraction beam will occur. The actual frequency of the diffraction beam can be derived as [12]:

 figure: Fig. 1.

Fig. 1. Schematic of optical phase shifting array using (a) micromirrors (b) MEMS gratings

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f+1=f0+vΛ,

where f 0 and f +1 are the frequencies of the incident and first-order diffraction waves respectively, and Λ is the grating pitch. Thus, the instantaneous frequency of the diffracted light beam is modulated by the in-plane velocity of the grating. The diffracted wave leaving the grating element thus becomes:

E+1=Acos(2πf+1t+ϕ1),

where A is the amplitude of the diffracted wave, and ϕ 1 is an arbitrary phase constant. By inserting Eq. (1) into Eq. (2), the wave field is given by:

E+1=Acos(2πf0t+2π0tv(τ)Λdτ+ϕ1)=Acos(2πf0t+2πdΛ+ϕ1),

where v(τ) is the velocity of the movable grating during a small time interval , and d is the in-plane displacement of the grating. Clearly, the phase modulation of the diffracted light beam, i.e. Δϕ=2πd/Λ, is dependent only on the ratio of the in-plane displacement to the grating pitch and independent of wavelength.

3. Experimental results

A prototype MEMS grating array has been developed using the SOI-MUMPS process [13] to demonstrate the operational principle. A scanning electron microscope (SEM) image showing a part of the device is given in Fig. 2(a). The device was fabricated on a doped silicon layer with a thickness of 25 µm on a silicon-on-insulator (SOI) wafer. The movable structures were then released by etching the silicon dioxide layer. The array with a 72% fill factor consists of 24 grating elements with each element driven by two sets of comb-drives to produce an in-plane translational motion to modulate the phase of the diffracted beam. Each comb-drive has a total number of 17 movable fingers with finger length of 23 µm, width of 4 µm, finger gap of 2 µm and overlap length of 8 µm. The grating element, having a period of 5 µm and an area of 110 µm×507 µm, was etched on a platform that is supported by two sets of folded-beam suspensions with beams of length 142 µm, width 2 µm and thickness 25 µm.

 figure: Fig. 2.

Fig. 2. (a). MEMS grating array developed using SOI micromachining for nondispersive optical phase shifting (b) schematic of the experimental setup.

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The in-plane motion of a grating element was first characterized. The grating element was driven by a push-pull mechanism with movable fingers biased at 80 V. Two differential driving voltages V x and -V x were applied respectively to the two sets of comb-drives. The in-plane displacement of the grating element was measured under an optical microscope. A linear relationship between the grating in-plane displacement x (in micrometer) and the driving voltage V x (in volts) was found and is given as follows:

x=0.065×Vx.

The resonant frequency of the grating element was measured as 6.3 kHz using the POLYTEC Planar Motion Analyzer (PMA-300, Polytec GmbH), which indicates that the device is capable of achieving sub-millisecond switching if properly controlled.

Next, the non-dispersive phase modulation of the device was demonstrated using a HeNe laser beam at wavelength 632.8 nm and a diode-pumped solid-state (DPSS) laser beam at wavelength 532 nm. A schematic showing the setup of the experiment is given in Fig. 2(b). The collimated laser beams were aligned normal to the device, and the first-order diffracted beams from the 24 grating elements were collected by a lens and focused onto a CCD camera. An optical slit was used to ensure that only the first-order beams were captured. In our experiment to demonstrate the operational principle, the odd-numbered grating elements were kept fixed and the even-numbered elements driven by a push-pull mechanism with a driving voltage of V x and a bias voltage of 80 V. As shown in Fig. 2(b), due to the in-plane motions of the grating elements, phase shifts are introduced to the first-order beams diffracted from the even-numbered grating elements, thus forming a dynamic grating with a grating period of about 306 µm along the array direction. The driving voltage V x was swept from -60 V to 60 V with increments of 2 V. The far-field diffraction pattern of the dynamic grating at each driving voltage was recorded. Figure 3 shows the experimental results for the green DPSS laser beam at 532 nm. The intensity distribution along a vertical line through the center of the diffraction pattern was plotted as a function of the grating in-plane displacement, which was estimated from the driving voltage V x using Eq. (4). The diffraction patterns at driving voltages of -10 V and 28 V are shown in inserts A and B of Fig. 3, respectively. Clearly, insert A indicates that the beams diffracted from all grating elements are in-phase, and thus the majority of the optical power went to the zeroth-order of the dynamic grating. Insert B indicates that the beams diffracted from the odd and even-numbered grating elements are 180 degrees out-of-phase, and thus the majority of the optical power is diffracted to the positive and negative first-orders. The in-plane displacement to produce this 180 degrees phase difference was thus determined to be 2.47 µm, which is in good agreement with Eq. (3) with the grating period Λ set to 5 µm. The same experiment was carried out with the red HeNe laser beam at 632.8 nm and the results are shown in Fig. 4. As shown in the figure, the in-plane displacement required to produce a 180 degrees phase shift to change the far-field diffraction pattern from insert A to insert B was again found to be 2.47 µm, which confirms that the phase shift produced by an in-plane moving grating is independent of wavelength and the proposed mechanism is nondispersive.

 figure: Fig. 3.

Fig. 3. Far-field diffraction pattern as a function of grating displacement for 532 nm wavelength laser beam

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 figure: Fig. 4.

Fig. 4. Far-field diffraction pattern as a function of grating displacement for 632.8 nm wavelength laser beam

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4. Potential application in broadband optical phased array

As mentioned in the previous sections, one promising solution to broadband optical phased array is to combine an achromatic Fourier transform lens with an array of nondispersive phase shifters. The proposed device will thus be useful in practical implementation of broadband optical phased arrays. Figure 5 shows schematically a 1D optical broadband phased array using the proposed MEMS in-plane movable gratings. As shown in the figure, broadband light is incident upon an array of MEMS gratings, each of which can be driven to execute an in-plane translational motion along a direction perpendicular to the grating lines. All grating lines in the array are aligned in the same direction. The broadband incident light is thus divided into multiple beams. Each beam is diffracted by an individual grating element. Light with different wavelengths is diffracted to different directions. Due to the in-plane motion of the grating element, a common phase shift independent of wavelength is induced on the light diffracted from it. Light beams diffracted from the whole array are then collected and recombined by an achromatic Fourier transform lens [3]. This type of lens system scales a common spatial frequency in one focal plane to a common location in the other regardless of the wavelength of the incident radiation. Hence, in phased array applications, the dispersion of the dynamic blazed grating along the y-axis (see Fig. 5) produced by the whole phased array and the dispersion produced by the individual grating element can be corrected simultaneously, forming a “white” light spot in the achromatic Fourier plane of the transformer. When the period of the dynamic blazed grating phase profile produced by the phased array to emulate a linear phase ramp varies, the “white” light spot in the achromatic Fourier plane moves up and down as shown in the Fig. 5. Broadband wide angle beam steering can thus be achieved by placing a conventional wide field-of-view lens in front of the system such that its focal plane coincides with the achromatic Fourier plane. This phased array system has the potential to achieve light weight, compact size, low power consumption, and low cost.

 figure: Fig. 5.

Fig. 5. Proposed 1D broadband optical phased array using MEMS gratings

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4. Conclusion

In conclusion, we have successfully demonstrated a proof-of-principle nondispersive optical phase-shifter array that utilizes in-plane translational motions of MEMS micro-grating elements to produce phase shifts in diffracted light beams. The phase shift is dependent only on the ratio of the grating in-plane displacement to its period, and thus independent of incident wavelength. The proposed MEMS nondispersive phase-shifter array may be useful in many multispectral applications such as steering a broadband light in an optical phased array, routing spectrally encoded signals and manipulating chromatic light in an optical imaging system.

Acknowledgments

Financial support by the Ministry of Education’s AcRF Tier 1 funding under Grant No. R-265-000-235-112 and R-265-000-211-112/133 is gratefully acknowledged.

References and links

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996). [CrossRef]  

2. J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE 3131, 111–123 (1997). [CrossRef]  

3. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981). [CrossRef]   [PubMed]  

4. S. A. Serati and J. E. Stockley, “Advances in liquid crystal based devices for wavefront control and beamstreering,” Proc. SPIE 5894, 180–192 (2005).

5. J. E. Stockley, G. D. Sharp, S. A. Serati, and K. M. Johnson, “Analog optical phase modulator based on chiral smectic and polymer cholesteric liquid crystals,” Opt. Lett. 20, 2441–2443 (1995). [CrossRef]   [PubMed]  

6. K. Wang and C. T. C. Ngyugen, “High-order medium frequency micromechanical electronic filters,” IEEE/ASME J. Microelectromech. Syst. 8, 534–557 (1999). [CrossRef]  

7. O. Solgaard, F. S. A. Sandejas, and D. M. Bloom, “Deformable grating optical modulator,” Opt. Lett. 17, 688–690 (1992). [CrossRef]   [PubMed]  

8. M. K. Lee, W. D. Cowan, B. M. Welsh, V. M. Bright , and M. C. Roggemann, “Aberration correction results from a segmented microelectromechanical deformable mirror and a refractive lenslet array,” Opt. Lett. 23, 645–647 (1998). [CrossRef]  

9. K. B. Li, J. P. Krishnamoorthy, O. Heritage, and Solgaard, “Coherent micromirror arrays” Opt. Lett. 27, 366–368 (2002). [CrossRef]  

10. G. Zhou, V. J. Logeeswaran, F. S. Chau, and F. E. H. Tay, “Line-addressable digital-deflection programmable micromirror array,” Opt. Lett. 29, 2581–2583 (2004). [CrossRef]   [PubMed]  

11. G. Zhou and F. S. Chau, “Helical wave-front laser beam generated with a microelectromechanical systems (MEMS)-based device,” IEEE Photon. Tech. Lett. 18, 292–294 (2006). [CrossRef]  

12. L. E. Drain, The laser Doppler technique (John Wiley & Sons, New York, 1980).

13. K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

References

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  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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
    [Crossref]
  2. J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
    [Crossref]
  3. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981).
    [Crossref] [PubMed]
  4. S. A. Serati and J. E. Stockley, “Advances in liquid crystal based devices for wavefront control and beamstreering,” Proc. SPIE 5894, 180–192 (2005).
  5. J. E. Stockley, G. D. Sharp, S. A. Serati, and K. M. Johnson, “Analog optical phase modulator based on chiral smectic and polymer cholesteric liquid crystals,” Opt. Lett. 20, 2441–2443 (1995).
    [Crossref] [PubMed]
  6. K. Wang and C. T. C. Ngyugen, “High-order medium frequency micromechanical electronic filters,” IEEE/ASME J. Microelectromech. Syst. 8, 534–557 (1999).
    [Crossref]
  7. O. Solgaard, F. S. A. Sandejas, and D. M. Bloom, “Deformable grating optical modulator,” Opt. Lett.  17, 688–690 (1992).
    [Crossref] [PubMed]
  8. M. K. Lee, W. D. Cowan, B. M. Welsh, V. M. Bright , and M. C. Roggemann, “Aberration correction results from a segmented microelectromechanical deformable mirror and a refractive lenslet array,” Opt. Lett. 23, 645–647 (1998).
    [Crossref]
  9. K. B. Li, J. P. Krishnamoorthy, O. Heritage, and Solgaard, “Coherent micromirror arrays” Opt. Lett. 27, 366–368 (2002).
    [Crossref]
  10. G. Zhou, V. J. Logeeswaran, F. S. Chau, and F. E. H. Tay, “Line-addressable digital-deflection programmable micromirror array,” Opt. Lett.  29, 2581–2583 (2004).
    [Crossref] [PubMed]
  11. G. Zhou and F. S. Chau, “Helical wave-front laser beam generated with a microelectromechanical systems (MEMS)-based device,” IEEE Photon. Tech. Lett. 18, 292–294 (2006).
    [Crossref]
  12. L. E. Drain, The laser Doppler technique (John Wiley & Sons, New York, 1980).
  13. K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

2006 (1)

G. Zhou and F. S. Chau, “Helical wave-front laser beam generated with a microelectromechanical systems (MEMS)-based device,” IEEE Photon. Tech. Lett. 18, 292–294 (2006).
[Crossref]

2005 (1)

S. A. Serati and J. E. Stockley, “Advances in liquid crystal based devices for wavefront control and beamstreering,” Proc. SPIE 5894, 180–192 (2005).

2004 (1)

2002 (1)

1999 (1)

K. Wang and C. T. C. Ngyugen, “High-order medium frequency micromechanical electronic filters,” IEEE/ASME J. Microelectromech. Syst. 8, 534–557 (1999).
[Crossref]

1998 (1)

1997 (1)

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

1996 (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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

1995 (1)

1992 (1)

1981 (1)

Bloom,, D. M.

Bright, V. M.

Chau, F. S.

G. Zhou and F. S. Chau, “Helical wave-front laser beam generated with a microelectromechanical systems (MEMS)-based device,” IEEE Photon. Tech. Lett. 18, 292–294 (2006).
[Crossref]

G. Zhou, V. J. Logeeswaran, F. S. Chau, and F. E. H. Tay, “Line-addressable digital-deflection programmable micromirror array,” Opt. Lett.  29, 2581–2583 (2004).
[Crossref] [PubMed]

Corkum, D. L.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Cowan, W. D.

Cowen, A.

K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

Dorschner, T. A.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Drain, L. E.

L. E. Drain, The laser Doppler technique (John Wiley & Sons, New York, 1980).

Friedman, L. J.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Hames, G.

K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

Hardy, B.

K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

Heritage, O.

Hobbs, D. S.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Holz, M.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Johnson, K. M.

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

J. E. Stockley, G. D. Sharp, S. A. Serati, and K. M. Johnson, “Analog optical phase modulator based on chiral smectic and polymer cholesteric liquid crystals,” Opt. Lett. 20, 2441–2443 (1995).
[Crossref] [PubMed]

Krishnamoorthy, J. P.

Lee, M. K.

Li, K. B.

Liberman, S.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Logeeswaran, V. J.

McManamon, P. F.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Miller, K.

K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

Morris, G. M.

Nguyen, H. Q.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Ngyugen, C. T. C.

K. Wang and C. T. C. Ngyugen, “High-order medium frequency micromechanical electronic filters,” IEEE/ASME J. Microelectromech. Syst. 8, 534–557 (1999).
[Crossref]

Resler, D. P.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Roggemann, M. C.

Sandejas, F. S. A.

Serati, S. A.

S. A. Serati and J. E. Stockley, “Advances in liquid crystal based devices for wavefront control and beamstreering,” Proc. SPIE 5894, 180–192 (2005).

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

J. E. Stockley, G. D. Sharp, S. A. Serati, and K. M. Johnson, “Analog optical phase modulator based on chiral smectic and polymer cholesteric liquid crystals,” Opt. Lett. 20, 2441–2443 (1995).
[Crossref] [PubMed]

Sharp, G. D.

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

J. E. Stockley, G. D. Sharp, S. A. Serati, and K. M. Johnson, “Analog optical phase modulator based on chiral smectic and polymer cholesteric liquid crystals,” Opt. Lett. 20, 2441–2443 (1995).
[Crossref] [PubMed]

Sharp, R. C.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Solgaard,

Solgaard, O.

Stockley, J. E.

S. A. Serati and J. E. Stockley, “Advances in liquid crystal based devices for wavefront control and beamstreering,” Proc. SPIE 5894, 180–192 (2005).

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

J. E. Stockley, G. D. Sharp, S. A. Serati, and K. M. Johnson, “Analog optical phase modulator based on chiral smectic and polymer cholesteric liquid crystals,” Opt. Lett. 20, 2441–2443 (1995).
[Crossref] [PubMed]

Tay, F. E. H.

Walsh, K. F.

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

Wang, K.

K. Wang and C. T. C. Ngyugen, “High-order medium frequency micromechanical electronic filters,” IEEE/ASME J. Microelectromech. Syst. 8, 534–557 (1999).
[Crossref]

Wang, P.

J. E. Stockley, S. A. Serati, G. D. Sharp, P. Wang, K. F. Walsh, and K. M. Johnson, “Broadband beam steering,” Proc. SPIE  3131, 111–123 (1997).
[Crossref]

Watson, W. A.

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 W. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Welsh, B. M.

Zhou, G.

G. Zhou and F. S. Chau, “Helical wave-front laser beam generated with a microelectromechanical systems (MEMS)-based device,” IEEE Photon. Tech. Lett. 18, 292–294 (2006).
[Crossref]

G. Zhou, V. J. Logeeswaran, F. S. Chau, and F. E. H. Tay, “Line-addressable digital-deflection programmable micromirror array,” Opt. Lett.  29, 2581–2583 (2004).
[Crossref] [PubMed]

Appl. Opt. (1)

IEEE Photon. Tech. Lett. (1)

G. Zhou and F. S. Chau, “Helical wave-front laser beam generated with a microelectromechanical systems (MEMS)-based device,” IEEE Photon. Tech. Lett. 18, 292–294 (2006).
[Crossref]

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[Crossref]

Opt. Lett. (5)

Proc. IEEE (1)

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[Crossref]

Proc. SPIE (2)

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[Crossref]

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Other (2)

L. E. Drain, The laser Doppler technique (John Wiley & Sons, New York, 1980).

K. Miller, A. Cowen, G. Hames, and B. Hardy, SOIMUMPs design handbook, http://www.memscap.com/mumps/documents/SOIMUMPs.dr.v4.pdf

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Figures (5)

Fig. 1.
Fig. 1. Schematic of optical phase shifting array using (a) micromirrors (b) MEMS gratings
Fig. 2.
Fig. 2. (a). MEMS grating array developed using SOI micromachining for nondispersive optical phase shifting (b) schematic of the experimental setup.
Fig. 3.
Fig. 3. Far-field diffraction pattern as a function of grating displacement for 532 nm wavelength laser beam
Fig. 4.
Fig. 4. Far-field diffraction pattern as a function of grating displacement for 632.8 nm wavelength laser beam
Fig. 5.
Fig. 5. Proposed 1D broadband optical phased array using MEMS gratings

Equations (4)

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f + 1 = f 0 + v Λ ,
E + 1 = A cos ( 2 π f + 1 t + ϕ 1 ) ,
E + 1 = A cos ( 2 π f 0 t + 2 π 0 t v ( τ ) Λ d τ + ϕ 1 ) = A cos ( 2 π f 0 t + 2 π d Λ + ϕ 1 ) ,
x = 0.065 × V x .

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