received his Maîtrise in electronics in 1996 and a DEA in Photonic in 1999 from University Louis Pasteur, Strasbourg, France. Since 1997, he has been an electronics teacher currently working at the Ecole Nationale Supérieure des Arts et Industries de Strasbourg (ENSAIS). Kiefer is a PhD assistant at the LSP laboratory, University Louis Pasteur, where he is currently developing an optical scanning system for reading and writing optical data on diffractive memories.
In this article, we describe a compact addressing system for memory reading which combines micro-mirrors (or optical MEMS: microelectromechanical systems), acousto-optics, and gratings. MEMS are more convenient for this application than scanners such as galvanometric, oscillatory, or polygon mirrors due to the large mechanical deflection angles and high level of integration achievable with MEMS devices.
Various movable optical micro-machined mirrors for beam-scanning applications have been developed in the last few years. This article focuses on resonant mirrors which can achieve high deflection angles (~±60º) with low driving voltages (15 to 20 V). However, resonant mirrors oscillate at low frequencies, imposing a limitation on the response time of systems with such devices.
Beam Deflecting System Properties
Properties of Micro-Mirrors
We used micro-mechanical scanning mirrors manufactured in a CMOS-compatible process. Figure 1
shows a mirror consisting of a plate suspended by two torsional springs.
The variation of capacitance C between the mirror plate and comb-like driving electrodes generates the plate's torsional movement. For an applied voltage U, the electrostatic torque M generated is:
where f is the deflection angle of the plate.
Figure 1: Diagram of a micro-mechanical scanning mirror
The size of the mirrors plates can range from 0.5 x 0.5 mm² up to 3 x 3 mm². The actuators are resonantly excited; in other words, they are continuously oscillating. Scan frequency depends on the size of the mirror plate and ranges from 0.14 KHz to 20 KHz. The mirror can achieve a mechanical scan angle of ±15º with a driving voltage of only 20 V.
When the actuator works in the synchronous mode, it is possible to access the angular position of the mirror plate by controlling the maximum deflecting amplitude and oscillating period. An advantage in using these mirrors is that the amplitude of the deflection can be monitored with the driving voltage U. For a large scan angle, the deflection angle varies linearly with the excitation voltage.
Properties of the Acousto-Optic Deflector (AOD)
AOD devices are based on the photo-elastic effect whereby an acoustic signal applied on an acousto-optic crystal produces a strain, which changes the optical properties of the crystal. The laser-beam diffraction geometry associated with the acousto-optical interaction is shown on Figure 2
, where L
is the acoustic wavelength. Let the angular frequency and the wave vector of the incident optical wave in the medium be denoted by wi
respectively and those of the acoustic wave by wa
. The acousto-optic interaction creates a scattered wave with wave vector m
By solving the equation that describes the light propagation in the acousto-optic crystal, we find that the diffracted optical waves in the medium have angular frequencies expressed as wm = wi + mwa and an approximate wave vector m = i + ma, where m = ±1, ±2, ±3...
Each diffracted order is separated from its neighbor by angle: qschift = lifa / n in which fa is the acoustic carrier frequency, n is the speed of sound in the crystal, and li the wavelength of the incident beam. To distinguish the different situations that occur, we introduce the following Q parameters:
(Klein and Cook parameter)
where L is the width of the acoustic beam. In practice the two following cases are used: Raman-Nath regime with Q < 1="" or="" bragg="" regime="" with="" q=""> 7.
In the Raman-Nath regime, multiple diffraction orders similar to those produced by a thin diffraction grating appear. For our application, the diffraction mode we selected is the Bragg regime. In this regime, the diffracted light beam appears predominantly in a single order (Figure 2).
Let q denote the angle between i and the acoustic wavefront (perpendicular to a). For an isotropic crystal, we find that the power in the principal diffracted beam varies with q, reaching a maximum at the Bragg angle q = qB given by:
where n is the index of refraction of the medium and c is free-space light velocity.
The frequency of a collimated acoustic beam can deflect an optical beam. The isotropic Bragg interaction is symmetricthe Bragg condition is satisfied if the angle between the incident optical beam and the diffracted beam is 2qB (Figure 2).
Figure 2: Bragg acousto-optic diffraction geometry showing a single diffracted order
Anisotropic interaction differs from isotropic interaction. The situation has been analyzed by Dixon. Anisotropy modifies the directions of phase matching into which the induced polarization rotates, altering the Bragg diffraction geometry. An anisotropic crystal such as Paratellurite (TeO2) has the advantage that the Raman Nath regime is not obtained, which means that multiple diffraction cannot occur. Therefore, anisotropic interaction offers an advantage over isotropic interactionit allows us to design an AOD device with a much wider bandwidth (for fixed diffraction efficiency) due, primarily, to a very slow shear acoustic wave in the  direction.
We used a TeO2
deflector that operates from 57 MHz to 107 MHz with a scan angle of around 2.7º. The advantage of the acousto-optic deflector is that the diffraction efficiency of the AO device for an incident laser beam can vary as a function of RF drive power; this means that it is easy to control the intensity of the diffracted beam intensity.
When an acousto-optic deflector is used as a scanner, precautions must be taken if the acoustic fill time t is comparable with the scan duration or period. If t is the transit time of the acoustic wave across the optical aperture of the device, it is necessary to wait t seconds before the cell aperture is filled to assure that the diffracted beam is present.
The maximal frequency with which the deflector can access random position is 1/t. For the TeO2 crystal we used, shear acoustic waves limit the transit time t to about 15 µs. To limit resolution loss, choose a scanning rate above this value.
AOD Angular Amplification
In the application in this article, the goal is to address more than one data packet. It is therefore necessary to have a scan angle as large as possible. For this reason, we considered using MEMS. The beam size for display addressing is about 1 to 1.5 mm. You can avoid diffraction by using a mirror size of 3 x 3 mm². The actuators have an oscillating frequency of around 200 Hz, which limits the access time of the display. To increase the response time of our system, we introduced an AOD.
The combination of an AOD and micro-mirrors allows us decreases in the access time. By placing micro-mirrors at calculated positions, it is possible to address several pages of the memory at the AOD rate. You can switch the addressing beam from one mirror to another at the AOD's maximum rate. By controlling the position of the mirror plate, we can switch the beam at a given position. To improve the set-up by reducing its size, it was necessary to increase the light deflection of the AOD by using a grating.
AOD Angular Amplification Using a Grating
We have seen that the principal problem of an AOD is a limited scan angle. For our display application we need to compact the system, requiring an increase of the angular deviation of light coming out of the AOD. For this purpose we use a grating. The Bragg relation gives the light deviation from a grating as:
where d is the pitch of the grating, a and b are defined on Figure 3, and m is an integer. By deriving Equation 1 as a function of a, we obtain for the first-order diffraction:
Equation 2 shows that we can increase the ratio db/da by adjusting db, with a maximum ratio for db close to 90º.
Figure 4 shows the theoretical amplification factor that we could obtain with a blazed grating (1200 grooves/mm) and a holographic grating. In the angular domain under consideration the amplification difference between the two gratings is negligible.
Figure 3: Schematic of a blazed grating showing incident and diffracted beam geometries
Figure 4: Theoretical amplification vs. normalized angle. The normalized angle 0º is the grazing angle for all types of gratings.
To display the angular amplification, we used a rotation stage (Figure 5
) that we can adjust with micro-motors. The precision of this kind of rotation stage is about 1/100 of a degree. A detector moving around the grating allows us to measure the angle of diffraction. To measure the angular amplification we create an angular variation of da
(~30) and measure db
. The angular amplification at a specific angle is given by ratio db
. To improve the signal-to-noise ratio, we use synchronous detection in which the incident laser beam is amplitude modulated by a chopper. Figure 6
is a picture of the diffraction grating.
Figure 5: The diffraction grating mounted on a goniometer
Figure 6: Photograph of the diffraction grating 2.5 x 2.5 cm²
To achieve a good amplification factor, we worked with the diffracted beam near 90º; in other words, the diffracted beam skims the grating surface. The grating has 1200 grooves per millimeter and we use a linearly polarized incident beam with an electric field parallel to the grooves, producing a better diffraction efficiency. The illumination was done with laser light at 632.8 nm.
Figure 7 shows the increase in angular amplification when we are close to the grazing angle, confirming the theoretical prediction. We could theoretically reach a very high amplification factor (Figure 4), but when the amplification factor increases, the diffraction efficiency decreases. For our case, the maximum amplification factor we obtain with an acceptable diffraction efficiency is around 10. To control the intensity of the diffracted beam and to have a response as flat as possible we can adjust the acoustic power by changing the RF power on the piezoelectric crystal.
We made all the measurements with a blazed grating. With this type of grating problems related to periodic errors in the grooves exist. Ghost orders of diffraction, which can create noise, appear. We can improve the situation by using a holographic grating with 2000 grooves/mm.
Figure 7: Angular amplification for a grating of 1200 grooves/mm at l = 632.8 nm
Addressing the Set-Up
As the mirrors are continuously oscillating, it is not possible to permanently address one data page of memory. We need to synchronize the AOD and the mirrors. With synchronization, the angular-encoding problem becomes a time-encoding problem. By knowing mirror parameters such as amplitude of deflection and oscillating period, it is possible to control the switching time of the AOD. This allows us to access one defined mirror, which lets us address a desired position on the memory. With the AOD we can redirect the laser beam on a chosen mirror at a given time.
The limiting factor of the system is not the commutation time of the digital direct synthesizer (DDS), which controls the acoustic frequency. System limitations depend on the fill factor t, which depends on the velocity of the acoustic wave (650 m/s for a shear wave with an incident angle of 48º in TeO2), and on the size of the optical aperture of the acousto-optic cell. In our case the fill time factor is about 15 µs, so we can consider the mirror to be fixed relatively to the AOD.
Since the scan angle depends linearly on the driving voltage for large angles in the synchronized mode
, our set-up is adjusted to operate in that mode. Synchronization of the mirror and the excitation voltage is done by a microcontroller shown in Figure 8
. This device controls the synchronization between the mirror plate and the voltage ramp. We use a photodetector (PD) to detect the crossover (Figure 9
) of the plate's oscillation. The PD generates a current used to start the voltage ramp excitation.
Figure 8 describes the synchronization set up. The CPU (microcontroller) generates a numerical ramp that a DAC converts to an analog signal. A power amplifier controls the excitation signal, the amplitude of the ramp varying from 10 to 20V.
Figure 8: Set-up of the synchronization system. The CPU controls the DAC and power amplifier.
Figure 9: To synchronize the system, the PD detects the crossover of the mirror to start the sawtooth excitation ramp voltage
Synchronizing the Mirror and AOD
The experimental set-up we used to test the synchronization between a mirror and the AOD is described in Figure 10
. The AOD is driven by the CPU to address the mirror at a calculated time depending on the mirror's position. That time is evaluated in order to address a defined point on the display. The CPU calculates that time depending on the points to address, oscillation amplitude, and the time period. The DDS controls the piezoelectric frequency of the AOD to address the mirror at a given time. The CPU controls a CCD camera.
Figure 10: View of the set-up needed to test system synchronization (grating is not in place)
The next step will be to synchronize a set of mirrors and the AOD to address the memory. We use a grating to improve the compactness of the system, as shown in Figure 11.
Figure 11: Schematic of the global experimental set-up for memory reading
This article has described the design of a high spatial and temporal bandwidth beam-deflecting system for holographic matrix-memory reading. A grating along with an acousto-optic deflector lets us improve angular and temporal properties. Our experimental results agree with theoretical predictions. This design offers an angular amplification factor as high as 10 and we expect to have an access time less than 100 µs on a wide angular range. We achieved synchronization of a mirror and the AOD. Integration in a multi-mirror system will lead to a fast and compact reading system.
We still need to study problems relating to beam deformation caused by grating and mirror defects. You can use the deflecting system we have described in display-addressing systems or in communication systems that require very short response time and a high scanning angle.
The authors would like to thank DVA for its support, and H. Schenk and P. Durr (Fraunhofer Institut Mikroelectronische Schaltungen und Systeme) for their help on micro-mirrors. The authors also gratefully acknowledge F. Le Fouiller and F. Darde (society A.A opto-electronic) for fruitful discussions on acousto-optic deflectors.