WO2002005009A1

WO2002005009A1 - Deformable grating modulator capable of both phase and amplitude modulation

Info

Publication number: WO2002005009A1
Application number: PCT/US2001/021715
Authority: WO
Inventors: Charles F. Hester
Original assignee: Opts, Inc.
Priority date: 2000-07-10
Filing date: 2001-07-10
Publication date: 2002-01-17
Also published as: WO2002005009A9; AU2001280504A1

Abstract

A grating-type spatial light modulator having two sets of grating bars (703, 705) provides simultaneous independent control of both the phase and amplitude modulation of an incident optical signal. The two sets of grating bars are interleaved and each set is independently controllable. The amplitude of incident light is modulated by controlling the relative distance between adjacent bars FO either set. The phase of the incident light is modulated by controlling the relative position of the tow sets of bars with respect to a fixed reference plane (707).

Description

DEFORMABLE GRATING MODULATOR CAPABLE OF BOTH PHASE AND AMPLITUDE MODULATION

Related Applications

This application incorporates (1) U.S. Provisional Patent Application No. 60/142,931, entitled "Adaptive Compressive Network," naming Charles F. Hester and Marshal K. Quick as inventors, filed on July 9, 1999, which application is incorporated entirely herein by reference; (2) U.S. Provisional Patent Application No. 60/183,793, entitled "Point Probe Memory With Light Modulator Read Out," naming Charles F. Hester and Charles A. Whitehead as inventors, filed on February 22, 2000, which provisional application is incorporated entirely herein by reference; (3) the U.S. Patent Application entitled "Grating Type Spatial Light Modulators And Method Of Manufacturing Grating Type Spatial Light Modulators," naming Charles F. Hester and Charles A. Whitehead as inventors, filed on July 10, 2000, which application is incorporated entirely herein by reference; (4) the U.S. Patent Application entitled "A Micromechanical Deformable Grating For Binary Optical Switching," naming Charles F. Hester as inventor, filed on July 10, 2000, which application is incorporated entirely herein by reference; and (4) the U.S. Patent Application entitled "Analog Compressive Network," naming Charles F. Hester and Marshal K. Quick as inventors, filed concurrently herewith, which application is incorporated entirely herein by reference.

Background Of The Invention

Field Of The Invention The present invention relates to a deformable grating light modulator that is capable of modulating both the phase and the amplitude of incident light.

Description Of The Prior Art The spatial light modulator is a frequently used component in optical processing and computing. It is a structure that allows a light beam to be controllably spatially (as opposed to frequency) modulated. There are many different types of programmable spatial light modulators, including, for example, modulators employing liquid crystal devices, magneto optical materials, and acousto optical materials. Various types of spatial light modulators are described in "Two- Dimensional Spatial Light Modulators: A Tutorial" by John A. Neff et al., Proceedings of the IEEE, Vol. 78, No. 5 (May 1990), pages 826-855, which is incorporated entirely herein by reference.

Light modulators are used for a variety of purposes, including inputting information into an optical system, modulating carrier light during an optical computation, such as in a Fourier filter, and as a neural network interconnect. Spatial light modulators are particularly useful as digital optical switches. Digital optical switches are employed in, for example, fiber-optic routing networks, printer heads, and displays.

One particular type of spatial light modulator is the deformable grating modulator, which uses mirrors formed on the surfaces of micromechanical switches. These devices electrostatically actuate these miniaturized mirrors to switch light from being reflected at one angle to being reflected at another angle. Microelectromechanical switches are easily manufactured using conventional semiconductor techniques, can be very small (several tens of microns), and have very simple moving parts. They can operate in either digital or analog fashion, and typically have a hinge or actuator that is electrostatically or piezoelectrically driven. Typically, a group of switches are arranged together as a set of parallel reflecting bars that form a grating. To provide a better understanding of the features of the invention, one conventional type of spatial modulator will now be described in detail. Referring to Figs. 1-3, this type of modulator 101 has a number of reflective parallel bars 103 suspended above a reflective surface 105. Each bar 103 is supported on either end by a support post 107. The modulator 101 also has one or more electrodes 201 corresponding to the bars 103.

Referring now to Fig. 2, when the electrodes 201 are inactive, the distance d between the bars 103 and the reflective surface 105 is λ/2 (or an integral multiple of λ/2), where λ is the wavelength of the light to be modulated. Thus, the light 203 reflected from the upper reflective surface of the bars 103 is in phase with the light 205 reflected from the reflective surface 105, so the modulator 101 acts as a mirror. This is the "off state of the modulator 101. To modulate light, a charge is applied to the bars 103, and an opposite charge is applied to the electrodes 201. The charge on the electrodes 201 attracts the charge on the reflective bars 103, and pulls all of the reflective bars 103 (i.e., the micromirrors) toward the reflective surface 105, as can be seen in Fig. 3. If all of the reflective bars 103 are pulled to a distance d of λ/4 (or an integral multiple of λ/4) from the reflective surface 105, then the light 203 reflected from the reflective surface of the bars 103 is opposite in phase from the light 305 reflected from the reflective surface 105. Thus, the destructive interference between light 203 and light 205 then prevents the modulator 101 from reflecting light to any distance. This is the "on" state of the spatial light modulator 101. As previously noted, each bar 103 is supported at either end by a support post 107. Accordingly, the end portions of the bars 103 serve as hinges and flex in order to allow the height of the center portion of the bar 103 to change. While these end portions must flex, however, they must also be stiff enough to support the reflective bar 103. Accordingly, both the bars 103 and the electrodes 201 must carry a large amount of electric charge in order to sufficiently flex the bars 103. One problem with all types of presently available modulators, however, is that they either suffer from poor overall space bandwidth or cannot represent full four quadrant complex numbers, i.e., they cannot perform full phase and amplitude modulation. Indeed, conventional liquid crystal modulators experience a coupled phase and amplitude modulation. That is, conventional liquid crystal modulators cannot control the amplitude of a light signal without simultaneously modifying the phase of that signal.

As a consequence of this phase and amplitude constraint, filter designers who program pattern recognition systems must use suboptimum designs based on the remapping of the filter to the limited constraint curve provided by the spatial light modulator. Moreover, using a spatial light modulator as an input device requires the input to have a coupled phase and amplitude, or by design be limited to only amplitude or only phase, thus limiting the operation to input constraint curves.

Being able to use both amplitude and phase modulation to represent complex numbers in optical processors would exploit the full capability of coherent optical processors. Past work has emphasized phase-only modulation, in particular binary phase-only modulation. The performance of conventional pattern recognition filters thus has been reduced due to this limitation. Moreover, layering of the optical processor, i.e., taking the output of one stage of processing and feeding it into the next stage, is best performed if full complex number representation is performed in the second stage. In particular, the performances of filters that open up the convex hull in pattern space have an inherent need for complex number representation. Accordingly, it would be desirable to have a spatial light modulator that is capable of simultaneously being able to independently modulate both the phase and amplitude of a light signal.

Summary Of The Invention

Accordingly, the invention is directed to a type of spatial light modulator that may advantageously provide simultaneous independent control of both the phase and amplitude modulation of an incident light signal. One embodiment of the invention is a grating type spatial light modulator having two sets of grating bars. The two sets of grating bars are interleaved and each set is independently controllable. The amplitude of incident light can then be modulated by controlling the relative distance between adjacent bars of either set. On the other hand, the phase of incident light can be modulated by controlling the relative position of the two sets of bars (i.e., the relative position of the halfway line between the two sets of bars relative to an arbitrary plane parallel to the bars).

Brief Description Of The Drawings Fig. 1 is a top view of a conventional micromechanical mirror type spatial light modulator.

Fig. 2 is a cross-sectional view of the spatial light modulator shown in Fig. 1 taken along section line 2-2'.

Fig. 3 is a cross-sectional view of the spatial light modulator shown in Fig. 1 taken along section line 3-3'.

Fig. 4 is a cross sectional view showing the relationship between a phase front produced by a deformable grating spatial light modulator and the spacing Δ between the bars of the grating.

Fig. 5 is a cross sectional view showing the relationship between the phase and amplitude of reflected light to the displacement of bars x and y with respect to a reference surface.

Fig. 6 is a cross sectional view of a deformable grating spatial light modulator according to one embodiment of the invention. Fig. 7 is a cross sectional view of a deformable grating spatial light modulator according to another embodiment of the invention Detailed Description Of Preferred Embodiments

Letting f(x,y,0) be the scalar field at the z = 0 plane. The field distribution from a reflective surface, such as a deformable grating spatial light modulator, at the coordinate (x,y,z) is

where the direction cosines are a - λ ω_x, β = λ ω_y, and ω_x and ω_y are the angular frequencies in the x,y plane. From this, we further know that: 1. lfa +β { \, then the effect of translation of the z axis is a linear phase factor exp(z^'2πz). 2. If the boundary

then the field distribution is amplified by A. The field distribution at one focal length behind a lens at coordinates (p,q) can be approximated by

U{p, + qy) dx dy where p and q are the input field distribution, i{x, y),

spatial frequencies ω_x = ^PX and ω_y = y-,f •

then the input is the sampled version of the original signal

s(x,y).

If i{x,y)- is Fourier transformed and A_x ≤ I 2τB,X an'"d^* Δ "^y <^* / I2B_J

where B_x and B_y are the spatial bandwidths of the signal s, then the signal spectrum is repeated at spacings V. and V. in p and q, respectively, in the Fourier plane.

/ "-x / ^y

Now considering a reflective surface consisting of equally spaced bars, a coherent wave impinging on the surface will undergo diffraction producing orders at angles according to spacing Δ and the wavelength λ of the light. This is graphically illustrated in Fig. 4, where the bars 401 and 403 reflect a coherent wave of light 405 to produce a phase front 407. A two-dimensional array of gratings forming a spatial light modulator (SLM) array (such as that described in copending U.S. Patent Application entitled "Adaptive Compressive Network," naming Charles F. Hester and Marshal K. Quick as inventors, filed concurrently herewith) can be used to input an image into, for example, the optical train of an optical processor for compression. The information input is seen as the sampled version of a complex function i(x,y), where (x,y) is a coordinate pair. Each grating has a characteristic function c(x,y) that is laid out in a grid for an overall SLM array, giving

with δ() being the Dirac delta function and

the sample spacing with uniformity in the two dimensions. The grating function has a fundamental frequency as determined by the internal sampling produced by the grating period, P. The grating function is

( c(x, y) - red X 2. ∑b{x,y)δ{x-jτ_x)δ(y - k...) W ' W i,k

where W is the grating width and b(x, y) is the bar function. The bar function represents the field over a single grating period . For the grating two offset bars of width P_g are indicated. With no loss of generality, the width may be just ^XA P_g. The bar function is constant in the y dimension. Thus, b(χ,y)= e^iΦV - [^_.- *] * * "^*** [ ^^T^] the bar fills the pixel vertically. For the index of refraction equal to 1 (i.e., the vacuum case), the

optical phase is ,^s where d, and cf-_are the displacement of alternate bias.

Thee close approximation gives to within a constant for the field of interest as

G{ώ)= \dxg{x)e-²' ^0& .

= βώufy ∑ [c(x,y) *i(x,y). c {x-nτ_x)-

Which can be rewritten as the Fourier transform 3 of a convolution. with Q> ÷ (tø.-Φ*)/z.

Then the Fourier transform of c(x,y) is

No ^ , _{) A}j^ ) - L^{C Φo} ,^'n [ *»*[] 5ivχ [ w J . dos [ d- z } V^ΛJ*

Finally, the right convolution term in f^j ecomes ^*" ° sin [ ₂. J 5>«c W*>^ J ^• 2<o> [ ® ^"i J where**indicates a double convolution. From the above it is seen that the translation of the grating with respect to the reference surface results in a phase modulation and the degree that the bars are separated from each other increases the amplitude of the modulation. This relationship is between the between the phase and amplitude of reflected light to the displacement of bars x and y with respect to a reference surface. As seen from this figure and the foregoing explanation, the phase of reflected light is proportional to x+y, and the amplitude of reflected light is proportional to x-y. That is, the phase of the reflected light is proportional to the midpoint between the two bars relative to a reference surface, while the amplitude of the reflected light is proportional to the distance between the two bars.

Those of ordinary skill in the art will appreciate that complex numbers can be represented and used for display and processing by assigning the amplitude A of a function value as the amplitude of the electric field and assigning the phase as the field phase, U(x,y)-Ae'^. From the foregoing, it will also be appreciated that this information can now be defined by, for example, deformable gratings in a spatial light modulator array, i.e., that a spatial light modulator array can be used to represent complex numbers. For a spatial light modulator array having gratings g(l,l) to g(n,m), each grating corresponding to a pixel, the information is sampled g(n,m)^~ f{x,y)-comb\ x The sampled ^rs J information is placed in an array of pixels, i(x,y) The pixel information array

is then mixed with a grating

Sample pitch and grating pitch being set such that P_S<P_S and P_s=nP_g. This results in the modulation of the grating locally at each pixel by g(n,m)= Ae"^.

One embodiment of a spatial light modulator grating that accomplishes this modulation is shown in Fig. 6. As seen in this figure, the grating 601 has a first set of grating bars 603 and a second set of grating bars 605. These bars are interleaved, such that each bar 603 is adjacent to only a bar 605 and each bar 605 is adjacent only to a bar 603. With this arrangement, the grating pitch for the grating is the length of a bar 603 and its adjacent bar 605.

Both the bars 603 and the bars 605 can be independently moved relative to, a fixed reference plane 607. Thus, bars 603 can be moved toward the reference plane 607 while the bars 605 remain stationary, and vice versa. From the foregoing explanation, it will be understood that this grating can accomplish modulation representing complex numbers by forcing of the grating bars such that the entire grating (i.e., both bars 603 and 605) is moved normal to the grating reference plane 607 at each pixel to a distance, D, thereby giving a light path change D = Y₂ Φ where φ = θχ #₂12, and differential movement of the grating bars, AD, an amount AD = A , with A Xθι-θ)l2 yielding an amplitude

#₂12), where B is the illumination amplitude and a net phase φ_N = 2 . Another embodiment of the invention is illustrated in Fig. 7. As with the previously discussed embodiment, the deformable grating spatial light modulator of Fig. 7 has two sets of independently controllable bars 703 and 705, that can be moved relative to a reference plane 707.

Unlike the previous embodiment, however, the bars 703 and 705 are arranged in pairs. That is, each bar 703 (except for an end bar) will be adjacent to both another bar 703 and a bar 705. Simliarly, each bar 705 (except for an end bar) will be adjacent to both another bar 705 and a bar

703. With this arrangement, the grating pitch for the grating is the length of two bars 703 and two bars 705. Thus, it will be appreciated that spatial light modulators according to the invention can mix information on a grating carrier to effect, by diffraction, large separation of modulation information in the Fourier plane. Moreover, because the modulation is well-separated in diffraction orders +1, 0, -1 of the grating pitch, the on to off states are of high dynamic range. The carrier modulation requires only two drive voltages per sample point, one for phase and one for amplitude, with each drive voltage controlling the position of one of two sets of bars. With alternate embodiments of the invention, a separate grating carrier, un-modulated can be used in conjunction with the primary carrier at 2:1 ration that will result in a side band that suppresses in band off state modulation and even higher dynamic ranges. The present invention has been described above by way of specific exemplary embodiments, and the many features and advantages of the present invention are apparent from the written description. Thus, it is intended that the appended claims cover all such features and advantages of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, the specification is not intended to limit the invention to the exact construction and operation as illustrated and described. For example, the invention may include any one or more elements from the apparatus and methods described herein in any combination or subcombination. Accordingly, there are any number of alternate combinations for defining the invention, which incorporate one or more elements from the specification (including the drawings, claims and summary of the invention) in any combination or subcombination. Hence, all suitable modifications and equivalents may be considered as falling within the scope of the appended claims.

Claims

I claim:

1. A deformable grating spatial light modulator for modulating both phase and amplitude of incident light, comprising: a first set of reflective grating bars; a second set of reflecting grating bars interleaved between the first set of reflective grating bars; a first electrode for controlling the first set of reflective grating bars; and a second electrode for controlling the second set of reflecting grating bars.