TECHNICAL NOTES

Practical realizations of N4 optical interconnects Freddie Lin

Physical Optics Corporation, Research Division, 20600 Gramercy Place, Torrance, California 90501. Received 19 September 1989. 0003-6935/90/355226-02$02.00/0. © 1990 Optical Society of America.

A novel and practical realization of N4 optical intercon­nects in a lensless optical system is presented. The new architectures take into consideration the limitations of spa­tial light modulators, optical components, and hologram size.

Parallel N4 optical interconnect schemes using a spatially multiplexed holographic array have been previously pro­posed by Ambs et al.1 and Caulfield.2 Using the potential of these architectures, the number of parallel interconnects can reach up to 1012. There are a variety of applications based on these N4 interconnect schemes. One of these applications is in optical three dimensions massive interconnects for paral­lel multiprocessor computers, neural networks, and informa­tion processing. This paper describes a new realization for N4 optical interconnects that does not have lenses in the optical reconstruction system. The proposed architecture eliminates a problem that has limited the usefulness of this application. The difficulty has been that most spatial light modulators (SLMs) are designed for near normal incidence.2

Because of this, they are not suitable for recording setups which require various incident angles. The effect of this difficulty on optical interconnect applications is discussed in another paper.3

Figure 1 shows a new way to record a N4 interconnect matrix. A collimated beam illuminates an SLM at one par­ticular incident angle (near normal, for example). A diffus­er, placed in the image plane of a 4-ƒ imaging optical system, will spread the incident pattern (modulated by the SLM) over a wide angular range. Since most SLMs are protected by substrates or packing plates, a 4-ƒ image system faithfully images the pixels of the SLM (which carry the pattern) onto

the diffuser. A hologram plate with a mask is placed at a proper distance z (depending on the desired recording size and the angle of spread of the diffuser. behind the diffuser. With an additional reference beam, the pattern from the SLM (Tij) will be holographically recorded in an element of the array. By changing the SLM pattern and moving the mask along both horizontal and vertical directions, one can easily fabricate an N4 interconnect matrix [i.e., (Tij)kl] with­out requiring various incident angles on the SLM. The drawback of this new recording architecture is that it reduces optical recording power. It is possible, however, to design an array of diffusers by combining them with diffraction grat­ings, which will direct the incident SLM pattern to a specific angular range. This will direct the light so that it does not have to spread over a wide angular range. Thus, in the recording process, the mask in front of the holographic plate and the diffuser array can be moved simultaneously.

In the reconstruction process (see Fig. 2), an encoded reference beam (with pixel akl), which is conjugate to the reference beam in the recording process and represents the input information, illuminates the holographic array. Each pixel covers one holographic element in the array. This encoded reference beam can pass through an SLM and an optical magnification system or originate from an array of laser diodes with collimating lenses. A photodetector array, which has the same packing density and pixel size as the SLM used in the recording process, is placed at the diffuser.

Fig. 2. Reconstruction of an N4 holographic interconnect matrix.

Fig. 1. Recording of an N4 holographic interconnect matrix.

5226 APPLIED OPTICS / Vol. 29, No. 35 / 10 December 1990

The beams diffracted from the holographic matrix elements will be directed back to the photodetector array.

Since there are many matrix elements in the holographic array, all of them add up pixel by pixel in the photodetector array. Thus the resulting signals detected by one of the detectors can be described as

This equation describes the parallel interconnects of an N × N input array to an N × N output array through an N4

holographic interconnect matrix. The two practical issues which still need to be considered are as follows:

(1) Equation (1) is an incoherent superimposition if laser diode sources which are mutually incoherent are used. If, however, coherent input from an SLM is employed, Eq. (1) incur a coherent summation problem. This phase problem can be reduced in two ways: The first involves placing a random phase mask4 which provides a spatially random dis­tribution of phase but with a constant phase over each pixel to the readout beam. The second solution involves inserting a moving diffuser which will average out the coherent inter­ference in the front face of the photodetector array.

(2) Because the hologram is made with diffuse light sig­nals, it suffers from a speckle noise problem. This problem reduces the resolution of the reconstructed image pattern when the size of each holographic element becomes smaller. This has led to the investigation of a number of artificial diffusers to increase the image quality and recording densi­ty.5,6 Furthermore, these artificial diffuser designs can also cause light to be distributed uniformly across the aperture of the holographic array.

One way to reduce the overall size of the holographic array is to tailor the system design to the diffraction limitation. In other words, the photodetector array should have the same resolution (or packing density) as the SLM; however, the former should have a fill factor much larger than the latter. For example, using the diffraction limitation equation w = 2λz/α, if the desired size of each holographic element is a = 400 μm (thus the total size of the array is 40 × 40 cm2 for N = 1000), the separation of the holographic array and detector array is z = 100 mm, and the operating wavelength is λ = 0.5 μm, then the width of the diffraction pattern between the first two zeros (i.e., the width of the main label) is w = 250 μm. To reasonably catch the incident beam power and reduce the crosstalk between adjacent detector pixels, a detector pixel separation of 2w with a fill factor of ½ (i.e., center-to-center separation is 500 μm and pixel size is 250 μm) can be em­ployed. The required SLM will have the same resolution as the photodetector; however, the size of the SLM pixel should be reduced to a smaller number (e.g., 50 μm); i.e., a fill factor of ~1/10 for an SLM design may be desired. To increase light throughput, an array illuminator7 can be used to illumi­nate this specific SLM. One can conclude that a specially designed SLM and photodetector array are required to re­duce the size of the holographic array.

The drawbacks of the above design are that both the SLM

and photodetector array require large size wafers (requiring 50-cm wafers with the above example) and may suffer from a nonuniform performance and fabrication problems. A gen­eral design rule is that the size of the SLM/photodetector array and N4 holographic array are inversely proportional. This can be alleviated by a specially designed coherent fiber bundle array. In the case of the SLM, the core and cladding size of each fiber should fit the pixel design of a conventional SLM in one end (e.g., a 50/125-μm fiber is good for an SLM with a 50-μm SLM pixel size and a 125-μm pixel separation). In the other end, the separation of fibers can be made to fit the desired fill factor, as described previously. In the case of a photodetector array, a tapered fiber optic bundle technol­ogy8 can be applied to a conventional photodetector array. A tapered fiber optic bundle has a smaller core size and a higher packaging density at one end and an enlarged fiber core size and a lower resolution at the other end. Again, the primary problem of this alternative approach, to reducing the size of the holographic array, is that none of these fiber optic bundle arrays is available commercially. Because of this, it is necessary that they be designed and fabricated as custom items.

In summary, a holographic array with a medium N (e.g., N = 256) can be physically realized with current state-of-the-art optical technologies. For a large size N4 holographic array (e.g., N > 1000), however, specific efforts are required for SLM, photodetector arrays, fiber bundles, holographic materials, and many others.

The author gratefully acknowledges his colleagues, Tin Aye and Yong Qiao, for their technical comments on this paper.

References 1. P. Ambs, Y. Fainman, S. H. Lee, and J. Gresser, "Computerized

Design and Generation of Space-Variant Holographic Filters. 1: System Design Considerations and Applications of Space-Vari­ant Filters to Imaging Processing," Appl. Opt. 27, 4753-4760 (1988).

2. H. J. Caulfield, "Parallel N4 Weighted Optical Interconnects," Appl. Opt. 26, 4039-4040 (1987).

3. J. Shamir, H. J. Caulfield, and R. B. Johnson, "Massive Holo­graphic Interconnection Networks and Their Limitations," Appl. Opt. 28, 311-324 (1989).

4. Y. Tsunoda and Y. Takeda, "High Density Image-Storage Holo­grams by a Random Phase Sampling Method," Appl. Opt. 13, 2046-2052 (1974).

5. A. Iwamoto, "Artificial Diffuser for Fourier Transform Hologram Recording," Appl. Opt. 19, 215-221 (1980).

6. I. Satoh, M. Kato, K. Fujito, and F. Tateishi, "Holographic Mem­ory System for Kanji Character Generation," Appl. Opt. 28,2634-2640 (1989).

7. F. B. McCormick, "Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings," Opt. Eng. 28, 299-304 (1989).

8. D. C. Harrison and B. E. Burke, "Large Area Focal Plane Com­prising Charge-Coupled Devices and Fiber Optics," Opt. Eng. 26, 897-901 (1987).

10 December 1990 / Vol. 29, No. 35 / APPLIED OPTICS 5227