Testing MEMS switches can be independent of data rate

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By Gary Mading and Jim Boyd

Must vendors upgrade to faster test equipment to support higher data rates? The basic principles of the MEMS switching process demonstrate why BER tests at the OC-3 data rate are valid for data rates up to OC-768.

The component choices for all-optical switching are numerous and include microelectromechanical systems (MEMS), the most common type of switch among equipment manufacturers. Although new optical switches promise to alleviate bandwidth bottlenecks, vendors may think that upgrading to higher data rates requires the incorporation of faster test equipment. However, validation testing on dispersionless all-optical MEMS switches is bit-rate independent, as is the switch itself. The physical concepts behind N x N optical MEMS switches help explain why conducting bit-error-rate (BER) tests on optical switching systems at the OC-3 data rate is valid for data rates up to OC-768.

Internal routing of light in a MEMS optical switch is by free-space propagation, and the optical beam is collimated and focused via refractive and diffractive lenses, respectively. Typically, light emerging from the end of an input single-mode fiber (SMF) is collimated by a microlens and routed through the switch by movable micromirrors to an output SMF. The light is refocused by another lens to a small spot centered on the core of the output fiber (see Fig. 1). Different fabrication techniques can result in various mirror-movement schemes. Some mirrors rotate about a given axis by one or more precise angles, directing the collimated beam in multiple directions. Others rotate about two orthogonal axes. Still others rotate 90° about an edge, "flipping" the mirror into or out of a light path (on and off). Semiconductor processing allows the fabrication of MEMS in two-dimensional arrays, which can scale to an N x N optical switch.

An optical beam experiences three processes within the switch: reflection by mirrors, collimation by lenses, and free-space propagation. Otherwise, the photons are in a fiber outside the switch. These processes are a function of geometry and are not affected by the data rate imposed upon the optical beam. Beam alignment, numerical aperture, and optical scattering also affect switch operation, but they are mainly a function of geometry and not at all affected by data rate. If all of these factors are not executed properly in the switch, the switch may not perform to expectations, but such a shortcoming can be detected at OC-3 data rates as well as at the higher, more costly data rates. In other words, optical integrity measured at the OC-3 rate ensures the same optical integrity as testing at the higher rates.

OPTICAL PROPAGATION
The effective core of the SMF is approximately 8 μm in diameter. When light leaves the end of the fiber, the propagation is Gaussian.1 The optical beam spreads according to the equation

where w(z) is the 1/e2 radius of the emerging beam at a distance z from the end of the fiber, w0 is the radius of the fiber core, and zR is the Rayleigh range given by zR = πw02/λ (see Fig. 2).

In an optical MEMS switch, the expanding beam is collimated with a lens. The collimated beam may propagate approximately 10.16 cm or 101.6 mm before reaching a focusing lens. Further, a factor of √2 is accepted in the expansion of the collimated beam due to diffraction. This results in a lower limit of approximately 224 μm for the radius of the collimated beam. This result, combined with the 4-μm active radius of the fiber, determines the focal length of the collimating lens to be 1.82 mm. Correspondingly, this is the focal length of a "ball" lens with an index of refraction n = 1.5 and a diameter of 2.42 mm. The lens should be placed so that its first surface is 0.61 mm from the end of the fiber. The collimated light will have a 1/e2 radius of 224 μm and will contain essentially all of the energy that exited the fiber except for reflection and scattering losses (see Fig. 3).

After traveling 10.16 cm or 101.6 mm through air, the radius will expand by the factor 1.414 to 317 μm. Geometrically, the focusing lens can collect all of this energy. Because most of the light energy is collected by the lens, reasonable insertion loss and very little crosstalk between channels is expected in a switch like this. However, the loss will depend in large part on the alignment and stability of fibers and lenses. The loss and crosstalk also depend on the alignment and stability of the mirrors with each other and with the optical axes of the lenses. Other factors include optical scattering and reflection losses at the lenses and mirrors, and how far the collimated beam travels and expands before it is refocused. These factors are affected by the optomechanical design and fabrication of the MEMS but not by the data rate; nor do they affect the data rate. The above factors can be controlled well enough to achieve a crosstalk level of -60 dB.2

These equations and results are derived for the case of an unmodulated, propagating beam. When the beam is pulse-modulated, the propagation of electromagnetic waves is described by Maxwell's equations, which are linear, first-order, partial-differential equations. In a medium with a linear response, the time development of the wave is independent of the spatial development. Optical fiber is a nonlinear medium, leading to chromatic dispersion and four-wave mixing. However, the path through the air in the optical MEMS is linear. The nonlinear response of the glass lenses causes dispersion, but the path through the lenses is only 2.42 mm in our example. In the case of a modulated beam, the lens has an effect only if the modulated beam has a different wavelength composition than a continuous-wave beam. Therefore, lens-derived dispersion is entirely negligible for optical MEMS switches of the type considered here.

PULSE MODULATION
When a pure sine wave is pulse-modulated as an on/off square wave, side bands are generated at fc ± (2n + 1)fm, where fcis the frequency of the optical carrier fm is the modulation frequency, and nis an integer. A typical value for fc in the telecom C-band is 193.5 THz. Consider an OC-768 data rate where fDR = 40 GHz, which corresponds to a modulation frequency of fm = 20 GHz.

A pure optical wave of infinite duration would have a frequency of fm, whereas if it were pulse-modulated at fm it would also contain frequencies fc ± (2n + 1)fm. However, even monochromatic laser light contains a slight spread of frequencies about the nominal center frequency. The spectral bandwidth of semiconductor lasers ranges from about 10 MHz for wavelength-locked DWDM lasers to several hundred gigahertz for run-of-the-mill lasers. Thus, depending on the laser source, pulse modulation could add to the spectral width. For example, modulating a DFB laser with OC-3 data does not increase the spectral width beyond its 10-GHz value, whereas using a OC-192 data rate increases the spectral width to 20 GHz. None of these frequencies will cause a problem in the lenses because the effect is so small.

The focal length, F, of a lens is a function of the frequency of the light: F = F(f). If there is a spectral width to the beam, the focal length will "smear," causing a variability in the collimation and focusing properties of the lens (see Fig. 4). The effect of data rate on focal length in our example is negligible. Indeed, one could go to data rates of 240 GHz before ΔF/F = 0.001. At this data rate, the focused spot at the re-entrant fiber would widen in the propagation direction by ±2 μm for the 16th odd harmonic, and proportionally less for the lower harmonics. Therefore, the energy in the optical path is sensibly unaffected by available data rates.

Optomechanical variations such as flexing of the mirror or the base of the MEMS structure is a potential source of data-rate-dependent errors for the switch, from time periods of 6.4 ns (OC-3 rate) to 25 ps (OC-768 rate). Assuming the mirrors are made of silicon 100 μm thick and 500 μm2, the fundamental mechanical plate frequency is about 1 MHz. A large oscillation amplitude could cause noticeable insertion loss in a switch path or interchannel crosstalk. However, the period of this vibration is much larger than OC-3 or higher data rates, and such low-frequency effects can easily be detected.

Gary Mading is the chief technology officer at gnubi communications, 17919 Waterview Parkway, Dallas, TX 75252; Jim Boyd is a consulting optical scientist. Gary Mading can be reached at gary.mading@gnubi.com.

REFERENCES
1. A. Ghatak and K. Thyagarajan, "Introduction To Fiber Optics," Cambridge University Press (1998).

2. D. J. Bishop and V. A. Aksyuk, Electron. Design 47 (7) (1999).

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