ASYMMETRIC FABRY-PEROT MODULATORS

Several groups in the early and mid-1990’s developed asymmetric Fabry-Perot modulators (AFPMs), generally in this AlGaAs/GaAs same material system [6-11]. Normally, the goal was to lower the voltage drive while improving the contrast ratio.  As such, peak contrast ratios greater than 20 dB (100:1) were observed [6, 7].   Most modulators that have claimed “low voltage operation” in the literature refer to a voltage drive 4 V or greater.  These low voltage designs also have quite small wavelength ranges, sometimes a fraction of a nanometer (e.g. [6]).  Perhaps the best result in the literature is the modulator of Yan et al. [9].  This device used only 2 V drive to achieve a contrast ratio of 3 dB over 5 nm, with a peak contrast of 7 dB (5:1).   Theoretical studies also looked at optimizing these modulators [12-15].

While these results are quite impressive in many regards, our goals were slightly different.  For short distance optical interconnects, it makes more sense to achieve decent contrast ratio over a wide range of wavelengths than to post an extremely high contrast ratio for a small range of wavelengths, as discussed in Chapter 3.  Furthermore, since the epitaxial growth techniques are complicated and expensive, a simpler, thinner epitaxial structure would be more practical and less costly in both time and dollars.  Finally, the thickness of a layer in an epitaxial structure cannot be perfectly determined during the growth.   Variations in conditions, especially temperature, cause variations in thickness and composition that can easily alter the absorption characteristics of the MQW region by several nanometers in wavelength.  Thus we were faced with the challenge of developing both a mathematical handle on a simple AFPM and a practical post-growth experimental technique for adjusting to growth variations.

TRANSFER MATRIX METHOD MODELING

Though this simple analytical solution is intuitively satisfying, in practice a computer simulation proved useful in order to vary several factors simultaneously, such as layer structure, wavelength, voltage, thickness, and refractive index.  The simulation needed to model a 1D stack of materials, representing all the refractive indices and absorptions as complex indices, and solving Maxwell’s Equations.  One of the most time- efficient techniques for solving this problem is called the transfer matrix method.

In the transfer matrix method, a matrix is composed for each layer and each interface, according to the rules for electromagnetic waves in dielectric media according to Maxwell’s equations.  The propagation of the wave and the continuity of the various vector quantities at boundaries can be represented by these matrices.   By successively applying these matrices to each other, it becomes possible to determine not only the

reflection and transmission characteristics of the dielectric stack, but also the electric fields or intensities as a function of distance inside the stack [17].

The software package MATLAB is optimized for matrix manipulation, so many calculations can be done in sequence, enabling optimization routines that run in real time. For example, the thickness of a particular layer can be altered between 100 and 200 nm in steps of only 1 nm, and the entire simulation can still finish in seconds.  Effects such as the Gaussian beam profile of the laser focus can also be included by superposing plane

waves.

For the refractive indices, published values were typically used where available, especially equations for interpolating the index for AlxGa1-xAs.  The MQW region was approximated as a bulk material with a complex index of refraction corresponding to its absorption, derived from the following experimental procedure.  First a p-i-n diode test structure was processed.  Then the device was inserted into our probe station setup and the photocurrent was measured as the voltage across the diode and the wavelength of an incident laser were varied.  Assuming that every photon subtracted from the optical beam corresponded exactly to one electron-hole pair collected electrically, the effective absorption coefficient of the MQW region can be calculated [1].  Then adjustments to the refractive index of the MQW region are derived via the Kramers-Kronig relations.  These steps result in data of the effective absorption coefficient and refractive index of the MQW region as a function of wavelength.  In the transfer matrix simulations, the MQW region was thus approximated as a quasi-bulk material with a complex refractive index that varied as a function of both wavelength and reverse bias.