Computer Science and Technology

Aerospace Design Techniques

The design of early airplanes was characterized by the "cut-arid-try" approach¹; that is, various reasonable designs were evolved and then sample airplanes² were built for trial in flight. This approach worked well as long as airplanes were fairly simple and inexpensive. But, for high-performance airplanes, the cut-and-try approach turned out to be prohibitively costly. When such an airplane is constructed, it has to fly. Modeling techniques, using computers, allow an airplane to be "flight tested" before it is built! So accurate is the simulation that nearly optimal designs can be developed on the drawing board³ and actual test flights are used only to verify the design and make minor modifications.

The Age of Space

The space age gave birth to its own complexities! Not only were the problems more difficult, but the answers had to be found faster. As the rocket flies toward the moon, researchers "fly" its trajectory in the computer. Lunar gravity, atmospheric drag, equatorial bulge of the earth, and the forces generated by corrective rocket bursts⁵ must all be taken into account together with several other forces and pertur­ bations. In some cases, the calculations must be made in real time while the rocket is plummeting through space at 25,000 miles per hour. There is no way of doing this without computers. Indeed, vir­ tually every branch of science would long have been stopped by mathe­ matical stone walls if the electronic computer had not come to the rescue. .. .._...

The Atomic Age

The atomic age brought out new complexities. Quantum mechanics forced the abandonment of the deterministic view of nature and the statistical approaches to science increased the number of required calculations by orders of magnitude. There was no simple way to pre­dict the behavior of neutrons in a slab⁶ of uranium involved in a chain reaction. Each individual particle had to be followed mathematically as it collided with its neighbors and produced new neutrons in everincreasing numbers. The children and grandchildren of each new wave of collisions had to be tracked as they made their way through the ura­nium and out into the surrounding world.

This kind of mathematical simulation is called a Monte Carlo procedure. In its simplest form, it consists of making numerous indi­vidual simulations of a process to see how it behaves under statistical variations.

Machine Language

A computer cannot understand English or any other human lan­guage directly. It understands only its own language, called machine language, which varies from one computer system to another. Instruc­tions in such a language consist of a sequence of letters and/or numbers that are unintelligible to us unless we are trained as computer systems experts (not just users or programmers) well-acquainted with that particular computer.

Prior to about 1958, a computer programmer had to write his instructions in such a machine language. This required very extensive training, much of which was wasted effort because, as newer computer systems were introduced, the language might change completely. Because of the tenuous connection between the appearance of machine language instructions and the language in which we think, computer programming was tedious and prone to error.

User-oriented programming languages

The disadvantages of direct machine language programming have now been overcome and the human-computer gap closed somewhat by the introduction of what are called user-oriented languages. These are ways of stating instructions by using English terms, although the instructions that result may not seem very much like our everyday conversation, they will at least have some degree of intelligibility to human beings.

The computer does not directly follow instructions that are expres­sed in such user-oriented languages; it wouldn't understand such ins­tructions. The instructions must be translated to machine language. This is done by a special preliminary program written by experts well-acquainted with the particular computer involved. This program is called the compiler¹.

The compiler does much more than interpret instructions; it also finds programming errors that might have occurred and describesthem to the user by printing out comments called diagnostics. If the user-oriented language program is free of such errors, it produces the machine language program, called the object program². When the com­putations are to be executed (performed), it loads the object program into the computer's memory. Your program will then be ready to use.

Many user-oriented languages have been proposed. During the 1969's, the two most important languages for general computer use were Algol and Fortran. Many computer systems have (or had) compi­lers for both languages so that either could be translated into machine language.

Algol and Fortran were intended primarily for scientific program­ming and another language, easier to understand, called Cobol, -was devised for the less sophisticated requirements of routine business programming. The real computer users — laboratory technicians, civil engineers, and biology professors —could now learn to code their own problems. Computer programming was thus no longer the exclusive stomping ground of a few thousand highly trained specia­lists.

The Asymmetric Slab Waveguide¹ ;

Dielectric slabs are the simplest optical waveguides. Because of their simple geometry, guided and radiation modes² of slab waveguides can be described by simple mathematical expressions. The study of slab waveguides and their properties is thus often useful in gaining an understanding of the waveguiding properties of more complicated dielectric waveguides. However, slab waveguides are not only useful as models for more general types of optical waveguides, but they are actually employed for light guidance in integrated optics circuits.

A dielectric slab waveguide is shown schematically in the figure. The figure shows a slab waveguide as it would be used in a typical integrated optics application. The core region of the waveguide is assumed to have refractive index ni and is deposited on a substrate with refractive index n₂. The refractive index of the medium above the core is indicated as n₃. The refractive index n₃ may be unity if the region above the core is air, or it may have some other value if the guiding region of index n_x is surrounded by dielectric materials on both sides. In order to achieve true mode guidance it is necessary that «i be larger than n₂ and n_s. In order to have a specific example we shall assume that

n_x> «₂>n₃ ■ (1-1.1)

If n₂ = n₃, we speak of a symmetric slab waveguide. In case that n₂ =£ n₃, the slab waveguide is asymmetric. The modes of symmetric slab waveguides are simpler than those of asymmetric slabs because they can be expressed either as even or odd field distributions. The lowest-order mode of a symmetric slab waveguide does not have a cutoff frequency⁴, which means that, in principle, this mode can propa­gate at arbitrarily low frequencies. By contrast, all modes of asym­metric slabs become cutoff if the frequency of operation is sufficiently low.

Like all dielectric waveguides the asymmetric slab supports a fi­nite number of guided modes which is supplemented by an infinite continuum of unguided radiation modes. Both types of modes are obtained as solutions of a boundary value problem. However, the guided modes can also be considered from the point of view of ray optics. Since ray optics is more clear than wave optics, we start the discussion by deriving the eigenvalue⁵ equation of the guided modes from geometrical optics, which is supplemented by some simple results of plane wave⁶ reflection and refraction at plane dielectric interfaces.

In integrated optics applications, slab waveguides are formed by various means, the simplest of which use the deposition of glass or plastic films on glass or plastic substrates. These films can be deposi­ted by various methods. One method of forming dielectric optical wa­veguides for integrated optics applications employs ion implantation techniques⁷. By bombarding the substrate material with suitable ions it is possible to alter the refractive index of the substrate so that a dielectric slab waveguide results.The depth at which the guiding re­gion appears below the substrate surface can be controlled by the choice of the energy that is used to accelerate the ion beam.

Many integrated optics applications use narrow dielectric strip waveguides instead of a continuous two-dimensional film. Such wave­guides are formed by ion implantation techniques or by the deposition of a thin film on top of a substrate which is subsequently etched away_i so that only the narrow strip waveguides are left.

The study of asymmetric slab waveguides serves as a valuable introduction to the entire field of dielectric optical waveguides. Because of their simplicity, slab waveguides provide insight into the mechanism of waveguidance by dielectric optical waveguides.