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A procedure is described for the synthesis of electro-optic shutters having arbitrarily prescribed characteristics of transmittance vs voltage. The procedure is an adaptation of the birefringent-network-synthesis procedure of Harris et al. The synthesized shutter consists of n identical cascaded cells between an input and output polarizer. The synthesis procedure prescribes the angles to which the cells should be rotated and the angle of the output polarizer. Although it is assumed in this paper that each cell contains a Kerr-effect material, the synthesis procedure is equally applicable if each cell utilizes the Pockels effect. The technique of this paper is of possible use in many situations where standard Kerr-cell (or Pockels-cell) shutters are now employed. By controlling the shutter’s transmission vs voltage characteristic, we are able to control the shape and duration of the transmitted optical pulse independently of the form of the applied voltage pulse. Thus by this procedure the duration of the optical pulse resulting from a given applied voltage pulse can be reduced. Possible applications are briefly discussed in the areas of high-speed photography and Q switching of lasers.

Part III of this series gave several theorems concerning lossless birefringent networks and their properties. This paper uses some of these results to develop two methods of synthesizing lossless birefringent networks containing only half the number of crystals normally required. The two methods are modifications of the synthesis procedure of Part I of this series, and require fewer crystals because the light makes two passes through the network. The two methods complement each other, for in one case the output and input coincide (i.e., are spatially degenerate) while in the second case, the output and input are spatially separated.

Part I of this series described a procedure for synthesizing birefringent networks having arbitrarily prescribed amplitude transmittance. The network resulting from that procedure consists of a series of identical cascaded birefringent crystals between an input and output polarizer. We refer to such a network as a “lossless birefringent network” since it contains no internal polarizers. The variables determined by the synthesis procedure of Part I are the angles to which the crystals and the output polarizer are rotated. This paper proves several general theorems concerned with lossless birefringent networks. These theorems deal with (1) uniqueness; (2) the effect upon the transmittance of changing the sign of the angles of the crystals and output polarizer; (3) the effect upon the transmittance of turning the network end for end; and (4) the symmetry relations which the crystal and polarizer angles must satisfy when certain restrictions are imposed upon the desired amplitude transmittance.

Part I of this series reported a procedure for synthesizing birefringent networks having a prescribed amplitude transmittance. The desired transmittance C(ω) was written as C(ω) = C_0 + C_1e^−iαω + C_2e^−i^2aω + ⋯ + Cne^−inaω, where the Ci could be arbitrarily chosen as long as each was real. The synthesis procedure of this paper is a generalization of the procedure of Part I and allows for the realization of C(ω) having complex Ci. The resulting network consists of n stages between an input and output polarizer, with each stage containing a birefringent crystal and (achromatic) optical compensator. The form of this network is essentially the same as the practical form of the network obtained from Part I, and hence the additional versatility is obtained at no extra cost in network complexity.

A procedure for the synthesis of birefringent networks having arbitrarily prescribed transfer functions is presented. The basic network configuration consists of n identical cascaded birefringent crystals between an input and an output polarizer. The crystals are cut with their optic axes perpendicular to their length. The variables determined by the synthesis procedure are the angles of the optic axes of the crystals and the angle of the output polarizer. Any transfer function which is periodic with frequency and whose corresponding impulse response is real and causal can, in theory, be realized. A network of n crystals allows the approximation of a desired function by (n+1) terms of a Fourier exponential series. Bandwidths of less than 1 Å appear possible.

The usefulness of three-dimensional vector diagrams in analyzing optical systems is described. The diagrams involved are three-dimensional plots of the positive frequency spectrum of the signal. By using two diagrams to represent a given signal, one for each of two orthogonal linearly polarized components, information on signal polarization is also conveyed. Devices or systems are analyzed by noting how the diagrams of the input signal are successively altered by passage of the signal through the system. The techniques described are most useful with systems containing birefringent and dichroic elements, and with signals containing one or a few discrete spectral components. The diagrams can be used to determine both the output (optical) signal and the (rf) signal resulting from its detection by a square-law photodevice. Examples considered include two types of amplitude modulator, a single-sideband modulator, and a balanced optical detection system.

Optical-damage tests were performed on multilayer dielectric mirrors containing ZnS as one of the constituents. Tests were made by use of the 1.08-μm output of a continuously pumped, repetitively Q-switched Nd: YAlO_3, laser. Two distinct types of coating damage were observed: (i) damage to the surface layer of the coating when that layer is ZnS; and (ii) damage to intermediate layers of ZnS. The damage threshold for the former is approximately 40 MW/cm^2 and for the latter, 105 MW/cm^2. Experimental evidence indicates that surface-layer damage is triggered by some change that takes place on the surface of the ZnS layer upon exposure to the atmosphere. Although the exact nature of the surface process was not determined, several methods were found for avoiding surface-layer damage.

Procedures have recently been given by Harris et al. and by Ammann for synthesizing single-pass and double-pass birefringent networks having arbitrary transmittance-vs-frequency characteristics. This paper describes the results of experiments which were performed on these two types of optical networks. A three-stage network was tested in the single-pass experiments, while three-, five-, and seven-stage networks were used in the double-pass experiments. Each stage of these networks consisted of a calcite crystal 2 cm in length followed by a quartz compensator. The transmittance characteristics of the networks were obtained by measuring network transmittance (at a fixed optical frequency) as a function of network temperature. Since the phase difference between fast- and slow-axis light components passing through a calcite crystal has the same functional dependence upon temperature as upon optical frequency, the transmittance-vs-temperature characteristic of a birefringent network will be the same as the transmittance-vs-frequency characteristic. This gives a very convenient, high-resolution method of measuring the transmittance of birefringent networks. The measured transmittances are shown together with values predicted by theory. The excellent agreement obtained serves both as a verification of the synthesis procedures and as a demonstration of the utility of the measurement technique.

Many of the commonly used types of polarizers and polarizing beam splitters consist of two appropriately oriented birefringent crystals (of the same material) which are cemented together. This paper describes modified forms of Glan–Thompson and Rochon prisms in which one of the two calcite (or quartz) halves is replaced by an isotropic material such as glass. In addition to a saving of calcite, these devices have other advantages which add to their usefulness. Two types of modified Glan–Thompson prisms and two types of modified Rochon prisms are described. The modified Glan–Thompson prisms behave as Glan–Thompson prisms for light entering one end, and as Rochon prisms for light entering the other end. The modified Rochon prisms, on the other hand, behave like Rochon prisms regardless of which end light enters. Several commercially available glasses are listed which can be used with calcite or quartz in these devices.

A second technique for the synthesis of birefringent networks having arbitrarily prescribed spectral transmittance is presented. The network consists of an input polarizer followed by n cascaded stages. Each stage contains (in general) a birefringent crystal, an optical compensator, and a polarizer. The quantities determined for each stage by the synthesis procedure are the angle to which the crystal is rotated, the amount of delay to be introduced by the optical compensator, and the angle of the polarizer. A desired function consisting of (n+1) terms of an exponential series can be realized by an n-stage network and, in certain cases, by a network containing fewer than n stages. The synthesis procedures of Part I and Part II are compared, and their relative merits discussed. Finally, two examples are given using the procedure of Part II.

Many devices operate between input and output polarizers. With such devices, the component of the incoming light which is polarized perpendicular to the transmission axis of the input polarizer is lost. We describe a modification which can be applied to many of these devices which allows all of the incoming light to be utilized, thereby enabling the device to be used with light of any polarization. The use of this modification on electro-optic shutters and AM modulators is discussed, and the results are generalized to show when and how the technique can be applied to other devices. The modification consists of replacing the input and output polarizers by calcite crystals whose end faces are flat and parallel. Double refraction occurs in the first calcite crystal, dividing the incoming light into ordinary and extraordinary rays. These rays emerge from the crystal traveling parallel to each other, but spatially separated. They are next operated upon by the device in question, which, in general, will alter their polarizations. The desired components may then be selected and recombined by the second calcite crystal followed by an iris. Experimental results are given for a KDP modulator which has been modified in this manner.

Part IV of this series gave two procedures (termed double-pass procedures) for synthesizing birefringent networks containing only half the number of crystals normally required. These techniques were applicable when the desired amplitude transmittance of the network satisfied certain restrictions. This paper describes additional double-pass procedures which apply to a substantially larger class of amplitude transmittances.