In the present communication, a procedure for the synthesis of an optical finite impulse response (FIR) birefringent filter
generating arbitrary spectral output is presented. The basic filter consists of a cascaded system of n identical retarders
between two polarizers at the two ends. A mathematical model of the optical FIR filter is introduced using the FIR
theory of digital filter design. The parameters determined by the synthesis procedure are the angles of the optic axes of
the individual crystals and the angle of the output polarizer. Classical FIR filter design method along with the optical
backward transfer technique has been used. Two different arbitrarily specified spectral output profiles have been studied.
However, the method is equally applicable for any periodic transfer function whose corresponding impulse response is
real and causal.
Phase retarders usually exhibit strong wavelength dependence. For this paper, the design and characteristics of an achromatic cascaded system of birefringent plates were studied. The combination of three retarders in a series had been previously proposed by Pancharatnam, and he discussed the possibility of fabricating reasonably good achromatic quarter-wave plates with a suitable level of retardance. This combination, however, still shows substantial variation in terms of retardance within 500 to 700 nm. Here, the combination of four plates for the construction of an almost achromatic quarter-wave plate, which has a variation of only ± 1 degree over the wavelength spectrum of 500 to 700 nm, is proposed. Moreover, spherical trigonometric considerations have been used by Pancharatnam for obtaining the transmission characteristics of a cascaded system. We, however, used the succinct and relatively simple Jones matrix formalism to derive a general expression for the equivalent retardation of this combination. The proposed arrangement of four birefringent plates promises better achromatic combinations.
Birefringent wave plates, often referred to as retarders, generally exhibit a strong wavelength dependence. However, there is a real need for achromatic retarders that exhibit identical characteristics over a broad wavelength range. In this paper, we have studied the design and characteristics of a cascaded system of birefringent plates in the near infrared region. Here we have studied a cascaded system of three birefringent plates using matrix analysis and designed a system which, by suitable reorientation of one of the plates, may perform both as an achromatic quarter-wave plate and half-wave plate, over the wavelength range of 1000 to 1800 nm. An inexpensive design for such an achromatic combination using crystalline quartz is described. The new arrangement of three birefringent plates proposed has the promise of producing achromatic combinations with fairly good accuracy.
A technique is described for the continuous variation of the resultant retardance and effective privileged directions of a cascaded system of three optical retarders. The system consists of a rotatable retarder sandwiched between two fixed, identical, parallel retarders. The primary aim of the study was to develop a simple technique for a variable retarder for monochromatic light, but the robustness of the system for a narrow band on either side of the design wavelength was also studied. Simulated plots show that a linear variation of the effective retardance from 0 to 2 is achievable, as is a linear variation of the effective azimuth from 0 to . It is also shown that these two parameters may be varied independently of each other.
Conference Committee Involvement (1)
XXXIX Conference of Optical Society of India International Conference on Optics and Photonics