Computation of bessel functions in light scattering studies

Area of Science:

• Computational physics
• Numerical analysis
• Electromagnetic theory

Background:

• Light scattering computations necessitate Bessel functions of various orders.
• Recurrence relations are the easiest method for computing Bessel functions, but prone to accumulating rounding errors.
• Existing methods may not provide sufficient accuracy for all applications.

Purpose of the Study:

• To describe satisfactory procedures for computing Bessel functions for cylinder and sphere scattering.
• To present methods that minimize rounding errors in Bessel function calculations.
• To address computations for both real and complex arguments.

Main Methods:

• For real arguments: Recurrence to high orders for Y(n)(z), estimation of J(n)(z) from two high orders of Y(n)(z), backward recurrence to maximum J(n)(z), and correction by forward recurrence.
• For complex arguments: Estimation of high orders of J(n)(z) without Y(n)(z), followed by backward recurrence.
• Implementation of stable recurrence procedures for Bessel functions.

Main Results:

• Demonstrated procedures for accurate Bessel function computation for cylinder and sphere functions.
• Successfully minimized cumulative rounding errors in recurrence calculations.
• Developed distinct, effective methods for real and complex arguments.

Conclusions:

• The described recurrence procedures provide accurate Bessel function values for light scattering computations.
• These methods enhance the reliability of numerical simulations involving Bessel functions.
• Applicable to a wide range of scientific and engineering problems requiring Bessel functions.