Getting started

ctmm is intended to form a backend to other software, rather than be used directly, in particular via the python bindings. The following brief example demonstrates how ctmm can be used directly from C to model a single layer of glass surrounded by air at normal incidence.

In order to use ctmm the header file ctmm.h must be included, and the shared library produced during the compilation step linked against.

#include "ctmm.h"

A ctmm_stack can then be created and initialised with

ctmm_stack stack;
stack = ctmm_create_stack(3, 633e-9, 0);

ctmm_create_stack takes three arguments, the number of layers (3), the illuminating wavelength (633e-9 nm HeNe laser here) and the angle of incidence (in radians).

Layer properties are set with the ctmm_set_ind and ctmm_set_d functions. All ctmm functions take a ctmm_stack as the first argument. For both the set index and set thickness (d) functions, the second argument is the layer number to set. For ctmm_set_ind this is follow by the real and imaginary components of the refractive index, likewise for ctmm_set_d this is followed by the layer thickness. For our air-glass-air example, the properties will be set with

ctmm_set_ind(stack, 0, 1, 0);
ctmm_set_ind(stack, 1, 1.5, 0);
ctmm_set_ind(stack, 2, 1, 0);

ctmm_set_d(stack, 0, 0);
ctmm_set_d(stack, 1, 0.25*(633e-9));
ctmm_set_d(stack, 2, 0);

The stack transfer matrix can then be evaluated with

ctmm_evaluate(stack);

If only the matrix is needed, a pointer to the ctmm_matrix transfer matrix can be obtained with

ctmm_matrix *tmat;
tmat = ctmm_get_matrix(stack);

The ctmm_matrix type is a typedefed struct with a single member, a fixed size array of ctmm_complex represeting a 4x4 matrix in row major order.

The ctmm_complex type is another typedefed struct that mimics the structure of the C99 complex type, and exists purely to simplify the process of writing ctmm for both C99 and non-C99 compliant compilers. On systems where the C99 complex type is available, the ctmm_complex type should be compatable.

Individual elements of a ctmm_matrix can be accessed with

ctmm_complex elm;
elm = ctmm_matrix_get(tmat, 0, 0);

In this case accessing the element (0, 0).

ctmm can also calculate the amplitude and power reflectivity and transmission coefficients for each polarisations, as well as the phase change on reflection and transmission with the following ctmm_rtc, ctmm_rts and ctmm_rtps functions

ctmm_complex rtc[4];
double rts[4];
double rtps[8];

ctmm_rtc(stack, rtc);
ctmm_rts(stack, rts);
ctmm_rtps(stack, rtps);

where rtc is an array of the amplitude reflectivity and transmission coefficients, rts is an array of the power reflectivity and transmission coefficients, and rtps is an array of the power coefficients, and the phase changes on reflection and transmission for each polarisation.

Once the stack is no longer needed, the allocated memory must be freed with

ctmm_free_stack(stack);