UM 2p5 parameters 4

User Manual Index > 2.5 Parameters

2.5.4 Keywords for mode seeking

– wavelength = λ [real]: Wavelength at which the simulation should be run. When material dispersion is not taken into account, all length are relative and the wavelength is relative to the lengths defined by the structure. When material dispersion is taken into account, all length, including the wavelength, are assumed to be expressed in micrometers. Other keywords affecting this value: start_lambda. (Synonyms: WAVELENGTH, wl, WL, lambda)

– n_eff_0 = nef f 0 [complex]: Defines the lower left corner of the region of effective index (in the complex plane) in which modes will be searched. By lower left corner we mean the corner of the rectangle of the complex plane with smallest real part and smallest imaginary part (see Fig. 2). (Synonyms: start_neff, start_index, lower left n_eff corner)

– stop_n_eff = stop_n_eff [complex]: Defines the upper right corner of the region of effective index (in the complex plane) in which modes will be searched. By upper right corner we mean the corner of the rectangle of the complex plane with largest real part and largest imaginary part (see Fig. 2). Important: start_n_eff has to be used before stop_n_eff is used. (Synonyms: upper right n_eff corner, final n_eff, stop n_eff, stop neff)

– n_eff_width = n_eff_width [complex]: Defines the region of effective indices in the complex plane in which to search modes by its width: The scanning region will go from n_eff_0 to n_eff_0+n_eff_width (see Fig. 2). (Synonyms: N_eff_width, N_EFF_WIDTH, n_width, N_WIDTH)

IMPORTANT NOTE: the real part of stop_n_eff and start_n_eff should always differ from values taken by the structure’s refractive indices, or severe numerical errors could stop the program’s execution. Indeed if nef f is exactly equal to the refractive index of the matrix (orbinclusions etc.), the value zero will appear as the argument of Hankel functions, which diverge in zero. Example: if you’re interested in finding the fundamental mode of a solid core MOF with matrix refractive index (1.45,0), and you expect the fundamental mode to have an effective index with real part close to 1.45, do not set the real part of stop_n_eff to 1.45, but to eg 1.449999.

– num_n_points = number_n_points [integer]: Defines the number of points par- allel to the real axis on which the determinant is computed for the initial determinant map. The determinant will be computed for num_n_points+1 points on each line paral- lel to the real axis (see Fig. 2). This parameter must be greater or equal 4. Its default value is 100. The ideal value of this parameter depends on the expected density of modes and the width of the scanning region. The density of modes in the nef f space depends on the complexity of the structure and the wavelength (it increases with de- creasing wavelength). If one approximately knows where a mode is (for example if a similar structure with a smaller number of rings has been studied before) a value of 20 or even 10 for num_n_points can be enough. For a large scan or for complex struc- tures values of 100 or 200 are more appropriate. When looking for a bandgap guided mode, values of 500 for a range of effective indices of 1e-2 are not excessive. If this parameter it too small, some modes might not be found, if it is too large, computing the map will be unnecessarily slow.

– num_ni_points = num_ni_points [integer] Defines the number of points parallel to the imaginary axis on which the determinant is computed for the initial determinant map (see Fig. 2). The map will be computed for num_ni_points+1 points for each value of the real part of nef f . This parameter must be either 0 (if (nwidth ) = 0) or greater or equal to 4. Its default value is 4 if (nw idth) = 0 and 0 otherwise. As the scan along the imaginary axis is exponential, a value of 4 (8 for some bandgap guided modes) is generally sufficient. If the structure has a very good confinement (ie. if the imaginary part of the effective index of the computed modes is expected to be less than 10−13 ), setting this parameter to zero is not only useful but necessary.

– start_mode = first mode [integer]: Sets the first class of symmetry [4] for which modes are searched. When modes belonging to a twofold degenerate symmetry class are sought, at least the first of the two degenerate symmetry classes must be included in the range of symmetry classes: If, say, classes 3 and 4 are degenerate, start_mode can not be set to 4, but must be set to 3 to find the modes belonging to symmetry classes 3 (and 4). (Synonyms: first mode, start mode)

– stop_mode = last mode [integer]: Sets the last class of symmetry [4] for which modes are searched. fibre will search for modes in all classes of symmetry between start_mode and stop_modes. (Synonyms: last mode, stop mode) Degenerate modes are computed simultaneously, so that it does not make a difference on computational time to ask for only one or both of two degenerate mode classes. A determinant map is computed for each non-degenerate mode class or pair of de- generate mode classes: computing the determinant map is the slow part of the code, so restricting the number of symmetry classes is a good way of saving time when a specific mode (eg the fundamental mode) is sought. When no symmetries are used, the only valid class of symmetry is 1, so that start_mode and stop_mode must be set to 1.

Action keywords

– suggest n_eff range = mode [character string]: This keyword adjusts the range of effective indices to find a specific mode specified as the argument. This has been implemented only for solid core MOFs with C6v symmetry, no jacket or cladding, matrix refractive index close to the refractive index of silica and low index inclusions with refractive index around 1. The range of classes of symmetry is adjusted to the class of symmetry of the considered mode. The argument should be one of the following values:

– fundamental Adjusts the range of effective indices and the class of symmetry to find the fundamental mode of the structure. (Synonyms: Fundamental,FUNDAMENTAL, FUND, fund, fundamental mode, 1)

– second Adjusts the range of effective indices to find the second mode of the structure. The automatic adjustment of the range of effective indices for the second mode is experimental and should not be relied upon. (Synonyms: 2, second mode)

Before suggest n_eff range is used, a structure (see Sec. 2.5.2) must have been defined.

– search modes (no arguments) Runs the simulation to find the modes. Before this keyword is used, a structure (see Sec. 2.5.2), the order of truncature of Fourier-Bessel expansion (see order, gorder and suggest order, Sec. 2.5.7), the wavelength (see wavelength, above), a range of effective indices (see n_eff_0, stop_n_eff, n_eff_width and suggest n_eff range) and the classes of symmetry to search for (see start_mode, stop_mode and suggest n_eff range) must have been defined. (Synonyms: modesearch, SEARCH MODES, MODESEARCH, mode search)