plot

Plots the surface thermal response.

Syntax

plot(fm, M, O, chi, f0, X_probe, Name, Value)

Description

Examples

Input Arguments

M - Material parameters \(N_m \times N_T\) real matrix | \(N_m \times N_T \times N_\mathrm{pump}\) real matrix | \(1 \times N_m\) cell

Material parameters include thermal conductivity, volumetric heat capacity, optical absorption coefficient, optical reflectivity (omitted if fm.c_args.phase_only is true), thickness in the z-direction, and thermal contact resistance for the film and substrate of the sample.

The shape of M may be either:

  • \(N_T\)-by-fm.fun_inputs.M.ncols, or
  • \(N_T\)-by-\(N_\mathrm{pump}\)-by-fm.fun_inputs.M.ncols
    • Use only when fm.fun_inputs.O.ncols equals 0.
    • If only one temperature is considered (\(N_T = 1\)), the first dimension may be dropped, so that M is an \(N_\mathrm{pump}\)-by-fm.fun_inputs.M.ncols matrix.

The axes of M represent:

  • Parameter variation wrt. temperature (\(N_T\)),
  • Parameter variation wrt. pump laser location (\(N_\mathrm{pump}\), if present),
  • Material parameter type, as listed in fm.fun_inputs.M.cols.

Additional constraints on M:

  • The size of the parameter axis (i.e., size(M,ndims(M))) must equal fm.fun_inputs.M.ncols.
  • If fm.c_args.log_args is false, all elements of M must be positive.
  • If fm.c_args.phase_only is false, elements corresponding to optical reflectivity must lie within [0,1].

Data Types: double | single

Examples:

If fm.c_args includes the following fields: 


film_isotropy: "iso"
 sub_isotropy: "iso"
inf_sub_thick: 1
   phase_only: 1
     log_args: 0

Then

  • fm.fun_inputs.O.ncols equals 0
  • fm.fun_inputs.M.ncols equals 8
  • fm.fun_inputs.M.ncols equals [kf, Cf, αf, hf, ks, Cs, αs, Rth]
O - Orientation parameters real matrix

Data Types: double | single

chi - Experimental parameters real vector

Data Types: double | single

f0 - Pump laser frequencies nonnegative real vector

Data Types: double | single

X_probe - Probe laser offsets nonnegative real 2-column matrix

Data Types: double | single

Parameter Nomenclature
  • kf:
  • kf:
  • kf
  • kf
  • kf
  • kf
  • M: Material parameters.
    • kf, ks: Isotropic thermal conductivity of the film and substrate.
    • kf⊥, ks⊥: Transverse (radial) thermal conductivity of the film and substrate (simple anisotropy).
    • kf∥, ks∥: Axial (longitudinal) thermal conductivity of the film and substrate (simple anisotropy).
    • kpfi, kpsi: \(i\)-th principal thermal conductivity of the film and substrate (complex anisotropy), with \(i \in \{1,2,3\}\).
    • kfij, ksij: \((i,j)\)-th component of the thermal conductivity tensor of the film and substrate, with \(i,j \in \{1,2,3\}\).
    • Cf, Cs: Volumetric heat capacity of the film and substrate.
    • αf, αs: Optical absorption coefficient of the film and substrate.
    • Rf, Rs: Optical reflectivity of the film and substrate.
    • hf, hs: Thickness of the film and substrate in the \(z\)-direction.
    • Rth: Thermal contact resistance between film and substrate.
  • O: Orientation parameters.
    • θf_az, θs_az: Azimuthal angle of the thermal conductivity axis of rotation for the film and substrate (simple anisotropy).
    • θf_pol, θs_pol: Polar angle of the thermal conductivity axis of rotation for the film and substrate (simple anisotropy).
    • θfai, θsai: \(i\)-th Euler rotation angle about the \(a\)-axis, defining the orientation of the principal thermal condcutivity axes of the film and substrate, with \(i \in \{1,2,3\}\), \(a \in \{X,Y,Z\}\).
    • vfi, vsi: \(i\)-th component of the unit vector along the thermal conductivity axis of rotation for the film and substrate (simple anisotropy), with \(i \in \{1,2,3\}\).
    • qfi, qsi: \(i\)-th component of the unit quaternion defining the orientation of the principal thermal condcutivity axes of the film and substrate, with \(i \in \{1,2,3,4\}\).
    • Rfij, Rsij: \((i,j)\)-th component of the rotation matrix defining the orientation of the principal thermal condcutivity axes of the film and substrate, with \(i,j \in \{1,2,3\}\).
  • chi: Experimental parameters.
    • sx, sy: Standard deviations of the pump laser's distribution in the \(x\)- and \(y\)-directions.
    • P: Pump laser power.
  • f0: Pump laser temporal frequency.
  • X_probe: Probe laser offsets, with each row being the \(x,y\)-coordinate of the probe wrt. the pump.

Output Arguments

See Also