In this section, we perform simulations for a 10m-long PCF and the input squared hyperbolic secant pulse with the envelope of\(\text{A}\left(0\text{,}\text{t}\right)=\sqrt{{\text{P}}_{0}}{\text{sech}}^{2}(\frac{t}{{T}_{0}})\). Here, T0 is the pulse width and P0 is the peak power. The central wavelength of the pulse is set at 800 nm which is desired for OCT in ophthalmology[30].
Figure 1 shows the cross section of the designed silica-based PCF used for generation of supercontinuum for OCT in ophthalmology. The air–hole diameters of the first, second, third, fourth and fifth ring are d1 = 0.26µm, 0.31µm, 0.36µm and 0.41µm, respectively. Also, the lattice pitch is 0.85µm.
Dispersion curves of the designed PCF for different values of first ring air-hole diameters d1 are shown in Fig. 2. We have used the dispersion relation as \(D=-\frac{\lambda }{c}\frac{{d}^{2}{n}_{eff}}{d{\lambda }^{2}}\) to plot dispersion curves where \({n}_{eff}\) is the effective refractive index of the fundamental mode [11]. As it is seen, by changing d1, the dispersion curve is changed where the flattest curve around 0.8µm is obtained for d1=0.41µm. By taking successive derivatives of each dispersion curve in Fig. 2, one can obtain the curves for different orders of the dispersion coefficients (\({\beta }_{m}={\left(\frac{{d}^{m}\beta }{d{\omega }^{m}}\right)}_{\omega ={\omega }_{0}}\)) versus the wavelength for the given d1 as shown in Fig. 3. However, for sake of brevity, only the curves for d1=0.41µm are shown in Fig. 3. Since the pump wavelength is chosen at 0.8 µm, the values of dispersion coefficients at this specific wavelength are required for simulation of GNLSE. Therefore, the linear and nonlinear parameters of the PCF calculated at 0.8µm for each air-hole diameter are listed in Table 1. Using these parameters and solving GNLSE via SSF method, one can simulate the SCG spectra as shown in Fig. 4. The pump peak power is P0=150W and pulse width is T0=1.5ps. As it is evident, the spectra depend on the air-hole diameter where the widest spectrum is achieved for d1=0.41µm. This is in consistent with the result obtained from Fig. 2 where the flattest dispersion curve was obtained for d1=0.41µm. The 10-dB width is usually used as a measure of the spectral width which is given in Table. 2. As it is obvious, the 10-dB width for the PCF with d1=0.41µm is maximum.
According to Table 2, the best bandwidth and resolution are obtained for the PCF with d1=0.41µm; therefore, we fix the air-hole diameter at d1=0.41µm for following simulations. In Fig. 5, the SCG spectra are shown when the pump width T0 is changed. Evidently, as the pulse width decreases, the spectrum is widened so that the widest spectrum is obtained for T0=30fs.This means that for T0=30fs, the 10-dB spectrum bandwidth is Δλ =62.0 nm which corresponds to the highest axial resolution of lc=4.5µm.
Table 3 lists the 10-dB bandwidths as well as the OCT axial resolutions calculated at each pump width T0 for the fixed air-hole diameter of d1 = 0.41µm. As it is seen the best bandwidth and resolution are obtained for the pulse width of T0 = 30fs; therefore, we fix the simulation parameters at T0 = 30fs and d1 = 0.41µm and then examine the role of pulse peak power in SCG spectrum and its 10-dB bandwidth. This is shown in Fig. 6 where the SCG spectra are plotted when the pump peak power is changed from P0 = 150W to P0 = 750W.
Table 4 lists the 10-dB bandwidths Δλ as well as the OCT resolutions lc calculated at different pump peak powers P0. It can be seen that by increasing the peak power, the SCG bandwidth and the OCT resolution are improved so that the best bandwidth and resolution are obtained for the pump with the peak power of P0=750W. Therefore, totally the best SCG bandwidth and OCT resolution are achieved when the squared hyperbolic secant pump pulse with P0=750W and T0=30fs is input into the PCF with d1=0.41µm. Obviously, this best bandwidth results in the best OCT resolution of 2.6µm for ophthalmology. This means that the supercontinuum generated from the designed PCF (see Fig. 1) is a very good candidate as a OCT source for ophthalmology since it can provide high quality images with resolutions as high as 2.6µm.