Optical Soliton Fundamental Power Calculator

Nonlinear optics & ultrafast photonics: Model fundamental ($N = 1$) temporal solitons, balancing anomalous group velocity dispersion ($\beta_2 < 0$) with self-phase modulation (SPM).

Pulse & Fiber Parameters

Pulse FWHM Duration $\tau_{FWHM}$ (ps):

Wavelength $\lambda$ (nm):

Dispersion Parameter $D$ (ps/(nm·km)):

Effective Mode Area $A_{eff}$ ($\mu\text{m}^2$):

Nonlinear Index $n_2$ ($10^{-20} \, \text{m}^2/\text{W}$):

Actual Peak Power $P_{peak}$ (W):

Soliton Dynamics & Characteristic Scales

Fundamental Soliton Power $P_0$

W (for $N = 1$ balance)

Soliton Order $N$

$N = \sqrt{L_D / L_{NL}}$

GVD Parameter $|\beta_2|$

$\text{ps}^2/\text{km}$ (anomalous)

Dispersion Length $L_D$

km ($T_0^2 / |\beta_2|$)

Soliton Period $z_0$

km ($(\pi / 2) L_D$)

Soliton Pulse Energy $E_0$

pJ ($2 P_0 T_0$)

Fundamental Soliton $\text{sech}^2(t/T_0)$ Envelope

At $N = 1$, the non-linear self-phase modulation chirp exactly cancels anomalous dispersion, maintaining invariant shape over thousands of kilometers.

Nonlinear Schrödinger Equation (NLSE) Physics

Pulse propagation in optical fibers is governed by the Non-Linear Schrödinger Equation (NLSE). When losses are neglected or compensated by distributed Raman amplification:

          $$i \frac{\partial A}{\partial z} - \frac{\beta_2}{2} \frac{\partial^2 A}{\partial T^2} + \gamma |A|^2 A = 0$$
          $$P_0 = \frac{|\beta_2|}{\gamma T_0^2} = \frac{3.11 \, |\beta_2|}{\gamma \tau_{FWHM}^2}$$
        

For a hyperbolic secant pulse $A(0, T) = \sqrt{P_0} \operatorname{sech}(T/T_0)$, anomalous group velocity dispersion ($\beta_2 < 0$) causes a positive chirp ($d\omega/dt > 0$), while the Kerr effect (SPM) produces a negative chirp. At $P = P_0$, the chirps balance precisely everywhere along the pulse.

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Optical Soliton Fundamental Power Calculator

Pulse & Fiber Parameters

Soliton Dynamics & Characteristic Scales

Fundamental Soliton $\text{sech}^2(t/T_0)$ Envelope

Nonlinear Schrödinger Equation (NLSE) Physics

Frequently Asked Questions