# Converting $\mathrm{ps/nm}$ to $\mathrm{ps}^2$

I have a dataset in the unit $$\mathrm{ps/nm}$$ for many different $$\lambda$$ which I want to convert to $$\mathrm{ps}^2$$.

I guess I can assume that I only deal with Gaussian bandwidths such that $$1\ \mathrm{ps}$$ corresponds to $$1\ \mathrm{THz}$$.

$$\Delta f = \frac{c\Delta \lambda}{\lambda^2} \approx 125\ \mathrm{GHz} \quad\text{for}\ \Delta \lambda = 1\ \mathrm{nm}\ \text{at}\ \lambda=1550\ \mathrm{nm}.$$

$$1\ \mathrm{ps}$$ corresponds to $$\lambda_d \approx 8\ \mathrm{nm}$$ at this wavelength.

Does that mean that I have to multiply by $$\lambda_d \approx 8\ \mathrm{nm}$$ if I want to convert from $$\mathrm{ps/nm}$$ to $$\mathrm{ps}^2$$?

Since you are wanting to "convert" between two units with different physical meanings, there is not a standard way to do this. Multiplying a number with units of $$\rm{ps/nm}$$ by any number with units of $$\rm{nm}$$ will give you a number with units of just $$\rm{ps}$$. You would need to multiply by a number with units of $$\rm{ps\cdot nm}$$ to get what you desire. What value you actually use is up to you, and must be interpreted accordingly based on the context of your problem.
Typically values are chosen that are good characteristic scaling numbers for the problem at hand. For example, if you are dealing with time scales of $$1\ \rm{ps}$$ and wavelengths of $$8\ \rm{nm}$$, then perhaps you could use a "conversion factor" of $$1\ \rm{ps}\cdot8\ \rm{nm}=8\ \rm{ps\cdot nm}$$. Without knowing more about your specific dataset or the experiment you are looking at, I don't think I can give more insight into what this conversion physically means though.