Converting to AC mains supply first is extremely inefficient. It is better to convert the DC from the PV panel directly to the voltage needed by the laptop.
You have given very little information so it is not possible to advise you on specific parts or schematics. In general, this is what you have to do:
1. See how much power you actually need to produce, this is the voltage from your existing AC charger (it will be marked on it) multiplied by the charging current taken by the laptop. If in doubt, use the current rating of the charger instead. Looking at my AC charger it says 20V / 3.2 A so the poutput power is 64 Watts.
2. Add on a factor to reflect the losses in the conversion circuit, I suggest a figure of 25%, you can probably do slightly better than that but lets look at it "worst case". The power requirement target is therefore 80W.
3. No matter how you do the voltage conversion, your PV panels should be capable of producing at least 80W.
4. Depending on your PV panels, you may have to step the voltage up or step it down. The voltage will depend on how much illumination reaches the panel but if you assume it has maximum rated output and the voltage is less than the laptop requires, use a boost regulator to increase the voltage. If the PV output is higher than required voltage, use a buck regulator.
These suggestions will give you optimal use of the laptop and its batteries, to some extent you can reduce the charging rate and allow longer for them to 'fill up' but you need to know the exact cell specification to determine how to do that. The type of regulator remains the same though.
Brian.