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This is because most of the people using them are indoors in a building where AC mains are available. You could measure the voltage coming out of the wall mount power supply and substitute your own battery pack. If you will never use the modem on AC, you can cut the output cord off and use it with your batteries. To be doubly careful, select the battery for higher than needed voltage and use a low drop out regulator to get the final voltage.
I have seen that most of the external modems use an AC power supply, probably because is easier to find from different suppliers and because you don't need any care about polarity.
If you need to supply the modem with a battery or a power supply with a DC voltage, it is easy, because most of them take the rectified voltage ( usually 9 Vac that becames about 13 Vdc after the rectifier and the capacitor ) and regulate it to 5 V dc through a 7805 or a LM2575 ( depends on the brand of the modem ).
For this reason any voltage among 9 and 14 Vdc will be OK to supply your modem.
BTW, don't care about the polarity at the power socket.
Of course this is true only if the modem is AC powered.
As far as I know, they need AC power supply to obtain positive and negative voltage to communicate with COM port. If you need to supply modem from DC supply, then you will need 2 sources and some alteration in your modem power stage.
If you so seriously doubt in it, then try to supply your modem by DC. You will break your modem or port.
I have made some multimodem (12 modems) station and had some experience. I had idea to make one supply source for all modems, tried to supply them by power DC supply, but my good friend has stopped me at right time.
Ok, you doubt - then search web ........ The Internet knows all.
It is a little known fact that some of these modems need an AC 12 to 15 Volts supply at around 250 mA. Supplying them with DC will lead to disaster since the rectifier circuits develop both +ve and -ve voltage rails for the chips and the RS-232 interface. Those circuits need an AC supply to do this.
There is no reason why you can't use a dc supply.
A dc supply of 25% more than the rated ac voltage
of the ac adapter, of either polarity of the jack will do.
For example if your modem runs on 9V ac then you can use
a 12V dc transformer, and the polarity of the plug is not
important because it is going to pass through an internal bridge
rectifier that will fix the polarity within the modem. Of course
the current must be adequate for the application.
I think ac adapters are easier to manufacture, by excluding
the bridge rectifier and the filter transformer.
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