Search a Path recursive for the existence of a search string in all matching files and dump it to a text file with PowerShell

I am used to grep under Linux a lot. So I was trying to device a way to search a bunch of files for a particular string. So I ended up writing the following bit of code as PowerShell function

function Search-PathString {
	[cmdletbinding()]
	param (
		[Parameter(
			Mandatory = $True,
			ValueFromPipeline = $True)]
		$SearchPath,
		[Parameter(
			Mandatory =$True,
			ValueFromPipeline = $False)]
		[string] $SearchString
		)
<#
	.SYNOPSIS
		Search a Path recursive for the existence of a search string in all matching files and dump it to a text file.
	.DESCRIPTION
		Search a Path recursive for the existence of a search string in all matching files and dump it to a text file.
	.EXAMPLE
		Search-PathString -SearchPath "*.log" -SearchString ""
#>
	Process {
		Get-ChildItem $SearchPath -Recurse | Select-String -Pattern $SearchString | Out-File "$SearchString.txt"
		}
	}

Enjoy the code and let me know if you have ways to make it smarter.