Better way to organize an upload file method in Laravel 5.2

I am a Laravel newbie so please forgive me for my code... I have a method, in a Laravel controller, that updates the current logged user profile (postProfileGeneral()). Logged user can upload a profile picture, and I manipulate the uploaded file (i.e. remove spaces, create unique name, etc.); since I'd like to reuse the upload routine, I put it on a separate method (_upload())... The code is this:

// get a unique file name
protected function _getUniqueFilename($path, $filename, $extension)
{
    $i = 2;
    $output = $filename . '.' . $extension;
    while(File::exists($path . '/' . $output)){
        $output = $filename . '_' . $i . '.' . $extension;
        $i++;
    }
    return $output;
}

// upload method, to reuse the routine
protected function _upload(Request $request, $field, $path = '')
{
    $path = ($path != '') ? $path : public_path();
    if ($request->hasFile($field)){
        $file = $request->file($field);
        if ($file->isValid()){
            $basename = $file->getClientOriginalName(); // get the original filename + extension
            $extension = $file->getClientOriginalExtension(); // get the original extension without the dot
            $filename = basename($basename, '.' . $extension); // get the original filename only
            $slug = str_slug($filename, '-'); // slug the original filename
            $name = $this->_getUniqueFilename($path, $slug, $extension);
            $file->move($path, $name);
            $output = $path . $name;
        }
    } else {
        $output = $request->input('cur_picture');
    }
    return $output;
}

// update profile
public function postProfileGeneral(Request $request)
{
    $picture = $this->_upload($request, 'picture', config('custom.users_path'));
    dd($picture);
    // rest of method here, not relevant
}

It works fine, but I feel there is a better way of doing this My questions are:

1. since the getUniqueFilename() and _upload() method can be reused in other controllers too (i.e. for uploading products pictures, or whatever) where should I put them to be generally available?
2. in the getUniqueFilename() method I must pass Request object as a parameter: is there a better way to do this? At last, I yet have my Request object available in the postProfileGeneral() method...

Thanks