I've created an example to show how to. Updated state definition would be:
  $stateProvider
    .state('home', {
      url: '/:foo?bar',
      views: {
        '': {
          templateUrl: 'tpl.home.html',
          controller: 'MainRootCtrl'
        },
        ...
      }
And this would be the controller:
.controller('MainRootCtrl', function($scope, $state, $stateParams) {
    //..
    var foo = $stateParams.foo; //getting fooVal
    var bar = $stateParams.bar; //getting barVal
    //..
    $scope.state = $state.current
    $scope.params = $stateParams; 
})
What we can see is that the state home now has url defined as:
url: '/:foo?bar',
which means, that the params in url are expected as 
/fooVal?bar=barValue
These two links will correctly pass arguments into the controller:
<a ui-sref="home({foo: 'fooVal1', bar: 'barVal1'})">
<a ui-sref="home({foo: 'fooVal2', bar: 'barVal2'})">
Also, the controller does consume $stateParams instead of $stateParam.
Link to doc:
You can check it here
params : {}
There is also new, more granular setting params : {}. As we've already seen, we can declare parameters as part of url. But with params : {} configuration - we can extend this definition or even introduce paramters which are not part of the url:
.state('other', {
    url: '/other/:foo?bar',
    params: { 
        // here we define default value for foo
        // we also set squash to false, to force injecting
        // even the default value into url
        foo: {
          value: 'defaultValue',
          squash: false,
        },
        // this parameter is now array
        // we can pass more items, and expect them as []
        bar : { 
          array : true,
        },
        // this param is not part of url
        // it could be passed with $state.go or ui-sref 
        hiddenParam: 'YES',
      },
    ...
Settings available for params are described in the documentation of the $stateProvider
Below is just an extract
- value - {object|function=}: specifies the default value for this parameter. This implicitly sets this parameter as optional...
- array - {boolean=}: (default: false) If true, the param value will be treated as an array of values. 
- squash - {bool|string=}: squash configures how a default parameter value is represented in the URL when the current parameter value is the same as the default value.
We can call these params this way:
// hidden param cannot be passed via url
<a href="#/other/fooVal?bar=1&bar=2">
// default foo is skipped
<a ui-sref="other({bar: [4,5]})">
Check it in action here