I have spent days trying to understand how to add new controllers to page with Angular. Their documentation sucks, but I have found that finally

modal.js

// https://github.com/angular-ui/bootstrap/blob/7b7cdf842278e86a677980d29bd74a1afd467ff1/src/modal/modal.js

angular.module('ui.bootstrap.modal', ['ui.bootstrap.transition'])

// ... some lines

// here $compile gets in by dependency injection... also spent hours debugging that :/
.factory('$modalStack', ['$transition', '$timeout', '$document', '$compile', '$rootScope', '$$stackedMap',
    function ($transition, $timeout, $document, $compile, $rootScope, $$stackedMap) {

// ...

// that one accutally creates popup / adds to DOM / compiles controller
$modalStack.open = function (modalInstance, modal) {

        // ...

        var body = $document.find('body').eq(0), // dirty body pickup
        
        // ...

        var angularDomEl = angular.element('<div modal-window></div>'); // ditry DOM creation
        angularDomEl.attr({
          'template-url': modal.windowTemplateUrl,
          'window-class': modal.windowClass,
          'size': modal.size,
          'index': openedWindows.length() - 1,
          'animate': 'animate'
        }).html(modal.content);

        // dirty compile
        var modalDomEl = $compile(angularDomEl)(modal.scope);
        
        // dirty add to DOM
        body.append(modalDomEl);
      };
      
      
/**
 * with little of VanillaJS and jQuery you can do that in less lines, but as everyone now loves angular it's worth understanding how they deal with such cases
 */