MD Settings: Restore focus after closing various dialogs.

chrome/browser/resources/settings/search_engines_page/search_engine_entry.js

 // Copyright 2015 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 /**
  * @fileoverview 'settings-search-engine-entry' is a component for showing a
  * search engine with its name, domain and query URL.
  */
 Polymer({
   is: 'settings-search-engine-entry',
@@ skipping 88 matching lines @@
     this.closePopupMenu_();
 
     this.showEditSearchEngineDialog_ = true;
     this.async(function() {
       var dialog = this.$$('settings-search-engine-dialog');
       // Register listener to detect when the dialog is closed. Flip the boolean
       // once closed to force a restamp next time it is shown such that the
       // previous dialog's contents are cleared.
       dialog.addEventListener('close', function() {
         this.showEditSearchEngineDialog_ = false;
+        this.$$('paper-icon-button').focus();
       }.bind(this));
     }.bind(this));
   },
 
   /** @private */
   onMakeDefaultTap_: function() {
     this.closePopupMenu_();
     this.browserProxy_.setDefaultSearchEngine(this.engine.modelIndex);
   },
 });