How to make gmail like search box with bootstrap - twitter-bootstrap-3

Question

I'm trying to implement input field with additional options similar to gmail search box. You can see it on the screenshots below.
When you click on a caret sign then additional form is shown up:
Currently, I'm struggling with making a nice looking form shown after clicking on the caret sign. Anyone knows how to achieve that with Bootstrap?
Here is a jsfiddle link:
https://jsfiddle.net/x1sfs9xb/1/
<div class="container">
<div class="row">
<div class="input-group">
<input type="text" class="form-control">
<div class="input-group-btn">
<button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown"><span class="caret"></span></button>
<ul class="dropdown-menu dropdown-menu-right">
<li>
<form action="#" class="form-horizontal">
<div class="row">
<div class="col-sm-12">
<div class="form-group">
<label class="col-sm-3 control-label" for="name">Input 1</label>
<div class="col-sm-9">
<input class="form-control" id="name" name="input1" type="text" />
</div>
</div>
</div>
</div>
<div class="row">
<div class="col-sm-12">
<div class="form-group">
<label class="col-sm-3 control-label" for="name">Input2</label>
<div class="col-sm-9">
<input class="form-control" id="name" name="input2" type="text" />
</div>
</div>
</div>
</div>
<p>
<input class="btn action-button pull-right" name="commit" type="submit" value="Save">
</p>
</form>
</li>
</ul>
<button type="button" class="btn btn-default"><span class="glyphicon glyphicon-search"></span></button>
</div>
</div>
</div><div class="row">
<div class="col-md-12">
<h1>Some content</h1>
</div>
</div>
</div>

Answer 1

You can achieve that by using a little CSS and JS:
CSS (your dropdown menu is relative to input-group-btn so you have to change position of that to static - now your dropdown menu is related to the input-group):
.input-group-btn {
position: static;
}
.dropdown-menu {
left: 0;
}
JS (get width of the input and assign it to your dropdown menu, also change it on browser resize):
var inputWidth = $('.form-control').outerWidth();
$('.dropdown-menu').css('width', inputWidth);
$(window).resize(function () {
inputWidth = $('.form-control').outerWidth();
$('.dropdown-menu').css('width', inputWidth);
});
JSFIDDLE