How to create a PowerShell object containing an array of objects that contain arrays of objects?

Question

I'm trying to build JSON output from PowerShell. I use PSCustomObject that contains an array of object. Each of those objects also contains an array of objects.

When I convert this into JSON, the inner array is an empty string.

Here's my code:

$(
    $item1 = [PSCustomObject]@{
        Name = "name1"
        Value = "value1"
    }
    $item2 = [PSCustomObject]@{
        Name = "name2"
        Value = "value2"
    }
    $item3 = [PSCustomObject]@{
        Name = "name3"
        Value = "value3"
    }
    $item2 | Add-Member -MemberType NoteProperty -Name ArrayOfObjects -value (New-object System.Collections.Arraylist)
    $item2.ArrayOfObjects += $item3

    $obj = [PSCustomObject]@{}
    $obj | Add-Member -MemberType NoteProperty -Name ArrayOfObjects -value (New-object System.Collections.Arraylist)
    $obj.ArrayOfObjects += $item1
    $obj.ArrayOfObjects += $item2
    $item2 | ConvertTo-Json
    $obj | ConvertTo-Json
)

The output is the following:

{
    "Name":  "name2",
    "Value":  "value2",
    "ArrayOfObjects":  [
                           {
                               "Name":  "name3",
                               "Value":  "value3"
                           }
                       ]
}
{
    "ArrayOfObjects":  [
                           {
                               "Name":  "name1",
                               "Value":  "value1"
                           },
                           {
                               "Name":  "name2",
                               "Value":  "value2",
                               "ArrayOfObjects":  ""
                           }
                       ]
}

While I would expect $obj | ConvertTo-Json to output this:

{
    "ArrayOfObjects":  [
                           {
                               "Name":  "name1",
                               "Value":  "value1"
                           },
                           {
                               "Name":  "name2",
                               "Value":  "value2",
                               "ArrayOfObjects":   [
                                                       {
                                                           "Name":  "name3",
                                                           "Value":  "value3"
                                                       }
                                                   ]
                           }
                       ]
}

Is this a PowerShell limitation on embedded arrays? Is it possible to construct such an object?

PSVersion: 5.1.17763.2183

PSEdition: Desktop