How to concatenate (take cross product of) two datetime arrays?

I have two arrays

Date = [datetime(2016,4,5), datetime(2016,5,4), datetime(2016,6,7)];
Time = duration(0,0:30:90,0,'Format', 'hh:mm:ss');

I want a product of these two arrays such that result is

ans =
5-Apr-2016 00:00:00
5-Apr-2016 00:30:00
5-Apr-2016 01:00:00
5-Apr-2016 01:30:00
4-May-2016 00:00:00
4-May-2016 00:30:00
4-May-2016 01:00:00
...

Answer 1

[Andrei Bobrov]

Date = [datenum(2016,4,5), datenum(2016,5,4), datenum(2016,6,7)];

a = bsxfun(@plus,Date,1/48*(0:3)');
out = datestr(a,'dd-mmm-yyyy HH:MM:SS');

Answer 2

[Guillaume]

This avoids conversion to datenum:

Date = [datetime(2016,4,5), datetime(2016,5,4), datetime(2016,6,7)];
Time = duration(0,0:30:90,0,'Format', 'hh:mm:ss');
[tidx, didx] = ndgrid(1:numel(Time), 1:numel(Date));
result = reshape(Date(didx) + Time(tidx), [], 1)

ndgrid is typically used to obtain the cartesian product of two sets.