How to derive the time axis for the ifft of an oscillating pulse?

Hello, I have an oscillating pulse in the frequency domain that I would like to ifft and find the time signal. My signal looks like:

And comes from the following code:

sampleRate = 1000;
freq = 500 : (1/sampleRate) : 1500;
intensityFreq = exp(-((freq-1000).^2));
signalFreq = sqrt(intensityFreq).*exp(-1i*10*(freq-1000));
plot(freq,signalFreq)

When I ifft, it doens't automatically produce the time axis, and also shows a similar oscillating pulse (in time) whose oscillations depends on the frequency range I used in the above code. For example, when:

freq = 500 : (1/sampleRate) : 1500;

is used (as in the code shown above), the ifft looks like:

While when:

freq = 980 : (1/sampleRate) : 1020;

Is used instead, the ifft looks like:

This makes no sense to me, since the frequency range shouldn't matter since signalFreq goes to 0 around these points anyway. Why does the altered frequency range affect the oscillations in the ifft so much? And how do I obtain the valid time axis for my output?

Any help is appreciated. If my explanation isn't clear I'll be happy to provide more detail.