Ok, since you're only after a single phone, you would need to monitor something (DHCP or ARP table) and look for the MAC address of your phone. It won't change, as it's (meant to be) globally unique per network interface.
However, there are some problems:
- DHCP leases last for a while. Just because there is a lease, that doesn't mean that the device is currently present
- ARP entries are cached, at least for a while. Just because you have an entry, doesn't mean that the device is currently present
- The device's IP address may change upon connection if it's been off the network for long enough for the DHCP lease to expire, so you can't rely on its IP address
- Your phone should attempt to register a DNS entry for itself, but unless you have a proper local DNS server (not just a relayer like most modem/routers are) then you won't be able to query the device's name to get an IP address to get its MAC address via ARP
- IPv6 Neighbour discovery might be another good one, but this involves an IPv6 stack on your network and phone and suffers the same problems as ARP.
- Monitor broadcast traffic for DHCP requests from your MAC in question. These shouldn't show up that often and are a safe sign that the device is currently on the network. But wow, that's a big overhead.
The best option is configure 802.1x. This involves a WiFi access point that supports WPA2-Enterprise and RADIUS server. Monitor the auth logs of your RADIUS server for the MAC of the devices in question and then send an email.