Setting aside various "technical" definitions of physician, the better question is, what is the "legal" definition of physician. Most states have a medical practice statute that clearly defines physician. In Michigan, my home state for example, MCL 333.17001 states that ONLY a licensed MD, DO, or podiatrist (DPM) is considered a physician under the Michigan Public Health Code and Michigan Compliled Laws Annotated. Legally, under the Michigan Medical Practice Act, therefore, only an MD, DO, or DPM is considered a physician. These professions ONLY treat HUMAN patients. Thus, vets cannot be physicians under the MI statute.
If an optometrist stated he/she was an optometric physician or physician in Michigan, he/she would be subject to misrepresentation and unauthorized practice of medicine charges and possible loss of license with pecuniary sanctions. MCL 333.17401 clearly states optometry is not the pratice of medicine, osteopathic medicine, or podiatric medicine. Likewise, chiros, dentists, psychologists, and other like professionals are NOT physicians in MI.
However, in some states, like Washington and Oregon, the legal definition of physician, I believe, includes: chiropractors (chiropractic physicians), optometrists (optometric physicians), psychologists (psychological physicians), and naturopaths from licensed ND schools (naturopathic physicians), and, I believe oral-maxofacial surgeons (the DDS only kind), who completed an OMFS residency, are also considered "physicians and surgeons" under those respective medical practice acts.
In WA and OR, an OD who says he's a physician (most likely with the qualifier "optometric") would be compliant with the law and not misleading, but if he moved to Michigan or other such strict MD/DO/DPM states, he'd be breaking the law and misleading the public.
I believe a few states define physician as MD, DO, and dentists (not pods); others, MD, DO, DPM, and dentists; and a few, only MD and DO. It wasn't all that long ago when DOs were not considered "physicians" in some states, but merely "osteopaths" under a different regulatory schema. In fact, it was only as recently as the 1960s and 1970s that DOs were given full medical practice rights in all states. Before that, they had special hospitals, restricted RxPs, and limits on their authority.
Interestingly, the legal definition of "surgeon" is often less restricted than physician, even though this seems somewhat contrary to logic (you'd think there would be stricter definitions for those who invade the body, but...). In many states, pods without specialized surgical residencies, and general dentists, can legally claim to be "podiatric physicians and surgeons/podiatric surgeons" or "oral surgeons" or "dental surgeons" without being an oral surgeon. If they passed themselves off as physicians, they might be in trouble, but surgeons...no problem!
Not meant to inflame the ODs, but I would think you'd be better off as optometrists without the physician moniker...why add the liability that the term creates? If you use that term, and it misleads others, whether intentionally or not, you could be held to the reasonable prudent standard of care of an OMD (physician), not an OD in a negligence suit.
Furthermore, I think the term is overused and misused. Chiros love to claim that chiropractic is merely another form of medicine like allopathic, osteopathic, and podiatric medicine. It's not a systemic field of medicine; rather it is a very specialized non-evidence based treatment modality, not a philosophical school of medicine. What's next: Psychological physician (PsyD, PhD), pharmaceutical physician (PharmD), nursing physician (NP), physician assistant physician (PA-C), veterinary physicians (DVM), physical therapy physician (DPT, MPT), audiometric physician (AuD), and for those Juris Doctors in the house, Legal Physicians (JD). Point: it can be overused and abused.
So, I would, an optometrist, like an MD, DO, PhD, vet, pharmacist, psychologist, dentist, and even a lawyer, is a "doctor", but may not legally be defined as a physician.