Gary Delane Boyd

Confocal Resonators Remarks on Their History

I joined Bell Telephone Laboratories in July 1959, after completing my doctorate at California Institute of Technology. I had obtained a BS (1954) and MS (1955) there also. My PhD thesis was on plasma physics under Prof. Roy W. Gould. The work involved sending modulated electron beams through a gas discharge.

I was interested in communication devices and so I went into James P. Gordon's department; Rudolf Kompfner was the Director and John Pierce was above him. It was a department that in the past was very concerned with microwave masers and low-noise microwave receivers. But this was winding down. The managers were looking for the next step. People were talking about communication with optical masers (lasers).

The Schawlow and Townes paper had just been published, Phys. Rev. Dec 1958, and contained an idea that fascinated me. The pump doesn't have to be coherent. Microwave masers are pumped with coherent sources simply because all the sources in the microwave region are coherent. But the Schawlow-Townes paper taught that there are incoherent optical sources which are also intense, and could be used as optical pumps.

John H. Sanders, from Oxford Univ., was in the group I joined and I started working with him for the few remaining months of his stay. He was using a resonator made with two flat mirrors separated by invar rods about 10 cm. long. He had chosen a microwave-excited discharge in He as the easiest way to go to obtain a population inversion. Time was short and his approach was, "Let's pump it hard and see if it oscillates."

After Sanders left, I decided not to continue this project. I didn't think the particular set-up was practicable. I was interested, however, in the Schawlow-Townes discussion of the plane parallel Fabry-Perot resonator. Because of my electrical engineering and waveguide background, I was not comfortable with this resonator nor with Schawlow and Townes' way of analyzing it. It had no axis, whereas waveguides do have axes. That is, the walls, whether cylindrical or rectangular, define a longitudinal axis. I thought that there had to be a better optical resonator, and I started to think about what an optical resonator should be like.

I looked into books on optical interferometry and in one book; Cannes' spherical interferometer was mentioned. It was not much used, but it did define a transverse axis and I started to look at its modes. I made one, using a brass assembly from Sander's set-up. I got curved mirrors, took a sodium lamp, and saw the interferometer fringes. The fringe spacing was much larger, for the central portion, than a comparable plane parallel interferometer. I immediately recognized that the alignment criterion was less sensitive than for the plane Fabry-Perot.

Schawlow and Townes had computed the walk-off loss for their version of a Fabry-Perot. What I and everybody wanted was a high-Q resonator that would avoid walk off losses. Looking at the Cannes interferometer from the ray point of view, I thought that perhaps it would have lower loss because the fringe patterns were so different from the plane interferometer.

Sometime in here, Fox and Li gave a seminar at Murray Hill, describing their numerical self-consistent field approach to the plane parallel Fabry-Perot. It was a significant advance over Schawlow and Townes. I was listening intently. W. D. Lewis, who had a strong antenna theory background, got up and suggested that curved wave fronts were also interesting and could be understood analytically. I didn't know this at the time, but in hindsight perceived that antenna people probably knew well that a Gaussian beam is unique in remaining Gaussian as it diffracts, and that this may have lay behind Lewis' remark.

It was a crowded lecture room because a lot of people were working on or interested in laser-related topics. Fox replied to Lewis saying, "Gary is working on such a structure." Immediately after, C. C. Cutler told me who Lewis was, and I went and called him at 5 p.m. after the secretaries had left so he answered his own phone and said come over. I assumed he was an MTS but when I found his office I was surprised, to say the least, that he was an executive director. We had a delightful conversation. I guess he suggested that I try an analytical self-consistent field treatment, similar to the numerical results for the plane parallel Fabry-Perot by Fox and Li, for my curved interferometer mirrors. He probably gave me a blackboard lecture on some of the mathematics.

I went back and started to write up the equations. At first I continued with my experiments on the spherical interferometer but afterwards, as the equations started to work out, I dropped the experiments as they were not necessary. At one point I discussed the integral (equation 5 of the paper) with Lewis and he pointed to results of Slepian and Pollack in the Bell Laboratories Mathematical Research group on this mathematics. So I went to them and got their papers. The integral equation is referred to as the finite Fourier transform. At my request their assistant F. J. MacWilliams extended their eigenvalue computations into the region of interest for us predicting low diffraction losses. I talked a good deal with Jim Gordon as I worked; he was very strong analytically. We talked sufficiently often that it began to seem to me a joint work and I put his name on it. I would have put Lewis' name on too, but he declined. I did do the brunt of the paper.

I would estimate this whole research effort began by about September 1959, and was completed before June 1960. The manuscript was submitted to the Bell System Technical Journal in September 1960,^[1] and I recall that I understood the material before Maiman's ruby laser was announced in July 1960.

After Maiman, I started thinking about how to demonstrate this laser (called optical maser at the time) resonator. I and my technician wanted to create curved mirrors on ruby. I knew nothing about grinding and polishing crystals so we found out how to do it. We had a rather poor piece of ruby and we ground curved ends onto it. Then I went to D. F. Nelson who had a laser flash lamp set-up and we flashed it and it lased! At the Berkeley Quantum Electronics conference in March 1961 I talked on our BSTJ article, which wasn't yet out, and also on the demonstration we had achieved.

Javan was a friend of Gordon's and I had casual interactions with Javan, Bennett, and Herriott. I definitely remember telling them, "don't use plane mirrors, and use curved ones." I don't remember whether these discussions occurred before their gas laser first operated or after. It wasn't until a month or two before the Berkeley conference that I actually succeeded in demonstrating that curved mirrors worked. But I remember I said, "God, at least order some curved mirrors." Javan, Bennett, and Herriott were fussing with this terribly difficult alignment and I knew they didn't need to anymore.

Herriott did listen and he ordered some. It took months to get mirrors in those days. Rigrod and Kogelnik had started on their Brewster window experiment and had ordered curved mirrors. Their focus in this experiment was to use curved mirrors instead of plane mirrors and to get rid of the internal mirrors, which had made the first HeNe laser into a mechanical kluge, with the distortable mechanical bellows that were necessary when the mirrors were internal. I think Herriott came in one day and said, "The curved mirrors have arrived." After that, the experiment worked. I believe I was told that it worked just holding one mirror in the hand and tilting it to get the different modes.