Manuscript ID: 413737 Type: research article Title: Coupling Light to Higher Order Transverse Modes of a Near-Concentric Optical Cavity Author: Christian Kurtsiefer; National University of Singapore Dear Dr. Kurtsiefer: Before making a final decision on your manuscript, I would like to give you an opportunity to address the reviewers’ concerns. The reviews are appended below. It is the policy of Optics Express to allow only one revision cycle; therefore it is important to respond to all of the reviewer points carefully and to make it evident that you have done so. For this reason, please provide a response letter to note any changes that have been made to the manuscript and indicate their locations. You will upload your response letter in the online system. Of course, you may not agree with the reviewers on every point. In this case, your responses and reasoning should be clearly presented because your manuscript might be sent for re-review upon resubmission. 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I couldn't find certain crucial parameters, like the radius of curvature of the mirrors and the measured finesse of the cavity. Please check. 2. I was intrigued by the argument in section 2.2 on identical effective mode volumes for all radial tranverse modes. Can the authors formulate a physical explanation for this, on top of the mathematical explanation mentioned in the manuscript? 3. The curves in Fig. 4 are not Lorentzian but suggest the presence of a sidemode. Do the authors understand the origin of the observed side peaks? Is this worth mentioning? Reviewer 2: Manuscript ID: 413737 Title: Coupling Light to Higher Order Transverse Modes of a Near-Concentric Optical Cavity Authors: ADRIAN NUGRAHA UTAMA, CHANG HOONG CHOW,, CHI HUAN NGUYEN, AND CHRISTIAN KURTSIEFER The authors presented a work to use a phase only spatial light modulator to shape the phase profile of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. Detailed implementation and characterization procedures are described, and good coupling efficiency are experimentally observed. The paper is well written with clear figures showing the key results. I have a few comments that hopefully the authors can provide more clarification to increase the quality of the paper: 1. Similar work has been demonstrated by using DMD and other types of SLMs. It is unclear to me that how the transmission coefficient is calculated. I suspect that the input power refers to the beam power after the beam is modulated by the SLM, but perhaps the real benefit of using phase-only SLM as compared to DMD based devices is the efficiency as compared to the input beam power out of the fiber. Some clarification and comparison would be recommended. 2. In Fig. 1, it is illustrated that higher order LG modes would result in smaller peak transmission in resonance. Can the authors explain what causes the reduction in peak transmission, especially in theory? 3. The authors states “In addition, all the radial transverse modes (LG modes with l = 0) at a particular critical distance d have identical effective mode volumes”. It is unclear to me how the math comes to such conclusion. Can the authors explain a bit more on this issue? 4. The definition of mode overlap after Eq.(9) needs more clarification as the mode profile U1 and U2 are not defined here. Since the LG modes are orthogonal to each other, why the mode matching efficiency is high between an input Gaussian beam and a high-order LG mode? 5. Some grammatical improvement is needed in Paragraph 2, section 3.1.2: “The detuning from the cavity resonance is expressed is corresponding units of light frequency”. 6. When the SLM is set to impose a super-position of multiple LG modes, what is the overall modulation efficiency as compared to the input power? 7. Fig. 5 shows that the mode matching efficiency varies as a function of phi, the relative phase between LG00 and LG10 modes. Can the authors explain a bit more here as I would assume the efficiency should remain constant for a rotationally-symmetric system? I am also not following the statement “in which case the in-phase component of the beam encodes the LG00 mode, while the quadrature component of the beam encodes the LG10 mode.” What is the in-phase and quadrature components of the beam? And which beam are we talking about here? 8. Fig. 7 reveals the impact of limited aperture of the mirrors to higher order LG modes. Is this limitation fundamental or related to particular mirrors used in the experiment? After the authors provides clarifications to the above questions, I would recommend the paper to be published in Optics Express. Reviewer 3: This is an original and thorough investigation of higher-order mode in near-concentric optical cavities and how they can be excited selectively with a spatial light modulator. With the increasing use of strong-coupling cavities in AMO physics, this is a timely paper, with applications to a wide range of quantum technologies in particular. The paper is well written, results are presented clearly and analyzed with care. This is a very good match for Optics Express, I recommend publication with only minor modifications: * How specific are these results to the specific mirror shape used by the authors, which integrates "anaclastic" lenses? Can we expect similar higher-order coupling efficiencies with a more conventional design? I would suggest to address this question more explicitely at a suitable place in the paper. * When mentioning small mode volumes in the near-concentric region and their potential for strong interaction between light and atoms [refs. 21-23], I would suggest to add a reference to work with near-concentric cavities in the Schleier-Smith group, such as Davis et al, PRL 122, 010405 (2019). * p. 10, "which on the same order as the mirror transmission and scattering losses": verb missing. --------Pre-Production Review-------- Please confirm that all of your funding sources have been added into your Prism submission in the Fees and Funding step. If your manuscript is accepted for publication, the Funding listing in your published paper will be pulled from this section. Do not use "et al." in your references. Revise your references to include the full author listings. For book reference publishers with "Press" as part of publisher name, delete "Press" and spell out "University”. 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