Experimental and theoretical study of the Gouy phase anomaly of light in the focus of microlenses

We report on the Gouy phase anomaly of light in the focus of cylindrical and spherical microlenses. The prime subject of our study concerns a discussion of how the very small size of microlenses affects the phase properties of light in their foci. We put emphasis on determining the amount of the Gouy phase shift for line and point foci within the limited axial space. Contrary to macroscopic lenses, the optical properties of microlenses are strongly governed by the effect of diffraction when their size tends to be comparable to the operation wavelength. In our study, we clearly show how such diffraction features affect the axial phase shift. For instance, phase singularities, which occur at discrete points on the optical axis where the total intensity vanishes for spherical microlenses, cause an additional axial phase shift when compared to the cylindrical microlens where those axial phase singularities are absent. The rotational symmetry of the Fresnel zones is the origin of such a difference between point and line foci.

[1]  P. Robinson,et al.  The gouy phase shift as a geometrical quantum effect , 1996 .

[2]  John M. Tamkin,et al.  Observation of the Gouy phase anomaly in astigmatic beams. , 2012, Applied optics.

[3]  H. Winful,et al.  Physical origin of the Gouy phase shift. , 2001, Optics letters.

[4]  Robert W. Boyd,et al.  Intuitive explanation of the phase anomaly of focused light beams , 1980 .

[5]  H. Herzig,et al.  Talbot Images of Wavelength-scale Amplitude Gratings , 2022 .

[6]  T. Tyc Gouy phase for full-aperture spherical and cylindrical waves. , 2012, Optics letters.

[7]  G. Brand A New Millimeter Wave Geometric Phase Demonstration , 2000 .

[8]  C. Sheppard Cylindrical lenses--focusing and imaging: a review [Invited]. , 2013, Applied optics.

[9]  D Subbarao,et al.  Topological phase in Gaussian beam optics. , 1995, Optics letters.

[10]  Hans Peter Herzig,et al.  Comparing glass and plastic refractive microlenses fabricated with different technologies , 2006 .

[11]  Myun-Sik Kim,et al.  Engineering photonic nanojets. , 2011, Optics express.

[12]  Myun-Sik Kim,et al.  Small-size microlens characterization by multiwavelength high-resolution interference microscopy. , 2010, Optics express.

[13]  T. Eiju,et al.  Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm. , 1987, Applied optics.

[14]  J. Schwider,et al.  Arraytests for microlenses , 1997 .

[15]  M. Nemes,et al.  Experimental proposal for measuring the Gouy phase of matter waves , 2010, 1012.3910.

[16]  H. Rigneault,et al.  Imaging the Gouy phase shift in photonic jets with a wavefront sensor. , 2012, Optics letters.

[17]  Wenfeng Sun,et al.  Complete presentation of the Gouy phase shift with the THz digital holography. , 2013, Optics express.

[18]  H. Herzig,et al.  Gouy phase anomaly in photonic nanojets , 2011 .

[19]  S. Habraken,et al.  Geometric phases in astigmatic optical modes of arbitrary order , 2009, 0912.1732.

[20]  Myun-Sik Kim,et al.  Longitudinal-differential interferometry: direct imaging of axial superluminal phase propagation. , 2012, Optics letters.

[21]  Myun-Sik Kim,et al.  Phase anomalies in Talbot light carpets of self-images. , 2013, Optics express.

[22]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .

[24]  Hongrui Jiang,et al.  Liquid tunable microlenses based on MEMS techniques , 2013, Journal of physics D: Applied physics.

[25]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[26]  J. Schwider,et al.  Digital wave-front measuring interferometry: some systematic error sources. , 1983, Applied optics.

[27]  E. Wolf,et al.  The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields , 2010 .

[28]  Takaaki Miyashita International standards for metrology of microlens arrays , 2005, SPIE Optical Metrology.

[29]  Mukunda,et al.  Bargmann invariant and the geometry of the Güoy effect. , 1993, Physical review letters.

[30]  D. Fischer,et al.  Generalized Gouy phase for focused partially coherent light and its implications for interferometry. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[31]  Keren Bergman,et al.  Optical interconnection networks for high-performance computing systems , 2012, Reports on progress in physics. Physical Society.