J. Eur. Opt. Society-Rapid Publ. 2026, 22, 47 Ó The Author( s), published by EDP Sciences, 2026 https:// doi. org / 10.1051 / jeos / 2026032 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Dispersive tuning of intrapulse polarization
Jia Xu 1, Ari T. Friberg 2, and Taco D. Visser 1, 3, * 1 Department of Physics and Astronomy, Free University, Amsterdam, The Netherlands 2 Center for Photonics Sciences, University of Eastern Finland, Joensuu, Finland 3 School of Physics and Electronics, Shandong Normal University, Jinan, PR China
Received 20 February 2026 / Accepted 24 March 2026
Abstract. We show how an interferometric setup containing a polarizing beam splitter and a slab of dispersive material allows control over the evolution of the instantaneous state of polarization of an optical pulse. With this proposed method the entire Poincaré sphere can be covered by varying the material’ s thickness. The ability to control the state of polarization over the duration of the pulse may be useful in a wide variety of applications.
Keywords: Pulses, Polarization dynamics, Dispersion, Interferometry.
1 Introduction
Optical pulses are used in a wide range of applications such as control of chemical reactions [ 1 ], observation of electron dynamics [ 2 ], time-resolved spectroscopy [ 3 ], nonlinear microscopy [ 4 ], the generation of entangled photons [ 5 ], and quantum key distribution [ 6 ], to name but a few. The state of polarization of an optical field is a fundamental property that determines how it scatters [ 7 ] andpropagates through a material medium [ 8 ]. Pulse shaping is concerned with spatio-temporal control of intensity and frequency. In addition, the ability to control the instantaneous polarization state provides another degree of freedom that can be exploited in all of the above-mentioned applications. This was examined by Gerber et al. by using an LCD inside a zero-dispersion compressor [ 9 – 11 ]. Here we present a theoretical analysis of an alternative method, based on optical dispersion, to manipulate the evolution of the instantaneous polarization state over the duration of the pulse.
We analyze an interferometric setup in which a polarizing beam splitter, such as a Wollaston prism, creates two orthogonally-polarized and fully correlated pulsed fields with equal amplitude, E x( t) andE y( t). Whereas one field, E x( t) say, is left unchanged, E y( t) ismodified by letting it travel a distance L through a deterministic, linear, and non-absorbing dispersive medium. The two fields are then recombined to form an output pulse whose polarization evolution is found to be strongly dependent on the thickness L of the dispersive medium. As an example we study a glasslike medium. We discuss two regimes. When the thickness L 10k, the polarization evolution of the output pulse is
* Corresponding author: t. d. visser @ vu. nl mainly governed by the time delay between the two pulses. When L 1000k, the polarization evolution is determined by both the time delay and the stretching of E y( t). We find that in both regimes it is possible for the instantaneous Poincaré vector to reach all points of the Poincaré sphere.
2 Plane-wave pulses
Consider a linearly-polarized pulse which is represented by an analytic signal E( z, t)([ 12 ], Sect. 3.1). Such a pulse can be expressed in terms of its spectral components by using the Fourier transform
Ez ð; tÞ ¼
with inverse relation
E
Z 1
E
0
ðz; xÞ ¼ 1 2p
Z 1
ðz; xÞe �ixt dx; ð1Þ
�1
Ez ð; tÞe ixt dt: ð2Þ
Since E( z, t) is an analytic signal with Ẽ( z, x)= 0ifx < 0, the lower limit of integration in equation( 1) is zero rather than �1. We assume that in a plane z = 0 the spectrum has a Gaussian shape around a center frequency x 0, i. e.,
E ð0; xÞ ¼ E 0 e � ð x�x 0Þ 2 = X 2; ð3Þ
where Ẽ 0 is a constant and X denotes the effective width. The spectrum must be zero for negative frequencies, and also only contain optical frequencies. Together this leads to the constraint
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