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Precision dispersion compensation for ultra-broadband bi-photons using a prism-pair with negative separation

Yaakov Shaked, Shai Yefet, Avi Pe

Published Mar 10, 2014• 0 citations

Abstract

The Brewster prism-pair is a major tool for dispersion control that produces tuned negative dispersion even when the prisms material has positive dispersion. We present a complementary technique for obtaining overall positive dispersion even when the material dispersion is negative, which is most useful for applications in the infrared, where the majority of the optical materials have negative dispersion. By adding a telescope between the prisms that images the first prism beyond the location of the second one, an effectively negative separation between the prisms can be obtained. This ability to flip the sign of the angular dispersion between the prisms provides a powerful new knob to the prism-pair system and allows higher degree of dispersion compensation. We demonstrate a prism-pair configuration, where both the 2nd and 4th order dispersion are compensated in the 1400-2400nm range, designed for a quantum optics experiment with ultra-broadband bi-photons. c 2014 Optical Society of America OCIS codes: 140.7090, 230.5480 Since the introduction of the Brewster prism-pair as a mechanism for dispersion control [1], it became a major tool for tuned dispersion compensation in ultrafast optical systems. Specifically, a prism-pair is commonly used to compensate for second-order dispersion (group delay dispersion - GDD). The angular dispersion that is created by the separation between the prisms tips always introduces negative GDD, even when the prisms material produces positive GDD. Thus, any negative dispersion can be achieved by the appropriate separation between the prisms; and tuned dispersion can be achieved by controlling the amount of prism material in the beam.

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The Brewster prism-pair is a major tool for dispersion control that produces tuned negative dispersion even when the prisms material has positive dispersion. We present a complementary technique for obtaining overall positive dispersion even when the material dispersion is negative, which is most useful for applications in the infrared, where the majority of the optical materials have negative dispersion. By adding a telescope between the prisms that images the first prism beyond the location of the second one, an effectively negative separation between the prisms can be obtained. This ability to flip the sign of the angular dispersion between the prisms provides a powerful new knob to the prism-pair system and allows higher degree of dispersion compensation. We demonstrate a prism-pair configuration, where both the 2nd and 4th order dispersion are compensated in the 1400-2400nm range, designed for a quantum optics experiment with ultra-broadband bi-photons. c 2014 Optical Society of America OCIS codes: 140.7090, 230.5480 Since the introduction of the Brewster prism-pair as a mechanism for dispersion control [1], it became a major tool for tuned dispersion compensation in ultrafast optical systems. Specifically, a prism-pair is commonly used to compensate for second-order dispersion (group delay dispersion - GDD). The angular dispersion that is created by the separation between the prisms tips always introduces negative GDD, even when the prisms material produces positive GDD. Thus, any negative dispersion can be achieved by the appropriate separation between the prisms; and tuned dispersion can be achieved by controlling the amount of prism material in the beam.

We demonstrate low-loss broadband tuned compensation of both the 2nd and 4th order dispersion of ultra-broad bi-photons, using a prism-pair with negative separation. The corrected spectral phase (

<\pi/20

) of the bi-photons spans nearly an octave in frequency (

\approx1330-2600

nm), as measured directly by a non-classical bi-photon interference effect. Due to the ultra-broad bandwidth, an ultra-high flux of bi-photons is available for quantum information experiments with extremely pronounced quantum correlations in both time and phase. Most experiments that explore these correlations require transform limited bi-photons, which are now achievable most efficiently with the prism-pair configuration.

The quantum correlation of octave-spanning time–energy entangled bi-photons can be as short as a single optical cycle. Many experiments designed to explore and exploit this correlation require a uniform spectral phase (transform-limited) with very low loss. So far, transform-limited single-cycle bi-photons have not been demonstrated, primarily due to the lack of precise, broadband control of their spectral phase. Here, we demonstrate the correction of the spectral-phase of near-octave spanning bi-photons to over an octave in frequency –2600 nm). Using a prism-pair with an effectively negative separation for shaping the bi-photons' spectral phase, we obtain a tuned, very low-loss compensation of both the second and fourth dispersion orders. An essential requisite for precise tuning over such a broad bandwidth is a measure of the spectral phase that provides feedback for the tuning even when the overall dispersion is far from compensated. This is achieved by a non-classical bi-photon interference, which enables direct verification of the corrected bi-photon spectral phase.

We have theoretically predicted and experimentally demonstrated an ultra-dispersive atomic prism made of coherently driven Rb atomic vapor. The prism posses spectral angular dispersion that six orders of magnetude higher than the prism made from optical glass; it is the highest spectral angular dispersion that has been ever shown (such angular dispersion allows one to resolve spatially light separated by a few kHz). The prism is working near the resonant frequency of atomic vapor, and its dispersion is optically controlled by coherent driving field.

Nonlinear SU(1,1) quantum interferometers based on non-degenerate optical parametric down-conversion exhibit strong unbalanced group velocity dispersion (GVD). This feature is intrinsic to this type of interferometer as correlated photons of vastly different frequencies propagate through a dispersive nonlinear crystal; consequently, the dispersion arises from the source itself. The resulting GVD degrades the axial point-spread function (PSF) in optical coherence tomography (OCT) with undetected photons; and physical compensation is less straightforward, in particular for non-degenerate broadband regimes due to the limited number of suitable materials. In this contribution, we analyze dispersion in bulk nonlinear interferometry and describe its implications for OCT imaging. Aspects of hardware compensation are addressed, and a novel empirical numerical method of compensation is proposed. The approach is based on the extraction of the phase component directly from the time-domain modality (high precision linearized quantum Fourier transform infrared spectrometer) and its injection into the mid-IR spectral-domain OCT signals (central wavelength of around 3770 nm) before the Fourier transform. The proposed method is compared with an alternative numerical technique. The results demonstrate a 2.2-fold improvement in axial resolution and outperform the alternative correction method in overall imaging performance.

Quantum sources that provide broadband biphotons entangled in both polarization and time-energy degrees of freedom are a rich quantum resource that finds many applications in quantum communication, sensing, and metrology. Creating such a source while maintaining high entanglement quality over a broad spectral range is a challenge, which conventionally requires various compensation steps to erase temporal, spectral, or spatial distinguishabilities. Here, we point out that in fact compensation is not always necessary. The key to generate broadband polarization-entangled biphotons via type-II spontaneous parametric downcoversion (SPDC) without compensation is to use nonlinear materials with sufficiently low group birefringence that the biphoton bandwidth becomes dispersion-limited. Most nonlinear crystals or waveguides cannot meet this condition, but it is easily met in fiber-based systems. We reveal the interplay of group birefringence and dispersion on SPDC bandwidth and polarization entanglement quality. We show that periodically poled silica fiber (PPSF) is an ideal medium to generate high-concurrence (>0.977) polarization-entangled photons over a broad spectral range (>77nm), directly and without compensation. This is the highest polarization-entanglement concurrence reported that is maintained over a broad spectral range from a compensation-free source.