Author: Ronen Shekel

One of the most beautiful experiments with SPDC light is that of induced coherence. It has originally been demonstrated and analyzed by Zou, Wang, and Mandel in 1991 [1, 2], and is discussed and utilized to this day. In this experiment two nonlinear crystals are used, set in a configuration as shown in Fig. 1.

A “green” pump beam generates via parametric down conversion “yellow” signal and “red” idler photons, both in the first crystal and in the second crystal. We then slightly change the length difference between the paths of the two yellow signal photons and measure their interference using a single photon detector (D1). The question arises – will we measure interference fringes? Are these signals coherent with each other?

induced coherence
Fig 1. The setup of an induced coherence experiment. BS – beam splitter. DM – dichroic mirror. NL – nonlinear crystal. D – single photon detector.

Well, since we cannot know which of the two signal photons we are measuring, we should indeed sum the amplitudes, and do observe interference. However, consider now a case where we block the path of the first idler photon (). Remarkably, even though signal photons can still originate from either the first or the second crystal, the fringes will disappear!

This may again be explained in terms of distinguishability. In Feynman’s words [3]:

If you cannot distinguish the final states even in principle, then the probability amplitudes must be summed.

Further examination of our system shows that blocking the first idler photon does affect the distinguishability between the two signal photons. If the signal photon is accompanied by an idler photon at the second detector (D2) then we know that it originates from the second crystal. If we don’t measure an idler photon – we know that it has been blocked, and that the signal photon originates from the first crystal. Thus, blocking the first idler photon reduces the indistinguishability between the two signal photons.

This is quite remarkable. Even when both processes have a low flux, and statistically, in no point in time the first idler and the second signal photon co-exist, the mere theoretical possibility of measuring the idler photon from the first crystal affects the coherence properties of the signal photon generated in the second crystal. For this reason, we say that the idler photon induces the coherence of the process.

In 2014, this effect has been utilized in the group of Nobel prize winner Anton Zeilinger, in the context of imaging [4]. Consider that we block only part of the path of this idler photon and swap the single photon detector with a sensitive camera. The area on the camera corresponding to the blocked area will show no interference, while the other area will show interference.

Measuring intensity that depends on the transmittance of an object is of course exactly what we want to do in imaging! Notice however the puzzling fact: the light measured by the camera never passed through the object, and the light hitting the object never reaches the camera!

A second modality for using induced coherence for imaging is for phase imaging: the phase accumulated by the idler photon is simply transferred to the signal photon. Such a modality provides interesting configurations such as where the light hitting the object is at a wavelength not detectable by the used camera. Alternatively, it also works when the object is completely transparent or even completely opaque in the wavelength detected by the camera.  

While this imaging technique is no doubt intriguing, providing materials for many new experiments conducted to this day [5], the exact quantum nature of the method has been debated. Indeed, in [6] it has shown that virtually all the features of the experiment can be realized in a quantum-mimetic fashion using classical light. The discussion has since continued, for example in [7] and [8].

In various undetected photon experiments different nonlinear crystals have been used, such as BBO or PPKTP, but in principle almost any nonlinear process could produce similar results [4]. If you want to join the discussion, get your own crystals at Raicol, where we provide the best  world-class  nonlinear crystals and find your own novel imaging modality!

[1]  Zou, X. Y., Lei J. Wang, and Leonard Mandel. “Induced coherence and indistinguishability in optical interference.” Physical review letters 67, no. 3 (1991): 318.

[2] Wang, L. J., X. Y. Zou, and L. Mandel. “Induced coherence without induced emission.” Physical Review A 44, no. 7 (1991): 4614.

[3] Feynman, Richard P. (Richard Phillips), 1918-1988. The Feynman Lectures on Physics. Reading, Mass. :Addison-Wesley Pub. Co., 19631965. Vol. III, chapter 03, “Probability Amplitudes”.

[4] Lemos, Gabriela Barreto, Victoria Borish, Garrett D. Cole, Sven Ramelow, Radek Lapkiewicz, and Anton Zeilinger. “Quantum imaging with undetected photons.” Nature 512, no. 7515 (2014): 409-412.

[5] Pearce, Emma, Osian Wolley, Simon P. Mekhail, Thomas Gregory, Nathan R. Gemmell, Rupert F. Oulton, Alex S. Clark, Chris C. Phillips, and Miles J. Padgett. “Single-frame transmission and phase imaging using off-axis holography with undetected photons.” arXiv preprint arXiv:2403.13389 (2024).

[6] Shapiro, Jeffrey H., Dheera Venkatraman, and Franco NC Wong. “Classical imaging with undetected photons.” Scientific Reports 5, no. 1 (2015): 10329.

[7] Kolobov, Mikhail I., Enno Giese, Samuel Lemieux, Robert Fickler, and Robert W. Boyd. “Controlling induced coherence for quantum imaging.” Journal of Optics 19, no. 5 (2017): 054003.

[8] Lahiri, Mayukh, Armin Hochrainer, Radek Lapkiewicz, Gabriela Barreto Lemos, and Anton Zeilinger. “Nonclassicality of induced coherence without induced emission.” Physical Review A 100, no. 5 (2019): 053839.

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Author: Dr. Noa Bloch

In nonlinear crystals, a special nonlinear process occurs. A pump photon is spontaneously converted into two complementary photons with lower energy. In this process both energy and momentum are conserved, i.e.   and .

In PPKTP Crystal or APKTP Crystal the  momentum mismatch of the process is compensated by the crystal reciprocal vector which is determined by the spatial frequency .

Vacuum energy and momentum fluctuations give rise to the spontaneous creation and annihilation of many random photons.

But the output photons of the SPDC (spontaneous parametric down-conversion nonlinear process) are the ones that conserve momentum and energy.

In type 1 SPDC  all the photon pairs which conserve momentum are positioned on a ring shaped structure:

In type 1 SPDC  all the photon pairs which conserve momentum are positioned on a ring shaped structure:

See a movie

Changing the temperature or wavelength of the crystal will change the phase matching condition thus radius of the rings will be changed as well as seen in the movie.

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A growing number of companies are switching to industrial RTP crystals for electro-optic Pockels cells

In the past year, there has been a growing trend for industrial companies to switch their traditional Pockels cell (PC) components, mostly KD*P, to industrial RTP Crystal.

The excellent EO properties of RTP, its simple setup and configuration, along with its attractive pricing, makes it a great alternative for current PC solutions. Industrial RTP enables increased ROI for a project, by saving time and money for the laser production line and across the product’s lifetime.


About RTP

RTP belongs to the KTP Crystal family. The outstanding electro-optical properties of RTP, together with its high damage threshold, enable its use in high-end laser applications, it is ideal for use in applications that require advanced characteristics, such as being non-hygroscopic, having high thermal stability, and for higher-repetition rates.

Raicol’s RTP PC is widely recognized for the following features:

  • Higher laser damage threshold
  • Non-hygroscopic material
  • Low absorption losses
  • No acoustic ringing (up to at least 200kHz)
  • Stability over a wide temperature range (10ºC –50ºC)


While providing many advantages over existing solutions, the advanced properties of RTP came with a price tag that prevented its widespread use for industrial applications.


Raicol’s new industrial RTP

Raicol’s new iRTP PC is the first product that brings the advantages of RTP to the EO mass market. The modified iRTP PC version of Raicol’s RTP is especially designed for the needs of the industrial laser market. Raicol’s iRTP PC is a standard off-the-shelf RTP PC that offers high performance EO cells at the price level of standard industry PCs.


iRTP vs KD*P Benefits

  • Improved thermal stability – iRTP has thermal stability over a wide range of temperatures, eliminating the need for thermal stabilization, thus eliminating the need for an oven or thermal control systems.
  • Reduce laser initiation time – RTP’s high thermal stability reduces laser stabilization and start up times, as well as the overall system initiation time.
  • Simple alignment – iRTP requires only 1D alignment to reach an optimum extinction ratio, in comparison to KD*P, which requires 3D axis control-significantly complexifying the alignment process.
  • Environmental stability- iRTP is a non-hygroscopic material with a temperature compensation design that allows it to function in non-controlled environments with a variety of temperatures and humidity levels.
  • Mechanical robustness and stability – iRTP’s requirement for only 1D alignment means that the iRTP package and mount has a simple and more mechanically stable design. The working parameters do not change throughout the laser’s lifetime, or during temperature changes, hence, requires little to no calibration over time.
  • Small size – The size and footprint of iRTP is much smaller compared to similar KD*P, due to a reduction in assembly, alignment, and temperature control components.
  • High repetition rate – iRTP supports a repetition rate up to 200 kHz.
  • Standard Pockels cell assembly – iRTP is an off-the-shelf product with standard industry EO cell specifications.
  • High damage threshold – iRTPs high damage threshold enables its use for high power lasers.

Do you have a question? Our experts will be happy to hear from you and advise you on the best product for you. Contact Us.

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