Author: Ronen Shekel
Quantum and classical ghost imaging
Ghost imaging, one of the first imaging techniques using quantum light, has captivated researchers since its inception in the mid-1990s. The concept of ghost imaging was first demonstrated in 1995 by Pittman et al. [1], using quantum light generated via spontaneous parametric down-conversion (SPDC), a nonlinear optical process that converts a pump photon into two lower-energy entangled photons.
In this experiment (Fig. 1a), the spatially entangled photons are separated, with one photon propagating through an object and being collected using a bucket detector with no spatial resolution, while the idler photon is sent to a multi-pixeled camera. By measuring coincidence events between the bucket detector and the camera, the object is reconstructed, despite the fact that the photons detected by the camera did not directly interact with it! This nonlocal characteristic led to the term “ghost imaging.”
The crux of this technique lies in the spatial correlations of the two photons: areas that are blocked by the object will not reach the bucket detector, so coincidence events will not occur with the corresponding pixels in the camera. But one must remember: correlations do not necessarily imply entanglement! Does quantum entanglement play a critical role in this technique? This was the subject of a debate that lasted several years.
In [2], for instance, theoretical arguments were presented, suggesting that entanglement is intrinsic to ghost imaging. However, in 2002, Bennik et al. [3] demonstrated ghost imaging using two classically correlated beams, randomly deflected at different angles. Others explored similar classical correlations using a rotating diffuser [4], generating correlated pseudo-thermal light (Fig. 1b).
Computational ghost imaging
An important fruit of this debate was that of computational ghost imaging, proposed by Shapiro [5], and demonstrated by Bromberg et al. [6]. In this method, only a single detector is used, and the high-resolution camera is replaced by a computation of the propagating field which is shaped using a spatial light modulator (Fig. 1c). The key point here is that we know everything about the photon propagating to the camera, so we can utilize this knowledge computationally and get rid of the physical camera. The object image is obtained by correlating the intensities measured by the bucket detector with the calculated field at the object plane.
While this computational approach already simplified the experimental setup, researchers soon realized [7] that the number of measurements could be significantly reduced by leveraging modern image processing techniques, particularly those that exploit prior knowledge about the image structure. Remarkably, for most imaging tasks, such information exists: natural images are sparse, that is, they contain many coefficients close to or equal to zero when represented in an appropriate basis. This property of natural images is at the core of modern lossy image compression algorithms, such as JPEG. The field of compressed sensing exploits this sparsity/compressibility to reduce the number of measurements needed for faithful image recovery. Utilizing this technique reduces the number of measurements required for a faithful reconstruction by an order of magnitude.
Current state and future directions
The fact that computational ghost imaging uses only a single detector provides experimental evidence that pseudothermal ghost imaging does not inherently rely on nonlocal quantum correlations. It is now also recognized that the quantum and classical methods produce images of a similar resolution. The main advantage of utilizing quantum light for ghost imaging is found at low light levels, at which the quantum modality exhibits greater visibility and a greater signal-to-noise ratio [8]. This could be especially important when imaging samples that are sensitive to high light levels. Further details comparing the classical and quantum modalities may be found in [9].
Almost 30 years since its first demonstration, many extensions, applications, and modalities of ghost imaging are still being explored. Are you interested in ghost imaging with quantum light? Or perhaps want to explore other use cases for quantum entanglement? Please check out our PPKTP crystal and BBO crystals, used for generating entangled photons, and join the conversation!
[1] Pittman, Todd B., Y. H. Shih, D. V. Strekalov, and Alexander V. Sergienko. “Optical imaging by means of two-photon quantum entanglement.” Physical Review A 52, no. 5 (1995): R3429.
[2] Abouraddy, Ayman F., Bahaa EA Saleh, Alexander V. Sergienko, and Malvin C. Teich. “Role of entanglement in two-photon imaging.” Physical review letters 87, no. 12 (2001): 123602.
[3] Bennink, Ryan S., Sean J. Bentley, and Robert W. Boyd. ““Two-photon” coincidence imaging with a classical source.” Physical review letters 89, no. 11 (2002): 113601.
[4] Valencia, Alejandra, Giuliano Scarcelli, Milena D’Angelo, and Yanhua Shih. “Two-photon imaging with thermal light.” Physical review letters 94, no. 6 (2005): 063601.
[5] Shapiro, Jeffrey H. “Computational ghost imaging.” Physical Review A—Atomic, Molecular, and Optical Physics 78, no. 6 (2008): 061802.
[6] Bromberg, Yaron, Ori Katz, and Yaron Silberberg. “Ghost imaging with a single detector.” Physical Review A—Atomic, Molecular, and Optical Physics 79, no. 5 (2009): 053840.
[7] Katz, Ori, Yaron Bromberg, and Yaron Silberberg. “Compressive ghost imaging.” Applied Physics Letters 95, no. 13 (2009).
[8] Moreau, Paul-Antoine, Ermes Toninelli, Thomas Gregory, and Miles J. Padgett. “Imaging with quantum states of light.” Nature Reviews Physics 1, no. 6 (2019): 367-380.
[9] Erkmen, Baris I., and Jeffrey H. Shapiro. “Ghost imaging: from quantum to classical to computational.” Advances in Optics and Photonics 2, no. 4 (2010): 405-450.
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Author: Yoad Michael
PPKTP Crystal is a quasi-phased-matched crystal that converts light of one wavelength into a different wavelength. The original purpose of this crystal was humble: It was designed to be an efficient frequency converter for laser system by second harmonic generation. However, with recent advances in quantum optics, the process of spontaneous parametric down conversion (SPDC) is now the dominating application of PPKTP.
SPDC is a process in which a strong pump beam is converted into correlated photon pairs, coined Signal and Idler. These correlations are the basis for various sources of quantum light, such as heralded single photons, time-energy or polarization entangled photon pairs, and squeezed light.
While it is convenient to consider only the quantum properties these light sources, the nonlinear properties of the interaction play a very significant role. For example, in PPKTP, the phase matching can be fully controlled such that: the signal and idler have the same polarization (type-0) or orthogonal polarization (type-2), same wavelength (degenerate) or separate wavelengths (nondegenerate), emitted along the direction of the pump beam (collinear) or at some angle (noncollinear). The type-0/type-2 is determined by the polling period and is something that needs to be determined at the manufacture stage, while degeneracy and collinearity can be fine-tuned by temperature (to avoid working at bizarre temperatures, it is advised to specify these parameters beforehand and adjust the polling period).
We can dive deeper into these differences. Polarization is not the only optical property that changes between type-0 and type-2 interactions; Spectral bandwidth, pair rate, and tolerance to temperature are also different. This is best illustrated by the wonderful work of the Ursin group [1], in which they compared type-0 and type-2 crystals as sources of polarization entangled photon pairs. As shown in Figure. 1, Type-0 is significantly broader than Type-2 and can be made nondegenerate by temperature tuning. In addition, the authors reported that the pair generation (per nm) of type-0 is about 10 times higher than that of type-2.
To make things a little more complicated, the dispersion and the length of the KTP Crystal also affects the spectral bandwidth and pair rate. Longer crystals generate more pairs at the cost of reduced spectral bandwidth, and signal/idler photons are much broader at telecom wavelengths (~1550) than they are at NIR (~810).
All these examples show that PPKTP is an extremely versatile component, and it is therefore important to first consider the needs of each application before choosing the right crystal. Below we present a few recent utilizations of PPKTP for various applications and provide our recommended crystal. We are proud to say that all this knowledge came from the brilliant researchers that use our PPKTP Crystals and shared their findings with the scientific community. Feel free to contact us if you think we are missing a key application or research work.
Boson Sampling and quantum interference
In Boson Sampling, quantum light is usually placed at the input of a large interferometer that includes multiple splitting and re-combining of beams. Boson Sampling relies on quantum interference (Hong-Ou-Mandel effect) and therefore benefits from high spectral purity. Special efforts were made by the Fedrizzi group for creating aperiodically polled crystals for high spectral purity at 1550nm [2], and a similar design was implemented by USTC’s photonic quantum supremacy experiment [3]. Recent quantum computing efforts by Xanadu [4] and QuiX [5] utilized PPKTP at the same wavelength region, due to both higher purity at these wavelengths and compatibility with peripheral platforms such as Silicon Nitride. Raicol has developed (through a collaboration with Prof. Ady Arie) a method for the design and manufacture of high spectral purity APKTP Crystals for Boson sampling and quantum interference close to the group velocity matching point of 1550nm.
Recommended Crystal: Type-2 APKTP or PPKTP at 775->1550. APKTP offers higher spectral purity while PPKTP offers higher pair rate.
Quantum Key Distribution
PPKTP plays a role in entanglement-based QKD as a source of polarization-entangled photon pairs. In this field there are many available options depending on whether the system is designed for free-space or fiber. In general, detector efficiency and the availability of 405nm lasers usually pushes these applications towards entanglement at 810nm [6, 7]. Type-2 crystals are easier to use because of their narrow linewidth, easy separation of the signal and idler with a polarizing beam splitter, and robustness to temperature, while type-0 crystals are broader and offer higher pair rate, making them good candidates for multiplexed QKD [8].
Recommended Crystal: Type-0 or Type-2 PPKTP at 405->810. Type-0 offers higher pair rate and spectral bandwidth, while Type-2 offers ease of usability.
Squeezed Light
Squeezed light usually utilizes the crystals in the strong pumping regime (unlike heralded single photons or polarization entanglement), and benefits from a strong nonlinear response, therefore making type-0 crystals the favorable option. Examples include the Furusawa group with 9dB of squeezing at 860nm [9], The Schnabel group has demonstrated 15dB and 13dB of squeezing at both 1064 and 1550nm [10, 11], and the Bowen group using the former for a demonstration of squeezing-enhanced microscopy [12]. Squeezed light can be generated anywhere from 780nm (390nm pump) to 3.8 microns and is a function of the exact specific application.
When choosing a crystal for squeezed light applications, the researcher should first decide if the squeezing is going to be generated in single-pass or in a cavity. For the former, a standard crystal suffices, while for an optimal parametric oscillator, monolithic or hemi-monolithic options are preferred [13].
Recommended Crystal: Type-0 ppKTP, optional hemi or fully monolithic.
Imaging With Undetected Photons
Imaging with undetected photons usually utilizes type-0 crystals with varying degeneracy. For fundamental research it is convenient to be able to detect both photons [14], while the Ramelow group generated a signal in the visible and idler at the mid-IR for microscopy applications [15].
Recommended Crystal: Type-0 PPKTP, with a period that is designed for nondegeneracy. No better example than Ramelow’s 660->800+3800.
We will try to update this list periodically, so visit this page every now and then!
Bibliography
[1] Steinlechner et al. “Efficient heralding of polarization-entangled photons from type-0 and type-II spontaneous parametric downconversion in periodically poled KTiOPO4”, JOSA B 31, 9, 2068-2076 (2014).
[2] Graffitti et al. “Independent high-purity photons created in domain-engineered crystals”, Optica 5, 5, 514-517 (2018).
[3] Zhong et al. “Quantum computational advantage using photons”, Science 370, 6523, 1460-1463 (2020).
[4] Madsen et al. “Quantum computational advantage with a programmable photonic processor”, Nature 606, 75–81 (2022).
[5] Taballione et al. “20-Mode Universal Quantum Photonic Processor”, arXiv:2203.01801.
[6] Yin et al. “Entanglement-based secure quantum cryptography over 1,120 kilometres”, Nature 582, 501–505 (2020).
[7] Mishra et al. “BBM92 quantum key distribution over a free space dusty channel of 200 meters”, Journal of Optics, 24, 7 (2022).
[8] Brambila et al. “Ultrabright Polarization-Entangled Photon Pair Source for Frequency-Multiplexed Quantum Communication in Free-Space”, arXiv:2205.10214.
[9] Takeno et al. “Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement”, Optics Express 15, 7, 4321-4327 (2007).
[10] Vahlbruch et al. “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency”, Physical Review Letters 117, 110801 (2016).
[11] Schönbeck et al. “13 dB squeezed vacuum states at 1550 nm from 12 mW external pump power at 775 nm”, Optics Letters 43, 1, 110-113 (2018).
[12] Casacio et al. “Quantum-enhanced nonlinear microscopy”, Nature 594, 201–206 (2021).
[13] Ast et al. “High-bandwidth squeezed light at 1550 nm from a compact monolithic PPKTP cavity”, Optics Express 21, 11, 13572-13579 (2013).
[14] Gilaberte Basset et al. “Video-Rate Imaging with Undetected Photons”, Laser & Photonics Reviews 15, 6 (2021).
[15] Kviatkovsky et al. “Microscopy with undetected photons in the mid-infrared”, Science Advances 6, 42 (2020).
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Author: Dr. Noa Voloch Bloch and Ori Levin
Difference Frequency Generation (DFG) and Sum Frequency Generation (SFG) are crucial processes in modern laser systems, allowing for the generation of new optical frequencies by mixing two distinct wavelengths. For professionals in industries such as defense, aerospace, medical, and industrial applications, selecting the right nonlinear crystal is critical to achieving optimal performance.
With over 50 years of experience in crystal growth, Raicol Crystals is at the forefront of providing high-quality nonlinear optical crystals and electro-optical components for laser systems worldwide. In this article, we will explore key aspects of DFG and SFG and how Raicol’s expertise in crystal manufacturing can significantly enhance the efficiency and precision of your laser systems.
1. What are Difference Frequency Generation (DFG) and Sum Frequency Generation (SFG) and How Do They Work? Difference Frequency Generation (DFG) is a nonlinear optical process in which two laser beams with different frequencies mix within a nonlinear crystal to produce a new output beam at the frequency difference between the two input beams. Conversely, Sum Frequency Generation (SFG) combines two input wavelengths to create a new beam at the sum of their frequencies. The crystals’ nonlinear susceptibility couples between the different laser input and create a new frequency output.
2. These techniques are essential for producing tunable sources of coherent radiation in the infrared, terahertz, and visible regions.
- Second Harmonic Generation (SHG) is a special case of Sum Frequency Generation (SFG) where two photons of the same frequency combine to produce a single photon with twice the frequency (or half the wavelength) of the input light. In this degenerate process, two identical photons from the fundamental beam are converted into one photon at the second harmonic through interaction with a nonlinear optical material.
The efficiency of this process depends critically on phase-matching conditions within the nonlinear crystal. SHG has become a widely used technique for generating new frequencies, particularly for accessing shorter wavelengths in laser systems and spectroscopic applications.
Raicol Crystals specializes in providing nonlinear crystals optimized for both DFG and SFG applications. By selecting the right material and engineering the crystal to meet specific wavelength requirements, Raicol ensures that DFG and SFG systems achieve high efficiency, precision, and stability. This makes their nonlinear crystals ideal for advanced laser systems requiring reliable and precise frequency control.
2. Which Nonlinear Crystals are Suitable for DFG and SFG?
- The efficiency of DFG and SFG processes depends significantly on the nonlinear crystal’s properties, including its nonlinear coefficient, damage threshold, and phase-matching capabilities. Commonly used nonlinear crystals for DFG and SFG include Potassium Titanyl Phosphate (KTP), Beta Barium Borate (BBO), and periodically poled lithium niobate (PPLN). These materials offer excellent nonlinear properties, high damage thresholds, and thermal stability in various wavelength ranges.
Raicol Crystals specializes in high-quality oxide-based nonlinear crystals, such as these, that are designed to handle high power, high efficiency, and thermal stability in laser systems. Additionally, Raicol’s ability to offer customized solutions means that customers can select the optimal material tailored to their specific DFG and SFG needs. Whether it’s for medical diagnostics, industrial applications, or defense systems, Raicol’s products ensure maximum performance in frequency generation applications.
3. How do Nonlinear Crystals Enhance DFG and SFG Efficiency?
- The efficiency of DFG and SFG heavily relies on the properties of the nonlinear crystal, such as its nonlinear coefficient, transparency range, and phase-matching capabilities. For maximum efficiency, the crystal must support the specific phase-matching conditions for the wavelengths of the input beams.
Raicol Crystals leverages over 50 years of expertise in crystal growth to provide customized solutions that enhance DFG and SFG efficiency. Their nonlinear crystals are optimized for high conversion efficiency, low losses, and the ability to handle high-power lasers. Raicol’s advanced manufacturing processes ensure that each crystal is precisely engineered to support the phase-matching conditions, allowing for superior performance in demanding applications.
Raicol’s tailored solutions enable clients to achieve the best possible output from their DFG and SFG systems, improving efficiency and ensuring reliable, high-quality results, particularly in critical industries like defense, aerospace, and medical diagnostics.
4. Why Choose Raicol Crystals for DFG and SFG Applications in Industrial and Defense Sectors?
- Raicol Crystals is a global leader in manufacturing nonlinear crystals, with deep expertise in the specific requirements of the defense and industrial sectors. Their advanced crystal solutions enable high-performance systems essential for applications like advanced radar, laser weapons, and high-resolution spectroscopy.
By offering customized nonlinear crystals that are engineered to meet the specific needs of these industries, Raicol ensures that its customers can achieve the precision and reliability required for mission-critical systems. Whether you’re designing next-generation defense technologies or enhancing industrial laser applications, Raicol’s nonlinear crystals provide the high performance necessary for success.
5. How Raicol Crystals Supports Medical Field with DFG and SFG Applications?
- In the medical field, DFG and SFG processes are used in non-invasive imaging techniques. The ability to generate precise wavelengths through these frequency generation methods enables improved resolution and sensitivity in medical imaging systems, making them valuable tools for diagnostics.
Raicol Crystals manufactures nonlinear optical crystals that are ideal for DFG and SFG applications in medical imaging. Their customized crystals ensure high frequency conversion efficiency, enhancing the performance of optical diagnostic devices. By optimizing the wavelength conversion process, Raicol’s crystals improve the clarity and accuracy of medical images, aiding in better diagnostic procedures and patient outcomes.
Conclusion: Why Raicol Crystals is the Optimal Choice for DFG and SFG Applications Difference Frequency Generation (DFG) and Sum Frequency Generation (SFG) play critical roles in many of today’s advanced optical technologies. For industries like defense, aerospace, medical, and industrial applications, the performance of DFG and SFG systems is intrinsically linked to the quality of the nonlinear crystals used.
Raicol Crystals, with over 50 years of expertise in crystal growth and a proven track record of providing high-quality nonlinear optical crystals, is the ideal partner for your DFG and SFG applications. Their commitment to precision, customized solutions, and high-performance products ensures that your frequency generation systems operate at peak efficiency and deliver optimal results.
Whether you’re enhancing the performance of existing laser systems or developing cutting-edge technologies, Raicol Crystals provides the knowledge, technology, and products needed to succeed.
Explore Raicol’s range of nonlinear optical crystals and electro-optical components to take your DFG \SFG systems to the next level.
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