### From present to past**:**

[See in #27 and #18 two questions (“WHY…?”) with explanations.]

**36. Quantum-based Bose-Einstein Condensation (BEC) of photons in everyday fibers.**

**“Bose-Einstein condensation (BEC) of photons in an Er-Yb co-doped fiber cavity”**

Paper 106. Nature Comm. **10**, 747 (2019) or 106. Nature Comm. **10**, 747 (2019), Supplementary Information.

and “**Bose-Einstein condensation (BEC) of photons in a long fiber cavity”. **Paper 108. Opt. Express **29**, 27807 (2021), or in pdf Opt. Express **29**, 27807 (2021).

Bose-Einstein condensation (BEC) was predicted in 1924-5 but it took 70 years to experimentally observe it. Such condensates, with a large portion of the particles occupying the ground-state at a nonzero temperature, were considered a new form of matter, a “*quantum phase*“, where the quantum regime covers many particles and rules their overall wave-function. BEC was experimentally demonstrated in 1995 by two groups with bosonic atoms at ultra-low temperatures of a few hundred nano-Kelvin (and therefore system cost of many million Dollars). They were awarded for this observation the 2001 Nobel Prize in Physics.

**We demonstrated** (Nature Comm. **10**, 747 (2019), and Opt. Express **29**, 27807 (2021)) **quantum-based BEC of photons in a standard one-dimensional (1D) erbium-ytterbium co-doped fiber cavity at, below and above room temperature **(cost of a few hundred Dollars). Photons are bosons, but usually their number is not conserved and therefore they have a zero chemical potential that cannot yield BEC. However, it can be different in some cases of cavities with gain and low photon loss-rates, as it is in our fiber system. The first paper (Nature Comm.** 10,** 747 (2019)) uses the standard linear dispersion relation in fibers and the BEC is based on a finite fiber cavity size effect in 1D. The second paper (Opt. Express **29**, 27807 (2021)) uses a special sublinear dispersion and therefore the photon-BEC there is valid also in the long fiber cavity limit.

**35. Photon thermalization in everyday fibers, showing broad Bose-Einstein spectra and lasing without an overall inversion.**

We found spectra that have not been seen yet in light gain media such as the probably most frequently used one, erbium-doped fiber (edf). Our observation differs from the commonly accepted view that photons in lasers are not in thermal equilibrium, and don’t show Bose-Einstein spectral distribution and Bose-Einstein condensation (BEC). We show thermalization of photons in standard one-dimensional (1D) edf cavities and even in open edf, and unusual Bose-Einstein spectra in a range that reach ~200 nm, and lasing without an overall inversion.

Paper: 103. Opt. Express **25**, 18963 (2017) or in pdf: 103. Opt. Express **25**, 18963 (2017)

Supplementary Video on the spectrum evolution of photon thermalization in an open erbiun-doped fiber

“**Breaking two laser axioms: Lasing without an overall inversion and thermal equilibrium”: **Paper 102: arXiv 1607 01681 (2016) (v. 1), or arXiv 1607 01681 (2016) (v. 2), or in pdf arXiv 1607 01681 (2017) (v. 2).

**34. Noise-mediated Casimir-like light pulse interaction in lasers. **

Optica **3**, 189(2016), (Paper 100), Supplementary material.

A new universal interaction mechanism between pulses mediated by noise in multi-pulse passively mode locked laser cavities. The interaction arises because of the suppression of the fluctuations of the radiation field, as does the attraction of conductors in the Casimir effect in quantum electrodynamics.

**33. Unusual (sub-linear) light dispersion in fibers**

Paper 107. “Nonlinear light mode dispersion and nonuniform mode comb by a Fabry-Perot with chirped fiber gratings, *Opt. Express* **28, **18135 (2020); or pdf: Opt. Express **28, **18135 (2020).

**32. Classical condensation phenomena in lasers.**

Theoretical prediction of classical condensation of laser light and experimental demonstration of it **in three different laser systems**: **(i)** many single-pulse eigen-modes in an actively mode-locked laser, **(ii)** a many-pulse laser system and **(iii)** a many-mode cw-laser. These condensations are based on weighting the modes/pulses in a loss-gain scale, [and not in an energy (frequency) hierarchy of regular BEC], in a noisy environment that has the role of temperature.

Papers:

**(i)** In an actively mode-locked laser: Theoretical Paper 89 (Phys. Rev. Lett. **104**, 173901 (2010)), and experimental Paper 91, (Opt. Express, **28**, 16520 (2010)). See also paper 97.

**(ii)** In a many pulse system in a loss-trap: Experimental Paper 99, (Optica **1**, 145 (2014)).

**(iii)** In a many-mode CW laser: Theoretical paper 96 (Opt. Express **20**, 26704 (2012), and experimental paper 101 (Opt. Express **24**, 6553 (2016)).

**31. “To BEC or not to BEC of photons in optical cavities?”.**

Papers: 96 (Opt. Express **20**, 26704 (2012) or in pdf: Opt. Express **20**, 26704 (2012), 97.

Conditions for classical condensation in lasers and questions on quantum-based photon-BEC.

**30. Presentation of “Many-Body Photonics”****.**

Paper 98, __(Optics & Photonics News (OPN) 24, 40, 2013).__

Statistical mechanics is key to understanding thermodynamic systems, but most people don’t think of it as a tool for describing what goes on in photonics. **Baruch Fischer** begs to differ. “Adding many-body physics to photonics is challenging and rewarding,” he said. “How otherwise can one deeply understand, for example, laser mode-locking and the role of noise there? It would be like being limited to watching the world around 0 K— frozen in an ice age with no water and no melting.”

**29. Light mode hyper-combs:**

Construction of hyper-combs, mode combs at any dimension (even higher than 3), from a one-dimensional actively mode-locked (AML) laser with a multi-frequency modulation. It is mapped to the S*pherical-M**odel* of magnetic spins in statistical-mechanics in any dimension which is the only one **soluble** many-body model in all dimensions, exhibiting a phase transition at dimensions higher than 2. The laser hyper-comb provides a rare physical realization of the S*pherical-Model in any (synthetic) dimension*, with potential to robust ultra-short light pulse generation. Paper 98 (*Opt. Express* **21**, p. 6196, 2013).

**28. Prediction and experimental observation for the first time critical behavior of light in passively mode-locked (PML) lasers, and also prediction and observation of the critical exponents. **

We showed the phase diagram of modes in PML lasers with externally injected pulses in the “*x-h-T* ” (= pulse strength – external pulse strength – noise) space, that is remarkably similar to the thermodynamic *n-P-T* (density – pressure – temperature) or *m-h-T* (magnetization – external magnetic field – temperature) phase diagrams of gas-liquid or magnetic-spin systems. We found “para-pulse” and spontaneous “ferro-pulse” regimes, similar to para- and ferro-magnetic phases, with a first-order phase-transition line (surface) between them that ends at a critical point (line). We verified all that experimentally.

**Videos from the experiment** showing the pulse change along two paths in the phase diagram:

– An ubrupt “para-pulse” to “spontaneous-pulse” phase transition,

– A smoother transition near the critical point.

**The critical exponents prediction and observation.** Papers 70, 90.

Those predicted to be the “classical” mean field values (β=1/2, γ=1, δ=3 ) which are exact in our laser light system. The experimental critical exponents were found to follow the theoretical prediction values.

**27. Inherent difference between active and passive mode-locking (AML and PML) via Many-Body Photonics.** Papers on AML: 60, 98; PML: 49, 54, 57, 63, 69); And an overall review: 97.

**WHY **are the shortest light pulses that can reach the few femto-seconds regime usually obtained by passive mode locking (PML) and not by active mode-locking (AML)**?**

**It can be inherently explained** by the many-body SLD view. It is connected to the one-dimensionality (1D) of regular lasers and mode systems, and the range of the interaction between modes. In one-dimensional many-body systems with a short range (near neighbor or finite neighbors) interaction between particles (spins, and here modes) there can be only limited string lengths of aligned spins (in the spatial domain, or in our case, phase-aligned modes in the frequency domain) without an overall ordering (phase-transition) at any temperature (or noise), even very low. The temperature (noise) can easily break a long aligned spin chain into two or more segments of aligned spins (modes), where the average segment length depends on the temperature or noise. Since such bond breaking can occur at every spin-spin (or mode-mode) site, with a minimal energy cost of one broken bond, the entropy in the free energy or the partition function dominates over the binding energy and eliminates any phase-transition to an overall alignment at any small temperature or noise. This is the case in AML in 1D with many modes under a regular modulation (where the modulation connects each mode to its neighbors), and therefore even very low noise (“temperature”) breaks the phase ordering and leaves only limited segment lengths of phase-aligned modes. Therefore, in AML not all the modes and the full frequency band participate in the phase ordering that provides the pulses in the time domain (Papers 60, 98). However, the mode system in PML lasers exhibits a phase transition at a nonzero noise to an overall ordered phase even in 1D due to the long range mode-mode interaction (absorptive four-wave mixing) induced by the saturable absorber (Papers 49, 54, 57, 63, 69, 97). AML, however, can overcome the dimensionality limitation by a complex modulation such as what we used for the mode hyper-combs (Paper 98) or with non-sinusoidal modulations. We note that the above arguments hold in the thermodynamic limit but they are applicable for systems with a finite but large number of particles (modes).

**26. ****Extension and solution of the SLD theory for any laser parameters beyond the soliton condition regime.** Papers: 79, 87.

It is done by a special gain-balance principle that we formulated and applied. The general parameter laser case is parallel to non-equilibrium thermodynamic systems. We emphasize that the “equilibrium” in our laser system, where noise has the role of temperature, in the soliton condition parameters regime is mathematically parallel to thermal equilibrium but it is not equilibrium in the thermodynamics sense. (Lasers are usually not in thermal equilibrium except special cases). The general laser parameters case (except where the soliton condition is met) is mathematically out of of “equilibrium”.

**25. Multi-pulse formation in a passively mode-locked laser in a cascade of first order phase transitions** (theoretical and experimental**). **Papers: 64, 84, 93, 95.

**Video from**** the experiment **on cascaded multi-pulse formation and annihilation of light pulse quanta in passive mode-locked lasers as the noise power (“temperature”) is varied (Paper 64):

**24. Many-Body Photonics: A new powerful approach for complex nonlinear light-wave systems – Statistical Light-mode Dynamics (SLD). **

Papers: 49, 52, 54, 57, 60, 63, 64, 69, 72, 79, 80, 84, 87, 88, 89, 90, 91, 93, 95, 96, 97, 98.

It is based on statistical-mechanics, analyzing many interacting light-wave mode systems, where noise takes the role of temperature. It provides a fundamental theory of pulses formation in passive mode-locking using an exactly solvable statistical mechanics model. It was the base for finding, theoretically and experimentally, that the mode system in passively mode-locked (PML) lasers undergoes a first order phase-transition when pulses are formed as usually the power is varied, and the same transition happens when the noise (the “temperature”) is varied. It explainins long standing questions on the power threshold and the abrupt transition to pulsation in PML.

PML is nothing but a first order phase transition. Exactly like in thermodynamics, it is a “Melting-Freezing” pathway of pulses (similar to gas-liquid-solid and ferromagnetic phase transitions). It thus replaces the *mechanics* view on those laser systems by a rich *statistical-mechanics* (*“thermodynamics”*) approach.

Passive mode-locking as a phase-transition was **globally solved for any laser parameters**: Paper 79.

**23. Experimental demonstration of “time-lens”, temporal differentiation of optical signals with a special fiber Bragg grating, “pulse-optics” and temporal Talbot-effect-based operations.** Papers: 45, 46, 50, 51, 56, 58, 59, 62, 65, 66, 67, 68, 71, 73, 75, 76, 77, 78, 81, 82, 83.

**22. Anderson Localization of light-waves: Experimental demonstration in random fiber grating arrays.** Papers: 74a, 74b.

**21. Localization of light: **Presentation and demonstration of two localization effects of light-waves in **“Optical Kicked Rotors**” – at the spatial frequency and temporal frequency domains. Papers: 40, 42, 43, 44, 48, 55.

**20. “Dispersion-Modes” (a new kind of modes in pulse lasers), and uses of the temporal Talbot self-imaging properties in dispersive fibers.** Papers: 44, 50, 51, 53.

**19. Invention of a novel tunable laser. (RF-addressed wavelength-switching.** Patents 7, 9, Paper 105, and Videos in paper 105: Video S1, Video S2.

It is based on a concept of cavity resonance activated wavelength selection (CRAWS) in mode-locked lasers. It gives superior features with nano-sec switching times and robust wavelengths, useful for WDM in fiber-optic communication.

**18. Induced saturable-gain and saturable-absorption gratings and wave-mixing in erbium-doped fibers and obtaining a ****new single mode, ultra-narrow linewidth fiber laser by special self-filtering effect in erbium-doped fibers.** Papers: *36a*, 36b, 39a, 39b, 41 and Patents 5, 8.

Fibers and fiber amplifiers that have had a tremendous impact on the field of optical communication, can also provide strong nonlinear and wave-mixing effects (induced gratings), with potential “all-optical” applications. For example, we have demonstrated a special fiber laser with an ultra-narrow line-width which is based on nonlinear wave-mixing (induced satuarable-absorption gratings) inside the laser cavity. Another example is a controllable filter based on dynamic saturable gain and absorption gratings in erbium-doped fibers.

**SO WHY** in usual lasers doesn’t the counter-propagating waves interference that can induce long saturable-gain gratings and distributed reflections provide a self line-narrowing mechanism and feedback for lasing even without mirrors**?**

**One simple answer is** that the reflections have a π (pi) phase-shift (a minus sign) with respect to their co-propagating waves (see papers *36a*, and 36b), and therefore destructively interfere with them. **Or, in a different way:** the interference that induces the saturable grating reduces the gain in “wrong” places: where the light intensities are high due to interference, the saturation grating provides a low gain, and a high gain where the intensities are low (**=** spatial hole-burning). Therefore, the overall gain is lowered, promoting oscillation at other close wavelengths that can use the unsaturated gain places due to different interference patterns, and thus enhancing line-broadening. However, it is opposite in saturable-absorption gratings, that can be obtained in the same medium, like edf, but un-pumped. Then the reflections have a phase 0 with their co-propagating waves and thus constructively interfere with them. Or again in a different way: in the interference pattern, the absorption is low (saturated) where the intensities are high and high where the intensities are low. Then the overall absorption for both counter-propagating beams is lowered, compared to a single beam propagation or no interference case. This is the idea behind our laser self line-narrowing (paper 39a, 39b) and the filters (paper 41) works that use induced saturable absorption gratings (un-pumped edf). The bad side of the induced gain grating part due to interference can be eliminated by setting orthogonal polarizations for the counter-propagating waves, or letting in the gain part propagation in only one direction that is possible in a ring cavity.

**17. A method for opticial “writing” and fixing microscopic structures for holographic image storage, and quasi-phase-matching for second harmonic generation in photorefractive SBN crystals. **Papers: 35, 37, 38 and Patent no. 6.

Besides fixing and storing volume holographic images, it enabled the formation of domain gratings and quasi-phase matching for optical narrow-band and broad-band second harmonic generation.

**16. Passive transverse-modes-locking with saturable-absorber. **Papers**:** 33a, 33b.

It was the first experimental demonstration of passive transverse-modes-locking of a laser with phase-conjugate mirrors. Passive mode-locking of longitudinal modes that was invented and known from the 19-sixties is the major way for obtaining very short light pulses; (see point 27 on passive and active mode-locking). It is based on the insertion of a saturable-absorber (SA) in a laser cavity that promotes short pulses generation by locking the phases of many longitudinal modes. Another way for obtaining energy compression that could be obtained in the transversal space dimension was not considered in the past, presumably because it requires the oscillator to support a large number of transverse modes with low losses with frequencies that are not necessarily equally spaced. In this work we demonstrated such a locking phenomenon by a special resonator formed by two photorefractive phase-conjugate mirrors that can support a large number of transverse modes. The SA was a film of Bacterio-Rhodopsin in a polymer matrix.

**15. Wave-mixing, phase conjugation and self-defocusing with Bacterio-Rhodopsin.** Papers: 30a, 30b.

It was a first use of bacteria-based medium for nonlinear wave-mixing.

**14. Presenting the concept of “Photorefractive Self-trapping ” and “Photorefractive Spatial Soliton”.** Papers: 28, 34 and Ph.D. Thesis by M. Segev (“Photorefractive wave-mixing and applications in Waveguides and Semiconductor Lasers”, Technion, Israel Inst. of Technology, Aug. 1990).

**13. Photorefractive self-defocusing, multi two-wave mixing and the Fanning Effect.** Papers: 28, 29.

**12. Use of phase conjugation and the Double Phase Conjugate mirror to self coupling of semiconductor lasers, laser arrays and fiber arrays.** Papers: 17, 22, 25, 31.

**11. The Double Color Pumped Photorefractive Oscillator** (Double phase conjugation with two beams having different colors). Papers: 24, 23, 26.

**10. Discovery and demonstration of the Double Phase Conjugation and the Double Phase Conjugate Mirror (DPCM), **also called Mutually Pumped Phase Conjugate Mirror.

Papers: 19, 17, 18, 21, 22, 25, 26, and Ph.D. Thesis by S. Weiss (“Dynamics of Photorefractive Oscillators and Cavities”, Technion, Israel Inst. of Technology, Sept. 1989).

It couples two complex optical waves (two beams with images), which can be mutually incoherent, pumping each other and generating for each of them their phase conjugate “time-reversal” replica.

**9. Self frequency detuning in Photorefractive Oscillators, and based on that a new Optical (Photorefractive) Gyroscope.** Papers: 14, 15, 16, 26, and Patent 2.

**8. Image transmission and interferometry through multimode fibers by phase-conjugation. ** Papers: 13, 18, 21.

**7. Demonstration of one-way optical field imaging through phase distortions (Phase-Conjugate Window). ** Paper 8.

**6. Invention of the first Self-Pumped (Passive) Phase Conjugate Mirrors. **Papers: 5, 10, 11, 12.

It generates a “time-reversed” waveform via a back-reflected light beam that carries pictorial information, without the need of external pumping. It is based on photorefractive nonlinear four-wave mixing where three waves besides the first one with the image, the two pumps and the phase conjugate wave, are self induced by oscillation. Thereafter other types of Self-Pumped Phase Conjugate Mirrors (SPPCM) or Passive Phase Conjugate Mirrors (PPCM) were found: the Semi-Linear, the Linear and the Ring PPCM (SPPCM).

**5. First demonstration of photorefractive wave mixing, photorefractive oscillation and (self-pumped) phase conjugation with SBN crystals.** Paper 6.

**4. Foundations of the research field – “Nonlinear Photorefractive Optics”.** Papers: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 34, 35, 37, 38.

**3. Formulation of the basic and complete equations for Nonlinear Photorefractive Four-Wave Mixing, and their analytical solutions. ** Papers: 4, 7, 12.

**2. Model and properties of Dipole-Glasses and Strain-Glasses.** Papers: 2, 3a, 3b.

**1. Magnetic and electric dipole interaction in two-dimensional metals. **(Oscillatory RKKY interaction in 2D). Paper 1.