Ti:S can indeed be LD pumped, as can Alexandrite: [O3], Solid-State Lasers - A Graduate Text, page 85, says 'Alexandrite can operate both as a 4-level vibronic laser and as a 3-level system analogous to Ruby. As a 3-level laser it has a high threshold, fixed output wavelength of 680.4nm at room temperature [680nm + 266nm = 191.205nm and 680.4 = 191.237nm], and relatively low efficiency. The absorption peak near 680nm has been exploited using diode laser pumps.'

​

As for about my idea of  Alexandrite at 750.4nm, yielding 196nm; Alexandrite absorption peaks are
420nm & 580nm, with my estimated ranges 370-470, 540-650nm based on the graph shown here:

http://www.northropgrumman.com/BusinessVentures/SYNOPTICS/Products/LaserCrystals/Documents/pageDocs/Alexandrite_absorption_chart.pdf

Found here:

http://www.northropgrumman.com/BusinessVentures/SYNOPTICS/Products/LaserCrystals/Pages/Alexandrite.aspx

​

Nd:YAG characteristics & absorption graphs, my estimated peaks: 590, 740, 750, 793, 810, [807.5nm]

Nd:YAG characteristics & absorption graphs, my estimated range: 350-370, 450-600, 790-830, 869, 885nm:

http://www.northropgrumman.com/BusinessVentures/SYNOPTICS/Products/LaserCrystals/Pages/NdYAG.aspx

​

Nd:YLF characteristics & absorption graph, my estimated range:  780-815, 865nm:

http://www.northropgrumman.com/BusinessVentures/SYNOPTICS/Products/LaserCrystals/Pages/NdYLF.aspx

Nd:YLF absorption peaks: 750, 793, 798, 804nm: 

http://www.alphalas.com/images/stories/products/laser_components/Laser_Crystals_ALPHALAS.pdf

​

​

Peaks:  Emission   Absorption (peak = |, range = ...)                             Absorption ranges

Nd:YAG      1064                 ..............|590           ||750.|808..        450-600, 790-830 etc

Nd:YLF      1047                                                  .||..   ||      780-815, 865

Ti:Sapphire  800                ......|495......                                  440-600

Alexandrite  750          ....|420..      ....|580....  |680                      370-470, 540-650

Ruby         694           .|400..    .....|554..                                 380-450, 500-600

TmHoCR:YAG  2081            ......................................|781            400-800

            Range:300       400       500       600       700       800       900    nm

                 +01234567890123456789012345678901234567890123456789012345678901 x 10nm

​

I also discovered TmHoCr:YAG lases at 2081nm, which could act as a substitute for the Nd:YAG-derived 2074nm in paper [O12]; after all, I did not have to go their route.

​

However even if these alternatives could produce sufficient power, I would still need a specialised summing crystal either for 700nm + 266nm, or 2081nm + 213nm. As before, I decided to acquire the different materials if they came up cheaply on eBay so I could experiment, but to concentrate on producing 213nm for the main project. 

​

​

NLO CRYSTAL PARAMETERS

 

​Unlike the researchers who wrote the 2003 paper [O12], I am unfamiliar with the optical, chemical and physical properties that define a NLO for its purpose, thus unable to specify the necessary parameters to order new crystals from manufacturers (NLOs are typically very expensive). Again, the only practical way forward was to buy surplus NLOs that had been used in similar applications. However the more I read about them, the more I realised I would have to be careful about my choice.

​

NLOs are manufactured from many compounds but a few kept cropping up, all having different properties, all having differing bandwidths, some better at high power, some more stable at temperature, most hygroscopic. BBO, KD*P, KTP and D*CDA are some of the more common:

 

The values below are taken from tables in [References: Optical Materials] 

​

BBO = BaB2O4 = Beta Barium Borate

Range 190nm - 3300nm
BBO   is moderately hygroscopic

BBO   has a damage threshold of 10GW/cm² @ 1064nm 1.3ns 10Hz / 120MW/cm² 8ns 10Hz @ 266nm

​

D*CDA = CsH2AsO4 aka CD*A / DCDA Deuterated Cesium D-hydrogen Arsenate

Range 260nm - 1100nm

D*CDA is VERY hygroscopic
D*CDA has a damage threshold of 360MW/cm² (Quantum Tech. datasheet DS707)

​

KD*P= KD2PO4 aka DKDP = Deuterated Potassium Dideuterium Phosphate

Range 200nm - 1600nm

KD*P  is moderately hygroscopic

KD*P  xtals are susceptible to thermal shock

KD*P  has a damage threshold of 6GW/cm² @ 1064nm 1.0ns 10Hz

​

KTP = KTiOPO4 = Potassium Titanyl Phosphate

Range 350nm - 2700nm

KTP   is non-hygroscopic

KTP   has a damage threshold of 2.4GW/cm² @ 1064nm 11ns 2Hz

​

LBO = LiB3O5 =  Lithium Triborate

Range 550-2600nm (Type I)

LBO   is moderately hygroscopic

LBO has a damage threshold of 19GW/cm² @ 1064nm 1.3ns 10Hz / 200MW/cm² @ 266nm 1.3ns 10Hz 

​

The star '*' in D*CDA or KD*P means the crystal was grown in heavy water [N27], and is referred to as 'deuterated'. Deuteration replaces hydrogen atoms with deuterium atoms, which increases:

the IR optical range of the material;

the electro-optic constant Fω;

the non-linear susceptibility constant Dx. 

​

A common way of countering hygroscopic issues is to immerse the xtal (also applies to pockels cell xtals) in a fluorocarbon liquid that meets the index matching characteristics of the operating wavelengths. The last paragraph in [N18], FastPulse NLO User's Guide, warns this liquid must first be filtered. 

​

KTP is regularly used in small milliwatt laser pointers, but is prone to photochromic damage (called grey tracking) during high-power 1064nm second harmonic generation which tends to limit its use to low-power and mid-power systems. KTP is also used as an electro-optic modulator (e.g. Pockels Cell), optical waveguide material, and in directional couplers. KTP crystals need stable temperature to operate if they are pumped with 1064nm IR to output 532nm green). Its low damage threshold renders it unsuitable for my project.

​

KDP / D*KDP pockels types are prone to ringing ([N5], Inrad BBO pockels Cells) which becomes evident the longer the crystal is biased - read into this frequency of pulses - but this should not affect me as LIBS will not require many pulses. This also applies to pockels cell crystals.

​

The following webpage gives a good introduction to the main criteria for NLO selection, explained in a very handy table reproduced below, that associates laser beam properties with NLO characteristics:

[N15] http://www.redoptronics.com/nonlinear-crystal-principal.html

​

Parameter For NLO Crystal Selection 

Laser Parameters                           Crystal Parameters

NLO Process                                Phase-Matching Type and Angle, deff

Power or Energy, Repetition Rate           Damage Threshold

Divergence                                 Acceptance Angle

Bandwidth                                  Spectral Acceptance

Beam Size                                  Crystal Size, Walk-Off Angle

Pulse Width                                Group Velocity Mismatching

Environment                                Temperature Acceptance, Moisture

​

The site goes on to explain Crystal Acceptance, Walk-off and Group Velocity Mismatch, the latter apparently of importance to super fast lasers and in this respect Ti-Sapphire is mentioned, but my interest is for low speed use (ns vs fs) so I assume I can ignore this for now. 

​​

TEMPERATURE TUNING

​

Often NLOs are contained within an assembly with a heating element and feedback temperature sensor. However BBO can also be cooled to advantage, therefore it is not safe to assume all HG assemblies with connectors for heaters/thermistors are likely to contain the same crystal type.

 

[G20] DeepSeek: 'Temperature and Angle Tuning:
The phase-matching condition can be fine-tuned by adjusting the temperature of the crystal or the angle of incidence. This allows some flexibility in the input wavelengths, but the range is still limited.

For example, angle tuning might allow a small shift in the input wavelengths (e.g., ±0.5nm to ±2nm), but this depends on the specific crystal and setup.'

​

CRYSTAL ACCEPTANCE

[N15] 'If a laser light propagates in the direction with angle Dq to phase matching direction, the conversion efficiency will reduce dramatically (see the right Figure). We define the acceptance angle (Dq) as full angle at half maximum (FAHM), where q = 0 is phase-matching direction. For example, the acceptance angle of BBO for type I frequency doubling of Nd:YAG at 1064nm is about 1 mrad-cm. Therefore, if a Nd:YAG laser has beam divergence of 3 mrad for frequency-doubling, over half of the input power is useless. In this case, LBO may be better because of its larger acceptance angle, about 8 mrad-cm. For NCPM, the acceptance angle is normally much bigger than that for CPM, for example, 2 mrad-cm1/2 for Type I NCPM LBO. ​In addition, you have to consider the spectral acceptance (Dl) of the crystal and the spectral bandwidth of your laser; crystal temperature acceptance (DT) and the temperature change of environment.'

​​

DIVERGENCE

​

[O1], Laser Safety Manual V4, from the university of Victoria, explains many laser parameters.
For instance, the section on beam divergence says: 'Although a laser beam is directional, some divergence (beam spread) does occur. This results in an increase in the beam diameter as the distance from the exit port of the laser increases. Beam divergence is measured in milliradians (17.45mrad = 1°) and lasers typically have a beam divergence of about 1mrad.'

​

[C18] provides links to online converters for mrad to degrees and vice versa.

​

The MK367 datasheet [O6] specifies divergence at '20% ~ 1.1mrad [0.06°] full angle', suggesting it would produce good power through BBO, but there is no mention of KT*P.

 

I asked DeepSeek the divergence of KT*P: 'The divergence of a laser beam, including one generated using a deuterated potassium titanyl phosphate (DKTP) nonlinear crystal, depends on several factors such as the laser cavity design, the quality of the crystal, and the beam waist. However, the divergence of the laser beam itself is not typically specified for the crystal alone but rather for the entire laser system. For a well-designed laser system using a DKTP crystal, the divergence can be quite low, often in the range of a few milliradians (mrad). For precise divergence values, you would need to consider the specific laser system and its design parameters.

a) Typical divergence:

1 to 5 mrad (milliradians) for many solid-state lasers using nonlinear crystals like DKTP.

b) High-quality systems:
Divergence can be as low as 0.5 to 1 mrad with optimized cavity design and beam shaping.'

​

Divergence may or may not be an issue for the MK580. I can attempt to improve it using a beam expander/reducer, and I can verify it using an optical shearing interferometer, aka 'optical shear plate'. This is why when a cheap one came up on eBay I grabbed it, although the interchangeable plate it came with is designed for a larger beam and I'm still waiting for a smaller plate to appear. The part I got is a Thorlabs SI-254P designed for a 10mm to 25.4mm beam however it may still be useful when paired with an expander: http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=2970

​​

WALK-OFF ANGLE

​

[N15] 'Due to the birefringence of NLO crystals, the extraordinary wave (ne) will experience Poynting vector walk-off. If the beam size of input laser is small, the generated beam and input beam will be separated at a walk-off angle (r) in the crystal and it will cause low conversion efficiency. Therefore, for focused beam or intra-cavity doubling, the walk-off is a main limitation to high conversion efficiency.'

​

Alternative wording from DeepSeek: 'In birefringent crystals, the walk-off effect (spatial separation of the ordinary and extraordinary rays) can limit the effective interaction length. A smaller beam radius can help mitigate this effect by reducing the spatial separation.'

​​

From the above I read: the larger and shorter the crystal, the better. DeepSeek also reveals the benefit of a tight focus:

​​​

FOCUS

​

Multiple papers I read indicated NLO output power is dependent upon a tight focus but none gave examples. When I asked an independent researcher if I should focus the beam into an NLO I was rebuffed with a firm warning that I might exceed the damage threshold of the material.

 

DeepSeek: 'what is the optimum pump beam radius for a laser nonlinear crystal harmonic?':​

​

The optimum pump beam radius for a laser nonlinear crystal in harmonic generation depends on several factors, including the type of nonlinear crystal, the wavelength of the pump beam, the phase-matching conditions, and the desired efficiency of the harmonic generation process. Here are some key considerations:

​

1. Phase Matching: The pump beam radius should be chosen to ensure good phase matching between the fundamental and harmonic waves. This often involves balancing the beam waist (radius) with the crystal length to maximize the overlap integral.

 

2. Walk-off Effect: In birefringent crystals, the walk-off effect (spatial separation of the ordinary and extraordinary rays) can limit the effective interaction length. A smaller beam radius can help mitigate this effect by reducing the spatial separation.

 

3. Focusing and Confocal Parameter: The beam radius is related to the focusing of the pump beam. The confocal parameter (Rayleigh range) should be comparable to or longer than the crystal length to ensure efficient interaction. The optimal beam waist ω0​ can be estimated using:

        __

       /λL

 ω0 ​≈ √ 2π

where λ is the wavelength of the pump beam and L is the length of the crystal.

 

4. Damage Threshold: The pump beam radius should be large enough to avoid exceeding the damage threshold of the crystal. High-intensity beams with small radii can cause optical damage.

 

5. Nonlinear Interaction Length: The effective nonlinear interaction length is influenced by the beam radius. A smaller beam radius increases the intensity, which can enhance nonlinear effects, but it also reduces the interaction length due to diffraction.

 

6. Empirical Optimization: Often, the optimum pump beam radius is determined empirically by varying the beam waist and measuring the harmonic output power. This experimental approach accounts for practical

factors such as crystal quality, alignment, and thermal effects.

 

Example Calculation
 

For a typical second-harmonic generation (SHG) process in a beta-barium borate (BBO) crystal with a pump wavelength of 1064nm and a crystal length of 10mm, the optimal beam waist might be around 20-50µm, depending on the specific conditions and desired efficiency.

 

Summary
The optimum pump beam radius is a trade-off between maximizing nonlinear interaction, maintaining phase matching, and avoiding damage. It is often determined through a combination of theoretical modeling and experimental optimization.

​​​

Addendum: above calculation checked & other wavelengths & lengths (see my NLOs listed below) added:

​

               Example above           My 2HG           My 3HG          My 4HG          My 5HG

        __     _____________     ____________     ____________     ___________     ___________

       /λL    /1064nm x 10mm    /532nm x 30mm    /355nm x 20mm    /266nm x 6mm    /213nm x 5mm

 ω0 ​≈ √ 2π   √       2π        √      2π        √      2π        √       2π      √     2π

​

            Answer = 41.15µm        = 63.03µm        = 33.62µm       = 15.94µm       = 13.02µm

​

​

Next I need to determine material damage threshold, see [References: Optical Materials].
 

​

This time I asked DeepSeek: 'How to calculate the optimum pump beam radius for a laser nonlinear crystal harmonic', expecting little more than above, but much more came back:

​

To calculate the optimum pump beam radius for a laser nonlinear crystal harmonic generation, you need to consider the trade-off between the nonlinear conversion efficiency and the damage threshold of the crystal. The goal is to maximize the conversion efficiency while avoiding damage to the crystal.

 

The optimum pump beam radius is determined by balancing the need for high intensity (small beam radius) to maximize nonlinear conversion efficiency against the need to avoid damaging the crystal (intensity below the damage threshold). The calculation involves determining the beam waist radius that allows the maximum power to be used without exceeding the crystal's damage threshold.

​

Key Parameters:

​

1. Nonlinear Conversion Efficiency
This depends on the intensity of the pump beam, which is inversely proportional to the beam area (i.e., smaller beam radius leads to higher intensity).

​

2. Damage Threshold
The crystal can only withstand a certain maximum intensity before it gets damaged. This limits how small the beam radius can be.

​

Steps to Calculate the Optimum Pump Beam Radius:

 

1. Determine the Damage Threshold Intensity (Imax):

 

a) This is typically provided by the crystal manufacturer or can be found in literature.
b) Imax is the maximum intensity (power per unit area) that the crystal can withstand without damage.

​

​

2. Calculate the Maximum Allowed Power (Pmax):

 

The maximum power that can be used without damaging the crystal is given by:

​

 Pmax = Imax x π x ω0²

​

where ω0 is the beam waist radius (the radius at which the intensity drops to 1/e² of its peak value).

​

​

3. Relate Beam Waist to Beam Radius:

 

The beam waist ω0 is related to the beam radius ω(z) at any position z along the beam path by:

            __________

 ω(z) = ω0 /1 + ( z  )² 

          √     ( zR )

​

where zR = π x ω0² is the Rayleigh range, and λ is the wavelength of the pump beam.

                λ

 

4. Optimize for Conversion Efficiency:

 

a) The conversion efficiency η for harmonic generation is typically proportional to the intensity squared (for second harmonic generation, 2HG):

​

​

 η ∝ I² ∝ ( P    )²

          ( πω0² ) 

​

b) To maximize η, you want to maximize I, but you are constrained by Imax​.

​

​

5. Set Intensity to Maximum Allowed:

 

a) To avoid damage, set the intensity I to Imax​:

​

 I =  P   = Imax

     πω0² 

​

b) Solving for ω0:

       ______

 ω0 = /   P   

     √  πImax

​

 

6. Consider Beam Propagation:

a) If the crystal is not at the beam waist, you need to account for the beam radius at the crystal position z:

            __________

 ω(z) = ω0 /1 + ( z  )² 

          √     ( zR )

​

b). Ensure that the intensity at the crystal does not exceed Imax.

​

​

7. Iterate for optium radius:

You may need to iterate the calculation to find the optimum beam radius that maximizes conversion efficiency while keeping the intensity below the damage threshold.

​

​

Example Calculation:
Assume:

 P = 1W (pump power)

 Imax = 1GW/cm² = 1^11W/m² (damage threshold)

 λ = 1064nm (pump wavelength) [why is this relevant here?]

 

Calculate w0:

       ______       ______________

 ω0 = /   P        /     1W        ≈ 5.64×10^−6m = 5.64µm

     √  πImax     √  π x 1^11W/m²

​

​​​​​

I asked DeepSeek another question:

​

'Calculate beam waist radius that maximizes conversion efficiency without exceeding the damage threshold for 1064nm with pump power 1W and damage threshold 1GW/cm²'

​

'To calculate the beam waist radius that maximizes conversion efficiency without exceeding the damage threshold, we need to ensure that the intensity of the beam does not surpass the damage threshold of the material. Here's how you can approach this problem:'

​

Given:
Wavelength, λ = 1064nm = 1064 × 10^-9m
Pump power, P = 1W
Damage threshold, Ith = 1GW/cm² = 1 × 10^9W/cm² = 1 × 1^12W/m² 

 

1. Relate intensity to beam waist radius
a) The intensity I of a Gaussian beam is given by:

​

 I =    2P  

      π x W0²

​

 where P is power of the beam and W0 is the beam waist radius

​

2. To avoid damage, the intensity must satisfy: I ≤ Ith

a) Substitute the expression for I:

​

    2P     ≤ Ith

  π x W0²

​

3. Solve for the beam waist radius W0

a) Re-arrange the inequality to solve for W0:

​

 W0² ≥   2P  

       π x Ith

 

       _______

 W0 ≥ /  2P   

     √  π x Ith

​

3. Plug the values:

 

       ______________

 W0 ≥ /     2 x 1    

     √  π x 1 x 1^12

​

      ______________

W0 ≥ √6.366 x 1^-13

​

W0 ≥ 7.98 x 1^-7m

W0 ≥ 0.798µm

​

4. Interpret the result

a) The beam waist must be at least 0.798µm to ensure the intensity does not exceed the damage threshold of 1GW/cm²

b) To maximize conversion efficiency, you would typically operate close to this minimum beam waist radius, as smaller beam waists lead to higher intensities and better nonlinear interaction. However, you must ensure the beam waist does not become smaller than 0.798µm, as this would exceed the damage threshold.

c) The beam waist radius that maximizes conversion efficiency without exceeding the damage threshold is approximately 0.798µm.
 

This is a different answer specifically for a Gaussian TEMoo beam, but there was no mention of this in the previous answer, so I revised my question:

​

'Calculate beam waist radius that maximizes conversion efficiency without exceeding the damage threshold for 1064nm with pump power 1W and damage threshold 1GW/cm²'

​

This time it again came up with the answer of 5.64µm so at least that's consistent.

​

DeepSeek appears to be my solution for determine laser parameters for NLO experimentation.

​

​

​​PRACTICALITY

​

Another factor critical to me alone, is my ability to actually focus to this extreme. Given I now know what to aim for, purely from practicality I shall aim to focus the 1064nm to 100µm and If I can achieve better, 50µm. 

​

Whatever the focus, I shall need a means of verifying it. see [References: Detectors & Visualisers].

​

OTHER CRITICAL FACTORS

 

This excellent site also provides invaluable cautionary information:

​

'In many cases, a nonlinear crystal used for nonlinear frequency conversion has a very long lifetime, which is longer than that of the whole laser system. The crystal material is essentially not modified during operation. However, a reduced crystal lifetime can occur under various circumstances:

​

Excessive optical intensities during operation may instantly damage a crystal. Unfortunately, nonlinear crystals often need to be operated not far from their optical damage threshold in order to achieve a sufficiently high conversion efficiency. This implies a trade-off between conversion efficiency and crystal lifetime. Note that even if the nominal intensity is below the nominal damage threshold, there may be problems due to fluctuations of the beam power or local intensity (e.g., if a beam profile has "hot spots"), or due to isolated defects in a crystal, which are more sensitive than the regular crystal material.

Even well below the threshold for instant damage, some crystal materials exhibit a continuous degradation within the used volume, e.g. in the form of "gray tracking". Such phenomena are particularly common for operation with ultraviolet light. Note that a gradual degradation can also lead into instant catastrophic damage via excessive heat generation.

Hygroscopic crystal materials deteriorate when they are not always kept in sufficiently dry air (or a dry purge gas). This applies e.g. to KDP and BBO, and in a lesser extent to LBO. It can be helpful to keep such a crystal at a somewhat elevated temperature, which makes it easier to keep it dry.
Operation of nonlinear crystals at temperatures below room temperature (in order to achieve phase matching) is generally problematic, as it may lead to condensation of water on the crystal surfaces if the surrounding air is not very dry. Even if the crystal material or coating is not sensitive to water, small water droplets may focus laser radiation more tightly than under normal operation, and thus damage the crystal material.

Crystals which are non-critically phase-matched in a crystal oven may exhibit problems when the crystal temperature is changed too rapidly or too often. In particular, anti-reflection coatings may be damaged due to different thermal expansion coefficients of the involved materials.

Crystal lifetime can also be strongly dependent on the material quality, although certain degradation phenomena appear to be intrinsic limitations of the material.

​

For high-power UV generation, nonlinear crystals may become consumables: they need to be replaced quite often within the lifetime of the whole laser system (e.g., every few hundred hours of operation). Often, several problematic aspects come together in the regime UV generation: crystal materials are generally more sensitive to ultraviolet light (having high photon energies), exhibit a higher absorption in that regime, and in case of ultrashort pulses the high group velocity mismatch enforces the use of a shorter crystal, which requires high optical intensities for a given conversion efficiency.'

​

Hot spots are also an issue with NLOs, as described here:

[N15], Principles of Nonlinear Optical Crystals - Conversion Efficiency, Red Optronics website: 'Note that even if the nominal intensity is below the nominal damage threshold, there may be problems due to fluctuations of the beam power or local intensity (e.g., if a beam profile has "hot spots"), or due to isolated defects in a crystal, which are more sensitive than the regular crystal material.'

​

ADD PAPER THAT SAYS COOLING BBO EXTENDS ITS LIFE

​

It was clear I would need to use crystals with a certain pedigree to stand any chance of harmonic generation, and as I read up about them, I realised most were composed of hygroscopic salt compounds, therefore unsealed, raw crystals were to be avoided. I also learned crystals were most efficient at certain temperatures dependent on their chemical composition, but are susceptible to thermal shock and could be destroyed by fluctuations sharper than 1°C per minute. I found hygroscopic ones were best operated in indexing fluid, which was typically FC-43 fluorocarbon, usually with a bubble for thermal expansion.

​

Eventually I realised my best choice was large, used crystal assemblies from laser companies Continuum and Quantel. These consist of large plastic cubes with metal guides inside on which the NLO is already installed. On eBay over time, I was able to acquire the following Nd:YAG harmonic converters.