From practical application consideration of nonlinear wave mixing process, the key properties of nonlinear optical materials can be characterized by (1) transparency range, (2) refractive index, (3) the strength of nonlinearity, (4) phase-matching scheme, as well as (5) damage threshold. Other factors such as mechanical hardness, thermal and chemical stability etc. will not be addressed here. The transparency range ensures the nonlinear wave mixing process is operated at no-absorption range. The material refractive index is related to phase matching design and mixing efficiency. The strength of nonlinearity and phase-matching scheme is the dominating factor for the wave mixing efficiency optimization of the selected nonlinear optical material. The damage threshold characterizes the maximum input/output power that the device can handle without inducing laser damage on surface or inside the material. Summary of transparency range and other key factors for selecting nonlinear materials are shown in table 1.
Table 1: Summary of key nonlinear material properties for efficient nonlinear wave mixing
Transmission spectrum (transmission in % vs. wavelength) describes accessible application wavelength window of selected optical materials. Example transmission spectrum is shown in figure 1, which gives transmission in % vs. wavelength for uncoated congruent LiNbO3 (CLN). The transmission in % is not shown to be 100% between the UV and MIR transparency range due to reflection of non-AR coated surfaces, which can be corrected with proper AR coating. However, the steep slope at near UV and near MIR range is due to material absorption. In addition, there is transmission dip near 2870 nm due to OH- absorption. Another example transmission spectrum is shown in figure 2, which gives transmission in % vs. wavelength of ordinary and extraordinary waves at near-UV and near-MIR region for uncoated materials of CLT, 7% doped MCLT and 5% doped MCLN. MCLT material family has wider transparency range (especially near UV range) as compared to that of MCLN, thus one would choose the MCLT material family if the application wavelength is beyond the transparency range of MCLN. Other than transparency range, there are several other factors (such as the strength of nonlinearity and feasibility for achieving effective phase-matching) to be considered for selecting proper nonlinear optical material.
Figure 1: Transmission curves of CLN
By looking into the transmission edges, figure 2 gives a transmission in percentage as a function of the wavelength in ordinary and extraordinary waves at near-UV and near-MIR region for uncoated materials of congruent lithium tantalate (CLT), 7 mol.% doped MgO doped CLT and 5 mol %. doped CLN. CLT material family has wider transparency range (especially near UV range) as compared to that of CLN, thus one would choose the CLT material family if the application wavelength is beyond the transparency range of CLN.
Figure 2: Transmission spectra of 1-mm-thick CLT, Mg7% -doped CLT, and Mg5% doped CLN in (a) UV region for ordinary wave, (b) UV region for extraordinary wave, (c) MIR region for ordinary wave, and (d) MIR region for the extraordinary wave. (Reference from: “Mg-doped congruent LiTaO3 crystal for large-aperture quasi-phase matching device”, Hideki Ishizuki and Takunori Taira, Vol. 16, Issue 21, pp. 16963-16970 (2008)).
Although typically the transmission begins to drop when the wavelength <400 nm and >4000 nm, the CLN is still applicable in those ranges but with a higher absorption loss.
The temperature dependent refractive index is described by the Sellmeier equation below
where the temperature-dependent parameter f is
and the Sellmeier coefficients are
This property describes the chromatic dispersion (refractive index vs. wavelength) and birefringence properties (refractive index vs. polarization), and thus determines the phase-matching condition, phase-matching bandwidth, etc. Example is shown in figure 3, which gives refractive index vs. wavelength for ordinary and extraordinary waves of MgO doped CLN (5% doped MCLN) and extraordinary waves of MgO doped SLN (1% doped MSLN).
Figure 3: Room temperature refractive index curves for 5% Mg-doped CLN and for 1% Mg-doped SLN, according to the Sellmeier parameters. (From , “Gayer et al., Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3, Appl. Phys. B 91, 343–348 (2008)”) with correction of no & ne
In the following, we will further address the importance of material dispersion (refractive index vs. wavelength) to nonlinear wave mixing process. For wave mixing of input fundamental wave in a nonlinear dielectric medium with effective d-coefficient to generate output second harmonic wave, the generated output second harmonic intensity (power) vs. input fundamental intensity (power) can be derived as:
Figure 4: This bandwidth property. When the mixing wavelength is deviated away from the designed center wavelength, phase-matching condition) will be changed and thus the efficiency will drop.
Figure 5: As a result of this group velocity mismatch (GVM), two pulses which are initially overlapping in time can be no longer overlap after some propagation distance. Thus, when nonlinear crystal with length exceeds the group velocity walk-off length, a distorted pulse output will be generated.
Strength of nonlinearity & Phase-matching configuration
Second order nonlinearity characterizes the strength of response for a dielectric medium to electric field. For convenience, we can define a two dimensional (6x3) nonlinear dielectric tensor, commonly known as Kleinman d-tensor, to describe the strength of nonlinearity:
In practical situation, depending on the crystal class, many tensor components actually can be reduced to zero for crystal structure symmetry reason. For example, the d-tensor of LiNbO3 (which is triangular 3m crystal class) can be expressed as
Where the nonlinear d coefficient is d22=2.59pm/V, d31=4.85pm/V, d33=25.3pm/V. Magnitude of the effective nonlinear coefficient deff with units of pm/V describes the nonlinear frequency mixing efficiency. For QPM configuration with polarization along z-axis, the effective deff will be reduced by a 2/π factor, i.e.deff=(2/π)d33.
The magnitude of the effective nonlinear coefficient deff with units of pm/V depends on the nonlinear tensor components djk and also depends on the phase-matching configuration. For QPM configuration with polarization along z-axis, the effective deff will be reduced by a 2/π factor, i.e. deff=(2/π)d33. Since the strength of such nonlinear interactions usually depends not only on the effective nonlinear coefficient, but also on the refractive indices of mixing waves. For comparison of different nonlinear crystal materials, one often uses a figure of merit (FOM), such as
Thus, the FOM for LiNbO3 with polarization along z-axis (d33) for non-critical phase-matching and quasi-phase-matching (QPM) will be 63.9 and 25.9, respectively. The FOM for other selected nonlinear materials are listed in Table 1. One should note that the wave mixing efficiency also depends on effective device length L, which is limited by
Phase-matching angle with spatial walk-off consideration: This is important factor for BPM, but in general is not critical for QPM, as QPM allows one to access desired polarization (usually is z-axis (d33)) without walk-off consideration.
Material dispersion for temporal walk-off consideration (i.e. GVM, for ultrafast pulse application).
Also practically available physical length for the selected materials. For example, one can get noncritical QPM in MgO:PPLN for type 0 or type II interaction with device length up to 80 mm if temporal walk-off is not the application limitation.
Damage threshold describes the highest power that a nonlinear material can sustain without causing surface or material damage or other undesired effects. The mechanism for laser induced damage threshold (LIDT) could be due to thermal effect, laser induced breakdown, surface damage etc. Additional undesired effect includes nonlinear self-focusing, photo-darkening (gray tracking), GRIIA (green-induced infrared absorption), etc. From practical application consideration, the laser induced damage threshold (LIDT) will depend on the engineering optimization of operation wavelength, peak/averaged power, spatial focusing condition, temporal pulse width, pulse energy, surface quality, and also integration packaging, etc.
(a) Damage by thermal effect:
Optical damage can arise due to energy absorption induced thermal damage. When materials are hit with rather high power CW or pulse lasers at certain wavelengths, which cause a substantial absorption of laser light, the absorbed energy will generate a substantial amount accumulated heat within the material and cause material overheated. The overheated spot will then possibly cause chemical degradation, burning, or cause mechanical breakdown due to thermally induced stress.
Figure 6 (a): illustrate the damage by thermal effect.
(b) Damage by laser-induced breakdown:
Laser induced damage (LIDT) may come from randomly distributed intrinsic faults/impurities or laser induced ionized free carriers, which cause materials to absorb input laser energy with value far above that would be experienced at lower intensity levels and thus cause the laser-induced breakdown:
Intrinsic randomly distributed faults or impurities: Most initial carriers are generated by intrinsic randomly distributed faults or impurities; in such a case, the tendency for damage involving such extrinsic effects substantially depends on the exact spot which is illuminated on a sample.
Ionized free carriers: high input peak power or multi-photon absorption might also be the starting point to generate some ionized free carrier, which causes subsequent strong absorption for induced damage. As the generated ionized free carriers have a limited lifetime, a sufficiently high optical energy must be provided within a short time to induce the damage. If the initial carriers are generated by multi-photon absorption, the related intrinsic damage process can be rather deterministic as it is largely defined and set by input laser parameters.
The physical mechanisms of laser induced damage (LIDT) for above two scenarios may depend on the pulse duration. For nanosecond and longer pulses, non-deterministic laser-induced damage is often observed, where the probability of damage increases smoothly around the threshold and damage is mainly through intrinsic randomly distributed faults or impurities. In such a case, a larger safety margin for safety operation is required to avoid laser damage through random impurities. For femtosecond pulses, deterministic laser-induced damage is often observed, where the damage is set in when the damage threshold is reached. Figure 6 (b) illustrates the damage by laser-induced breakdown.
Figure 6 (b): illustrate the damage by Laser-induced Breakdown.
Normally, doubling the laser beam area should allow one to apply two times more power until damage occurs. However, a larger beam will also make the input laser more likely to hit a “bad spot” on a sample. Therefore, this kind of scaling may not work perfectly for some optical components where LIDT is dominated by randomly distributed intrinsic faults or impurities. Thus, for large beam spots, one may see damage more frequently at a given intensity.
(c) Damage by material surface:
Optical damage can arise on its surfaces due to a higher density of microscopic defects, which could be due to Intrinsic distributed faults/impurities (like what occurs inside the bulk materials) or surface scratch/dirt, or any other surface contamination (such as mechanical oil or outgases epoxy compound). With all possible higher density microscopic defects on surfaces than the same type of bulk material, LIDT for surface normally is lower than that for bulk. The LIDT for optical surfaces may substantially depend on the exact surface treatment. In addition, dielectric coatings can also cause a substantial reduction of power handling capability.
Figure 6 (c): illustrates the damage by material surface.
(d) Other Damages/Degradation:
Photo-darkening/Gray-tracking: photo-darkening (photo-induced absorption) is transmission losses resulting from absorption or scattering grow with time when they are irradiated with light at certain wavelengths. In many cases, the photodarkening mechanism involves the formation of color centers or other microscopic structural transformations in the medium. Photodarkening can lead to serious performance degradations and lifetime limitations of optical devices. Typically MgO:PPCLN has neglectable gray-tracking issue. However, in some material such as KTP, a gray line is observed when the crystal is irradiated by visible or UV light. The induced absorption is attributed to polarons, where carriers may in that case be captured e.g. by Ti4+ ions or by Fe3+ impurities in the KTP. Gray tracking is usually reversible and disappears within a few hours after irradiation. Its strength depends on the crystal quality and thus on the fabrication method, as well as some important parameters such as the pulse duration and pulse repetition rate.
GRIIA: The GRIIRA (green induced infrared absorption) results from the impurity inside the materials (for example, in LiNbO3 with unbalanced ratio of Li+ and NbO3-). The induced absorption appears to be related to the formation of polarons (electrons trapped by antisite niobium ions), also called color centers, which can result e.g. from two-photon absorption. The effect can be greatly reduced by doping the material with magnesium oxide (MgO) and/or by using stoichiometric material, which contains fewer of the intrinsic niobium antisite defects. At the same time, both methods can also reduce the tendency for photorefractive beam distortions due to the increase of ionic conductivity.
Photorefractive effect: The photorefractive effect is seen in certain material that responds to light by altering their refractive index. Such an effect could be useful for some applications, but is undesired effect for nonlinear wave mixing applications, as the change of refractive index vs. light intensity will cause the change of phase-matching condition for power variation and also cause spatial and temporal instability for beam distortion. Similar to GRIIA in LiNbO3 materials, such an effect could possibly be reduced by magnesium oxide (MgO) doping and/or by using stoichiometric material.
Nonlinear-self focusing/thermal lensing: For high laser intensities, nonlinear self-focusing or thermal lensing may occur within a sample, which may lead to even further focusing at high intensity center and finally results in optical damage.
Figure 6 (d-1): illustrates the damage by photo-darkening/gray-tracking and GRIIA.
Figure 6 (d-2): illustrates the damage by photorefractive effect and nonlinear-self focusing/thermal lensing.
One should also notice that it might be difficult to define the damage threshold “precisely” due to the combination of many possible damage mechanism/design factors and also accumulation effects. For example, material might not exhibit any easily detectable damage initially but does react to multiple pulses with the same parameters in the long term. This could be due to that small hidden defects were only created in the first few pulses but grows to significant sizes which eventually cause optical damage in the long term. Thus, from safety operation point of view, it is always good to keep sufficient engineering margin. Example laser damage threshold for selected nonlinear materials is shown in table 1 and also for MgO:PPLN material is shown in the table 2
Table 2: Example laser damage threshold for MgO:PPLN under different wavelength, laser conditions, focusing parameters, and intensity.
Effective date: August 1, 2018
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