Absorptive Long-Pass Filters

• Absorptive long-pass filters are optical, IR, and RF devices that suppress high-energy radiation through intrinsic material absorption while allowing longer wavelengths to pass.
• They operate based on the Beer–Lambert law and material-specific absorption coefficients, offering minimal angular sensitivity compared to interference filters.
• Applications include optical calorimetry, cryogenic IR management, and quantum microwave circuits, ensuring high suppression of out-of-band signals.

Absorptive long-pass filters are optical, microwave, or RF devices engineered to suppress undesired lower-wavelength (higher energy) radiation via intrinsic material absorption, while transmitting longer-wavelength (lower energy) signals with high efficiency. In contrast to interference-based filtering, these devices employ physical media with wavelength-dependent absorption coefficients, leading to cutoff behavior set by intrinsic material properties, film thickness, or device geometry. Absorptive long-pass filters are critical for applications requiring minimal out-of-band reflection and robust angle-insensitive performance, including dual-readout calorimetry, cryogenic IR-thermal management, and high-fidelity quantum measurement chains.

1. Physical and Optical Principles

The operation of absorptive long-pass filters relies on the exponential attenuation of incident radiation according to the Beer–Lambert law: $T(\lambda) = \exp[-\alpha(\lambda)\,d]$ where $T(\lambda)$ is the wavelength-dependent transmittance, $\alpha(\lambda)$ the spectral absorption coefficient, and $d$ the absorber thickness. The cutoff wavelength $\lambda_c$ is conventionally defined at $T(\lambda_c) = 0.5$, yielding $\lambda_c$ set by both $\alpha(\lambda)$ and $d$.

Unlike interference filters, which display strong angular and polarization dependence due to multiple-beam interference, absorptive filters exhibit minimal angular sensitivity. The spectral roll-off is determined by the absorption spectrum of the material, typically dispersive organic dyes (in visible/near-IR) or engineered composites (for mid-IR/far-IR, RF, or microwave regimes). In multi-material composites, effective medium approximations (e.g., Maxwell–Garnett theory) yield the overall absorption constant, which can be tailored by powder loading or matrix tuning (Munson et al., 2017).

2. Material Systems and Fabrication

Typical absorptive long-pass filters for optical applications are produced as thin ($\sim$100 μm) films composed of organic dyes embedded in polymers (e.g., gelatin, cellulose nitrate) on transparent carriers. Prototypical commercial examples include Kodak-24 and Kodak-25 (λc = 590 nm and λc = 595 nm, respectively), which use proprietary dye chemistries to tune the absorption edge (Benaglia et al., 4 Dec 2025).

For infrared and sub-millimeter bands, absorptive layers are often composites of dielectric-matrix polymers loaded with reststrahlen powders (e.g., CaCO₃, MgO with 5–20 μm granularity). These are typically spray-deposited or laminated to thicknesses matched to absorption requirements (e.g., 50 μm). The spectral characteristics can be precisely engineered by adjusting the volume fraction and composition of the powders (Munson et al., 2017).

In the microwave domain, absorptive long-pass (“low-pass” in RF terminology) filters are implemented by filling coaxial sections with lossy dielectrics such as Eccosorb CR-124. Here, the filter’s attenuation function and cut-off frequency are primarily set by the length of the lossy section and the complex permittivity of the absorber, which shows frequency-dispersive loss (Paquette et al., 2022).

3. Spectral Performance and Cutoff Characterization

Transmittance and attenuation spectra are measured using spectrophotometric methods—typically UV/VIS/IR spectrophotometry with well-collimated beams for the optical regime (Benaglia et al., 4 Dec 2025), or Fourier-transform spectrometry for the IR/far-IR (Munson et al., 2017). The cutoff is operationally defined at $T(\lambda_c) = 50\%$, and the spectral transition width is given by the dispersion of $\alpha(\lambda)$ near cutoff.

A typical data summary for Kodak-24 (100 μm) is shown below:

Wavelength (nm)	$T(\lambda)$ (%)	$\alpha(\lambda)\,[\mathrm{m}^{-1}]$
500	0.2	$7.6\times10^4$
550	5.8	$5.2\times10^4$
580	34	$1.1\times10^4$
590	50	$6.9\times10^3$
600	75	$2.9\times10^3$
650	85	$1.6\times10^3$

For polymer/gelatin-based filters, the absorption edge width (transition from 10% to 90% transmission) is dictated by the dye dispersion and is generally broader than for high-order interference filters, but exhibits superior angle invariance. By numerical convolution of $T(\lambda)$ with an emitter's spectral output, the overall suppression fraction for unwanted light (e.g., PWO scintillation) can be estimated (Benaglia et al., 4 Dec 2025).

4. Integration in Scientific Applications

Optical Calorimetry

The discriminative readout of Cherenkov light in hybrid electromagnetic calorimeters places strict requirements on filter performance to suppress scintillation background. In (Benaglia et al., 4 Dec 2025), Kodak-24 and Kodak-25 (100 μm) were implemented directly in front of SiPMs to block $>$99.9% of PWO scintillation while transmitting Cherenkov photons (λ $>$ 600 nm). These absorptive filters maintained cutoff position and attenuation for incidence angles up to 20°, in contrast to interference filters showing 20–40 nm blueshifts and degraded performance at off-normal angles.

Infrared Filtering in Cryogenic Systems

For IR rejection in cryogenic bolometer setups, composite filters with powder-loaded absorptive layers on silicon exhibit $>$99.8% blocking of thermal IR power from 300 K blackbody sources, while transmitting with $T > 99\%$ within the 70–170 GHz signal band. Thermal management is enhanced by mounting on high-conductivity silicon substrates with metamaterial antireflection coatings, ensuring minimal temperature gradients and negligible in-band thermal reradiation (Munson et al., 2017).

Microwave Attenuation for Quantum Circuits

Absorptive microwave long-pass filters, realized as Eccosorb-filled coax segments, demonstrate deep stopband attenuation ($>$120 dB), smooth error-function time-domain response, and true absorptive (reflectionless) behavior for both passband and stopband. These properties are essential for eliminating standing waves and out-of-band reflections that degrade quantum circuit performance (Paquette et al., 2022). At cryogenic temperatures, power handling up to 100 nW is attainable with noise temperatures below 100 mK.

5. Modeling, Design Metrics, and Cascadability

Device modeling proceeds via direct application of the Beer–Lambert exponential for optical filters, Maxwell–Garnett effective medium theory for composites, and full transmission-line analysis for microwave sections. Key design equations from (Benaglia et al., 4 Dec 2025, Paquette et al., 2022), and (Morgan, 2012) include:

• For optical filters:

$$S/S_0 = \int EM(\lambda)\,T_c(\lambda)\,T_f(\lambda)\,d\lambda \,/\, \int EM(\lambda)\,T_c(\lambda)\,d\lambda$$

giving the fraction of unwanted emission transmitted.

• For absorptive microwave filters:

$|H(\omega)| \approx \exp[-\alpha(\omega)\,L]$

with cutoff defined by $\alpha(2\pi f_c)L = \ln\sqrt{2}$.

Cascadability is a central feature of reflectionless absorptive long-pass cells (Morgan, 2012), in both lumped-element and distributed versions. Each cell—engineered to present $S_{11} = 0$ at all frequencies—may be inserted arbitrarily in system chains, e.g. to incrementally build up stopband rejection or suppress standing waves. Each cell in a third-order Inverse Chebyshev prototype topology contributes 14.47 dB of stopband attenuation at the $\sqrt{3}\,f_c$ frequency, with insertion loss scaling as the number of cells.

6. Angular Dependence and Comparison to Interference Filters

A defining advantage of absorptive long-pass filters is their robustness to variations in incidence angle. Experimental data for Kodak-24, Kodak-25, and comparable absorptive types indicate negligible shift ($< 1$ nm) in cutoff over angles 0°–20°, maintaining blocking efficiency for diffuse or highly oblique photon fields. In contrast, multilayer interference filters exhibit significant blue-shifting of the cutoff ($\Delta\lambda_c \sim 20$–40 nm at 20°), leading to spectral leakage and insufficient suppression in applications with broad angular emission. Consequently, absorptive filters are strongly favored where angular isotropy or large acceptance is required (Benaglia et al., 4 Dec 2025).

7. Practical Integration, Limitations, and Design Recommendations

Table: Absorptive Long-Pass Filter Types and Key Properties

Filter Type	Cutoff ($\lambda_c$/f_c)	Suppression
Kodak-24 (optical, 100μm)	$\lambda_c$ = 590 nm	$>$99.9% (PWO)
Kodak-25 (optical, 100μm)	$\lambda_c$ = 595 nm	$>$99.9% (PWO)
Everix Abs-580 (optical, 260μm)	$\lambda_c$ = 580 nm	$>$99.9% (PWO)
Composite Si filter (IR, 50μm)	$\nu_c$ = 3.6 THz	$>$99.8% (300 K)
Eccosorb CR-124 (RF, e.g. 50 mm)	$f_c$ = 300–400 MHz	$>$120 dB

Design recommendations (Benaglia et al., 4 Dec 2025, Munson et al., 2017, Paquette et al., 2022):

• Use thin ($\sim$100 μm) absorptive filters for minimum geometric loss and maximal angular uniformity.
• Avoid interference filters in applications with broad angular photon distributions.
• Evaluate filter materials for undesirable fluorescence or afterglow, as some absorbers may re-emit pulsed signals (e.g., Hoya-O56).
• For RF/microwave filters, match absorber-filled section geometry to system impedance, and manage thermalization rigorously in cryogenic environments.
• Incorporate complete wavelength- and angle-dependent transmission models in system-level Monte Carlo to predict performance.

In summary, absorptive long-pass filters are essential tools for precision photon or signal discrimination in high-performance scientific instrumentation, offering unmatched angular stability, deep attenuation, and flexibility for system integration across optical, IR, and RF/microwave domains (Benaglia et al., 4 Dec 2025, Munson et al., 2017, Paquette et al., 2022, Morgan, 2012).