**Core Concept**
The question tests the student's ability to identify the causative agent of an orbital cellulitis in the context of maxillary sinusitis, based on the presence of irregularly branching septate hyphae on a Gram stain smear.

**Why the Correct Answer is Right**
The presence of irregularly branching septate hyphae on a Gram stain smear is characteristic of a fungal infection, specifically *Aspergillus*. Aspergillus species are common causes of fungal sinusitis and orbital cellulitis, particularly in immunocompromised individuals such as diabetics. The hyphae of Aspergillus are septate, meaning they have walls dividing the hyphae into separate cells. The irregular branching pattern is also distinctive of Aspergillus.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not match the description of the causative agent. The Gram stain smear shows septate hyphae, which is not characteristic of *Staphylococcus*.
* **Option B:** This option is incorrect because *Streptococcus* is a bacterial cause of orbital cellulitis, not a fungal cause. The Gram stain smear shows septate hyphae, which is not characteristic of *Streptococcus*.
* **Option C:** This option is incorrect because *Pseudomonas* is a bacterial cause of orbital cellulitis, not a fungal cause. The Gram stain smear shows septate hyphae, which is not characteristic of *Pseudomonas*.

**Clinical Pearl / High-Yield Fact**
In cases of orbital cellulitis, especially in immunocompromised patients, a high index of suspicion for fungal sinusitis should be maintained. The presence of septate hyphae on a Gram stain smear is a key diagnostic clue for fungal sinusitis.

**Correct Answer:** D.